Thermal Modeling of Flow in the San Diego Aqueduct, California, and its Relation to Evaporation By HARVEY E. JOBSON GEOLOGICAL SURVEY PROFESSIONAL PAPER 1122 UNITED STATES GOVERNMENT PRINTING OFFICE,WASHINGTON : 1980 UNITED STATES DEPARTMENT OF THE INTERIOR CECIL D. ANDRUS, Secretary GEOLOGICAL SURVEY H. William Menard, Director Library of Congress Cataloging in Publication Data Jobson, Harvey E. Thermal modeling of flow in the San Diego Aqueduct, California, and its relation to evaporation. (U.S. Geological Survey professional paper ; 1122) Bibliography: p. 23-24. Supt. of Docs. no.: I 19.1621122 1. San Diego Aqueduct, Ca1if.—Temperature—Mathematical models. 2. San Diego Aqueduct, Calif.—Evaporation—Mathematical models. I. Title. II. Series: United States. Geological Survey. Professional paper ; 1122. TC764.J62 628.1’5 79-20943 For sale by the Superintendent of Documents, US. Government Printing Office Washington, DC. 20402 Stock Number 024-001-03266-0 Pa e Abstract ____________________________________________ 1g Data and model calibration _____________________ Introduction ________________________________________ 1 Data available _____________________________ Model development __________________________________ 2 Model calibration _________________________ The flow model ________________________________ 2 Model verification and discussion _______________ The Eulerian temperature model ________________ 3 Summary and conclusions _____________________ The Lagrangian model _______________________ 1-- 7 References _____________________________________ ILLUSTRATIONS FIGURE 1.Map showing San Diego Aqueduct showing data-collection points CONTENTS 2—21. Graphs showing: 2. 3. 4. 01 q 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. The effect of the dispersion coefficient on the computed temperatures in the San Diego Aqueduct on August 18, 1973, in comparison with measured temperatures ___________________________________________________ Variation of stage and discharge for the flow transients on December 10 and 11, 1973 ___________________ Comparison of wind function values for July 30, 1973, as computed with and without heat transfer between the water and the bed _____________________________________________________________________________ . Variation of the wind function, with windspeed for the San Diego Aqueduct during July 25 through 28, 1973 . Variation of the wind function, with windspeed for the San Diego Aqueduct during July 29 through August 1, 1973 ___________________________________________________________________________________ . Variation of the wind function, with windspeed for the San Diego Aqueduct during August 2 through 5, 1973 . Variation of the wind function, with windspeed for the San Diego Aqueduct during August 6 through August 9, 1973 ___________________________________________________________________________________ . Variation of the wind function, with windspeed for the San Diego Aqueduct during August 10 through August 13, 1973 ___________________________________________________________________________________ Variation of the wind function, with windspeed for the San Diego Aqueduct during August 14 through August 17, 1973 _________ , __________________________________________________________________________ Variation of the wind function, with windspeed for the San Diego Aqueduct during August 18 through August 21, 1973 ___________________________________________________________________________________ Computed wind function values for the San Diego Aqueduct. Every other point plotted for the 28-day period starting July 25, 1973 _____________________________________________________________________________ Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the calibration period _____________________________________________________ Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the first verification _______________________________________________________ Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the second verification ___________________________________________________ Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the third verification _______________________________________________________________________ Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the fourth verification _____________________________________________________ Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the fifth verification _____________________________________________________ Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the sixth verification _____________________________________________________ Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the seventh verification ___________________________________________________ Computed monthly average daily evaporation from the San Diego Aqueduct during the study period, July 25, 1973, to July 24, 1974 _____________________________________________________________________________ _____ 22 _____ 23 _____ 11 _- 12 ______ 12 __ 13 _____ 13 _____ 14 _____ 14 _____ 15 ..... 16 _____ 17 _____ 19 _____ 20 _____ 21 11111 22 _____ 23 ,,,,, 24 ,,,,, 24 III IV TABLE 9°?» OSLO P1 2ha~fin 5 = Reflectivity; CONTENTS TABLES — Page . Coefficients for use in equation 3 to determine the centerline depth in the San Diego Aqueduct ________________________ 3 . Summary of modeled data for the San Diego Aqueduct ______________________________________________________________ 9 . Daily values of the wind function coefficients for the San Diego Aqueduct ____________________________________________ 18 . Summary of energy budget terms for individual water parcels passing through the San Diego Aqueduct ________________ 19 . Evaporation rates for the San Diego Aqueduct during the study period, July 25, 1973, to July 24, 1974 ________________ 22 SYNHMDLS = Cross-sectional area of the channel; Rh = Hydraulic radius; = Surface area of a reservoir; 3 = Time-step number, before which the water tempera- : Specific heat of water at constant pressure; ture is assumed to have been constant; = Coefficient in equation 3; S" = Sun altitude in degrees; = Heat storage capacity; T = Cross-sectional average water temperature; = Coefficient in equation 3; t = Time; = Time step; Ta = Air temperature; = Longitudinal dispersion coefficient; Tb = Arbitrary reference temperature; = Length, in meters of the subreach (1,299 m); T; = Initial temperature of a water parcel as it enters the = Rate of evaporation; system; = Vapor pressure of air; To = Final temperature of a water parcel as it passes the = Coefficient in equation 3; downstream end of the channel; = Saturation vapor pressure of air evaluated at a tem- T“. = Wet-bulb air temperature; perature equal to that of the water surface; U = Cross-sectional average velocity; = Increase in heat content of the slab between time zero U... = Shear velocity; and t resulting from a unit increase in surface tem- V = Wind speed; ‘ perature at time zero; Vj = Volume of water in subreach j; = Heat flux leaving the water caused by longwave radia- W = Top width of the channel; tion being emitted by the water; x = Longitudinal coordinate; = Heat flux leaving the water as a result of the latent y = Distance above the insulated bottom of the slab at heat of vaporization; which temperature ATE is computed; 2 Heat flux conducted from the water to the air as sensi- Y,- = Centerline water depth in subreach j; ble heat; YM( k) = Recorded centerline water depth at recorder k; = Net flux to the water caused by incoming radiation Z = Thickness of the bed slab; from the sun and the sky; or = Constant in wind function; = Flux of thermal energy from the bed to water; y = Psychrometric constant; = Heat flux added to the water by rain falling directly on AH(i) = Heat flux to the water from the bed during any time its surface; step iDT to (i + 1)DT to result from a unit increase in = Rate of absorption of thermal energy at the water sur- water temperature at time zero; face per unit area; ATB = Temperature rise within the slab; = Rainfall rate; AT(jDT) = Change in water temperature to occur at jDT; = Thermal diffusivity; A9 = Difference between the virtual temperature of the air = Latent heat of vaporization of water; and the water surface; 2 Empirical mass-transfer coefficient in the wind func- e = Emissivity of water; tion; p = Density of water; = Atmospheric pressure; 0' : Stefan-Boltzman constant for black-body radiation; = Discharge at cross-section j; r = Travel time required for a parcel to flow through the = Diversion discharge; system; and = Coefficient of correlation; d1 = Empirical wind function. CONVERSKDJTABLE Factors for converting metric units to inch-pound units are shown to four significant figures. Multiply metric unit By meter (m) 3.281 kilometer (km) 0.6214 centimeter (cm) 0.03281 millimeter (mm) 0.3937 meter per second (m/s) 3.281 cubic meter per second (m3/s) 0.02832 kilopascal (kPa) 10.00 To obtain inch-pound unit foot (ft) mile (mi) foot (ft) inch (in) foot per second (ft/s) cubic foot per second (ft3/s) millibar (mb) THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA, AND ITS RELATION TO EVAPORATION By HARVEY E. JOBSON ABSTRACT The thermal balance of the 26-kilometer-long concrete-lined San Diego Aqueduct, a canal in southern California, was studied to de- termine the coefficients in a Dalton type evaporation formula. Meterologic and hydraulic variables, as well as water temperature, were monitored continously for a 1-year period. A thermal model was calibrated by use of data obtained during a 28-day period to determine the coefficients which best described the thermal balance of the canal. The coefficients applicable to the San Diego Aqueduct are similar to those commonly obtained from lake evaporation studies except that a greater evaporation at low windspeeds is indicated. The model was verified by use of data obtained during 113 days (excluding the calibration data). These data verified that the de- rived wind function realistically represents the canal evaporation. An annual evaporation of 2.08 meter was computed; this amount is about 91 percent of the amount of water evaporated annually from nearby class A evaporation pans. INTRODUCTION Because of its large influence on many facets of the ecosystem, water temperature is clearly an important water-quality parameter. The rates of most chemical and biological reactions are temperature dependent, as are the spawning and growth cycles of most fish. The accuracy of any water-quality model is, therefore, sensitive to the accuracy of the thermal model upon which it must depend. The accuracy of a temperature model, likewise, is very dependent on the accuracy of the estimated exchange of energy between air and wa- ter. Finally, evaporation is a major component of the surface exchange process. Evaporation is, therefore, a key element in any water-quality model in addition to being a troublesome factor in computing the water balance of a river system. While evaporation from lakes and reservoirs has re- ceived considerable attention, there has been almost no quantitative evaporation measurements from open channels. The purpose of this study and report is to develop a thermal model for open channels and to de— termine the applicable coefficients for a Dalton-type evaporation formula. Dalton’s law is often expressed as E : [11(90 —e(l) (1) in which E=rate of evaporation in units of length per time; i11=an empirical coefficient or wind function; ea=saturation vapor pressure of air evaluated at a temperature equal to that of the water surface; and ea=vapor pressure of the air. For the purposes of this report, the wind function is assumed to have the form ¢=a+NV (2) in which V=windspeed and intercept, a, as well as the mass-transfer coefficient, N, are assumed to be con- stant for the canal. The evaluation of the coefficients a and N is difficult for open channels. Southern California offers an excel- lent average climate for the study of the coefficients in the wind function because the sensitivity of surface exchange to windspeed is large in this area of low humidity and high natural water temperatures. The San Diego Aqueduct, operated by the Metropolitan Water District of southern California, was chosen for determination of these coefficients as it has a rela- tively shallow depth, usually steady flow, and a sim- ple hydraulic regime as well as being located in a hot, dry climate. Meterologic data including incoming solar radia- tion, incoming atmospheric radiation, windspeed, wind direction, air temperature, wet-bulb air temper- ature, and rainfall were recorded at each end of the canal for a 1-year period beginning July 25, 1973. In addition, the water temperature at each end, the depth at five locations, and the rates of flow at the canal inlet and diversions were monitored. All these data have been presented previously (Jobson and Sturrock, 1976). The interpretation of these data is accomplished by the use of a one-dimensional, finite-difference, thermal-balance model. The model, which uses both the Eulerian and Lagrangian reference frames, pre- dicts the temperature at the lower end of the canal as a function of (1) the upstream temperature, (2) the rate of surface exchange due to radiation, rainfall, evaporation, and conduction to the air, (3) the ex- change of energy between the bed and the water, and 2 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA (4) longitudinal mixing within the channel. The con- tribution of each surface exchange and mixing process to the predicted temperatures is tabulated by use of a model written in the Lagrangian reference frame. This tabulation allows the coefficients in the wind function to be ascertained. Data collected during 141 days were complete enough for use in calibrating or verifying the thermal model. These 141 days existed in eight groups of con- tinuous data. Every month except January, February, September, and October were represented in the data sets. The model was developed and calibrated using data obtained during the first 28 days of the study. Cali- bration in the sense used here implies the determina- tion of the two coefficients in the wind function (eq. 2) which allow the model to best describe the thermal regime of the canal. The model, with the two derived coefficients, was then verified using the remaining 113 days of data. The wind function coefficients found to apply to the San Diego Aqueduct are similar to the values obtained from lake—evaporation studies except that a larger evaporation at zero windspeed is indi— cated. The following sections describe the flow and tem- perature models and the model calibration, including a discussion of a sensitivity analysis. The model ver- ification is then presented. The report is concluded by presenting an estimate of the total evaporation from the canal throughout the year. MODEL DEVELOPMENT The temperature in an open channel is dependent on both hydraulic and meterologic variables. The flow, on the other hand, can usually be assumed to be inde- pendent of water temperature unless thermal strat- ification is significant. Flow in the San Diego Aqueduct was modeled independently of the tempera— ture, and a data set was written for each time step which contained the average centerline water depth in each subreach and the discharge at each grid point. This data set was then used as input to the tempera- ture model. THE FLOW MODEL The San Diego Aqueduct is a concrete-lined open canal originating near Hemet, Calif, about 120 km southwest of Los Angeles and flowing generally south for about 26 km (see fig. 1) on a slope of 0.00012. The canal’s trapezoidal shape has a 3.66 In bottom width and side slopes of 1.5 to 1. At full capacity it delivers about 28 m3/s, but generally it flows near half ca- pacity. During the study the flow varied from 7 to 24 117°00' I 33°45' BLACK MOUNTAIN 10 KILOMETERS EXPLANATION A Gaging station Meteorologic station Evaporation pan Underground aqueduct CALIFORNIA canal Study site I FIGURE 1.—San Diego Aqueduct showing data-collection points. MODEL DEVELOPMENT 3 m3/s. The maximum design depth is 3.05 m with a 0.305 m freeboard. The operation of the canal is such that the flow re- mains steady for several days in a row. Changes usu- ally occur in steps. Because of equipment failures, shutdowns for canal maintenance, and so forth, only 141 of the 365 days were modeled. Changes in dis- charge ranging from 12 to 60 percent occurred on only 5 days of the 141 days. Although the flow in the canal was generally steady, it was not uniform. Either thechannel rough- ness or the bottom slope varied slightly with distance along the canal. To account for the nonuniformity of the flow between the five water level recorders (see fig. 1), longitudinal profiles of the centerline depth were measured under five different steady flow condi- tions. For computational purposes, the canal was schematized into 20 subreaches of equal length. Each subreach and.the cross section at its upstream end were represented by the index j. The mean depth in each subreach was determined for each flow. An anal- ysis of these observed depths indicated that the follow- ing expression could be used to determine the cen- terline water depth in each of the 20 subreaches. YM(4) ~ YM(3) 5 . Y.- = C.- + d. ——————— + 2 e“. YM(k) (3) Q(21) k=1 in which Yj=centerline water depth, in meters, for subreachj (j=1, 2, . .. 20 with j=1 at the upstream end); 0,, dj, and em. are constants shown in table 1; YM(k)=recorded stage, in meters, at gaging station k, (k=1, 2, 3, 4, 5 with k=1 for the gaging station in the farthest upstream; and Q(21)=discharge at the downstream end of the canal, in cubic meters per sec- ond. The constant e“. interpolates the depth from the two nearest gaging stations in proportion to the dis- tance from each station. The term involving d,- ac- counts for backwater effects and the constant C,- ac- counts for any vertical displacement of the bed in the subreach. The standard error of estimate for equation 3, among the five flow conditions, ranged from a low of 0.004 m for subreach 12 to a high of 0.069 m for sub- reach 14. The median value for all subreaches was 0.031 m. The water volume in each subreach was computed from I Vj = (3.658 + 1.5Yj) YjDX (4) in which Vj = volume of water in subreach j, in cubic meters; Yj = mean centerline water depth in meters (from equation 1); and DX = length, in TABLE 1.—Coefficients for use in equation 3 to determine the center- line depth in the San Diego Aqueduct [All depths are expressed in meters. The value of dJ is assumed zero if the abso- lute difference YMM) — YM(3) is less than 0.04 m and the sign of d, is negative if YM(4) 7 YM13) is negative] Sub- ejk iffCh 0’ d1 12:1 k:2 )2: 12:4 12:5 1 —0.029 0 1.0 0 0 0 0 2 — .055 0 .841 0.159 0 0 0 3 — .047 0 .689 .311 0 0 0 4 — .052 0 .537 .463 0 0 0 5 — .028 0 .385 .615 0 0 0 6 — .021 0 .235 .765 0 0 0 7 + .024 0 .081 .919 0 0 0 8 + .008 0 0 1.0 0 0 0 9 + .182 0 0 .559 0.441 0 0 10 + .150 0 0 .259 .741 0 0 11 + .139 0 0 0 1.0 0 0 12 — .019 0.074 0 0 .872 0.128 0 13 + .144 .428 0 0 .759 .241 0 14 + .294 .507 0 0 .646 .354 0 15 + .226 .519 0 0 .533 .467 0 16 + .202 .606 0 0 .420 .580 0 17 + .078 .492 0 0 .308 .692 0 18 + .125 .399 0 0 .195 .805 0 19 + .070 .158 0 0 .082 .918 0 20 0 0 0 0 0 .500 0.500 meters, of the subreach (1,299 m). The discharge at each cross section was then computed from the dis- charge into or out of the canal and continuity us- ing the expression 620‘): Q0 +1)+QD(j)+[V(j, i +1/2)—V(j, i—1/2)]/DT(5) in which Q(j)=discharge at cross-section (j) and time iDT, V(j, i—1/2)=volume of water in subreach j at time (i—l/z) DT; DT=time step (1 hour used in flow model); and QD(j)=discharge diverted from subreach j during the time step. Three diversion points exist. Diversions near Simpson and the South End (fig. 1) were seldom used, and the third, downstream of Newport, is insig- nificant in size. The volume at time step i+1/2 was de- termined from the average of the depth determined at time step i and time step i+1. THE EULERIAN TEMPERATURE MODEL Applying the principle of conservation of thermal energy to a one-dimensional open channel, the gov- erning equation becomes y 92 _ 9:2 HTW H. at +U ax ‘DI 6x2 Acp + Rhcp (6) in which T=cross-sectional average water tempera- ture; t=time; U =cross-sectional average velocity; 4 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA x=longitudinal coordinate; DI=longitudinal disper- sion coefficient; HT=rate of absorption of thermal energy at the water surface, per unit area; W=top width of the channel; A=cross-sectional area of the channel; c=specific heat of water at constant pressure; p=density of water; Hp=rate at which the water ab- sorbs heat from the bed, per unit area; and Rh=hy- raulic radius. It is usually found that the cross- sectional temperature variation is small for natural channels (Dingman and Weeks, 1970; Jones, 1965; and Rawson, 1970). Water temperatures were mea- sured at four points in the vertical in the San Diego Aqueduct and vertical stratification was never ob- served. The specific heat and density are assumed to be constant, and the product of the dispersion coefficient and the area is assumed to be independent of x. All other varialbes, U, W, HT, A, Hp, and Rh, can be functions of both x and t. Equation 6 is an Eulerian expression; it is a de- scription of the variation of temperature with respect to a fixed coordinate system. This equation was solved numerically by the finite-difference technique using an implicit six-point forward difference scheme. The method of Stone and Brian (1963) was modified by giving the spatial derivative evaluated at the new time step a weight of 0.55 and the derivative evaluated at the old time step a weight of 0.45. This modification is similar to the method proposed by Fread (1974) for a four-point scheme. A 20-minute time step was selected for use in the temperature model because it was an even multiple of the data re- cording frequency (10 minutes) and because of economic reasons. Once the time step was determined, the distance step was selected such that the average value of U DT/DX was about 1.0 in order to optimize the accuracy of the numerical scheme. Using the same cross sections as in the flow model, the canal length was divided into 20 subreaches (21 grid points). The last two terms in equation 6 were evaluated by use of meterologic and hydraulic data; the data were evaluated at a time midway between the time steps. If the water temperature is required in evaluating these terms, however, the old value at the cross section was used. It can be easily demonstrated, by use of nu- merical experiments, that use of the old temperature values has little effect on the accuracy of the solution provided DT W/A [6(HT/cp)/6T] < 0.2. For a water depth greater than 50 cm, this restriction reduced to 6(HT/Cp)/8T S 700 cm/day. Jobson (1973) has shown that this criteria will be met except under very excep- tional conditions. The value of 6(HT/Cp)/6T will be recognized as the kinematic surface exchange coef— ficient. _ The next to the last term in equation 6 represents the rate at which the water absorbs energy from the atmosphere. The San Diego Aqueduct contains several inverted siphons to carry the water under roadways or drainageways. When a subreach contained a siphon the effective surface area of the subreach was reduced to account for the fact that no surface exchange can occur unless there is a free surface. Siphons were as- sumed to have no effect on the velocity or volume of water in the subreach. For purposes of this report, the surface exchange will be expressed as the sum HT=HN_HD+HR_He_Hh (7) in which HN=net heat flux to the water caused by in coming radiation from the sun and the sky; Hb=heat flux leaving the water caused by longwave radiation being emitted by the water; HR =heat flux added to the water by rain falling directly on its surface; He=heat flux leaving the water as a result of the latent heat of vaporization of the evaporated water; and Hh=heat flux conducted from the water to the air as sensible heat The net incoming radiation is composed of four components: The solar radiation incident to the water surface less the reflected component plus the incom- ing atmospheric radiation less its reflected component. The solar radiation incident to an exposed horizontal surface was measured directly at each end of the canal. During times when the entire water surface was exposed to the sun, the percentage of the incident solar radiation to be reflected was determined by use of the expression: R=1.18 Saw-77 (8) in which R =reflectivity and Sa=sun altitude in de- grees (Anderson, 1954). Equation 8 was developed for clear sky conditions, but it is used here under all weather conditions. Cloud cover, which was fairly rare, appears to have a fairly small effect on the reflectivity for sun altitudes above 30°. For low sun altitudes, the water surface was shaded by high banks on either side of the canal. Shading was accounted for by increasing the reflectivity. For the purposes of determining the shading due to the banks, the canal was assumed to flow directly south (fig. 1) and the top of the bank was assumed to be 16.38 m from the centerline of the channel. The average bank height was found to be 8.11 m, mea- sured relative to the invert of the canal. For each time step, the location of the sun (azimuth and elevation) was determined. Knowing the sun’s azimuth, an al- titude for complete shading of the water surface and for complete exposure were determined. If the water MODEL DEVELOPMENT 5 surface was completely shaded, the value of reflectiv- ity was assumed to be 0.9. In other words it was as— sumed that the diffuse component of solar radiation (about 10 percent) would be available even in the shade. If the water surface was completely exposed, equation 8 was used to determine the reflectivity. The reflectivity was assumed to vary directly with the sun’s altitude ranging from a value of 0.9 for com- plete shading to the value given by equation 8 for complete exposure. The amount of incoming atmospheric radiation was measured directly. Unfortunately, this measurement proved to be very difficult, and reliable values are not available for all the 141 days. In some cases, the in- coming atmospheric radiation was estimated by use of a method proposed by Koberg (1964). Three percent of the incoming atmospheric radiation was assumed to be reflected (Anderson, 1954). The longwave radiation emitted by the water sur- face was computed using the Stefan-Boltzman law for blackbody radiation. Hb=ea(T+273.16)4 (9) in which e=emissivity for water (0.97); cr=Stefan- Boltzman constant for black-body radiation; and 273.16 converts to the kelvins when the water tem- perature, T, is given in degrees Celsius. The energy added by rainfall, which was a very rare occurrence, was determined by HR=cpi(T,,.—T,,) (10) in which i=rainfall rate; Tw=wet-bulb air tempera- ture; and Tb is an arbitrary reference temperature which is taken to be zero. The other terms in equation 7 are related to the rate of evaporation, E. The thermal energy utilized by evaporation is expressed as He=pLdJ(eo—ea) (11) in which L=latent heat of vaporization of water. Heat exchange by conduction has received rela— tively little attention because its magnitude is usually small in comparison to the evaporation heat ex- change. Assuming that eddy diffusivities of heat and mass are equal, which leads directly to the Bowen ratio concept, the conduction term can be expressed as in which y=the psychrometric constant (0.0061 P”); Pa=atmospheric pressure in kilopascals; and Ta=air temperature that should be measured at the same elevation as the vapor pressure. The last term in equation 6 represents the thermal flux at the bed of the canal. In the past, attempts have been made to model the bed conduction term; the heat flux has been estimated to be the product of the ther- mal conductivity and the temperature gradient Within the bed. Measurements of bed temperatures are difficult to take so are seldom available. In addition, bed conditions are seldom uniform. Even though the bed conduction term has been shown to be significant (Brown, 1969; Pluhowski, 1970) for shallow depths, it is usually ignored. The concrete and earth under the San Diego Aqueduct were approximated as an infinitely thick conducting medium; the thermal properties of which were estimated. The thermal conductivity of flowing water is much greater, because of turbulence, than that of the concrete and soil; so the surface tempera- ture of the bed can be assumed to equal water tem- perature. Mathematical expressions for the temperature dis- tribution and heat fluxes within a semi-infinite medium which result from an arbitrary temporal variation in surface temperature are relatively simple (Carlslaw and Jaeger, 1959, p. 64). Unfortunately, these expressions converge slowly and their use in a numerical model would be expensive. On the other hand, if the bed were considered to be a slab, insu- lated on the bottom and of an arbitrary thickness, Z, the equations are still fairly simple but converge much faster. If the temporal variations in surface temperature are cyclical, the heat fluxes determined by the semi-infinite and finite thickness slab equa- tions become indistinguishable as the slab thickness increases. In fact, assuming a diurnal water tempera- ture swing of 5°C and thermal properties for concrete, the surface heat fluxes for a slab only 25 cm thick are within 7 percent of the values for a semi-infinite medium. The heat exchange between the water and the bed ‘ was, therefore, estimated by considering the bed to be a homogenous slab, insulated on the lower face and with a top-surface temperature equal to that of the overlying water. The heat flux into or out of the bed was then determined as a function of the past history of the water temperature. Only the thermal diffusiv- ity and heat-storage capacity of the bed needed to be assumed. A slab thickness of 25 cm was assumed; this thickness is believed to be sufficiently thick to give the desired accuracy. The temperature distribution within a slab, ini- tially at constant temperature, for which the surface is subjected to a unit increase in temperature at time 6 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA zero is given by (Carslaw and Jaeger, 1959, p. 102) * _i °° (—1)" ATE—1 7Tn=02n+1 exp [—k(2n + 1)27r2t/4Z2] cos [(2n + 1) 77y/2Z] (13) in which ATE = the temperature rise within the slab; k = the thermal diffusivity; Z 2 thickness of the bed slab; and y = the distance above the insulated bottom of the slab at which temperature (AT8) is computed. The increase in the heat content of the slab can be evaluated at any time by multiplying equation 13 by the heat-storage capacity, then integrating over the total thickness g g (—1)" Ha) =CvZ(1 — 7,2 ”:0 m exp [—k(2n + 1)27T2t/4Z2] sin .[(2n + 1) 7r/2]) (14) in which H( t) = the increase in heat content of the slab between time 0 and t resulting from the unit in- crease in surface temperature at time zero; and CV the heat-storage capacity of the slab which is the product of the density and specific heat. Of course this heat must have been provided from the overlying water. Equation 6 is solved by use of a finite-difference ap- proximation that advance in time by discrete steps of duration at DT. The heat flux from the slab to the wa- ter AH(i) during any time interval iDT to (i + 1)DT which results from a unit increase in water tempera- ture at time zero, can be computed as AH(i) =H(iDT) —H [(i + 1) DT]. (15) The AH(i)’s describe the time variation of the re- sponse of the system to a unit change in water tem- perature. Water temperature fluctuations can be approxi- mated by a series of step changes, and the heat flux is linear with respect to temperature; so the superposi- tion principle is used to determine the heat flux from the bed to the water for any temperature history by use of the equation Hp(iDT) = kg ATUeDT) AH(i —k) (16) in which Hp(iDT) is the heat flux to the water from the bed during the time iDT to (i + 1)DT; ATUeDT) is the change in water temperature which occurred at kDT (k s 1'); AH is given by equation 15; and the wa- ter temperature is assumed to have been constant for times before t = (i — 72)DT. Equation 16 is solved for each cross section and each time step in a tempera— ture model. The water temperature was assumed to have been constant before the model started (AT = 0 for k < 0), and the bed conduction term was limited to a 24-hour memory (3 = i — 72, since DT = 20 min- utes). Thermal diffusivity and heat-storage capacity of the bed material are the only additional parameters which are needed to include the bed conduction term in a thermal model. Heat-storage capacities are rela- tively easy to estimate. A thermal diffusivity of 0.01 cm2/s was found to work best for the concrete-lined canal. No water was added to the canal, and the diversions had no effect on the temperature of the water remain- ing in the canal except insofar as they affected the depth and velocity. The effect of the diversions are ac- counted for in the flow model, and no special precau- tions were needed in the temperature model. The flow and temperature models were coupled in that the output of the flow model was used as input to the temperature model. Hydraulic data at times mid- way between the time steps of the temperature model were obtained by straight-line interpolation between the values generated by the flow model. The dispersion coefficient in equation 6 represents the combined results of several physical processes (Jobson and Yotsukura, 1973), and the estimation of its value is difficult. Fortunately, the predicted tem- peratures are not very sensitive to the assumed value of the dispersion coefficient. Figure 2 is presented to illustrate this insensitivity. The temperature mea- sured at the downstream end of the San Diego Aqueduct on August 18, 1973, is shown in the figure, as well as the predicted temperatures obtained by solv- ing equation 6 with two different values of the dis- persion coefficient, DI. One value of D1 was assumed to be equal to 7,500 Rh U ,, where U * is the shear ve- locity and the other assumed Dr=250 Rh U *. Changing the dispersion coefficient by a factor of 30 changed the predicted temperature at any time by less than 0.08 Celsius degree. The vertical scale, in figure 2, has been expanded during part of the day to illustrate that the value of 7500 RhU, appears to overly smear small temperature variations, The large dispersion coefficient was observed in the Missouri River by Yot- sukura, Fischer, and Sayre (1970), and the small value represents the approximate mean of all the measured values summarized by Fischer (1973). A value of Dx/Rh U r=250 is used throughout this report and the value of Rhwas evaluated for the section near the center of the canal reach. MODEL DEVELOPMENT 7 29 l — 25.8 M 00 — 25.6 ~ 25.4 N \J 25.2 TEMPERATURE, IN DEGREES CELSIUS N a: EXPLANATION Observed Computed Dx/Rh U... = 250 O Computed Dx/Rh U* = 7500 I I I 25 1 l I o 12 18 24 TIME OF DAY, IN HOURS FIGURE 2.—The effect of the dispersion coefficient on the computed temperatures in the San Diego Aqueduct on August 18, 1973, in comparison with measured temperatures. THE LAGRANGIAN MODEL Equation 6 is an Eulerian equation, meaning that it is a description of the variation of temperature with respect to a fixed coordinate system. Another descrip- tion, the Lagrangian, considers the variation of the temperature of a given parcel of fluid or fluid lump, as the parcel moves through the system. In the Lagran- gian framework, one conceptually follows an individ- ual fluid parcel while keeping track of the factors which tend to change its temperature. Applying the thermal continuity equation to a unit mass of fluid, the Lagrangian equivalent of equation 6 is Q dt 62T 6x2 HTW Acp Hp —R,.cp (17) : DI Integrating both sides of equation 17 over the travel- time, one obtains 62T 6x2 HTW Acp £1; Rhcp To—T. =f (D, >dt (18) in which To = final temperature of the water parcel as it passes the downstream end of the channel reach; T,~ 2 initial temperature of the water parcel as it en- ters at the upstream end of the reach; and T = travel- time required for the parcel to be convected through the system. Expanding the right-hand side of equa- tion 18 yields 2 Ta—T,=f’ BIZ—Edit +JT (HN—HD+HR)A—v;)—dt +J Rig") dt ’ W {4; {L(eo—ea)+yL(T—Ta)}:4? dt. (19) Equation 19 is extremely useful to a modeler because it allows the contribution of each exchange process to be isolated and evaluated. For example, integrating the first term in the second integral would determine the net temperature rise of a parcel due to absorbed atmospheric and solar radiation. Comparison of this value to the total temperature change (To — T.) then is a measure of the sensitivity of the predicted tem- peratures to errors in measurements of solar or atmo- spheric radiation. One of the main purposes of this report is to deter- mine the coefficients in the wind function which are applicable to the San Diego Aqueduct. Equation 19 provides a powerful tool for investigating the wind function. To make use of this tool we must assume that the wind function, 11;, applicable to a particular water parcel, is constant. Solving for the wind func- tion by factoring it out of the integral gives 8 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA BZT T,—T,,+f; {0, W W T H +(HV—H¢,+HR) A—Cp }dt+f0 ff]; dt (1;: The wind function in equation 20 is computed as a residual in that it is the average value which must be used during the traveltime, T, to force the energy bud- get of the Lagrangian parcel to balance. Any mea- surement error or any physical process which is not correctly modeled will manifest itself as an error, or scatter, in the value of the wind function computed by use of equation 20. Nevertheless, if measurements are carefully made on a well-selected site, the results can be consistent and useful. ,4. Before equation 20 can be solved, the variation of water temperature with time and distance must be known or assumed. The resulting wind function value, however, is not very sensitive to this water tempera- ture distribution. Equation 6 was used, before the ap- plication of equation 20, to estimate the internal water temperature distribution. In the solution to equation 6, the wind function was assumed to be re- lated to the windspeed as shown in equation 2. The final result was obtained by use of an iterative process in which (a) the coefficients in equation 2 were as- sumed; (b) equation 6 was solved for the 28-day cali- bration period; (c) equation 20 was solved for the wind function at 1,890 equally spaced times during the cal— ibration period; ((1) the wind function values were plotted against the windspeeds representative of the time of passage of the water parcel and new estimates of the coefficients in equation 2 obtained; and (e) if the new estimates were significantly different from the previous estimates, the process was repeated. Equa- tions 6 and 20 were solved using numerical tech- niques and the process converged very rapidly. Each term in equation 20 was calculated separately so that the relative contribution of each physical process to the total temperature changes of any particular fluid parcel could be determined. DATA AND MODEL CALIBRATION DATA AVAILABLE Meterologic data including incoming solar radia- tion, incoming atmospheric radiation, windspeed, wind direction, air temperature, and wet-bulb air temperature, were continuously recorded at each end of the canal for a 1-year period beginning July 25, 1973. In addition, the water temperature at each end, the depth at five locations, and the flow rate were con- tinuously monitored. 7 W [a {L(eo —ea) +yL(T—T,,)} E dt (20) The water temperature and all meteorologic data, except rainfall which was a rare occurrence, were re- corded every 10 minutes in digital form on magnetic tape. The five stages were recorded continuously on analog charts. The charts were digitized to give hourly stages. During times of steady flow, the dis— charges were furnished by the Metropolitan Water District from current-meter measurements and (or) gate ratings. After February 28, 1974, a continuous analog record of discharge was available from a sonic flow meter. Before February 29, 1974, unsteady flow rates were computed from Manning’s equation using the farthest upstream stage measurement. The roughness coefficient applicable in the Manning equa- tion was determined during the periods of steady flow. For further information concerning the site layout or the data collection effort, the reader is referred to Jobson and Sturrock (1976). Because of equipment malfunctions and times when there was no flow in the canal, the data for all 365 1 days of the study were not complete. A total of 141 days were judged to have sufficient data to calibrate or verify the thermal model. These 141 days existed in eight groups of continuous data. The length and dates for each group are shown in table 2. The smallest group contained 4 consecutive days and the largest group 45 days. To be considered acceptable for analy- sis, certain criterion had to be met. These were: 1. The water temperature must be available at both ends of the canal. 2. Flow data must be reasonably complete. 3. All meterologic parameters, except atmos- pheric radiation, must be available at either the Cottonwood (upstream) or the Skinner (downstream) station. Even during the 141 days, many time periods of short duration existed for which the data were not complete. .For example, there were frequent gaps in the wet-bulb temperature record because the wick of the wet-bulb probe dried out for short periods of time. Because the model requires a complete data set for operation, the observed data were copied on a tempo- rary data file and all missing or questionable data were filled in or replaced before the model was run. If a parameter was missing for only an hour or so, the missing values were interpolated. If a longer period of record was missing, the missing values were assumed to be equal to the values observed at the other station. DATA AND MODEL CALIBRATION TABLE 2.—Summary of modeled data for the San Diego Aqueduct [RMS : root mean square] Error in Length computed Mean daily flow rate. in Beginning Ending of temperature (°C) cubic meter per second Group record —_—-—— ————-———-— Df in Standard data Date Hour Date Hour hours Mean RMS Mean deviation 1 07—25—73 1440 08—21—73 0400 638 +0.01 0.14 13.03 0.41 2 11—28—73 1720 12—12—73 1440 334 - .08 .23 6.65 1.58 3 12—19—73 1000 12—24—73 1140 122 — .16 .22 11.10 .69 4 03—07—74 2220 03—10—74 1200 62 + .01 .12 23.58 .56 5 03—13—74 920 03—21—74 2400 207 — .04 .14 19.36 5.30 6 04-18—74 1020 05—01—74 1240 314 — .07 .22 13.95 1.07 7 05—08—74 1520 06—22—74 1420 1079 — 16 .26 15.98 1.35 8 07—05—74 1040 07—23—74 1420 436 — 13 .23 20.34 .20 Vapor pressures and wet-bulb temperatures were handled with special care. Vapor pressures were com- puted from the observed wet- and dry-bulb tempera- tures at both stations before any missing records were filled. Then the vapor pressure was treated as if it were a measured parameter so that in no case was the vapor pressure computed from wet- and dry-bulb tem- peratures obtained at different locations. It was observed that the diurnal range in atmos- pheric radiation differed depending upon the sensor type (Eppley or Gier-Dunkle)1 used in its detection. Although daily mean values appeared consistent, the observed diurnal variation appeared to be too large for both sensor types (Jobson and Sturrock, 1976). It was assumed, therefore, that the incoming atmospheric radiation did not vary during a day, and the daily av- erage value was used. During the calibration period July 25, 1973, to August 21, 1973, the atmospheric radiation was observed at both ends of the canal by use of Eppley pyrgeometers. Between November 28, 1973, and March 10, 1974, only the Eppley pyrgeome- ter at Skinner was used. After March 13, 1974, the incoming atmospheric radiation component was esti- mated by use of the procedure outlined by Koberg (1964). MODEL CALIBRATION No flow model calibration, as such, was involved in this study. As stated previously, the flow was un- steady for only 5 of the 141 days, and the stage was continuously monitored at five points along the canal length. The mean and standard deviation between the daily average flow rates for each data group is shown in table 2. Knowing the flow rate into the canal, as well as the canal depth as a function of time and dis- tance (from eq. 3), the discharge at any point and time was uniquely determined from continuity consider— ations (eq. 5). In order to illustrate the response of the ‘The use of brand names in this report is for identification purposes only and does not imply endorsement by the US. Geological Survey. system to a typical transient, the observed stages as well as the discharge values at the inlet and outlet are shown in figure 3 for transients which occurred on De- cember 10—11, 1973. The Cottonwood, Simpson, New- port, South End, and Skinner gages are 0.3, 9.1, 13.5, 25.0, and 26.0 km downstream of the canal entrance respectively. The Cottonwood discharge is computed from the observed stage at Cottonwood, and the Skin- ner discharge is determined from equation 5. Before October 1, 1973, the roughness of the canal was observed to be constant with a value of 0.0175 but after October 1, the observed roughness appeared somewhat erratic (Jobson and Sturrock, 1976, p. 69). The results of the thermal model obtained for the sec- ond period, November 28 to December 12, 1973, seemed to be more consistent when the roughness was assumed to be 0.0175 than when it was assumed to be 0.0151 as published by Jobson and Sturrock (1976). Therefore, the results for this period were obtained by assuming the Manning’s roughness coefficient to be 0.0175. The modeled and observed temperatures on the 5 days when unsteady flow occurred were critically re- viewed, but no systematic error that appeared to be related to inadequate flow model results could be de- tected. A sensitivity analysis, conducted in some pre- liminary runs during the calibration period, indicated that neither the RMS (root-mean-square) error in pre- dicted temperatures nor the derived coefficients in the wind function were extremely sensitive to discharge errors. A one percent increase in computed discharge increased the intercept coefficient, a, in equation 2 by about 4 percent and decreased the mass-transfer coef- ficient, N, by about 4 percent. It was also determined by a sensitivity analysis of data input for the calibration period that the intercept was not very sensitive to errors in the measured solar radiation or the assumed thermal diffusivity of the bed, but that it was fairly sensitive to errors in the ob- served atmospheric radiation. A one percent increase 10 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA I I | I I I I I | I I I I I | 2 H I _________________________________ ,r""' _ Cottonwood ’/‘/ __ _ > / _/_. ._ I’ / ———————————— ; —/ _——_—_ ,’ Simpson //"‘ — “— — — — — /-’--"‘ U, _- ----------------- >/,__,-___-______/ _ E southEndA i7 '- — —————— ———7 , L” — Skinner -’ _ E / Z ___________ -\_.—/ LL; 1_ Newport/ _ (D < +— _ m _ 0 | l I l l I | I I 15 I | I | I I I I I D Z o _ 0 Lu :0 I n ________________ L“ Cottonwood ,” g 10 — ,>’ CE / LII—J Lu Skinner E _ 9 m I) D Z -_ 5 — __ Lu (3 o: < I — U .— 2’3 0 0 I I I I I I I I I I I I I | I 0000 0600 1200 1800 0000 0600 1200 1800 2400 DECEMBER 10,1973 DECEMBER 11,1973 FIGURE 3.——Variation of stage and discharge for the flow transients on December 10 and 11, 1973, in the values of solar radiation, atmospheric radia- tion, and thermal diffusivity changed the intercept by +0.4, +3, and 0.1 percent, respectively. The fitted mass—transfer coefficient, on the other hand, was somewhat sensitive to errors in solar radiation but not to errors in atmospheric radiation or bed diffusivity. One percent increases in solar radiation, atmospheric radiation, and thermal diffusivity changed the mass- transfer coefficient by +2, +0.6, and —0.02 percent, re- spectively. In summary, the computed Coefficients in the wind function were sensitive to certain measured parame- DATA AND MODEL CALIBRATION 11 ters such as flow rate and radiation, but measurement errors were not unreasonably amplified. The RMS error in computed temperatures was not very sensitive to assumed value of thermal diffusivity of the bed as long as it was within the range of 0.008 cm2/s to 0.015 cmZ/s. Outside this range, the RMS error increased rapidly. By comparison, the range of thermal diffusivities observed in concrete dams on the Tennessee River was from 0.0061 cmz/s for Bull Run Dam to 0.0141 cm2/s for Norris Dam (Troxell and others, 1956). If the assumed thermal diffusivity was outside the indicated range, the computed values of the wind function did not appear to be linearly related to windspeed. Figure 4 illustrates the effect of thermal diffusivity on the wind function values computed for July 30, 1973. With the diffusivity set equal to zero, the wind function values for the day define a loop rather than a straight line. Assuming diffusivities larger than 0.015 cmz/s also created a loop, but the loop progressed counterclockwise with increasing time. Equation 20 was solved for the wind function at 1,890 equally spaced times during the 28-day calibra- tion period. The average windspeed, during the transit of each parcel, was also tabulated, and the wind function values were plotted as a function of windspeed. The results are shown in figures 5 through 11. Also shown in each illustration is a straight line of best fit for the day as well as the correlation coefficient. A composite of all of the results shown in figures 5—11 is shown in figure 12 along with the equation ¢=3.02+1.13 V (21) in which the wind function is given in millimeters per day per kilopascal when the windspeed, V, is given in meters per second. Equation 21 was derived by use of a regression analysis on all 1,890 values of windspeed and wind function during the calibration period, and it was used in equation 6 for all days in the analysis procedure. Equation 21 is considered to be the princi- pal result of this study. An idea of the total variability of the wind function can be obtained from figure 12. As can be seen from ‘0 l l I A < 8 E EXPLANATION 9 0 Thermal diffusivity = 0.01 cmZ/s : 8 — A Thermal diffusivity = 0 —_ uJ n. >. < D E a 6 ~ U) 0: w [— Lu E _I 2' 4 E Hour of water exit E e; 2 9 l— _ _. O 2 Z 3 u. D E E 0 L l l O l 2 3 4 WINDSPEED, IN METERS PER SECOND FIGURE 4.—Comparison of wind function values for July 30, 1973, as computed with and without heat transfer between the water and the bed. 12 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA 12 | JULY 25,1973 «1 = 2.5 + 1.2V 10— I JULY 26. 1973 r =0,98 w = 2,8 +1.3V 12 I 10’ JULY 27, 1973 r =0i87 w=3i6+0.8V a _ WIND FUNCTION, ill, IN MILLIMETERS‘PER DAY PER KILOPASCAL I 1 JULY 28, 1973 7 =0.95 w’ = 2.9 +1,2V FIGURE 5.—Variation of the wind function, with windspeed for the San Diego Aqueduct during July 25 through 28, 1973. 2 3 4 0 1 WINDSPEED, IN METERS PER SECOND 12 i 10 _ JULY 29,1973 r =0.95 w = 32 + LIV V l JU LY 30, 1973 7 =0.97 w = 3.1 +1.0V 12 I 10 JULY 31, 1973 r =0.97 w = 2.4 +1.2V WIND FUNCTION, ‘1’. IN MILLIMETERS PER DAY PER KILOPASCAL o I I AUGUST 1, 1973 r =0.92 w=2i4+1.lV 1 i FIGURE 6.—Variation of the wind function, with windspeed for the San Diego Aqueduct during July 29 through August 1, 1973. 2 3 4 0 1 WINDSPEED, IN METERS PER SECOND DATA AND MODEL CALIBRATION ‘2 I I I I I 10 _ AUGUST 2,1973 A _ AUGUST 3,1973 _ r =0.57 7 =0.93 w=3.4+015V w=l.7+lI5V o I I I I I I ‘2 I I I I I I 10 _ AUGUST 4, 1973 _ _ AUGUST 5, 1973 _ r =0‘93 r =0194 w=l,7+1,6V w=2.l+L2V WIND FUNCTION, 11!, IN MILLIMETERS PER DAY PER KILOPASCAL I I I I 3 4 0 I 2 3 4 WINDSPEED, IN METERS PER SECOND O .1 N’— __ \ FIGURE 7.—Variation of the wind function, with windspeed for the San Diego Aqueduct during August 2 through August 5, 1973. ‘2 I T AUGUST 6,1973 AUGUST 7,1973 r=0,81 r=0.76 w=2.0+|.5V U I I I I I I ‘2 I I I I I I 10 AUGUST 8, 1973 _ _ AUGUST 9, 1973 a ' r = 0.98 II: = 32 +1.1V WIND FUNCTION, 11’, IN MILLIMETERS PER DAY PER KILOPASCAL o I I | 0 I I | 0 I 2 3 4 0 1 2 3 4 WINDSPEED, IN METERS PER SECOND FIGURE 8.—Variation of the wind function, with windspeed for the San Diego Aqueduct during August 6 through August 9, 1973. 14 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA ‘2 I I I I I I 10 _ AUGUST 10, 1973 _‘ _ AUGUST 11, 1973 _ r=0.94 r=0.95 w=32+L2V w=335+131V 2 _ E _. _ 0 I I I I I I 12 T I I I I I 10 _ AUGUST 12, 1973 g _ AUGUST 13,1973 _ r = 0.92 r :0‘61 w=3I2+L2V w=3.5+0I9V WIND FUNCTION, III, IN MILLIMETERS PER DAY PER KILOPASCAL 0 I I I I I I 0 I 2 3 4 0 1 2 3 4 WINDSPEED, IN METERS PER SECOND FIGURE 9.—Variation of the wind function, with windspeed for the San Diego Aqueduct during August 10 through August 13, 1973. ‘2 I I I I I 10 g AUGUST 14, 1973 _ # AUGUST 15, 1973 _ r =0382 r = 0.78 w=3.9+0.6V w=3.2+1,lV 2 fl _ _ A I I I I I I ‘2 I I I I I I 10 _ AUGUST 15, 1973 - 7 AUGUST 17,1973 fl r =0.85 7 =0.91 w=238+1.6V w=3.l+l.4V WIND FUNCTION, w, IN MILLIMETERS PER DAY PER KILOPASCAL 0 | | I I | | 0 I 2 3 4 0 1 2 3 4 WINDSPEED, IN METERS PER SECOND FIGURE 10.—Van’ation of the wind function, with windspeed for the San Diego Aqueduct during August 14 through August 17, 1973. WIND FUNCTION, III, IN MILLIMETERS PER DAY PER KILOPASCAL DATA AND MODEL CALIBRATION AUGUST 18, 1973 r =0,90 w = 36 +0i6V | I AUGUST 19, 1973 r =0.93 W = 31 +1.0V 2 ._ _. w o I | I I I ‘2 I I I I I 10 _ AUGUST 20,1973 _ AUGUST 21,1973 I =0.92 Ib=2.7+l.lV Iv =0i6+2.5V 3 . o’ .0 _ ._ o I I I I I o 1 2 3 4 o 1 2 3 WINDSPEED, IN METERS PER SECOND 15 FIGURE 11.~—Variation of the wind function, with windspeed for the San Diego Aqueduct during August 18 through August 21, 1973. WIND FUNCTION, III, IN MILLIMETERS PER DAY PER KILOPASCAL FIGURE 12.—Computed wind function values for the San Diego Aqueduct. Every other point plotted for the 28-day period starting 10 w=3i01+1.l3V ’c ' ° 2 3 WINDSPEED, IN METERS PER SECOND July 25, 1973. 16 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA figures 5 through 11, the data for any particular day generally defines a reasonably straight line, but the mass-transfer coefficient and intercept varies from day to day. Ignoring the results for 2 of the 26 com- plete days, the intercept varies from 1.7 to 3.9 and the mass-transfer coefficient varies from 0.5 to 1.6. Nevertheless, equation 21 seems to be fairly well de- fined by the data and indeed it is entirely possible that the intercept and mass-transfer coefficient are somewhat dependent on wind direction or other meteorologic factors which vary from day to day. With the wind function defined by equation 21, equation 6 was capable of predicting the downstream temperature during the 28-day calibration period with a RMS error of 0.14°C. A sample of the predicted and measured temperatures is shown in figure 13. MODEL VERIFICATION AND DISCUSSION The ability of equation 21 to accurately define evap- oration from the San Diego Aqueduct was verified by solving equation 6, wherein the wind function is de- fined by equation 21, for the remaining 113 days of data. These days were scattered throughout the year and included days in the months of November, De— cember, March, April, May, June, and July. Visual verification with typical results is illustrated in figures 14 through 20 which contain the observed and modeled temperatures during the first 4 full days of each of the seven groups of verification data. The mean and the RMS error in the predicted tempera- tures for each group are shown in table 2. The overall RMS error during the 113 days of verification is 023°C. Errors tend to be smaller during the winter; this should be expected because of the smaller diurnal range. The observed temperatures during March 1974 (figs. 16 and 17) appear somewhat erratic possibly be- cause of instrumentation errors. The temperature re- corder at the lower end of the canal definitely mal- functioned soon after March 21, 1974. Overall, the 29 I I I | I I I l I I I I I I I I I I I | I EXPLANATION ------ - Modeled Observed 28 b — - —— Observed upstream I‘ , A\ — I “ /\ ‘ \ I \ \ 27 — I — I ‘ ’lfI /’/ \\\ 26 T x/ \- J m\ / \\ / x - TEMPERATURE, IN DEGREES CELSIUS 25:— \ -¥ \\\ l \\\ \\-Il \\ \ 24-— ’ ~— 23 I I I I I I | I I I I I I I 4L I i I | | I | | 26 27 28 29 JULY 1973, IN DAYS FIGURE 13.—Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the calibration period. MODEL VERIFICATION AND DISCUSSION 17 17 I I I I I I I I I I I | I I I I I I I I I I I I I EXPLANATION — —————— Modeled Observed 16 " — — — —- Observed upstream TEMPERATURE, IN DEGREES CELSIUS 12— 11_JIIIIIII.III.I NOV. 30 DAY IN 1973 FIGURE l4.—Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the first verification. DEC. 3 results of the verification appear to be very good. The results illustrated in figures 14—20 are believed to verify that equation 21 predicts representative evaporation rates during all seasons of the year. On the other hand, the results shown in figures 5 through 11 suggest that the wind function coefficients in equa- tion 21 vary from day to day. In order to determine if these coefficients varied in any systematic manner throughout the year, equations 6 and 20 were solved simultaneously for the seven verification periods in the same manner as for the calibration period. Plots similar to those shown in figures 5—11 were inspected, and the daily values of the wind function coefficients were determined. Table 3 contains a tabulation of the results for all days in which the correlation coefficients for the linear regression exceeded 0.7. \Fewer results are shown for the cooler months. Dur— ing this time, evaporation became a small factor in the energy budget so that random errors in the other components were amplified. Although significant scat- ter in the daily mass transfer coefficients exist, no seasonal pattern is apparent. The intercept values, on the other hand, appear to increase between March and July. Since the intercept values are fairly sensitive to errors in the atmospheric radiation term and no ac- tual measurements of this term was available after March 13, 1974, little emphasis is placed on the ap- parent trend. Figures 13 through 20 demonstrate that equation 21 provides accurate predictions of water temperature when incorporated in a thermal model. But before the accuracy of equation 21 can truly be verified, it must be demonstrated that the accuracy of the predicted temperatures is reasonably sensitive to the evapora- tion rate. The diurnal variation in water temperature at the canal entrance is very small as can be seen in figures 13 through 20. The San Diego Aqueduct is fed by a pipeline which passes under the San Jacinto Mountains just upstream of the canal entrance. The ability of the model to start with a relatively constant inflow temperature and to accurately predict the diurnal swings at the downstream end implies that 18 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA TABLE 3.—Daily values of the wind function coefficients for the San Diego Aqueduct TABLE 3.—'Daily values of the wind function coefficients for the San Diego Aqueduct—Continued Mass transfer Interce t (a) Correlation ( ) [mm/d-kPa‘m/s] Mass transfer Intercep‘t (a) Correlation ( ) Pa} [mm/d‘kPam/s] Date [mm/d- Pa] coefficient Date [mm/d coefficient 07—26—73 2.80 1.30 0.98 05—19—74 1.80 1.40 0.88 07—27—73 3.60 .80 .87 05—20—74 1.20 1.80 .90 07—28—73 2.90 1.20 .95 05—21—74 1.40 1.50 .79 07—29—73 3.20 1.10 .95 05—22—74 1.60 1.30 .83 07—30—73 3.10 1.00 .97 05—23-74 1.90 1.00 .84 07—31—73 2.40 1.20 .97 05—24—74 1.80 1.40 .71 08—01-73 2.40 1.10 .92 05—26—74 2.60 3.60 .86 08—03—73 1.70 1.50 .93 05—27—74 3.10 1.60 .97 08—04—73 1.70 1.60 .93 05~28—74 1.20 1.60 94 08—05—73 2.10 1.20 .94 05—29—74 1.80 1.10 .92 08—06—73 2.00 1.50 .81 05—31—74 .70 .90 .91 08—07—73 2.60 2.00 .76 06—01-74 1.30 .90 .95 08—08—73 3.40 1.60 .85 06—02—74 2.30 .60 .86 08.09_73 3.20 1.10 .98 06—03— 74 1.90 .90 .88 08— 10—73 3.20 1.20 .94 06—04—74 2.00 .80 .90 08—11—73 3.60 1.10 .95 06-05—74 2.00 .80 .94 08—12—73 3.20 1.20 .92 06—06474 2.40 .80 .94 08—14—73 3.90 .60 .82 06—07—74 .10 1,00 .87 08—15—73 3.20 1.10 .78 06—08—74 1.00 .90 .93 08—16—73 2.80 1.60 .85 06—09—74 2.40 .40 .73 08—17—73 3.10 1.40 .91 06—10—74 2.30 .60 .93 08—18—73 3.60 .60 .90 06— 1 1—74 1.90 1.00 88 08—19-73 3.10 1.00 .93 06—12474 1.50 1.30 .90 08—20— 73 .60 2.50 .92 06—13—74 240 .90 .95 11—30—73 2.60 1.10 .72 06—14—74 2.50 .60 .89 12—11—73 2.50 1.80 .88 06—15—74 2.50 .40 .85 12—22—73 -.80 2.60 .84 06—16—74 2.70 .80 .93 03—18—74 —1.10 6.00 .88 06—17—74 2.40 .70 .97 03—20—74 —1.70 2.50 .74 06—18—74 2.10 .80 .97 03—21—74 —1.50 5.00 .81 06—19—74 2.30 .80 .89 04—19—74 “2.20 3.60 .80 06—20—74 1.90 1.00 .94 04—20—74 1.10 2.50 .73 06—21—74 2.30 .80 .97 04—22—74 1.60 2.50 .86 07—06—74 2.80 .70 .97 04—23— 74 1.40 1.70 .82 07—07—74 2.00 .80 .97 04—24—74 —2.00 3.00 .91 07—08~74 1.50 1.20 .90 04—25—74 .80 1.60 .95 07—09—74 2.40 .80 .95 04—26—74 .50 2.00 .86 07—10—74 .80 1.50 .91 04—27—74 .30 2.40 .89 07—11—74 1.90 .90 .82 04—28-74 .80 2.10 .92 07—12—74 2.60 .50 .90 04—29-74 1.60 1.20 .72 07—13—74 2.70 .60 .82 05—10—74 —3.90 4.60 .92 07'16—74 2.20 .80 .92 05—11-74 —1.70 3.80 .95 07—17—74 2.40 .50 .90 05—12—74 .40 2.30 .84 07—18—74 3.30 .60 .84 05—13—74 —3.60 3.50 .91 07—20—74 1.70 1.10 .89 05—16—74 —1.00 2.30 .92 07—21A74 1.90 .80 .94 05—17—74 —.70 2.40 .94 07—22«74 1.70 2.00 78 05—18—74 .60 1.70 .94 the surface exchange, including evaporation, is being accurately modeled. The study site was selected such that it would be in a climate where a' large part of the total surface ex- change is due to evaporation. Equation 19 provided the means of evaluating the contribution of each pro- cess to the energy budget of an individual water par- cel passing through the canal. In order to illustrate the relative contributions of each process, the mean and standard deviation of each major term in equation 19 are tabulated in table 4 for each group of data. It is seen that evaporation H., as well as the net radiation, HN—Hb, are major components of the energy budget. Conduction to the air or the bed are small compo— nents. Comparing the RMS error in the predicted temperature (table 2) to the temperature change due to evaporation (table 4), it is seen, that except perhaps for a short period in March when there may have been instrument malfunction, the evaporation must have been modeled fairly well. It is concluded, therefore, that the evaporation from the San Diego Aqueduct is realistically represented by the wind function of equa- tion 21. In order to compare equation 21 with existing wind functions, a simple seventh-root velocity law was used to convert windspeeds for all equations to a common reference height of 4 m, which was the approximate height of the anemometers used in this study. No cor- rection was made for the measurement height of the vapor pressure, and it was assumed that the effect of averaging data over periods of time of 1 day or less had no effect on the coefficients in the wind function. MODEL VERIFICATION AND DISCUSSION 19 TABLE 4.—-Summary of energy budget terms for individual water parcels passing through the San Diego Aqueduct Mean and standard deviation of temperature increase, Beginning in degrees Celsius, to result from the indicated cause Group date [Standard deviations in parentheses] Observed temperature Incoming Back Conduction Conduction increase radiation radiation Evaporation to the air to the bed 1 07-25—73 —0.21 2.78 -1.95 —1.00 0.0 0.00 (0.86) (1.00) (0.05) (0.35) (0.16) (0.09) 2 11—28—73 -0.54 3.12 -2.80 —0.71 —0.13 0.01 (0.73) (0.88) (0.33) (0.22) (0.21) (0.12) 3 12—19—73 —0.33 1.94 —1.82 —0.37 —0.08 0.01 (0.55) (0.56) (0.02) (0.15) (0.11) (0.06) 4 03—07-74 —0.22 1.20 —1.06 —0.25 —0.14 0.00 (0 44) (0 40) (0 02) (0.05) (0 05) (0 03) 5 03—13—74 +0.12 1.58 —1.31 —0.12 —0.02 0.00 (0 62) (0.69) (0 29) (0.25) (0 19) (0 05) 6 04—18—74 +0.01 2.53 —l.84 —0.58 —0.08 0.01 (1 00) (1.14) (0 04) (0.29) (0 13) (0.11) 7 05-08—74 —0.08 2.52 —1.82 —0.68 —0.08 0.01 (0 98) (1.11) (0.22) (0.31) (0 13) (0.09) 8 07—05—74 —0.06 2.27 — 1.57 —0.72 0.0 0.00 (0 86) (1.04) (0 03) (0.35) (0 13) (0 08) 17 I. I r I I I ‘I I | I | I | I I I I I I I I I EXPLANATION — ------ Modeled Observed 16 — —- - — Observed upstream _ 15— - TEMPERATURE, IN DEGREES CELSIUS DECEMBER 1973, IN DAYS FIGURE 15.—-Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the second verification. Harbeck (1962) summarized evaporation studies inputs and having surface areas ranging from 4X 103 made on reservoirs having little or no artificial heat to nearly 1.2x108m2. He proposed the relation 20 2.43 lb .— _— _ Arms (22) in which A, is surface area of the reservoir, in meters squared; and V is the windspeed at the center of the reservoir, in meters per second. The major difference between equation 21 and 22 is that Harbeck assumes no evaporation will occur unless a measurable windspeed exists. This is probably a reasonable as- sumption if the windspeed is measured near the cen- ter of a large lake, but it is probably unrealistic for computation of evaporation from streams. Near streams and rivers the rough terrain limits wind- speeds to values less than the stall speeds of most anemometers during a fairly larger percentage of the time. In addition the flow velocity generates a relative motion between the water and air even at zero windspeeds. For a surface area of 150 m2, (the aver- age width of the canal was about 9 m) equations 21 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA and 22 intersect at a windspeed of about 4 m/s. Above an artificially heated water surface, free con- vection may significantly increase the rate of evapora- tion. For artificially heated reservoirs, Ryan and Stol- zenbach (1972) present the formula ¢=0.95(A0)‘/3+0.91V (23) in which A6 is the difference between the virtual tem- perature of the air and the water surface. The virtual temperature is the temperature at which dry air would have the same density as the moist air mixture assuming constant pressure. They suggest that the value of A0 should be taken as zero for water bodies with no thermal loading. The mass-transfer coeffi- cients (slope) in equations 21 and 23 differ by 19 per- cent. A commonly used formula was developed by Meyer in 1942 and published by Linsley, Kohler, and Paulhus (1958). 17 I I I I I I | I | I I I I I I I I I I | | | I I I EXPLANATION ------ - Modeled Observed 16 — — — — — Observed upstream 15 14 13 TEMPERATURE, IN DEGREES CELSIUS 12 11..I.111..ILI| MARCH 1974. IN DAYS FIGURE 16,—Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the " third verification. MODEL VERIFICATION AND DISCUSSION w=2.7+0.66 V. (24) Although the mass-transfer coefficient is smaller, the intercept in formula 24 is only 11 percent less than that for equation 21. The Tennessee Valley Authority (1972), as well as Ryan and Stolzenbach (1972), have given excellent summaries of many of the existing empirical wind function formulas. Equation 21 is, however, believed to be the only equation ever developed from the ther- mal balance of an open channel. In summary, the wind function for the San Diego Aqueduct (eq. 21) in- dicates a larger evaporation at low windspeeds than is indicated by most lake evaporation formulas, but the mass-transfer coefficient is within the range of values which have been reported. For the average windspeed at the San Diego Aqueduct, about 1.5 m/s, equation 21 indicates a slightly greater evaporation rate than would be indicated by most lake evaporation for- mulas. In order to estimate the evaporative water loss from 21 the San Diego Aqueduct, equations 1 and 21 were solved using daily averaged values of windspeeds, water temperature, and vapor pressure for each end of the canal (Jobson and _Sturrock, 1976). The evapora- tive rate at each end of the canal was computed for each day, and the resulting monthly averaged evap- oration rates were determined. The monthly average results are shown in figure 21 as well as in table 5. Because of missing data, mainly the vapor pressures of the air, a considerable amount of interpolation was required to estimate monthly evaporation rates. Using days when the daily average vapor pressure was available at both ends of the canal, a monthly value of the ratio of these vapor pressures was estab- lished. Missing vapor pressures were interpolated using these ratios as well as the monthly mean values and any other factors considered to be significant. Missing water temperatures were interpolated by pay- ing special attention to the seasonal variation of the mean difference in the water temperatures at the ends of the canal. Very few windspeed data were missing. 18 I I I I I I I I I I I I l I I I I I I I I I I I I | I I I I EXPLANATION - ------ Modeled Observed 17 _ — - — Observed upstream _ U) D (7) J A 8 16 — y ‘ — ‘D .. I ”L; I \ I \ I .1 \ 5 I \ \ Lu I \\ D 15 — ‘\ _ E ‘ , / v x u; \‘ I , \ A \ / \ m \ _ / \ / \ 12 \ ’ \ / \ \ < / x D: f a. \ . \ \ _ Lu 14 — r \ / I ‘ ~ g / \ / ., '— m, l [I 13 _ — 1 2 I I I I I I I I I I I L I I I I I l I I I I I L 14 l 5 16 17 MARCH 1974, IN DAYS FIGURE 17 .—Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the fourth verification. 22 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA 22'I'I'I'I’I'l'l EXPLANATION — ————— — Modeled Observed — — — Observed upstream TEMPERATURE, IN DEGREES CELSIUS IIIIIITF‘I l Illlll APRIL 1974, IN DAYS FIGURE 18.—Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the fifth verification. The annual evaporation rate for the canal was esti- mated to be 2.08 m. This number is significantly larger than the estimated lake evaporation for the re- gion of 1.32 In (Kohler and others, 1959) and slightly greater than the regional estimate for evaporation from a class A evaporation pan of 1.78 In. On the other hand, the average pan evaporation during the study, from class A evaporation pans maintained at each end of the canal by the Metropolitan Water Dis- trict, is shown. in table 5 along with the computed TABLE 5.—Evaporation rates for the San Diego Aqueduct during the study period, July 25, 1973, to July 24, 1974 Water loss by the Canal, in Pan thousands of coefficient cubic meters Evaporation rate in millimeters per day Month Canal CISEZA January __________ 1.99 2.57 0.77 15.4 February __________ 2.19 4.30 .51 4.3 3.45 .72 19.8 6.90 .75 43.7 6.97 .95 55.3 9.65 .96 78.2 10.65 .90 81.6 9.80 .81 59.7 September ________ 7.89 — — 57.6 October ____________ 7.41 6.72 1.10 55.8 November ________ 4.48 3.35 1.34 31.0 December __________ 3.39 2.74 1.24 22.4 Total ____________________________________________ 524.8 Norm—1,000 m3 = 0.811 acre feet. ‘Represents composite of 1973 and 1974 data. canal evaporation and a monthly pan coefficient. As- suming a pan evaporation of 8.3 mm/d during Sep- tember, the annual pan loss was observed to be 2.29 In giving an annual observed pan coefficient of 0.91. Comparing the computed canal evaporation with the observed pan evaporation values, one again reaches the conclusion that evaporation rate from the San Diego Aqueduct is a little greater than reservoir evaporation for the same area. The evaporation rates estimated above were con- verted to water use by multiplying the average evap- oration rate for each day by the effective surface area of the canal for that day. The surface area was com- puted from the mean daily stage values in conjunction with the shape of the canal and the data contained in table 1. The monthly water losses are also shown in table 5. The water loss for February is very low be- cause the canal was empty during much of the month. Flow was continuous for all other months. The July value represents the loss during July 26—31, 1973, plus the loss during July 1—22, 1974, prorated to 31 days. Even during June, July, and August, the evaporative loss represents less than 0.2 percent of the total flow. SUMMARY AND CONCLUSIONS A one-dimensional temperature model has been de- veloped by use of flow and meteorologic data collected SUMMARY AND CONCLUSIONS 23 25 I | I | I | I l I l I | I | I | I l I l I | I l l l I l EXPLANATION ------- Modeled Observed 24 — — —— — -— Observed upstream TEMPERATURE, IN DEGREES CELSIUS MAY 1974, IN DAYS FIGURE 19.——-Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the sixth verification. on the San Diego Aqueduct in southern California. Analyzing the problem from both the Eulerian and Lagrangian point of view, it was possible to determine the two coefficients in a Dalton-type evaporation for- mula (eq. 21) by balancing the energy budget of the. canal. The model was calibrated, that is, the coefficients were determined, using 28 days of data and verified with 113 different days of data. During all seasons of the year, equation 21 appears to realistically represent the evaporation from the canal. Equation 21 is believed to be the first wind function ever derived from the thermal balance of an open channel. The derived wind function for the San Diego Aqueduct indicates a larger evaporation at low windspeeds than would be indicated by most lake evaporation formulas, but the mass-transfer co- efficient is within the range of values commonly re- ported. An annual canal evaporation of 2.08 m is indi- cated; this figure is about 91 percent of the amount of water evaporated annually from nearby class A evap- oration pans. REFERENCES Anderson, E. R., 1954, Energy budget studies, in Water-loss inves- tigations: Lake Hefner studies, Technical Report: US. Geologi- cal Survey Professional Paper 269, p. 71—120. Brown, G. W., 1969, Predicting temperatures of small streams: Water Resources Research, v. 5, no. 1, p. 68—75. Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of heat in solids (2d ed.): New York, Oxford University Press, p. 104. Dingman, S. L. and Weeks, W. F., 1970, Temperature and ice dis- tribution in the North Saskatchewan River below the Edmon- ton generating plant: Cold Regions Research and Engineering Laboratory, Hanover, NH, Special Report 152, 31 p. Fischer, Hugo B., 1973, Longitudinal dispersion and turbulent mix- ing in open channel flow: Annual Review of Fluid Mechanics, p. 59—78. Fread, D. L., 1974, Numerical properties of implicit four-point finite difference equations on unsteady flow: National Oceanic and Atmospheric Administrative Technical Memorandum NWS HYDRO— 18, 38 p. Harbeck, G. E., Jr., 1962, A practical field technique for measuring reservoir evaporation utilizing mass-transfer theory: US. Geological Survey Professional Paper 272—E, p. E101—E105. Jobson, Harvey E., 1973, The dissipation of excess heat from water systems: American Society of Civil Engineers, Journal of the Power Division, v. 99, no. P01, p. 89—103. Jobson, Harvey E., and Sturrock, A. M., Jr., 1976, Comprehensive monitoring of meteorology, hydraulics and thermal regime of the San Diego Aqueduct, California: US. Geological Survey Open-File Report 76—628, 102 p. Jobson, Harvey E. and Yotsukura, Nobuhiro, 1973, Mechanics of heat transfer in nonstratified open-channel flows, in Shen, Hsieh Wen, ed., Environmental impact on rivers (River mechanics III): Fort Collins, 0010., Hsieh Wen Shen, 67 p. Jones, E. J ., 1965, Temperature in California streams; part 1, evaluation of thermograph records: US. Geological Survey open-file report, 31 p. Koberg, Gordon, E., 1964, Methods to compute long-wave radiation from the atmosphere and reflected solar radiation from a water 24 THERMAL MODELING OF FLOW IN THE SAN DIEGO AQUEDUCT, CALIFORNIA 28 l I | I l I l I l I l I | I | I | I | I I I l I l I l I l I | EXPLANATION - ------ Modeled Observed 27 —- _ - — Observed upstream _ U) 3 :7) .1 LLI o u: LU Lu :2: 0 Lu 0 E Lu. n: 3 i.- < 1: Lu 0. 2 Lu '— lilililllililililillilililJ 22 6 7 8 9 JULY 1974, IN DAYS FIGURE 20.—Comparison of the modeled and observed temperatures at the downstream end of the San Diego Aqueduct during the first 4 days of the seventh verification. Linsley, R. K., Jr., Kohler, M. A., and Paulhus, J. L. H., 1958, Hy- Z >_ 10 — — drology for engineers: New York, McGraw-Hill, 98 p. E g — _ Plukowski, E. J ., 1970, Urbanization and its effect on the tempera- : o: 8 — — ture of the streams on Long Island, New York: US. Geological n: 31' — — Survey Professional Paper 627—D, 110 p. Z w 6 ._ — Rawson, J ., 1970, Reconnaissance of water temperature of selected 2% _ —— streams in southeastern Texas: Texas Water Board, Austin, < E 4 _ __ Tex., Report 105, 12 p. g E __ _ Ryan, P. J., and Stolzenbach, K. D., 1972, Environmental heat fi 3' 2 _ transfer, in Engineering aspects of heat disposal from power a g _ _ generation: Mass. Institute of Technology, Cambridge, Ralph 0 M. Parsons Laboratory for Water Resources and Hydro- J F M A M J J A S O N D dynamics, summer session, 75 p. MONTH Stone, H. L., and Brian, P. L. T., 1963, Numerical solution of con— FIGURE 21.—Computed monthly average daily evaporation from the San Diego Aqueduct during the study period, July 25, 1973, to July 24, 1974. surface: US. Geological Survey Professional Paper 272—F, p. F107—F136. Kohler, M. A., Nordenson, T. J., and Baker, D. R., 1959, Evapora- tion maps of the United States: US. Weather Bureau Technical Paper 37, Washington, DC, 13 p. vective transport problems: American Institute of Chemical Engineers Journal, V. 9, no. 5., p. 681—688. Tennessee Valley Authority, 1972, Heat and mass transfer between a water surface and the atmosphere: Water Resources Research Laboratory Report 14, Norris, Tenn., 147 p. Troxell, George Earl, and Davis, Harmer E., 1956, Composition and Properties of Concrete: New York, McGraw-Hill, 334 p. Yotsukura, N. B., Fischer, H. B., and Sayre, W. W., 1970, Meas- urement of mixing characteristics of the Mississippi River be- tween Sioux City, Iowa and Plattsmouth, Nebraska: US. Geological Survey Water-Supply Paper 1899—G, 29 p. mm , if?!“ csumaw Shorter Contributions to Geophysics, 1979 Mountain Breathing—Preliminary Studies of Air-Land Interaction on Mauna Kea, Hawaii By ALFRED H. WOODCOCK and IRVING FRIEDMAN Porosity and Density of Kilauea Volcano Basalts, Hawaii By GORDON R. JOHNSON Diabase Dikes in the Haile-Brewer Area, South Carolina, and Their Magnetic Properties By HENRY BELL III, KENNETH G. BOOKS, DAVID L. DANIELS, WILLIIAM E. HUFF, JR., and PETER POPENOE Aerial Gamma-Ray Survey in Duval, McMullen, Live Oak, and Webb Counties, Texas By JOSEPH S. DUVAL and KAREN A. SCHULZ GEOLOGICAL SURVEY PROFESSIONAL PAPER 1123—A—D UNITED STATES GOVERNMENT PRINTING, WASHINGTON: 1980 UNITED STATES DEPARTMENT OF THE INTERIOR CECIL D. ANDRUS, Secretary GEOLOGICAL SURVEY H. William Menard, Director Library of Congress Catalog—card No. 80—600006 For sale by the Superintendent of Documents, US. Government Printing Office Washington, DC. 20402 Stock Number OZ4—001—03277—5 CONTENTS [Letters designate the separate chapters] (A) Mountain breathing——preliminary studies of air—land interaction on Mauna Kea, Hawaii, by Alfred H. Woodcock and Irving Friedman. (B) Porosity and density of Kilaeua Volcano Basalts, Hawaii, by Gordon R. Johnson. (C) Diabase dikes in the Haile—Brewer area, South Carolina, and their magnetic properties, by Henry Bell III, Kenneth G. Books, David L. Daniels, William E. Huff, Jr., and Peter Popenoe. (D) Aerial gamma—ray survey in Duval, McMullen, Live Oak, and Webb Counties, Texas, by Joseph S. Duval and Karen A. Schulz. CONVERSION FACTORS Metric unit Inch-Pound equivalent Metric unit Inch-Pound equivalent Length Specific combinations—Continued millimeter (mm) : 0.03037 inch (in) liter per second (L/s) : .0353 cubic foot per second meter (m) : 3.28 feet (ft) cubic meter per second : 91.47 cubic feet per second per kilometer (km) : .62 mile (mi) per squ)ail‘(e kilometer square mile [(ft“/s)/mifl] [ m-“/s / m2 Area meter per day (m/d) = 3.28 feet pear dgyiéhgidrgbge con uc v y square meter (in?) : 10.76 square feet (ftz) meter per kilometer : 5.28 feet per mile (ft/mi) square kilometer (ka) : .386 square mile (miz) (m/km) hectare (ha) = 2-47 acres kilometer) per hour : .9113 foot per second (ft/s) km/ Volume ( meter per second (m/s) : 3.28 feet per second cubic centimeter (cm3) : 0.8g1 cugic inch (in3) meter sq)uared per day : 10.764 feetmsquared pertday (ftz/d) liter (L) : 61, cu ic inches (mZ/d ransmissivi y cubic meter (“‘75) = 35-31 cubic feet if“) cubic meter per second :: 22.826 million gallons per day cubic meter : .00081 acre-foot (acre-ft) (mg/S) (Mgal/d) ' 3 ——< i . gig? hectometer (hm ) ; 3:113 figisfefgt) cubic meter) per minute 2264.2 gallons per minute (gal/min) liter : 1.06 quarts (qt) (mi/mm liter = .26 gallon (gal) liter per second (L/s) : 15.85 gallons per minute cub": meter : -00026 mlligflngi‘iglons (Mgal 01' liter per second) per : 4.83 gallonslperirrsi/nfléte per foot . _ ‘ _ meter [(L/s /m] ga /m n ] cubic meter _ 61290 barrels (bbl) (1 bbl_42 gal) kilolrinetelr) per hour : .62 mile per hour (mi/h) Weight m meter per second (m/s) : 2.237 miles per hour gram (g) = 0.035 ounce, avoirdupois (oz avdp) gram per cubic : 62.43 pounds per cubic foot (lb/ft3) gratin t (t) : 1.0332 pound,havoirgu6)§8slb()lb avdp) centimeter (g/cm“) me ric ons : .1 tons s ort ( _ . __ v v gram per square _ 2.048 pounds per s uare foot 1b ft2 metric tons _ 0.9842 ton, long (2,240 lb) centimeter (g/cm?) ‘1 ( / ) Specific combinations gram tPel‘ tSquare = 0142 pound per square inch (lb/in?) cen ime er kilogram per square : 0.96 atmosphere (atm) k 1centimeter (kg/cm?) 98 0 9 Temperature ’ a r s . a . t lgengtiIInneItgr quare b r ( 869 a m) degree Celsius (°C) 1.8 cubic meter per second (rm/s) cubic feet per second (ft3/s) degrees Celsius (temperature) degrees Fahrenheit (°F) [(1.8>< ”C) +32] degrees Fahrenheit Mountain Breathing—Preliminary Studies of Air-Land Interaction on Mauna Kea, Hawaii By ALFRED H. \VOODCOCK and IRVING FRIEDMAN SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 GEOLOGICAL SURVEY PROFESSIONAL PAPER 1123~A FIGURE 1. 2. 3. TABLE 1. CONTENTS Page Abstract _________________________________________________________________ A1 Introduction _____________________________________________________________ 1 Acknowledgments _________________________________________________________ 2 Observations _____________________________________________________________ 3 Latent heat loss to the air _________________________________________________ 5 Source of heat ___________________________________________________________ 5 Sensible heat of inflowing air as source of latent heat in outflowing air ___ 5 Conduction of heat into the mountain __________________________________ 5 Snow and rainwater as a sensible heat source __________________________ 6 Discussion and speculations _______________________________________________ 6 Conclusions ______________________________________________________________ 8 References cited __________________________________________________________ 8 ILLUSTRATIONS Page Photograph showing north-northeast view over Mauna Kea summit area _____________________________ A2 Graph showing time-related differences in average direction and volume of airflow in the drill holes, summit cone of Mauna Kea, Hawaii ____________________________________________________________ 3 Graph showing temperature versus depth over time in a summit-cone drill hole over a period of about 6 months, Mauna Kea, Hawaii __________________________________________________________________ 4 TABLES Page Comparative temperature, water vapor, and speeds of motion of air flowing out of the drill hole on the summit cone and in the free air above, Mauna Kea, Hawaii ______________________________________ A3 Deuterium in water vapor from 2-liter samples of nearly saturated air flowing from the summit-cone drill hole, Mauna Kea, Hawaii ______________________________________________________________________ 4 Deuterium in snow, graupel, permafrost, and lake waters of the Mauna Ke-a summit area, Hawaii ______ 7 III SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 MOUNTAIN BREATHING—PRELIMINARY STUDIES OF AIR-LAND INTERACTION ON MAUNA KEA, HAWAII By ALFRED H. WOODCOCK 1 and IRVING FRIEDMAN ABSTRACT Air moves in and out of the porous ash and cinder of the summit of the dormant volcano Mauna Kea, Hawaii (alti- tude about 4200 m), presumably in response to pressure changes in the atmosphere. Measurements have revealed an average airflow of about 20 kg m"2 d‘l. The air enters the porous ash relatively dry and leaves nearly saturated; the excess water vapor averages about 6.6 gm kg". This vapor flow produces an estimated average latent heat loss to the at— mosphere from the interior surfaces of the mountain of about 3.9 W m‘” (0.94 cal m‘2 5“). Thus it appears that a sen- sible heat source, which is probably geothermal, exists within the mountain. A negative thermal gradient in the summit cone and deuterium analyses of exhaled water vapor indicate that the vapor source is, in part, permafrost. INTRODUCTION The summit cinder cone on Mauna Kea, Hawaii, is the site of several astronomical observatories of the Institute for Astronomy, University of Hawaii. Figure 1 shows an aerial view of this and other cones which lie well above the moist trade-wind air of the lower atmosphere on the island of Hawaii (lat 19°49’34” N., long 155°28’20” W.). Prepara- tory to the construction of the Mauna Kea observa— tory buildings in 1967 and 1975, exploratory holes were drilled about 12 m down into the cinder at the sites. These holes (76 and 100 mm in diameter) presented an opportunity to obtain the vertical tem- perature distribution in the summit cone. In March 1967 the first author visited the first of these holes to make a series of temperature-depth measurements. At the time a rapid flow of air out of the drill hole was noted. This flow was so interesting that the temperature study was delayed and instead measurements were made in the hole of the speed, direction, temperature, and water vapor of the flow- ing air. Unfortunately the observatory construction 1Prasent address is Department of Oceanography, Hawaii Institute of Geophysics, Honolulu, HI 96822. program in 1967 required that the hole be filled after a short time, thus preventing the accumulation of comprehensive amounts of information about the flow. In 1975 two more drill holes (100 mm in diam- eter and 12 m deep) in the summit cone were made available for study by the Institute for Astronomy. One was used to continue the airflow (air breath— ing) study, and the other was used to measure the temperature changes with depth and time. Again the time interval between the drilling and construc- tion at the site was too- short to permit conclusive results. However, the combined exploratory data collected during these two intervals are sufiiciently interesting and unique to warrant publication now. We hope that the results will lead to a more complete study of the interaction of alpine atmos- pheres and mountain regions such as the Mauna Kea summit. The occurrence of pressure-induced breathing of air through porous earth is well established but its role in the transfer of water vapor and latent heat to dry atmospheres remains unexplored. Penetration of air through cave surfaces into porous limestone has been studied (Wigley, 1967), and there is evi- dence of atmospheric-pressure effect upon water- table levels in soils (Peck, 1960; Turk, 1975). Yen (1963) has done much experimental work on vapor transport through porous snow, and Geiger (1971) reported that moist air adds water to porous dry sandy soils as they breathe about 22 m3 m—2 d—1 under the influence of wind-produced pressure changes. This paper presents the preliminary observations made in the Mauna Kea drill holes and estimates of their meaning in terms of water vapor and latent heat flow from the mountain to the atmosphere. Previous work near the top of Mauna Kea (Wood- A1 A2 cock, 1974) revealed a deep layer of permafrost, although the mean air temperature (about 4°C) had been thought to be too high for the occurrence of permafrost there. Also, a negative temperature gradient was found in the sediments under nearby Lake Waiau (fig. 1) (altitude 3970 m), a surprising find near the top of a dormant volcano in the tropics (Woodcock and Groves, 1969). Study of the loss of latent heat from the mountain may eventually aid in explaining these anomalous phenomena. ACKNOWLEDGMENTS Lother Ruhnke and Bernard Mendonca of the Mauna Loa observatory, US. National Oceanic and Atmospheric Administration, also made a series of measurements of the flow in the Mauna Kea drill SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 holes. These data are included in the average quan- tities presented in figure 2. We thank the staff of the Institute for Astronomy and the Infra-red Tele- scope Facility of the University of Hawaii for mak- ing the drill holes available. The vane and hot-wire anemometers were loaned to us by C. M. Fullerton and R. C. Taylor of the Cloud Physics Laboratory, Hilo, and the Meterology Department, University of Hawaii, Honolulu, respectively. Kenneth Hardcastle of the US. Geological Survey, Denver, Colo., carried out all the deuterium measurements, and R. L. Soroos of the US. Geological Survey made the drill- hole ash samples available to us. Kerry Wilson of the Cloud Physics Laboratory derived the free-at- mosphere mixing-ratio values from the Hilo radio- sondes, and Paul Ekern aided our literature search. The gas analyses were carried out under the direc- FIGURE 1.—View north-northeast over Mauna Kea summit area, showing some of the many pyroclastic cones there. Waiau Cone and Waiau Lake are in the foreground, and the summit cone, Puu Wekiu, and the observatory of the Institute for Astronomy are in the middle distance to the right. (Photograph by A. J. Abbott.) MOUNTAIN BREATHING, OF AIR-LAND INTERACTION OF MAUNA tion of J. J. Naughton, Department of Chemistry, University of Hawaii. G. P. Wollard, recently de- ceased former Director of the Hawaii Institute of Geophysics, long encouraged and supported the work on Mauna Kea. These studies have been supported in major part by the US. Ofl‘ice of Naval Research. Hawaii Institute of Geophysics contribution no. 828. OBSERVATIONS Flow in and out of the holes in the summit cone was measured with a calibrated sensitive Taylor (Biram’s type) totalizing vane anemometer with 100-mm inside diameter, which was carefully fitted into the top of the holes for each measurement period. A correction of +12 percent, determined from calibration runs at the Hilo Cloud Physics Observatory, was found to be required when the vane anemometer registered flow into the hole (that is, when the anemometer vane reversed). At airflow rates too low to» be registered correctly by the vane anemometer, a hot-wire anemometer was used. The speed and direction of air motion in the holes was measured for a total of 111.5 hours, including two 24—hour periods, during which the mean flow was derived from 274 separate readings. Figure 2 presents an average of the volume and direction of flow :per unit of interior surface area of the two drill holes (that is, 2.93 and 3.8 m2). The average outflow was 26.9 m3 m—2 d“, derived from the sums of the product of the units of flow and its duration KEA, HAWAII A3 llllllll Out of hole Into hole I 11111111111 0 4 8 llllllllllllll 62.300 AIR PRESSURE, IN PASCALS —62.400 i111 [III I I l 12 16 20 24 AIR FLOW IN HOLE, IN LITERS METER'2 SECOND" NOON HOURS, LOCAL STANDARD TIME FIGURE 2.—Time-related differences in average direction and volume of airflow in the drill holes, summit cone of Mauna Kea, Hawaii. In histogram each block represents average volume derived from totalizing anemometer readings during time interval. Black dots show representative semidiurnal air pressures at Mauna Kea observatory. (fig. 2). This outflow amounts to 21.0 kg m—2 d“, based upon a mean air density of 0.78 kg HP3 at a pressure of 623 millibars (List, 1951, p. 298) or 62,300 pascals. TABLE 1.-—Comparative temperature, water vapor, and speeds of motion of air flowing out of the drill holes on the summit cone and in the free air above, Mauna Kea, Hawaii [T0, dry-bulb temperature; TN‘ wet-bulb temperature; RH, relative humidity; 11, mixing ratio; m, about; L, liter] Free air Out-flowing air Date and T T T T Flow local standard D N RH N _ Wing D w RH .11 voluLne Flow rate time (°C) (°C) (percent) (9 k9 1) (m s 1) (°C) (°C) (percent) (9 k9") (L s 1) (m s 1) May 5, 1967, 0920-- 8.0 —1.8 27 3.1 7.2 3.8 3.8 100 8.5 5.6 0.71 July 25,1967, 0830 5.4 .9 53 5.0 6.9 4.3 4.2 99 8.7 14.1 1.8 Auq. 7,1967,1400- 6.7 4 39 4.0 4.2 3.6 3.6 100 8.3 2.4 .3 Auq.8,1967, 0730- .5 0 93 6.2 NB 4.0 4.0 100 8.6 3.7 .5 Sept. 9, 1967, 1035 7.9 -1.1 18 2.0 8.9 5.7 5.0 93 9.0 2.7 .9 Oct. 15, 1975, 1506 5.5 -1.4 31 .0 m4 7.8 7.2 94 10.5 2.3 .29 Nov. 18,1975,1240 8.2 -2.6 7 .8 «3 6.7 6.6 99 10.3 3.5 .45 Nov. 19, 1975, 1300 6.7 —1.8 20 2.1 (1) 7.6 7.3 97 10.7 3.8 .49 Dec. 17, 1975, 1315 - .4 -5.8 31 19 3.0 6.2 5.8 95 9.5 4.7 .61 Jan. 21,1976,115O -3.7 —5.7 69 3 4 7.0 5.0 4.7 97 .9 19.8 2.53 Jan. 22, 1976, 1155 - .2 - .6 94 6 0 2.3 5.3 5.0 96 9.0 6.9 .88 Mar. 9, 1976, 1424- 8 -1.6 88 6 0 3.3 5.0 5,0 100 9.2 5.3 .68 Mar. 10, 1976, 1520 -3.0 -4.4 78 4.0 9.0 4.8 4 6 97 8 8 6.2 .79 Apr. 7,1976,1338- 5.8 -3.5 11 1.1 NS 5.2 4 7 94 8 8 6.3 .80 May 6, 1976, 1457-— 3.4 .9 72 5.9 7.6 6.2 5 5 93 9 3 5.6 .72 May 7,1976, 1428-- 2.2 -1.8 53 4.0 5.2 6.2 5 5 93 9 3 4.4 .56 1 Near calm. A4 A sling psychrometer was inserted into the drill hole during outflow to measure the wet-bulb (Tw) and the dry-bulb (TD) temperatures during the 1967 period (table 1). Because of the relatively low flow rates, the Stevenson Screen hygrometric formula- tion, adjusted for atmospheric pressure effects, was used to derive relative humidities and mixing ratios (Great Britain Meteorological Office, 1964). How- ever, for all the 1975 and 1976 Tw and TD measure- ments during outflow in the drill hole, an Assmann ventilated psychrometer was used. The free-air Tw and T], readings were made from a shielded sling psychrometer. The standard psychrometric formu- lation (List, 1951, p. 365) was used to derive rela- tive humidity and mixing ratios from the Assmann and sling psychrometer readings. 0 I I I I I I I I I _ _‘,, _ ._ _1 _ + I- Temperature taken in: “ ‘ 1975 4— ANov. 19 __ + _ g _ ODec. 17 a- / 1 E 1976 + E 6_ A Jan. 21 _ Z l Mar. 9 .. ‘ _‘— + _ E 0 Apr. 7 it __ _ o 8” I: May 7 / +\ 10 — .__ + _ r __ _ 12- 6 __+ _ 1 I I I I I 1 | | -2 o 2 4 6 8 10 18 TEMPERATURE, IN PERCENT DEGREES CELSIUS WATER FIGURE 3.—Temperature versus depth over time in a summit- cone drill hole over a period of about 6 months, Mauna Kea, Hawaii. Annual thermal wave not evident below 8 In. To avoid confusion below 7 m, observations at same depth that correspond within 0.1°C or less are represented by closed circles. Adjacent digits show number of observa- tions represented by closed circles. Graph at right shows percent water (weight HgO/weight dry ash) in drill—hole core samples taken October 15, 1975. SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 TABLE 2.——Deuterium in water vapor from 2-L samples of nearly saturated air flowing from the summit-cone drill hole, Mauna Kea, Hawaii [Deuterium analyses were made using conventional techniques. The water vapor was converted quantitatively to hydrogen gas by reaction with hot uranium metal. The gas was analyzed by a double collecting 6 in. (204 rim) 60° Nier-type mass spectrometer. Analyses are reported relative to Vienna Standard Mean Ocean Hater (SMOH), having a 2 sigma of 0.5 permil. 6D °/“ = R - R sam le standard , z Rstandard x 1000 where Rsample _ Dmsample’ Rstandard Dmstandard’ and the standard is Vienna snow.) Sampling Water content 6 D °/a° depth in ole (mg) (m) Date Time Dec. 17, 1975 ---------- 1109 13 -177 2.5 1330 15 -174 2.5 1450 15 «182 2.5 Apr. 7. 1976 ----------- 1049 11.3 -156 2 1148 13.6 ~159 2 1327 14.1 ~159 2. 1505 13.1 -163 2 May 6, 1976 ------------ 1425 16.0 -157 1.5 1428 17.2 -163 3.3 1430 16.8 —166 6.1 1432 16.2 ~177 11.9 Table 1 shows only a part of the numerous psy- chrometric data used to estimate the net latent heat flow from the holes. For the sake of brevity, the data from which the mean local free-air mixing ratio (2.62 g kg“) was derived are not shown. This mix- ing ratio is based upon a total of 86 readings of TD and Tw, at least five readings on different days in each month of the year. They included the local free-air mixing ratio (W) values shown in table 1. The mean local free-air mixing-ratio value is about 1 g kg—1 greater than the mean mixing ratio at 4.2 km in the atmosphere away from the influence of Mauna Kea. This free-atmosphere average was de- rived from 3 years of twice-daily radiosonde data (1972, 1973, 1974) at the National Weather Service, Hilo, about 30 km east of Mauna Kea. Upslope winds during part of the day probably account for this 1 g kgt1 increase in water vapor at the Mauna Kea summit (J. Z. Jefferies and D. R. McKnight, written commun., 19618). The above local air-temperature measurements and those of ground temperature made by therm- istor in a third drill hole (fig 3) are corrected, where necessary, for instrumental errors. These errors are discussed in a publication concerning other recent uses of the instruments (Woodcock, 1974). To learn more about the origins of the water vapor coming from the drill holes, samples for deu- terium analysis were taken in 2-L (liter) evacuated stainless steel flasks. A plastic tube, lowered into the hole and drained of surface air during rapid out- flow of air, was then attached to the flask valve. While taking the outflow air samples, the valve was MOUNTAIN BREATHING, OF AIR-LAND INTERACTION OF MAUNA KEA, HAWAII opened slowly to avoid condensation effects due to rapid pressure changes. The deuterium concentra- tions of the air samples were measured at a labora- tory of the US. Geological Survey at Denver, Colo. (table 2). LATENT HEAT LOSS TO THE AIR From the data of figure 2 and table 1, and the mean local air-mixing ratio (that is, 2.62 g kg—l), we estimated the average amounts of latent heat coming out of the drill holes. This evaporative heat loss from the interior of the holes (He) is propor- tional to the mixing-ratio difference (AW), as noted below. H..=L(AWM), where Ho=heat loss in W m“2 or watts per square meter, L =1atent heat of water vaporization (2.49><106 J kg“1 or joules per kilo- gram) (see footnote 2), AW =average difference in water-vapor con- tent between entering and exiting air (about 6.6 g kg—l), and M =average weight of exiting air (about 21 kg m—2 drl). Using the above relationships, taken from the mean data of table 1 and figure 2, we found that an average of 3.9 W m“: (0.94 cal m—2 s“) left the interior surfaces of the drill holes, representing about 137 g m‘2 d—’ water (about 50 mm yr—l). It may seem unreasonable to suggest a mean annual exchange from extrapolation of these few days’ observations, because we do not know how rep— resentative the quantity may be. However, we believe that it is useful to do so at this exploratory stage in the study, as a flow of dry air in and moist air out as the air pressure changes is almost certainly a long-term fact in this summit region. SOURCE OF HEAT In suggesting that the mountain is the source of the sensible heat represented by the loss of water vapor to the atmosphere, it is necessary to show that other potential sources of heat are inadequate. SENSIBLE HEAT OF INFLOWING AIR AS SOURCE OF LATENT HEAT IN OUTFLOWING AIR Transport of sensible heat into the mountain in- terior due to airflow (H,) is proportional to the tem- 2This quantity becomes 2.82x10‘i J kgil if permafrost proves to be the only vapor source. However, until more is known about the source, we assume the conservative value of 2.49X10“ J kg“. A5 perature excess of the inflowing air over that of the outflowing air and is derived as follows: H,=C,, (ATM), where H,.=sensible heat transport (cal m—2 d“) , C,,=specific heat capacity of dry air (about 1004 joules per kilogram kelvin) , AT=temperature excess of inflowing air over outflowing air (°C), and M=weight of flowing air (21.0 kg m—2 d—l). Using the above equation, we estimate that the air entering the mountain (that is, 21.0 kg m—2 d—l) should have a mean temperature exceeding that of the air leaving the mountain by 161°C in order to supply the mean latent heat found in the air coming out of the mountain. The average temperature of the exiting air is estimated to be about 5°C (table 1), which means that the average temperature of the entering air should be about 21°C. In other words, if the interior of Mauna Kea were dry, the exiting air would have a mean temperature of about 21°C. Actually, the mean air temperature at the Mauna Kea summit is about 4°C (Woodcock, 1974). Thus the sensible heat of the air is an unlikely source of the latent heat in the outflowing air. The fact that airflow into the mountain seems confined to the evening and night hours (fig. 2) when the air is colder (J. Z. Jefferies and D. R. McKnight, written commun., 1968) makes it probable that the air is, on the average, a sink rather than a source of sensible heat. CONDUCTION OF HEAT INTO THE MOUNTAIN Until more is known about the thermal conduc- tivity of the ash, cinder, and lava flows of Mauna Kea summit cones, this source of sensible heat can- not be estimated. However, a brief consideration causes us to conclude that it is almost certainly negligible. Even if we assume that the mountain is solid basalt (thermal conductivity about 0.005 cal cm—l cm—2 s—1 °C—1), a mean negative tempera- ture gradient of about 20°C m—1 would be required for conduction to transfer 3.9 W m—2 (0.94 cal m—2 s“) into the mountain. A negative gradient is present on the summit cone (fig. 3), but it is only about 01°C mt‘. This is about twice that found un- der Lake Waiau, where downward heat flow of about lucal cm*‘-’ s—1 (4.18><10“2 W m—Z) has been esti- mated (Adams and others, 1976). Actually, the Mauna Kea summit area is made up largely of porous vesiculated ash and cinder, which have a very much lower thermal conductivity than solid basalt. Thus, conduction of sensible heat into Mauna A6 Kea is discarded as a source of the latent heat com— ing out in the air. SNOW AND RAINWATER AS A SENSIBLE HEAT SOURCE The few years of data available indicate that pre- cipitation at the Mauna Kea observatory is only about 250 mm yr—l, largely in the form of snow. If no evaporation or sublimation occurred at the surface and all this water seeped into Mauna Kea at a temperature of 10°C, it would carry in less than 10 percent of the heat coming out as latent heat. As melt-water temperatures on Mauna Kea are found to be near 0°C, it is more likely to be a sink for sensible heat within the mountain than a source. DISCUSSION AND SPECULATIONS The sums of the daily outflow amounts, derived from the product of the average rates and the times in figure 2, exceed the inflow by a factor of about 1.7. Also, the direction of flow seems to have little if any relationship to the local semidiurnal pressure changes. At this stage in the study we can only assume that these effects are due to horizontal pres- sure gradients across the summit region and that these gradients are caused perhaps by local differ- ences in winds, air temperature, and summit-cone surface and subsurface conditions. Pyle (1959) has indicated the variability of local diurnal pressures arising from island mountain effects in Hawaii. In deriving the estimates of average flow in and out of the summit cone, we have simply summed the daily in-and-out flow amounts from the holes and divided by two. Thus, we have assumed that the total inflow and outflow observed (about 53 800 L m—2 dt1 or liters per square meter per day) occur- red generally over the summit cone and that the local inflow deficiency was balanced approximately by a proportional excess of inflow elsewhere on the mountain summit. In making these estimates of airflow and water vapor flow into and out of the summit cone, we also assumed that the flow through each square meter of the walls of the drill holes was the same as the average flow from a square meter of the mountain- top surface. This may not be a valid assumption, because the porosity of the pyroclastic cones of the summit area probably differs horizontally from place to place, and perhaps vertically as well. (Porter, 19723., b, discussed the morphology of Mauna Kea cones.) However, we have no reason to think that the area of our drill holes in the summit SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 cone is either more or less porous than elsewhere on the summit cone. In this respect it was encouraging to find that the flow in the second drill hole, about 100 m from the first, corresponded closely to that in the first hole. However, we are unable to answer the question of whether the flow in these two holes is representative of the average air and vapor mo- tion in and out of the mountaintop. Clearly, more work is required. The depth of penetration of air into the mountain structures is not known, but the possibilities for internal transport of heat and water via the air- penetration mechanism are apparent. This transport will be a function of differences in the pressure and temperature of the water-saturated air as it moves from place to place within the mountain. The air will extract heat and water vapor from wet, warmer surfaces and will add heat and water to colder sur- faces. These exchanges will be superimposed upon adiabatic processes as the air moves up and down. The trend should be one of smoothing out differ- ences in temperature and water distribution within the mountain. (For example note in figure 3 the rather uniform distribution of water despite the preceding 9—month dry period.) The water-vapor flow out of the summit seems to require a large heat source. We note that the heat loss due to the excess vapor flow 3.9 W rrr2 (94X10*“ cal cmt2 s4) is many times the earth’s mean geothermal flow in oceanic areas near Hawaii (about 1 or 2X10’“ cal cm*” s“ or 4.2-8.4>--- do ---~ —189 Do. ——»- do —~~- -l69 Do. >--— do~——— —73 Do. Permafrost ~82 to —93 8 samples from depths between 0.4 and 14 in. Nov. 21, 1954 Water »»»»»» —23 take Haiau, level not recorded. Lake Naiau, level unusually low. (0.8 m below sill depth). Lake Naiau. overflow 91 m3 d“. Sept. 4, 1970 -..— do .... —18 Apr. 10, 1971 undo »..- .52 very nearly between these limits (table 2), as would be expected if the average vapor source were a mix- ture of evaporate from old snowmelt and perma- frost melt. We assume that fractionation occurs and that the residual (heavier) liquid, from which vap- orization has occurred, does not accumulate but drains away to greater depths. The light exhaled vapor might also be explained if the vapor (relative humidity 50 percent) is light when it enters the mountain (that is, 8D=250 permil), and if the 3D value of the vapor added by sublimation of permafrost is about —90 permil. The final 8D value of the vapor would be about —175 permil. Because measurement of the deuterium of a local air sample from Mauna Kea (Friedman and others, 1964, p. 199—200) revealed the expected relatively heavy value of —160 permil, the preceding explanation is unlikely. Waters from deep Within Mauna Kea, orig-i- nating from low-altitude precipitation, are excluded as a possible vapor source as they are all much heavier (Friedman and Woodcock, 1957). Four factors incline us to regard permafrost as the most probable source of the light vapor: (1) ice is the only known adequate local source of such light vapor (table 3); (2) the 8D decreases with depth and duration of outflow, indicating a deeper light-vapor source (table 2); (3) after a long dry summer we found the lightest vapor exhaled (Dec. 17 samples, table 2) ; and (4) we found a negative temperature gradient in the summit cone (fig. 3). Thus, it appears that deuterium and temperature A8 measurements both indicate the presence of perma- frost below the observatory site. Extrapolation of the temperature curve below the depth of near-zero annual amplitude (fig. 3) suggests that 0°C and ice occur at about 60-m depth. In the future, with more data available on the average of SD of snow and on the proportions of light and heavy water in the outflowing vapor, we may be able to estimate the rate of melting of the permafrost from the latent heat loss in this vapor. CONCLUSIONS A source of heat in the Mauna Kea summit cone of nearly 4 W m—3 (1 cal m—2 s—‘) is indicated by the net outward flow of water vapor due to mountain breathing. Most, if not all, of this heat is apparently derived from Within the mountain and not from the atmosphere at the summit. The source of the water vapor appears to be melt from old snow and from permafrost. REFERENCES CITED Adams, W. M., Watts, George, and Mason, George, 1976, Estimation of thermal diffusivity from field obser- vations of temperature as a function of time and depth: Am. Mineralogist, v. 61, nos. 7—8, p. 560—568. Friedman, Irving, and Woodcock, A. H., 1957, Determination of deuterium-hydrogen ratios in Hawaiian waters: Tellus, v. 9, p. 553—556. Friedman, Irving, Redfield, A. C., Schoen, Beatrice, and Harris, Joseph, 1964, The variation of the deuterium content of natural waters in the hydrologic cycle: Rev. Geophysics, v. 2, no. 1, p. 177—224. SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 Geiger, Rudolph, 1971, The climate near the ground: Cam- bridge, Mass., Harvard University Press, 611 p. Great Britain Meteorological Oflice, 1964, Hygrometric tables, Part II (2d ed.): London, England, Pub. 265b. Lee, W. H. K., and Uyeda, Seiya, 1965, Review of heat flow data, Chapter 6 in Terrestrial heat flow: Am. Geophys. Union Geophys. Mon. Ser. No. 8 (Natl. Acad. Sci.-Natl. Research Council Pub. 1288), p. 87—190. List, R. J., 1951, Smithsonian Meteorological Tables (6th re- vised ed.) Smithsonian Misc. Colln., v. 114 (pub. 4014), 527 p. Peck, A. J., 1960, The water table as affected by atmospheric pressure: Jour. Geophys. Research, v. 65, n0. 8, p. 2383— 2388. Porter, S. C., 1972a, Buried caldera of Mauna Kea volcano, Hawaii: Science, v. 175, no. 4029, p. 1458—1460. 1972b, Distribution, morphology, and size frequency of cinder cones on Mauna Kea volcano, Hawaii: Geol. Soc. America Bull., v. 83, no. 12, p. 3607—3612. 1972c, Holocene eruptions of Mauna Kea volcano, Hawaii: Science, v. 172, no. 3981, p. 375—377. Pyle, R. L., 1959, The diurnal pressure oscillation on a heated mountain island: Jour. Meteorology, v. 16, no. 5, p. 467— 482. Turk, L. J., 1975, Diurnal fluctuations of water tables in- duced by atmospheric pressure changes: Jour. Hy- drology, v. 26, p. 1—16. Wigley, T. M. L., 1967, Non-steady flow through a porous medium and cave breathing: Jour. Geophys. Research, v. 72, no. 12, p. 3199—3205. Woodcock, A. H., 1974, Permafrost and climatology of a Hawaii volcano crater: Arctic and Alpine Research, v. 6, no. 1, p. 49—62. Woodcock, A. H., and Groves, G. W., 1969, Negative thermal gradient under alpine lake in Hawaii: Deep-Sea Re- search, supp. v. 16, p. 393—405. Yen, Yin-Chao, 1963, Heat transfer by vapor transfer in ventilated snow: Jour. Geophys. Research, V. 68, no. 4, p. 1093—1101. Porosity and Density of Kilauea Volcano Basalts, Hawaii By GORDON R. JOHNSON SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 GEOLOGICAL SURVEY PROFESSIONAL PAPER 1123—B Tabulation of data and comparison oflhe densities and porosz'tz'es of samples from two depositional enoz‘ronments FIGURE 1. 2. TABLE 1. CONTENTS Page Abstract _________________________________________________________________ B1 Introduction ______________________________________________________________ 1 Techniques _______________________________________________________________ 1 Basalts of Kilauea Iki ____________________________________________________ 3 Basalts of the east rift zone ______________________________________________ 4 Summary and conclusions _________________________________________________ 6 References cited __________________________________________________________ 6 ILLUSTRATIONS Page Locations of K1—76—1 and HGP—A drill holes, Island of Hawaii ______________________________________ B1 Porosities of basalt from drill hole K1—76—1, Kilauea Iki, Hawaii ___________________________________ 4 TABLES Page Densities and porosities of basalt from Sandia Corporation drill hole K1—76—1, Kilauea Iki, Hawaii ______ B3 Densities and porosities of basalt from University of Hawaii drill hole HGP—A, east rift zone of Kilauea Volcano, Hawaii ______________________________________________________________________________ 5 III SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 POROSITY AND DENSITY OF KILAUEA VOLCANO BASALTS, HAWAII By GORDON R. JOHNSON ABSTRACT Bulk-density and grain-density measurements were made on samples of basalt from the Kilauea Volcano region of Hawaii. Samples were obtained from two drill holes: a shal- low hole at Kilauea Iki pit crater, and a deep hole at the lower east rift zone. Water-accessible porosities were cal- culated from calipered measurements of bulk density and measurements of grain density made using Archimedes’ principle. Helium-accessible porosities were calculated from calipered measurements of bulk density and measurements of grain density made using helium pycnometry. Grain density apparently decreases with depth in the Kilauea Iki drill hole owing to (1) rapid cooling and simultaneous trapping of heavy minerals in the upper material and (2) settling of heavy minerals from the deeper material that was cooled at a much slower rate. No such relationship can be deter- mined from grain-density measurements of east rift zone drill-hole samples. Helium-accessible porosities and corre- sponding water-accessible porosities of most individual samples from the Kilauea Iki drill hole are nearly the same. In contrast, helium-accessible porosities of many individual samples from the east rift zone drill hole are much greater than corresponding water-accessible porosities. The sample depths involved for the two drill holes and the depositional environments of the rocks probably account for the rela- tionships between helium-accessible porosities and water-ac- cessible porosities determined for one hole differing from those determined for the other. INTRODUCTION Sixty-eight samples of Hawaii basalts were col- lected from cores of two drill holes, one (Kl—76 1) in Kilauea Iki pit crater and the other (HGP—A) in the lower east rift zone of Kilauea Volcano (fig. 1) ; both are on the island of Hawaii. Data about the porosity, dry bulk density, and grain density of the samples are tabulated in tables 1 and 2. The Kilauea Iki samples are tholeiitic basalts from mag- ma deposited in December 1959. The measured Kilauea Iki core samples were collected at l-m in- tervals from near the ground surface to a depth of 43 m. The samples from the east rift zone drill hole came from cored intervals at depths of 139 to 1965.5 m. 155° ISLAND 19° 30' KILAUEA VOLCANO K1 -76-1 1 Q/Kilauea Iki (v ‘ pit craters-t 20 KILOMETERS FIGURE 1.—Locations of K1—76—1 and HGP—A drill holes, Island of Hawaii. TECHNIQUES At US. Geological Survey laboratories in Denver, 0010., the cores were drilled and trimmed with diamond tools to obtain uniform cylindrical samples 25.4 mm in both diameter and length. These samples were then dried overnight in a vacuum oven and weighed to an accuracy of 0.001 g. The sample weights, recorded as Wm, were later used to calcu- late grain volume and grain and bulk densities. Grain Volumes were determined on the small samples using two techniques: (1) helium pycnom- Bl B2 etry and (2) the buoyancy, or Archimedes’, prin- ciple. Basically, helium pycnometer measurements utilize an inert gas to compare the pressure—volume relationship of a sample with that of a steel ball of known volume. Accepting the validity of the perfect gas law with the imposed conditions, the unknown volume of the sample can be derived. Helium is used because it is an inert, nonadsorbing gas and has a small molecular diameter that allows it to penetrate easily into minute sample pores. A method using Archimedes’ principle consists of weighing a water— saturated sample suspended from a fine wire and stirrup in a water bath. Before weighing, the samples are soaked in a partial-vacuum environment for several days to attain complete saturation. Grain volume V, is then calculated as V0: Wary—‘Wsull , p where WW, is the submerged or suspended weight and ‘p is the density of water. To obtain grain vol- umes by either of the above methods assumes that, depending on the method, helium or water com— pletely invades all sample pores. The bulk volume of a solid consists of the total of the volumes of solid material and of voids. Bulk vol- umes for these samples were determined by measur- ing the length and diameter of each cylindrical sample. An average of several readings, each accu- rate to 0.1 mm, was used to calculate bulk volume. Bulk volumes were also obtained using submerged weights and saturated sample weights. The satu- rated samples were towelled to a surface-dry condi- tion and weighed in air. Bulk volumes were calcu- lated using the equation Vb: Wsat—Wsfl, p where WW were saturated surface-dry weights. (1) (2) Grain and dry bulk densities of the samples were obtained from the volume determinations. Dry bulk density (DBD) was calculated as the ratio of Wm, to the calipered volume, whereas bulk density deter- mined by Archimedes’ principle (DBA) was calcu- lated as the ratio of WW to Vb. Grain density was also calculated two ways: (1) the ratio of Wary to the grain volume obtained by helium pycno-metry (SGH) and (2) the ratio of Wm to V9 (SGA). True measurements of grain volumes, and hence of grain densities, require that all pores are helium or water saturable. If complete saturation is not achieved, then measurements of grain volume will be erroneously large, and apparent grain density will SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 be correspondingly low. In contrast, DBA calcula— tions are not affected by incomplete saturation but rather by the size and quantity of pores that occur at the surface of samples. When saturated samples are removed from water to be weighed in air, the effects of towelling and the low surface tension of water result in all but the very small surface pores becoming unsaturated. Thus WW will be reduced, Vb will be abnormally low, and DBA will be greater than the actual dry bulk density. Helium-accessible and water-accessible apparent porosities were determined from measurements of DBD, DBA, SGH, and SGA. Apparent porosity (Pa) is commonly expressed as Pa = 100 <_V_P>, Vb where V, is the volume of fluid-accessible pores and Vb is bulk volume. However, because grain volume, measured both by Archimedes’ principle and helium pycnometry, includes those pores that are isolated to either water or helium, Vp may be expressed as (3) Vp 7- Vb — V”, (4) where V, is grain volume. By substitution, p.=1oo(1—Zy_). (5) VI) and expressed in terms of bulk and grain density, P,,=100 (1——Di>, (6) II where Db is either DBD or DBA, and D, is either SGH or SGA. Because values of SGH are nearly the same as intrinsic grain densities in many rock types, helium—accessible porosities in these rocks will ap- proach total porosities. Total porosity may be ex- pressed as V. P,=100 (1— J ), Vb as in equation 5, except that in this case V, is the volume of grains only, not that of grains and isolated pores. In many rocks, such as clean sandstones, water- accessible porosities are equivalent or nearly equiv- alent to total porosities, because the interstices be- tween grains are large enough to permit easy pene- tration by water. In other rocks, such as the basalt from Kilauea Volcano, porosity is controlled mainly by fractures that act as capillaries interconnecting larger vesicular pores. This association of large- diameter pores with restricted openings (fractures) (7) POROSITY AND DENSITY OF KILAUEA VOLCANO BASALTS, HAWAII is one type of so-called inkwell pores. If the fractures are not too restrictive to water penetration, then saturation can be easily achieved by capillarity. However, if the fractures are so tight as to resist water penetration, then saturation can be achieved only if sufiicient pressure is applied to overcome the restrictive effects of the surface tension of water. Nevertheless, water-accessible porosities are meas— ured on samples that have been saturated at pres- sures of about 1 atmosphere, and these porosities may therefore be much less than helium-accessible porosities measured on the same samples. Con- versely, the water-accessible porosity of a sample cannot truly be greater than its helium-accessible porosity. BASALTS OF KILAUEA IKI Because of the vesicularity of most of the basalt samples of Kilauea Iki, values of DBA are, for many samples, much greater than corresponding values of DBD. The obviously vesicular samples listed in table 1 have noticeably high values of DBA, but other samples have values of DBA that are as much as 0.09 g/cm3 greater than corresponding DBD values. Consequently only DBD was considered when cal- culating water-accessible porosities, because porosi- ties calculated using values of DBA would be erroneously low and, when compared with helium- accessible porosities, would lead to the false assump- tion that most of the basalts of Kilauea Iki have significant quantities of isolated pores. Figure 2 compares the helium-accessible porosities with the water-accessible porosities of the basalt samples of Kilauea Iki. Whereas a direct comparison indicates that porosity as a function of depth is apparently about the same for both types of porosity (fig. 2A) , the ratio of PHe to P1120 plotted for all samples (fig. 23) shows an interval at 32 to 35 m where samples haVe isolated pores and another probably similar zone below a depth of 41 m. Additionally, a single sample at 7 m has a significant amount of isolated porosity. Otherwise, the helium- and water-accessible porosities are more or less equivalent in these samples. Because values of SGH for many samples are in the upper range of grain density of basalts (3.1- 3.2 g/cm3), helium porosities in these samples are probably about equivalent to total porosities. How- ever, grain density apparently decreases somewhat with depth. This decrease in grain density is prob- ably real but could be due to the effect of porosity that is isolated to both helium and water invasion. B3 TABLE 1.—Densities and porosities of basalt from Sandia Corporation drill hole K1—76—1, Kilauea I ki, Hawaii [DBD, dry bulk density using calipered volume; DBA and SGA, dry bulk density and grain density using bulk and grain volume determined from Archimedes' principle; SGH, grain density using volume obtained by helium pycnometry. PH , helium-accessible porosity, in percent; PH 0, water-accessible pogosity, in percent. g/cni3 = Mg/m3] 2 Depth DBD DBA SGA SGH PHe PH20 of core, 3 M DB_D in meters (g/cm ) 100“" SGH)‘100(1'SGA) 0.99 1.860 12.359 3.046 3.144 40.8 38.9 1.91 2.342 12.614 3.169 3.198 26.8 26.1 2.87 2.405 12.615 3.095 3.196 24.7 22.3 3.73 2.342 12.558 3.147 3.197 26.7 25.6 4.70 2.695 12.732 3.118 3.139 14.1 13.6 5.59 2.655 12.770 3.056 3.109 14.6 13.1 6.53 2.872 2.890 3.014 3.099 7.32 4.71 7.39 2.811 2.876 3.215 3.217 12.6 12.6 8.31 2.699 12.827 3.196 3.192 15.4 15.6 9.22 2.549 12.657 3.164 3.193 20.2 19.4 1013 2.678 2.745 3.208 3.235 17.2 16.5 1100 2.767 2.830 3.180 3.205 13.7 13.0 11.96 2.416 12.566 3.158 3.192 24.3 23.5 12.88 2.821 2.846 3.113 3.139 10.1 9.38 13.84 2.793 2.798 3.117 3.117 10.4 10.4 14.71 2.789 2.811 3.104 3.119 10.6 10.1 15.62 2.782 2.825 3.104 3.104 10.4 10.4 16.56 2.248 12.578 3.035 3.055 26.4 25.9 16.56 2.730 2.783 3.073 3.092 11.7 11.2 17.45 2.821 2.822 3.095 3.120 9.58 8.85 18.31 2.794 2.838 3.103 3.117 10.4 9.96 19.30 2.643 2.726 3.074 3.098 14.7 14.0 20.57 2.655 2.706 3.025 3.053 13.0 12.2 21.65 2.568 2.649 2.938 2.954 13.1 12.6 23.24 2.451 12.638 2.994 3.013 18.7 18.1 24.16 2.714 2.746 3.057 3.078 11.8 11.2 25.07 2.575 12.665 3.023 3.035 15.2 14.8 25.96 2.758 2.790 3.008 3.052 9.63 8.31 27.20 2.782 2.802 3.023 3.081 9.70 7.97 28.32 2.751 2.764 3.027 3.054 9.92 9.12 28.93 2.804 2.837 3.016 3.046 7.94 7.03 29.90 2.764 2.790 3.008 3.084 10.4 8.11 30.99 2.782 2.835 3.027 3.062 9.14 8.09 32.54 2.849 2.873 2.981 3.094 7.92 4.43 33.45 2.867 2.880 2.991 3.092 7.28 4.14 34.47 2.847 2.851 2.982 3.052 6.72 4.53 35.38 2.788 2.802 2.972 3.044 8.41 6.19 36.60 2.781 2.807 3.004 3.037 8.43 7.42 37.57 2.677 2.717 2.994 3.023 11.4 10.6 39.04 2.645 2.714 3.024 3.050 13.3 12.5 39.80 2.844 2.859 2.995 3 007 5.42 5.04 41.17 2.877 2.894 3.013 3 059 5.95 4.51 42.11 2.882 2.895 3.019 3 047 5.42 4.54 43.03 2.811 2.852 2.957 3 038 7.47 4 94 Averages--- 3.061 3 098 1Denotes DBA of samples with noticeably large vesicles. If isolated porosity does in fact exist in samples from greater depth, powdered samples will then ex- hibit higher values of grain density than will their solid counterparts, because isolated pores are de- stroyed in the process of pulverization. Nevertheless, the SGH of a powdered split of the 21.65 m sample was determined to be 2.934 g/cm3, or nearly the same value as the SGH of the 21.65 no solid sample (table 1). The most probable explanation for the decrease in grain density with depth is that the near-surface lava cooled rapidly, thus trapping heavy minerals, B4 SHORTER CONTRIBUTIONS T0 GEOPHYSICS, 1979 O | l l O I. I I I l l l T l I o. o c O. 0 o o ' © @ 0' U) 10— 0' 00 fl — c: 0- Lu 0- E 0'3 2 9 o- o o- z o o ui 20— o_ — — — O 0' < a o- c. ° 3 0 - (D o . a 0- °' 9 30* 8. ' EXPLANATION ‘ ‘ Ed 8 .° - Helium-accessible porosity, PHe E o o' . o Water-accessible porosity, PHzO o. s 0' D 40_ o 0' __ _ _ o o o. o . 50 l l l I I l 1 I I I I I 1 0 1o 20 30 40 501.0 1.5 2.0 A POROSITY, IN PERCENT B PHe/PHZO FIGURE 2.—Porosities of basalt from drill hole K1—76—1, Kilauea Iki, Hawaii. A, Porosity values and their relationship to depth. B, Porosity values as a function of technique, showing zones of isolated porosity. while the deeper lava cooled much more slowly, allowing heavy minerals to settle at some level below the depth of the drill hole. Richter and Moore (1966) reported extreme variability, from 2 to 37 percent, in olivine content in samples from another drill hole at Kilauea Iki; the amount of olivine phenocrysts also affects the chemical composition and results in a corresponding increase in magnesia. Because both olivine and magnesia have specific gravities of about 3.2, their relative abundance from sample to sample should account for the differences in SGH and SGA values shown on table 1. BASALTS OF THE EAST RIFT ZONE In contrast with the samples from the Kilauea Iki drill holes, most of the samples from the drill hole on the lower east rift zone are dense, fine-grained basalts. According to Kingston and others (1976), all cores collected below 914.4 m show some degree of chloritic alteration. Samples taken near the sur- face are normal olivine-bearing tholeiitic basalt. However, none of the samples measured in the lab- oratory contains large vesicles to the extent that erroneous values of DBA would be expected. Ac- cordingly, most values of DBA are within 0.02 g/cm3 of their corresponding DBD, and for only one sample, collected from 139.3 m, is the DBA as much as 0.07 g/cm3 higher than its value of DBD. For these samples either DBD or DBA could be used with comparable results to calculate water-accessible porosity, but to be consistent, only porosities calcu- lated from values of DBD are shown on table: 2. Unlike Kilauea Iki samples, porosity—depth re- lationships and porosity ratios for the east rift zone samples are not graphed, because these samples are from widely spaced cored intervals; thus, the values of porosity do not necessarily represent a continuous function with respect to depth. The ratios of helium- accessible to water—accessible porosities (table 2) show that at core intervals at depths greater than POROSITY AND DENSITY OF KILAUEA VOLCANO BASALTS, HAWAII BS TABLE 2.—Densities and porosities of basalt from University of Hawaii drill hole HGP—A, east. rift zone of Kilauea Volcano, Hawaii [080, dry bu1k density using calipered vo1ume; DBA and SGA, dry bulk density and grain density using bulk and grain volume determined from Archimedes' principle; SGH, grain density using volume obtained by he1ium pycnometry. P , he1ium—accessib1e porosity, in percent; PH 0’ water-accessib1e porosity, in percent. g/cm3 = ngfi3] 2 Depth DBD DBA SGA SGH PHe P1420 i of core, 3 080 _ 080 P in meters (g/cm ) 100(1' SGH) 100(1 SGA) H20 138.99 2 810 2.838 3.038 3.046 7.74 7.50 1.03 139.29 2.603 2.669 3.019 3.042 14.4 13.8 1.04 139.60 2.696 2.709 3.026 3.077 12.4 10.9 1.14 681.23 2.546 2.538 2.837 2.949 13.7 10.3 1.33 682.14 2.892 2.884 2.966 12 917 0.86 2.49 0.34 682.29 2.908 2.893 2.964 12 909 0 03 1.89 0.02 682.75 2.810 2.801 2.948 12 878 2 36 4.68 0.50 876.60 2.560 2.566 2.740 2 894 11 5 6.57 1.75 877.37 2.348 2.355 2.960 12 869 18.2 20 7 0.88 1117.55 2.767 2.758 2.937 3 013 8.16 5 79 1.41 1118.46 2.614 2.615 2.910 3 041 14.0 10 2 1.37 1120.14 2.719 2.697 2.829 3 053 10.9 3 89 2.80 1355.44 2.811 2.815 3.078 12.942 4.45 8.67 0.51 1356.97 2.503 2.511 2.786 2 996 16.4 10.2 1.61 1358.19 2.666 2.663 3.138 12.995 11.0 15.0 0.73 1644.85 2.799 2.807 2.970 3.142 10.9 5.76 1.89 1645.46 2.822 2.816 2.980 2.983 5.40 5.30 1.02 1647.14 2.682 2.688 2.914 2.981 10.0 7.96 1.26 1838.40 2.883 2.866 2.945 3.003 4.00 2.11 1.90 1839.16 2.856 2.843 2.948 3.096 7.75 3.12 2.48 1839.32 2.826 2.826 2.953 3.122 9.48 4.30 2.20 1840.08 2.843 2 865 2.954 2.991 4.94 3.76 1.31 1964.89 2.397 2.385 2.960 3.067 21.8 19.0 1.15 1965.50 2.418 2.411 2.946 2.971 18.6 17.9 1.04 1Denotes SGH of samp1es with noticeably 1arge vesic1es. 139.60 m, water-accessible porosity is, in most samples, much less than helium-accessible porosity. Only samples collected from the core interval at about 139 m, a single sample at 1645.46 m, and those at 1964.89 m and 1965.50 m, near the bottom of the drill hole, have nearly equivalent water-accessible and helium-accessible porosities. Unfortunately, reliable SGH measurements could not be made on those samples that are footnoted in table 2. Unstable and nonreproducible instrument readings indicated that the permeabilities of the samples were so tight that they resisted invasion by helium. However, these same samples were appar- ently more water saturable than helium saturable, because their SGA values in all cases were greater than their corresponding SGH values. Paradoxically, accurate values of SGH must always be equal to or greater than corresponding values of SGA. According to the Hawaii Geothermal Project Well Completion report HGP—A (Kingston and others, 1976), all samples collected below 366 m to a depth of 1219 m contain secondary zeolites that are mod- erately abundant. One possible explanation for the obviously low SGH values of the samples footnoted in table 2 is that certain zeolites act as molecular sieves (Evans (1964), among others) and thereby are permeable to small molecules in such a way that excess amounts of helium would be held in the crystal lattices. Thus, when measured on these samples, grain volumes could be larger than actual B6 grain volumes, and values of SGH would be corres- pondingly low. This explanation assumes the mineralogy of the zeolite to be that which would act as a molecular sieve to helium molecules. If so, then this type of zeolite is in significant abundance in three core in- tervals: (1) from 681.23 to 682.75 m, (2) from 876.60 to 877.37 m, and (3) from 1355.44 to 1358.10 m. Obviously, helium-accessible porosities are much too low in all the footnoted samples from these three core intervals, and it is possible, although indeter- minable, that the values of SGH for other samples taken from these intervals are also erroneous. Be- cause values of SGH for such samples from these core intervals cannot be relied on, helium-accessible porosities must be considered therefore to be errone— ously low. SUMMARY AND CONCLUSIONS The porosity relationships graphed in figure 23 show that the fractures in the basalt 0f Kilauea Iki are, for the most part, open and accessible to water penetration. The few samples that exhibit water— aecessible porosity that is anomalously low compared with helium-accessible porosity might represent layers of basalt that have tight fractures, although SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 under an increased hydrostatic pressure these frac- tures could be open to water penetration. In con- trast, many samples from the drill hole at the east rift zone have p-orl'osities that are isolated to water penetration. Most of the tight east rift zone lavas are presumed to have been formed subaerially (Kingston and others, 1976), whereas the lavas of Kilauea Iki were formed at or near ground surface. A general decrease in grain density with depth indicated by the Kilauea Iki samples is probably due to a near-surface concentration 0f heavy minerals and possibly to a settling and depletion of heavy minerals in the deeper zones. No such relationship is evident from grain density measurements of samples from the east rift zone drill hole. REFERENCES CITED Evans, R. C., 1964, An introduction to crystal chemistry: Cambridge, Cambridge University Press, 410 p. Kingston, Reynolds, Thom, and Allardice, Ltd., 1976, Hawaii geothermal project well completion report HGP—A: Honolulu, University of Hawaii Research Corp, and U.S. Energy Research and Development Administration, 34 p. Richter, Donald H., and Moore, James G., 1966, Petrology of the Kilauea Iki lava lake, Hawaii: U.S. Geological Sur- vey Professional Paper 537—B, p. Bl—BZG. Diabase Dikes in the Haile—Brewer Area, South Carolina, and Their Magnetic Properties By HENRY BELL III, KENNETH G. BOOKS, DAVID L. DANIELS, WILLIAM E. HUFF, JR., and PETER POPENOE SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 GEOLOGICAL SURVEY PROFESSIONAL PAPER 1123-0 Paleomagnetie poles are calculated for Upper Triassic and Lawerjurassie dikes revealed by magnetic data FIGURE 1. TABLE 0: CONTENTS Page Abstract _________________________________________________________________ Cl Introduction ______________________________________________________________ 1 Magnetic setting __________________________________________________________ 2 Geologic setting __________________________________________________________ 9 Diabase dikes _________________________________________________________ 10 Sampling procedures ______________________________________________________ 11 Laboratory procedures ____________________________________________________ 13 Results __________________________________________________________________ 14 Conclusions ______________________________________________________________ 17 References cited __________________________________________________________ 17 ILLUSTRATIONS Sketch map of the Appalachian region of the Eastern United States, showing the location of the Haile— Brewer area, South Carolina, known occurrences of dikes of Triassic and Jurassic age, and areas of outcrop of the Newark Group __________________________________________________________________ Aeromagnetic map of the Camden—Kershaw area, north-central South Carolina _______________________ Geologic map of the Haile—Brewer area, South Carolina ______________________________________________ Profiles obtained by means of an airborne magnetometer carried at 122-m elevation and profiles obtained by means of a truck-mounted magnetometer ________________________________________________________ Two-dimensional magnetic profiles of a simulated geologic profile calculated for 4.6 m and 122 m elevation TABLES Major- and minor—oxide composition, trace-element content, and normative mineralogy of a large diabase dike. Lancaster County, SC. ___________________________________________________________________ Magnetic properties and normative magnetite and ilmenite contents of a large diabase dike, Lancaster County, SC. __________________________________________________________________________________ Definition of terms used in the sampling hierarchy __________________________________________________ Results of spinner-magnetometer measurements on specimens of diabase dikes from the Haile—Brewer area, South Carolina, untreated and after cleaning by subjection to alternating magnetic fields of intensities of 100, 200, and 300 oersteds ___________________________________________________________________ Paleomag'netic directions and paleomagnetic pole positions for diabase dikes and dike swarms in the Haile—Brewer area, South Carolina _____________________________________________________________ Summary of magnetic data and paleomagnetic pole positions for diabase dikes and dike swarms in the Haile—Brewer area, South Carolina ____________________________________________________________ III Page Page C12 13 13 14 16 17 SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 DIABASE DIKES IN THE HAILE—BREWER AREA, SOUTH CAROLINA, AND THEIR MAGNETIC PROPERTIES By HENRY BELL III, KENNETH G. BOOKS, DAVID L. DANIELS, WILLIAM E. I-IUEF, 111., and PETER POPENOE ABSTRACT The aeromagnetic map of the Haile-Brewer area, east- central South Carolina, shows numerous strong narrow northwest-trending anomalies that are associated with dia- base dikes. These diabase dikes were sampled by means of core—drilling equipment to obtain oriented samples on which magnetic properties were measured for paleomagnetic orien— tation. The pole positions calculated for the various dikes are in two groups that are close together but that have opposing polarity. The paleomagnetic pole positions calculated are within the range of those obtained from diabase intrusive rocks in eastern North America that are considered to be Late Triassic and Early Jurassic in age. INTRODUCTION Sedimentary and igneous rocks of the Newark Group (Upper Triassic and Lower Jurassic) in the Eastern United States crop out in extensively faulted narrow basins. The igneous rocks are pre- dominantly diabase and gabbro that have been em- placed as dikes and sills. Commonly, the diabase dikes are emplaced in faults cutting not only fossil- iferous sedimentary rocks within the basins but also, as in the Haile—Brewer area, South Carolina, Pale- ozoic or Precambrian crystalline rocks in areas widely distributed beyond the basins, as P. B. King has emphasized (1961, 1971). The igneous rocks, including the diabase dikes, that are in these basins have been much studied, particularly in regards to their petrography, structural setting, and relation to the rifting that preceded continental drift and the opening of the Atlantic Ocean. In West Africa, particularly Mauritania and Liberia, and in northern South America, in Brazil, Guyana, Surinam, and French Guiana, there are diabase dikes and dike swarms very similar in ap- pearance and probably in age to the Widespread diabase dikes in eastern North America. P. R. May (1971, fig. 1) has pointed out that the orientation of all these dikes is such that if the continents sur— rounding the Atlantic Ocean were restored to a pre- continental-drift configuration, these widely sepa- rated dikes would all seem to radiate from a common center located somewhere near the south- east coast of the United States and perhaps on the Blake Plateau. In the Eastern United States, particularly in Pennsylvania, these diabase intrusive rocks are asso- ciated with deposits of iron, copper, and other minerals, but the relation of the diabase to the mineralizing process is obscure. In the Haile—BreWer area, South Carolina, diabase dikes cut gold-bear— ing rocks but appear to be younger than the min,- eralizing processes. Although the diabase dikes are not known to be related to the mineralization in South Carolina, they are nevertheless part of the geologic environment where investigations into the geologic, geochemical, and geophysical setting of the gold mines have been carried out. Aeromagnetic data indicate that the dikes are even more abundant and widespread than previously believed from geologic reconnaissance mapping of mining areas. They may indicate areas of abundant pre—Mesozoic fracturing, or perhaps other features, as yet unrecognized, that might lead to favorable areas for ore deposits. Paleomagnetic studies offer a method for placing the diabase dikes in the Haile- Brewer area more precisely into the context of the geologic and chronol‘logic framework of Mesozoic rocks in eastern North America. For this purpose, many of the dikes have been sampled, and their magnetic properties and paleomagnetic-pole posi— tions have been obtained. The results are summar- ized in this report. Figure 1 shows the location of Cl C2 SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 EXPLANATION D‘abase dike of Triassic and Jurassic age—Mainly in Piedmont province of Appalachian region; unmapped in many areas 7/ Ouiu'ops of Newak Group of late % Triassic and Early Jurassic age—Mainly sedimentary rocls but induding intrusive stools and sills in most areas. and inierbedded lava in §yc§ . -g‘a‘fi 40* some nonhern areas —-- Normal {auls—Ai borders of areas of oucrop of Newark Group ------- Boundaries of maior geologic provinces «"1‘“ 7 MID KILOMETERS 200 MlES FIGURE 1.—Sketch map of the Appalachian region of the Eastern United States, showing the location of the Haile—Brewer area, South Carolina, known occurrences of dikes of Triassic and Jurassic age, and areas of outcrop of the Newark Group. (Modified from King 1961.) the Haile—Brewer area in South Carolina, the wide distribution of diabase dikes in the Appalachian region, and areas where the dikes cut sedimentary rocks of Late Triassic and Early Jurassic age. MAGNETIC SETTING A total-intensity magnetic map of part of South Carolina, including the area of the Haile and Brewer mines, is shown in figure 2, which is modified from a map by the U.S. Geological Survey (1970). The data were acquired by means of airborne instru- ments along flight traverses that were about 122 m above the ground, approximately 0.8 km apart, and oriented east and west. The Doppler system was used for navigational location. The data, contoured relative to» an arbitrary datum, show the total- intensity magnetic field in gammas. The aeromagnetic map (fig. 2) shows numerous areas of anomalies that are closely spaced, moder- ately high in amplitude, linear, and positive; the anomalies reflect sharp, narrow variations in the intensity of the Earth’s magnetic field. Many of DIABASE DIKES IN THE HAILE—BREWER AREA, SOUTH CAROLINA these linear positive anomalies are conspicuously alined, trend northwest, and have steep gradients that reflect sources having tops near the surface of the ground. The anomalies are clearly related to diabase dikes that crop out in the area. The flight lines trending approximately due east are partic- ularly well oriented for revealing these narrow, lin- ear magnetic anomalies. If the flight lines had been oriented parallel to the anomalies, their recognition would have been much more diflicult for several rea- sons; for example, the anomalies might have been between flight lines and might not have been re- corded, or the large differences in magnetic response between adjacent flight lines might have been inter- preted as an instrumental or other technical dif— ficulty. The steep northwest-trending anomalies are not evident either on the northwest part of the map or on the southeast part. In a large part of the area shown on the magnetic map (fig. 2) centered near lat 34°30’ N., long 80°45’ W., the level of magnetic intensity is so great that the magnetic contrast due to the linear anomalies is lost. The geologic map of the Haile—Brewer area shows that the Liberty Hill quartz-monzonite pluton is in this area (fig. 3) and that it is cut by diabase dikes, at least locally and in the peripheral parts of the pluton. Apparently the magnetic intensity of the quartz monzonite is nearly the same as that of the diabase dikes. The high- intensity magnetic anomalies in the southeastern part of the map area near lat 34°15’ N., long 80°37’ 30” W. also obscure the dike anomalies. There, broad northeast-trending anomalies coincide with a steep gradient in gravity data and may reflect faulting in subsurface rocks (Popenoe and Bell, 1975). Strong linear northwest-trending magnetic anomalies have been recognized southeast of the area shown in figure 2; these anomalies have been interpreted as reflecting diabase dikes deeply buried beneath Coastal Plain sedimentary rocks (Popenoe and Zietz, 1977). The widths of the northwest-trending linear aero— magnetic anomalies indicate tabular magnetic sources, which are inferred to be Wider or less steeply dipping than field experience and reconnais- sance mapping show the diabase dikes to be. In order to locate the magnetic anomalies as precisely as possible on the ground and to confirm that the anomalies overlie diabase dikes, as inferred, a ground-magnetometer survey was made using truck- mounted equipment. Traverses were made along roads that crossed the anomalies shown by the air- borne survey. The equipment, described by Zablocki (1967), consists of an encapsulated flux-gate mag- C3 netometer suspended from 3 to 4.6 m above the ground on a boom behind the vehicle. Kane, Har- wood, and Hatch (1971) used similar equipment in New England to test and map magnetic anomalies previously located by airborne surveys. The results of the ground traverses in South Car- olina were similar to the results in New England and indicated that the sources of several anomalies were diabase dikes not previously discovered. In addition, the ground traverses showed that in a few places Where data from airborne instruments indi- cate a broad anomaly, the ground traverse shows many small anomalies not evident in the data from the airborne survey (fig. 4). These smaller anom- alies in the ground data commonly seem to result from closely spaced thin dikes, which are not: indi- cated as individual anomalies in data from the airborne-magnetometer survey. In Meriwether County, Ga., a single linear magnetic anomaly de_ tected by airborne methods proved to be as many as four distinct diabase dikes when studied at ground level (Rothe and Long, 1975). In New England, Kane and others (1971) found that airborne equip- ment could not detect single rock units having thicknesses of less than about 15 m. By means of a two-dimensional technique, mag- netic profiles were calculated to test the assumptions that broad magnetic anomalies result from closely spaced thin dikes; a small part of profile A—A’ in figure 4 was used as a model. The model, shown in figure 5, consists of tabular bodies simulating diabase dikes ranging from 7.6 to 30.5 m in thick- ness, extending an infinite length perpendicular to the profile, dipping at 80° W. or 80° E., extending to an infinite depth, and having parallel contacts. The magnetic properties used to calculate the pro- files were chosen to be representative of all the known diabase dikes in the Haile—Brewer area and were in some cases averages of as many as 37 dikes. Two profiles were calculated, at 4.6 m above the ground and at 122 m, and they were compared with the observed profiles obtained from the airborne and truck-mounted magnetometers. The results, illustrated in figure 5, show calcu- lated profiles that resemble closely the observed pro- files. The results suggest that many of the linear magnetic anomalies shown on the aeromagnetic map (fig. 2) likewise may represent an unknown number of dikes of various thicknesses and spacings, all trending at any particular location in nearly the same direction. On the aeromagnetic map (fig. 2), all the anomalies that have identifiable diabase-like outcrops are shown as a dike or dike swarm. In C4 SHORTER CONTRIBUTIONS T0 GEOPHYSICS, 1979 80°33 7 ’30" SOUTH CAROLINA Index map showing Iomtion of Camden—Kashaw area : /.6’ ,/ fr ' f1 ' ~ {gig/{fl 7 Approximate boundary of aeromagnefic survey 34°15! I V I] H ’ 434015, 80°52'30" 45' 80°37’30" FIGURE 2.——Aeromagnetic map of the Camden—Kershaw area, north-central South Carolina. (Modified from US. Geo- logical Survey, 1970.) DIABASE DIKES IN THE HAILE—BREWER AREA, SOUTH CAROLINA C5 2230” 80°15’ 34°40’ EXPLANATION Magnetic contours—Showing total intensity magnetic field of the earth in gamma: relative to arbitrary datum. Hachured to indicate closed areas of lower magnetic intensity, dashed where data are incomplete. Contour intervals are 20 and 100 gammas Flight path—Showing location and spacing of data NOTE—Aeromagneflc survey flown 122 m above ground, 1967 Linear magnetic anomaly-associated with diabase dike or inferred to be associated with diabase dike or dike swarm—A, B, 676, etc. refer to dike or dike swarm discussed in text and listed in table' 6 Site of one or more drill cores for paleomagnetic studies—Showing number listed in table 5 Truck-mounted magnetometer traverses and aeromagnetic profiles shown in figure 4 5 10 15 2'0 KILOMETERS l 5 10 MILES FIGURE 2.—Continued. C6 SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 81‘15' 34'45’ 81‘00’ , 80'45' 35’00' \ < 5? Howie-Condor \,' \ x I i », \ , / ~ — \ / l '\ \ .. \ /_\ 33 Gael/1452795 . I 7 I - " ‘1 V 7 I 7 Ia // o ,h l— o 10 20 MILES l 1 l J ~ A F ' l I , , 0 10 20 KlOMETB’iS ,,,,,,, _ _, ‘ i, 34‘00’ 80°30’ , , 34' 1 5' 80° 1 5' 80°00’ DESCRIPTION OF MAP UNITS GRAVEL, SAND, CLAYEY SAND, AND CLAY (HOLO- W GABBRO (UPPER PALEOZOIC)—Coarse-grained, dark, CENE TO CRETACEOUS)—Coastal Plain deposits with 1% olivine-bearing, grades to diorite locally, nor-itic in part. In- Middendorf Formation (Upper Cretaceous) at the base ’ cludes the Dutchmans Creek Gabbro of McSween (1972) overlain by younger upland deposits; deeply weathered, and QUARTZ MONZONITE (BIOTITE QUARTZ MONZONITE, much redistributed by leaching, colluvial and aeolian processes. GRANODIORITE, TON ALITE, AND GRANITE) (CARBON- Middendorf Formation probably absent where less than 50 IFEROUS)—Pink and gray porphyritic, coarse-grained, in- feet thick cludes fine-grained and subporphyritic facies; commonly with DIABASE (TRIASSIC AND JURASSIC)—Black to dark-gray abundant inclusions near contacts dikes than less than 0.3 m to 342 m thick; miner-ans dikes in § GRANI’IOID ROCKS UNDIVIDED(LOWER PALEOZOIC T0 Kershaw County projected on the basis of clowspaced airborne \\:\ UPPER PRECAMBRIAN)—Includes the Great Falls granitic and ground geophysical data ‘ piuton of Fullagar (1971) and quartz porphyry in Lancaster Co.,S.C. CONGLOMERATE, SANDSTONE,SHALE, AND CLAY- CAROLINA SLATE BELT UNDIFFERENTIATED (PALEO- m STONE (TRIASSIC)—Various shades of red, brown, purple, C5 ZOIC AND UPPER PRECAMBRIAN)—Argillite,tuffaceous and gray undifferentiated. Conglomerates in southernmost . argillite, and graywacke, includes felsic and mafic volcani- outcropa contain many fragments of argillite, phyllite, and elastic rocks and volcanic flows. Metamorphic rocks, pre- schist derived from nearby sources in the Carolina slaté belt dominantly in greenschist or lower greenschist facies. North FIGURE 3.—Geologic map of the Haile-Brewer area, South Carolina. (Modified from Bell and Popenoe, 1976.) DIABASE DIKES IN THE HAILE-BREWER AREA, SOUTH CAROLINA C7 80'30' ’ 35-15' 80'15' —' , ~ » -_ 2., ‘ CORRELATION or MAP UNITS \\ ,m, I {L _ I 1 _ Holocene to -m Jurassic and Triassic Paleozoic Carolina , slate belt Paleozoic and(or) brian Contact—Dotted where concealed D —v—U—- Fault-Dashed where largely a shear zone; dotted where concealed or projected on geophysical data. U. upthrown side; D, downthrown side —1—> Major anticline—Dashed where projected F_,’°' Bearing and plunge of fold axa in tightly folded rocks ' Strike and dip of beds— Inclined Vertical Strike and dip of foliation— Inclined Vertical Strike and dip of foliation— i, inclusion in igneous rock H8 ii: 1?. Strike and dip of fracture cleavage— Little or no recrystallization in plane of cleav~ age Inclined Vertical hike Bearing‘aand plunge of lineation— ; Variety of linear feature shown by letter; . Geology mpiled flan OWEN and c, crinkles on bedding, foliation, or cleavage; V, ‘ 'Bdi “$5 a, b); Stmkey “958); X, intersection of bedding and cleavage A Randazzo, Swe and Whaler . . . ‘ (19701; Waskom and Buflei (1971); 5‘ Mm "“nt "e“ 0' Pmmt rmumk Nystrum “972); 14—4, Line of section shown in Bell and Popenoe (1976) 34°30’ 79'45' 34'45’ 79' 30' DESCRIPTION OF MAP UNITS of the J onesboro fault extended, includes the McManus For- least in part, to the Wildhorse Branch and Persimmon Fork mation of Conley and Rain (1965) Formations of Secor and Wagener (1968) MICA GNEISS (PALEOZOIC AND UPPER PRECAM— AMPHIBOLITE (LOWER PALEOZOIC)—Darkdgreen, gray, n _ BRIAN)—Layered biotite gneiss and biotite schist, hornblende and black amphibolite, includes some hornblende schist and gneiss and hornblende schist with granitic layers common. hornblende gneiss, diorite,’and metagabbro Probably equivalent to large parts of the Carolina slate belt I : GRANITOID GNEISS (LOWER PALEOZOIC AND UPPER north of the Jonesboro fault extended except the metamorphic _ 8 PRECAMBRIAN)—Undivided granitoid sneisses, sneissic grade is almadine-amphibolite granites, and schists characteristic of the Charlotte belt ARGILLITE AND SLATE (LOWER PALEOZOIC)—-Gray HORNFELS AND CONTACT METAMORPHIC ROCKS—In- “ and greenish-gray, thinly bedded and laminated argillihe and eludes dark saccharoidal rocks at the contact of the Liberty slate - ,Hill and Pageland plutons; biotite gneiss with some sericite .. v A > VOLCANICLASTIC ROCKS (LOWER PALEOZOIC)-Tuffs . schist adjacent to the Lilesville pluum Around the Liberty : >V4 ,f : and flows are common near Kershaw. Muscovite, chlorite, Hill plumn mapped largely on the basis 0f geophysical data INTENSELY SILICIFIED ROCKS—Vicinity of the Brewer mine; contains massive topaz locally phyllite, and muscovite-quartz schist, largely felsic but with some interbedded mafic units. Probably equivalent, at FIGURE 3.—Continued. SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 L Part of profile J F shown in figure 5 —I 1200 " "—' 5 m0 .— 3 _ f 400 — 0 Data from alrbome magnetometer g 2000 A I A' S " I I I: ' z 1600 H E_ I l I II I III I 1200 V ' g 800 400 0 n L I 76-8 Dam from truck-mounted magnetometer 1200 B 3' 8 c: é c) Data from airborne magnetome‘z B 1600 1200 8 0 TOTAL INTENI'TY MAGNETIC FELD. IN GAMMAS F 9 § :1 D D Data from trudl-mounted magnetometer 0 500 IIIJU 1500 METERS 0 IMO 2WD 3000 4000 FEET BCPLANATION _£L.__l 76-3 Diabase dike—Solid symbol ‘ndlcatm outcrop. number Indicate paleomagieflc sample site lnduded In table 5; open symbol hdlcatas location ptolected from nearby outaopor Inferred from aaomagneflc data FIGURE 4.—Comparison of profiles obtained by means of an airborne magnetometer carried at 122 m elevation with profiles obtained by means of a truck-mounted magnetometer. Locations of profiles are shown on figure 2. DIABASE DIKES IN THE HAILE— Calculated magnetic profile at 122 in elevation 100— TOTALNTENUTYWFELDJNGAMMAS WEST /0bserved magnetic profile GROUND LEVB. BREWER AREA, SOUTH CAROLINA 09 Observed magnetic profile from airbome magnetometer at 122 m elevation obtained by means of a truck-mounted magnetometer at 3—4.6 m elevation / Nil—"W Sinulated geologic profile (part of profileA—A’ shown In figire 4) striking N. 60° E., showlng dikes dipping 80° E. or 80° W. Bikes are 7.6, 15.2, or 30.4 m thick and are of infinite length and depth. Magnetic propafles used are: magietic vector with azinuth of 84", lndination 25°. and intensity 0.0027 emu (electromagnetic unit).Convetsion 2.7 X 10—6 Nm (2.7 X 10-3 emu/cc) 500 1000 METERS ‘3 F l | o l l I 500 1000 1500 20m 2500 3000 FEET FIGURE 5.—Two-dimensiona1 magnetic profiles of a simulated geologic profile calculated for 4.6 m and 122 m elevation. addition, all comparably long anomalies are shown as a dike or dike swarm, even though no outcrop of diabase has been found. Other less pronounced or less continuous anomalies that may also be thin diabase dikes are not identified on figure 2. All these anomalies indicate that the total number of diabase dikes in the area is very much larger than pre- viously known. GEOLOGIC SETTING The geologic map of the Haile—Brewer area (fig. 3) shows that diabase dikes seen in outcrop or in- terpreted from the aeromagnetic map are not uni- formly distributed. The dikes tend to be particularly abundant in parts of Kershaw and Lancaster Counties and along the Wateree River near the CIO boundary between Kershaw and Fairfield Counties. There the dikes are cutting metamorphosed volcani- clastic rocks and argillites of the Carolina slate belt and to a lesser extent the coarse-grained Liberty Hill pluton, which intrudes rocks of the slate belt. The Pageland pluton, however, is cut by several diabase dikes, including a dike more than 300 m thick. Included within the volcaniclastic unit in the Haile—Brewer area are sparse dark metamorphosed dikes, perhaps originally of andesitic or basaltic composition, which are not reflected in the aero- magnetic data. Neither were they detected by the truck-mounted magnetometer, perhaps, because they are thin, are discontinuous in outcrop, and are prob- ably low in magnetite content. Figure 3 shows diabase dikes extending as far as the limit of aeromagnetic data into areas where Coastal Plain sedimentary rocks are at the surface. Diabase dikes in the Haile-Brewer area are not known to cut either Cretaceous or younger sedi- mentary rocks. The strong magnetic anomalies ex- tending from known diabase in areas of crystalline rocks into areas covered by rocks of the Coastal Plain reveal that the dikes extend beneath the over- lying sedimentary rocks, where their orientation and extent can be interpreted from the magnetic data. DIABASE DIKES The dikes in the Haile—Brewer area are all olivine- bearing tholeiitic diabase that is commonly inter- granular or subophitic, is less commonly porphyritic, and contains feldspar or olivine phenocrysts. Mega- scopic variations in the dikes are mainly variations in grain size, texture, and abundance of olivine and feldspar phenocrysts. The average modal analysis of 16 thin sections of diabase from South Carolina re- ported by Chalcraft (1976) is given as follows: Volume (percent) Plagioclase _____________ 53.3 Clinopyroxene ___________ 30.9 Olivine _________________ 11.2 Magnetite—ilmenite ______ 2.5 Biotite _________________ Trace Alteration products ______ 1 3.3 Total _____________ 101.2 1Average of 13 thin sections containing more than traces of altera- tion products. In the field, the black to dark-gray diabase com- monly has a weathering rind of characteristic orange—brown soft residuum. Many of the dikes weather spheroidally, and cores of the weathering spheroids, called core stones, are displaced as float SHORTER CONTRIBUTIONS T0 GEOPHYSICS, 1979 and are commonly found scattered on the ground surface below the dike outcrop. In some thin dikes, a columnarlike jointing is perpendicular to the dike walls, and some dikes have distinct fine-grained chilled margins. No systematic thickness measurements of diabase dikes have been made; thus, neither the average thickness nor the most common thickness is known. However, the thickness of a dike sampled in, the present study was measured or estimated Wherever the dike contacts could be at least approximately located. The thicknesses range from a few centi- meters to more than 300 m. The most common thick- nesses appear to be about 3 m and about 15 m. The largest dike, carefully measured by Steele (1971) Where it is exposed in a deep road cut in Lancaster County, is 1,123 feet (342.3 m) thick. Dikes. of this thickness appear to be very rare. Several artificial outcrops, perhaps as long as 100 m, were found where as many as nine dikes ranging in width from less than 15 cm to as much as 22 m crop out. Where several thin dikes are close together, correlation of specific dikes from outcrop to outcrop is complicated by the similarity in appearance of the dikes, their nearly parallel strike, and their apparently anas— tomosing character. Steele (1971), as a result of his studies of the thick dike in Lancaster County, concluded that the unusual thickness of that dike resulted from two injections of magma. The bifurcated character of the long aeromagnetic anomaly associated with the dike may indicate that, indeed, more than one dike did coalesce to produce an exceptionally thick dike. The dike probably coalesced before the magma in either dike cooled, because no textural indication of chilling between them is obvious. In general, the diabase dikes in the Haile—Brewer area have the conspicuously oriented trend of about N. 45° W. that is characteristic of these dikes in the southeastern piedmont (fig. 1). However, the strike of individual dikes is locally varied. The dip of the dikes is commonly vertical, or nearly so. In the Wadesboro Triassic and J urassic(?) basin a short distance northeast of the Haile—Brewer area, diabase dikes trending northeast, as well as those trending northwest, appear to be common (Randazzo, Swe, and Wheeler, 1970; Randazzo and Copeland, 1976). Some of the northwest-trending diabase dikes are cut and offset by faults that paral- lel the southeastern border faults of the Wadesboro basin. At least two episodes of diabase-dike emplace- ment in the Wadesboro basin seem to be clearly in— dicated; therefore, several episodes of dike emplace- DIABASE DIKES IN THE HAILE—BREWER AREA, SOUTH CAROLINA ment in the nearby Haile—Brewer area might also be expected, but they have not been recognized. Although diabase dikes similar to dikes in the Triassic and Jurassic basins have been recognized and mapped in the Haile mine and elsewhere in the Haile—Brewer area, the airborne-magnetometer sur- vey shows that the dikes are very much more num- erous in the deeply weathered rocks than previously realized. Most commonly, the dikes crop out in stream beds, where dense unweathered diabase makes an obstruction that diverts the course of the stream. These obstructions and diversions produce local topographic expressions that reveal the trend of the dikes. Other outcrops along ridges or on inter- fluvial areas commonly are poorly exposed pave- ments or consist of clusters of boulders or‘ cobble— size fragments. Bouldery ridges and trails of float cobbles are clear indications in areas of residual weathering that at least one diabase dike is present in the immediate vicinity, but the true: nature and attitude of the dike or dikes are generally concealed. Detailed mapping of the dikes is impeded not only by deeply weathered country rocks in which the dikes are found but also by the common deeply weathered condition of the dikes themselves and by the heavily vegetated countryside. In these areas, the aeromagnetic map is particularly helpful as an aid to mapping. In petrographic and chemical studies, Ragland, Rogers, and Justus (1968), Weigand and Ragland (1970) , and Smith, Rose, and Lanning (1975) have divided the Triassic diabase into groups differing in chemistry, probable origin, and age. Weigand and Ragland (1970) separated eastern North American diabase dikes into three varieties. These are an olivine-normative diabase, a high-TiO2 group, and a low-TiO2 group. They further divided the high-TiO2 rocks by recognizing a subgroup of dikes having a high iron-oxide content. Smith and others (1975, p. 945) found that in Pennsylvania, copper and titanium contents were reliable indicators of diabase type. They divided the diabase intrusive rocks into three groups—Rossville, York Haven, and Quarry- ville types—having differing mineralogy and chem- istry and corresponding approximately to the three varieties of Weigand and Ragland (Smith and others, 1975, p. 949—950). The Quarryville type cor- responds to the olivine-normative variety, the York Haven type corresponds to the high-TiO2 quartz- normative variety, and the Rossville type corre- sponds to the low-TiO2 quartz-normative type. Table 1 gives the chemical composition, trace-element con- tent, and normative mineralogy of eight oriented C11 samples of the 342.3 m-thick dike in Lancaster County that were collected for magnetic studies. Most samples are quartz normative, but those col- lected near the margins are olivine normative. Table 2 summarizes the magnetic properties, measured during this study, of the eight samples for which chemical data are presented in table 1. Steele (1971) gave detailed analytical and petrographic data for 95 samples from this same dike. The magnetic properties closely reflect the norma- tive mineralogy. Both the induced magnetism and the remanent magnetism are distinctly lower near the western margin than in the central part of the dike. The sample from near the eastern margin of the dike is similar to the sample from the western margin in content of normative olivine, magnetite, and ilmenite; the magnetic properties are also sim- ilar, except that the remanent magnetism of the sample from the eastern margin is unaccountably high. Using K-Ar age determinations of samples of Triassic diabase intrusive rocks collected in Con- necticut and New Jersey, Armstrong and Besancon (197 0) attempted to test the hypothesis that more than one period of intrusion occurred in the Newark Group rocks. They reviewed previous work of a similar nature that seemingly indicated that the ages of the volcanic rocks in the Newark Group (Upper Triassic and Lower Jurassic) are about 190 to 195 my (million years). Armstrong and Besancon found that K-Ar age determinations on diabase dikes gave results that were consistently and statistically older than the rocks the dikes cut. They (1970, p. 25) came to the conclusion that the diabase dikes in eastern North America are not suitable for “defining a point on the geologic time scale,” either because of a loss of Ar from low-grade metamorphic rocks; at zeolite or prehnite—pumpellyite facies conditions or because of extraneous excess Ar. SAMPLING PROCEDURES The diabase dikes were sampled for study of paleomagnetic properties, beginning with the large dike in Lancaster County in 1969; a few dikes were sampled in 1975, and most of the remaining dikes described in this report were sampled in the spring of 1976. All the samples except those collected in 1969 were obtained by drilling outcrops using the methods described by Doell and Cox (1965) and using equipment similar to that they described. The nature of the outcrops in the Haile-Brewer area and the general thinness of the dikes required 012 SHORTER CONTRIBUTION S TO GEOPHYSICS, 1979 TABLE 1.—Major- and minor-oxide composition, trace-element content, and normative mineralogy of a large diabase dike, Lancaster Co unty, S.C. [Rapid rock analysis by P. L. Elmore, Gillison Chloe, James Kelsey, Lowell Artis, Hezekiah Smith, and J. L. Glenn, all of the U.S. Geological Survey. Spectrographic analysis by J. L. Harris, U.S. Geological Survey . Samples are approximately equally spaced across the dike; sample 677 is near the west margin, and sample 683 is near the east margin of the dike. L, present but below limit of detection; leadered where not calculated] Sample __________________________ 677 676 678 679 680 681 682 683 Major- and minor-oxide compositions [Rapid rock analyses, in weight percent] 5102 ______________________ 50.0 50.5 51.1 51.0 51.4 51.0 51.2 50.4 A1203 _____________________ 18.3 17.3 17.0 17.2 16.9 17.0 17.2 17.9 F9203 _____________________ 1.2 2.5 2.4 2.0 2.3 2.5 2.9 1.2 FweO ______________________ 7.1 7.8 7.9 7.7 7.4 7.8 6.8 7.6 MgO _____________________ 6.5 5.5 5.5 5.8 6.0 5.8 6.1 6.2 09.0 ______________________ 12.0 10.4 10.5 10.9 10.7 10.4 11.2 11.7 Nazo _____________________ 2.4 2.5 2.5 2.4 2.4 2.2 2.4 2.2 K20 ______________________ .62 .91 .99 .87 .90 .87 .85 .66 H20+ ____________________ .89 .82 .74 .97 .63 .76 .12 .95 HzO— ____________________ .21 .28 .26 .23 .25 .44 .25 .25 T100 ______________________ .56 76 76 .67 .72 .76 .65 .60 P20; ______________________ .05 .10 .10 .09 .09 .10 .09 .07 MnO _____________________ .15 .17 .17 .18 .19 .19 .18 .15 C02 ______________________ <.05 <.05 <.05 <.05 <.05 <.05 <.05 <.05 Total _______________ 100 100 100 100 100 100 100 100 Trace-clement contents [Spectrographic analyses, in parts per million] Ag _______________________ L L L L L L L L Ba _______________________ 150 150 200 200 200 200 100 150 C0 _______________________ 70 30 50 30 30 50 20 30‘ Cr _______________________ 500 200 300 200 200 200 150 300 Cu _______________________ 70 100 100 70 100 100‘ 100 70 Mo _______________________ 5 5 5 5 5 5 3 5 Ni _______________________ 150 100 100 100 100 100 70 100 Pb _______________________ 3 10 7 3 3 3 3 3 Sc ________________________ 70 70 70 70 70 70 30 50 Sr ________________________ 150 200 200 200 200 200 150 150 V ________________________ 200 200 200 200 200 200 100‘ 150 Y ________________________ 30 3O 50 30 30 50 20 30 Zr ________________________ 50 70 100 70 70 100 30 70 Ga _______________________ 10 15 15 10 10 10 10 15 Yb _______________________ 3 3 5 3 3 5 2 3 CIPW mineral norms [In weight percent] Quartz ___________________ ____ 1.01 1.30 .99 1.79 2.81 1.57 -_.._ Orthoclase: ________________ 3.67 5.42 5.87 5.15 5.34 5.17 5.04 3.91 Albite ____________________ 20.34 21.30 21.22 20.34 20.37 18.72 20.36 18.68 Anorthite _________________ 37.40 33.53 32.33 33.65 32.79 34.14 33.74 37.14 Diopside __________________ 17.67 14.35 15.58 16.12 16.01 13.77 17.16 16.68 Wollastonite __________ (9.02) (7.29) (7.91) (8.19) (8.17) (7.01) (8.80) (8.48) Enstatite _____________ (5.08) (3.87) (4.16) (4.38) (4.55) (3.79) (5.18) (4.57) Ferrosalite ____________ (3.57) (3.19) (3.52) (3.55) (3.30) (2.98) (3.19) (3.63) Hypersthene ______________ 11.59 18.13 17.68 18.28 18.03 19.18 16.24 19.18 Enstatite _____________ (6.80) (9.93) (9.58) (10.09) (10.44) (10.74) (10.06) (10.70) Ferrosalite ____________ (4.79) (8.20) (8.10) (8.19) (7.59) (8.44) (6.19) (8.49) Magnetite _________________ 1.74 3.65 3.49 2.90 3.34 3.65 4.22 1.74 Ilmenite __________________ 1.06 1.45 1.45 1.28 1.37 1.45 1.24 1.14 Apatite ___________________ .12 .24 .24 .21 .21 .24 .21 .17 Olivine ___________________ 5.41 ____ ____ ____ ____ ____ ____ .29 Forsterite _____________ (3.04) ___1 ____ ____ ____ _-__ ____ (.16) Fayalite ______________ (2.36) ____ -___ ____ ____ ____ ____ (.14) Calcite ___________________ .12 .11 .11 .11 .11 .11 .11 .11 Total _______________ 99.11 99.18 99.26 99.04 99.38 99.24 99.89 99.05 that special care be taken to insure that the rock drilled was in its original place and not rotated or moved by erosion or other disturbances. Outcrops of diabase in the beds of streams, along the shores of Wateree Lake, and in deep road cuts: where both contacts between dike and country rock are exposed gave the greatest confidence that the dikes were suit- able for sampling. Other outcrops on bouldery ridges or flat pavement outcrops inspired less confidence that they were undisturbed. At these places, it was not always possible to determine that an outcrop was not a large spheroidal weathering boulder DIABASE DIKES IN THE HAILE—BREWER AREA, SOUTH CAROLINA 013 TABLE 2.—Magnetic properties and normative magnetite and ilmenite contents of a large diabase dike, Lancaster County, SC. [wt. percent, percent by weight. K, Ji, Jr, and Jr+Ji are in 10’4 emu (electromagnetic units)/cm3. Ji:0.554K. Koenigsberger ratio: Qer/Ji] Proportions, r ' . No mative normative Inclina- magnetite . - K . _ Total tion of Sample ,Jnfigfim p115): 355353. 13.25233? $22226...- IEQEJE‘J. £5125: mag)?”- $315353} (wt. _ . . bility, K tion, Ji tion, Jr ratio, Q Jr—i— :11 zation eu $52525: (gears. weereeu 677 ___________ 2.80 62 38 0.67 0.37 6.06 16.37 6.43 7 676 ___________ 5.10 72 28 17.90 9.91 9.96 1.01 19.87 20 678 ___________ 4.94 71 29 14.60 8.08 6.88 .85 14.96 20 679 ___________ 4.18 69 31 10.70 5.92 3.36 .57 9.28 44 680 ___________ 4.71 71 29 15.00 8.31 9.14 1.10 17.45 38 681 ___________ 5.10 72 28 15.8 8.75 3.40 .39 12.15 —25 682 ___________ 5.46 77 23 13.4 7.42 3.04 .41 10.46 20 683 ___________ 2.88 60 40 10.2 5.65 19.0 3.36 24.65 18 slumped from its original position or that the out- crop was not part of a large mass of colluvium that had slumped or slid as a unit. Probably some such disturbed outcrops were sampled and may be the cause of unrealistic results and a source of error. An attempt was made at each site location to ob- tain at least three drill cores spaced about a meter apart. At some sites, the outcrop of diabase was too small to be conveniently drilled more than once or twice, or the diabase proved to be too deeply weathered to provide satisfactory samples. At other locations, only the fine-grained, chilled margin of the dike proved to be sufficiently unweathered to drill. Cores were obtained from a total of 39 sites. Of these, only 27 were used in statistical calculations and measurements of remanent magnetism, for the various reasons just mentioned. All sites drilled, however, are shown on figure 2. In the laboratory, the drill cores were cut into as many 23-mm-l’ong specimens as possible. Usually one to five specimens were cut from each core, and the total number of specimens involved is 163. These Were all measured and compared to obtain a single direction and intensity of remanent magnetism for each core. Table 3 shows the hierarchy of names used in the sampling and statistical calculations. TABLE 3.—-Definition of terms used in the sampling hierarchy Dike or dike swarm. Diabase dike or several closely spaced dikes associated with a linear magnetic anomaly on which there is at least one drilling site. Labeled “Dike A," “Dike B,” etc. Site. Outcrop of diabase suitable for drilling by means of a portable diamond drill and from which a drill core was collected. Labeled “76—1,” “75—2,” “676,” etc. Core or drill core. Drill core obtained at a site; 1—3 cores obtained at each site; each core 20—40 cm long. Labeled “a,” “b,” “c,” etc. Label follows site designation. Specimen. One to five 23-mm-long pieces cut from individual drill cores; magnetic properties were measured on these specimens. Labeled “A,” “B,” “C,” etc. Label was added to site and core designations but is not included in tables. LABORATORY PROCEDURES Measurement of NRM.—In the laboratory, the specimens were given random sequential numbers, and their natural remanent magnetism (NRM) was measured. The instrument used and the procedures followed were the same as those described by Doell and Cox (1965). The data obtained from the spinner magnetometer were reduced, and the declination and inclination of the magnetic fields of the specimens were plotted by various computer programs (R. W. Bowen, R. R. Doell, and C. S. Grommé, unpublished computer program, 1966). Alternating-field cleaning.—The plot of the data from the spinner magnetometer showed that there is much scatter in the NRM of the specimens. In order to decrease the dispersion in the data not related to the paleomagnetic field, all specimens were subjected to an alternating field of 100 Oe (oersteds) to remove the extraneous magnetism. One hundred oersteds was chosen as the best level for cleaning all specimens, after specimens from several locations had been cleaned at incremental steps from 37 0e to as much as 500 Oe. The 100-Oe level of cleaning is close to the 150-Oe level found to be satisfactory by Beck (1972) and deBoer (1967, 1968) for samples of diabase from Pennsylvania and New England. Calculation of paleomagnetic-pole positions—In order to interpret the data obtained, most re- searchers ‘of paleomagnetism rely on parametric sta- tistics for dispersion on a sphere (Fisher, 1953). In order to calculate a paleomagnetic-pole position, the variations inherent in the specimens have been aver- aged for each hierarchy in the sampling program. The specimens from each site Where at least three cores were obtained have been averaged to produce the mean declination and mean inclination of the NRM. These data together wtih the mean decli- nations and mean inclinations calculated after the specimens had been cleaned at 100, 200, and 300 Oe C14 DIABASE DIKES IN THE HAILE—BREWER AREA, SOUTH CAROLINA TABLE 4.——Results of spinner-magnetometer measurements on specimens of diabase dikes from the Haile—Brewer area, South [D, declination, in degrees; I, inclination, in degrees; 1:, estimate of Fisher‘s (1953) precision parameter; Site No. of Natural remanent magnetism Lfgggigg Maggi?“ No. av‘é‘ififa D I Is 0195 34.33 80.67 76—1 3 18.9 10.6 27.9 23.8 34.40 80.72 76—2, at ___- 355.5 —7.1 ___- ____ 76—2,b ____ 354.8 —15.0 _-__ ___- 34.40 80.72 76-3, a ___- 50.6 —20.6 ___- ____ 76—3,b ___- 41.3 ——20.0 ___- ___- 34.40 80.72 76—4, a ____ 341.7 15.2 ____ ____ 76—4, b ___- 346.4 24.3 ___ ____ 34.39 80.69 76—8 5 341.7 27.3 4 3 41 6 34.52 80.59 76—9,a ___- (1) (1) ___- ____ 76—9,b ___- 59.9 14.0 ____ __ 34.51 80.59 76—10 4 162.6 —58.0 13.2 26.2 34.52 80.57 76—12, a ___- 10.3 32.9 ____ ___- 76—12,a ___- 8.2 31.5 ___- _-__ 76—12, b ___- 2.1 40.0 ___- __ 34.55 80.60 76—13 4 9.6 24.0 41.9 14.4 34.60 80.59 76—15 4 13.2 68.8 12.7 26.8 34.61 80.60 76-17 4 15.1 38.5 10.7 29.5 34.58 80.56 76—19,a ____ 149.0 42.5 ____ ___- 76—19,b ___- 200.7 28.1 _ __ ____ 34.55 80.53 76—20 4 319.2 18.4 2.6 72 7 34.40 80.81 76—21 6 87.3 17.0 1.3 ___- 34.40 80.82 76—22, a ___- 174.9 12.8 ___- ____ 76—22, b ___- 184.8 72.7 ___- ____ 76—22, b ___- 162.6 70.7 ___- ____ 34.40 80.82 76—23 ____ 178.5 21.3 ___ __ _ 34.40 80.81 76—24 4 161.3 39.5 2 5 74.4 34.40 80.83 76—25 3 115.0 —15.2 1 1 0.0 34.40 80.83 76—26, a ___- 235.6 9.8 ___- ___- 76—26,b ____ (1) ___- ___- ___- 34.40 80.83 76—27 3 197.5 16.5 17.7 30.2 34.40 80.83 76—28, a ___- 96.0 29.5 ____ ____ 76—28, b ____ 100.3 26.6 __ ___- 34.41 80.85 76—29 5 102.9 —62.8 1 8 85 6 34.42 80.85 76—30, a ____ 303.0 22.0 ___- ____ 76—30, b ____ 145.3 32.7 _ ___ 34.45 80.86 76—31 5 52.6 2.8 106.6 7 4 34.65 80.50 676 9 7.6 19.9 40.4 8 2 34.57 80.60 75—1 ___- 311.6 45.1 ____ ____ 34.60 80.60 75—2, a ___- 77.2 39.9 ___- ___- 75-2,b ___- 3.0 30.6 ___- ____ 1 Not measured. are shown in table 4. Data from specimens, cleaned at 100 Oe, from sites on the same linear magnetic anomaly (fig. 2), and therefore presumably on the same diabase dike, have then been averaged to pro- duce a mean virtual geomagnetic-pole (VGP) posi- tion for individual dikes. Data from sites on closely spaced thin dikes in a dike swarm have been com- bined and used to calculate a VGP for the dikes in that swarm. The paleomagnetic direction, paleopole position, and statistical parameters for each dike, calculated from data derived from specimens cleaned at 100 0e, are shown in table 5. No correction for structural rotation or folding of the rocks in which the dikes are emplaced has been applied to the data. RESULTS The VGP calculated for each dike or dike swarm (table 5) results from combining data having vari- ous reliabilities. For instance, the calculated pole for dike A is a combination of data from three sites on an aeromagnetic anomaly (fig. 2) that extends about 16 km in the volcaniclastic unit near the contact with the Liberty Hill pluton. The data from these three sites give conflicting results. One site, 7 6—10 (table 4), is an outcrop in the bed of a stream; it has ample area for core drilling and yields significant statistical results. The second site, 76—9 (table 4), is a roadcut, 0.32 km to the northwest, where only two cores were obtained; perhaps as a result of undetected dis- turbance by road builders, these two cores yield divergent results that are not significant for pole calculations. The third site, 76—13, is 2.74 km north- west of the second site. Although also an artificial exposure, it yields results that are Within acceptable statistical limits but have a magnetic direction that is nearly 180° from that of sit-e 76—10 on this DIABASE DIKES IN THE HAILE—BREWER AREA, SOUTH CAROLINA C15 Carolina, untreated and after cleaning by subjection to alternating magnetic fields of intensities of 100, 200, and 300 oe’rsteds 0195‘, radius of cone of confidence at 95 percent probability level, in degrees; 0e, oersted] Magnetism remaining after cleaning at the indicated intensities 100 Oe 200 Oe 300‘ Oe D I k a95 D I 1c 0195 D I k 0195 6.8 4.6 81.4 13.8 359.1 —0.9 101.3 12.3 353.4 —21.8 5.9 56.1 12.8 —12.4 ___- ___- ___- ___- ___- ___- ___- ____ ___- __-_ 15.6 —19.8 ____ ___- ____ ___- --__ ___- ___- --__ ___- ____ 41.7 ——26.4 ____ ___- ___- ___- ___- ___- ___- ____ ___- ___.. 43.0 —24.9 ___- ____ ___- ___- ___- ___- ____ ___- ___- ____ 349.4 13.2 ___- ___- ___- ___- ____ ____ ___- ___- ____ ___.- 0.1 3.0 ___.. ___- ___- ___- ___- ____ ___- ____ ___- ___- 238.3 53.7 2.2 68.4 219.6 39.8 1.6 ____ 157 0 57.6 1.4 0.0 5.5 16.3 ___- ___- ___.. ___- ___- ___- ___- ___- ____ __-_ 11.8 12.7 ___- _-__ -___ ____ ___ ___- ___ ____ ___- ___- 175.8 —24.4 3.6 56.6 174.3 4.6 5 2 61 1 184.4 20.0 5.8 56.6 16.6 33.1 ___- ___- ___- ____ ____ ___- ___- ____ ___- ____ 10.1 27.2 ___- ___- ___- ___.. ___- ___- ___- ___.. ___- ___- 4.5 32.4 ____ ___- ___- ___ __ _ __ _ ___- ____ ____ ___- 3.5 20.2 126.8 8.2 357.6 17.9 36.8 20.6 340.8 13.4 11.7 37.8 11.7 60.1 158.8 7.3 15.6 58.2 104.3 7.5 22.3 46.3 15.4 17.6 9.1 32.4 39.4 14.8 2.4 36.2 17.1 22.9 336.2 50.8 5.3 44.2 169.7 44.4 ___- ___- ___- ___- ___- ___- ___- -___ ___- ___- 197.2 28.0 ___- ___- __-_ ___- ___- ___- ___- ____ ____ ____ 234.3 66.0 3.2 60.9 264.5 64.8 3.6 77 1 302.8 59.5 2.4 0.0 33.0 63.9 2.5 54.4 10.4 68.2 1.9 ___- 343.7 68.0 2.2 ____ 187.3 13.4 ___- _-__ ____ ___- ___- ___- ___- ___- ____ ___- 179.3 61.0 ___- ____ ___- ___- ____ ___- ____ ___- ___- __-_ 179.6 62.1 ____ ___- ___- _-__ ___- ___- ___- ___- ___- ___- 184.2 14.0 ____ ___- ___- ___- ___ ___ ___- ____ ___- ___- 196.4 52.0 2.2 82.3 199.8 52.2 1 4 0.0 209.6 55.6 1.5 0.0 153.0 47.6 1.4 0.0 157.4 48.8 1 4 0.0 198.9 65.5 1.5 0.0 205.9 11.0 ___- ___- ___- ___- ___- ___- ___- ___- ___- __-- 183.3 11.3 ____ ___- ___- ___- ___- ___- ___- ____ __-_ ___- 190.4 6.7 56.3 16.6 182.0 0.4 23.1 26.3 194.5 2.8 56.6 16.5 111.7 21.8 ____ ___- ___- _-__ ___- ___- ____ ____ ___- ___- 140.7 21.0 ___- ___- 162.2 9.2 _-__ ___- ___- ____ ____ ___- 179.7 -3.5 2.0 75.3 167.8 —11.9 1 0 00 _-__ ___.. ___- ____ 358.3 42.4 _-__ ____ ___- ___- ___- ___- ___- __-_ __-_ _-__ 182.8 32.3 ____ ____ 175.2 25.2 ___- ____ ___- ____ ____ ___- 15.0 9.7 320.4 4.3 16.8 5.2 15.7 24.0 ____ ___- __-_ ___- 5.6 17.9 30.1 9.5 ___- ___- ____ ____ ____ ____ ___- -___ 22.1 36.7 ___- ___- 17.8 36.6 ___- -___ ___- ___- ____ ____ 94.0 35.3 ___- ____ 101.0 34.5 ___- ____ 114.5 29.3 _-__ ___- 10.0 35.4 ___- ____ 11.4 35.1 ___- ___- 1.1 37.4 ___- ___- aeromagnetic anomaly. The reason the data are so divergent is not known, but it may be that unrecog- nized multiple dikes are present or that the aero- magnetic anomaly or some other factor has been mis- interpreted. The consequences of combining data from these sites are reflected in a large radius of the cone of confidence for the paleomagnetic direction and a small precision parameter, k, for the VGP from this dike. Dike B (fig. 2) is a 28.2-km-long segment of an aeromagnetic anomaly on which three sites were drilled. Suitable cores were obtained from only two of the sites, which were 2.09 km apart. The VGP obtained by combining data. from all specimens from these two sites yielded a pole position having a small cone of confidence at the 95-percent level, a large precision parameter, k, and normal polarity. It seems likely therefore, at least for the distance between the two sites, that this aeromagnetic anomaly results from a diabase dike for which the VGP is reliable. Data from two sites on Dike C produced a. reliable VGP with reverse polarity. The diabase drilled at the two sites, however, differs in lithology in both hand specimens and thin section. At one site, the rock is porphyritic and contains abundant feldspar phenocrysts, which in thin section are much clouded with opaque alteration products and calcite. The other site, in contrast, is a more typical nonpor- phyritic diabase. Apparently the appearance of the diabase changes along strike. On Dike D, four sites were drilled, but only two sites provided the required cores and specimens that when combined met accepted reliability criteria. Dike 676 is the dike in Lancaster County that is more than 305 m thick. The data for this dike give a reliable VGP. 016 SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 TABLE 5.—Paleomagnetic directions and paleomagnetic pole positions for diabase dikes omd dike swarms in the Haile—Brewer area, South Carolina [0195, radius of cone of confidence at 95 percent probability level; k, estimate of Fisher’s (1953) precision parameter; Lat. and Long., latitude and longitude of the Virtual geomagnetic pole (VGP); P, polarity; N, north-seeking (reverse) polarity: S, south-seeking (normal) polarity; 5m and 5p, semiaxes of the confidence oval about the VGP] Paleomagnetic direction Paleopole position Dike Mean Mean (sites included) decli- incli- 95 l Lat. N. Long. E. P 5m 6p nation nation a 6 (degrees) (degrees) (degrees) (degrees) (degrees) (degrees) A (76—9, 76—10, 76-13) __________ 6 23 52 2 67.13 83.55 S 56 30 B (75—2, 76—17) ________________ 12 36 15 25 72.18 58.48 S 18 10 C (76—19, 76—20) ________________ 190 43 17 29 29.32 88.38 N 21 13 D (75—1, 76—12) ________________ 13 32 8 116 69.37 61.49 S 9 5 676 ____________________________ 3 16 8 49 63.44 91.45 S 8 4 E (76—22 to 76—30 inclusive) ____ 182 19 14 5 45.37 96.03 N 15 8 F (76-15) ______________________ 11 60 7 158 78.76 331.07 S 11 8 G (76—31) ______________________ 15 9 4 320 57.34 70.62 S 4 2 H (76—2, 76—3, 76—4) ____________ 16 —-12 23 9 46.70 75.24 S 23 12 I (76—1) _______________________ 7 5 14 81 57.37 86.73 S 14 7 EXPLANATION A. Dike, weathered, probably about 14 m thick; core stones sampled; fine to very fine grained; abundant olivine, some much altered: opaque min- erals conspicuous; inter-granular texture. B. Dike, probably about 15 m thick; fine to medium fine grained; olivine bearing, partly altered; opaque minerals sparse. C. Dike, outcrop in road gutter and stream bed; no contacts seen; in part porphyritic; in thin section, possible relict olivine; pyroxene altered; all plagioclase much clouded with opaque alteration material; some clots of calcite with very fine quartz; sparse chlorite; opaque minerals abundant. Dike, outcrops as bouldery ridge and on flood plain; about 23 m thick; fine grained; olivine sparse, altered; intergranular texture, 676. Dike, sampled in deep road cut; about 342 m thick; described by Steele (1971); contains as much as 5 percent olivine and 4 percent opaque minerals; inter-granular texture. E. Group of closely spaced thin dikes; most range in thickness from 0.6 m to 2.7 m but group includes one dike 21 m thick; most dikes are well exposed at location site; some have abundant transverse joints; dike trends range from N. 3° W. to N. 27° W F. Dike, weathered outcrops are crumbly; fine to medium grained; abundant large unaltered olivine; abundant opaque minerals both fine and very fine; intergranular texture. G. Dike, weathered; core stones sampled; strikes N. 30° W.. dips vertically; abundant transverse joints; about 3 m thick. H. Group of 3 closely spaced thin dikes, 1 m, 3 m, and 3.4 m thick, respectively; crops out in road gutter; some dikes show unweathered very fine grained chilled margins and have coarser grained weathered interiors. I. Dike, outcrop in road cut, weathered; core stones sampled. In table 5, E represents a dike swarm of as many as nine closely spaced dikes ranging in thickness from 0.6 m to 2.7 m; the swarm also includes one dike about 21 m thick. Because these dikes are so closely spaced and because they have similar trends and similar appearances, they have been considered as if they were the result of a single intrusion of magma along closely spaced fractures. The paleo- magnetic direction that results from combining data. from these sites meets the standards for re- liability; the data provide a cone of confidence with- in the 95-percent probability level at 14°. The dike swarm, however, has a reverse, north-seeking, polarity. Data. are used from only one site on each of the dikes F, G, and I, but the results of paleomagnetic- direction and paleopole-position calculations give small cones of confidence and large precision param- eters, k. In table 5, H represents a. dike swarm of as many as six dikes, ranging from about 0.2 m to about 3.6 m in thickness, emplaced in the coarse-grained Liberty Hill pluton. Only three of the dikes, however, were suit-able for core drilling. Possibly one of these thin dikes may be represented by a small anomaly in each of the aeromagnetic profiles (fig. 4, south- westernm‘ost open-dike symbol in each profile) ob- tained by means of a truck-mounted magnetometer. The VGP’s calculated for the dikes designated A through I and 676 seem to fall into three groups on the basis of their positions and polarities (table 5). The average positions of the paleopoles of each of these three groups are presented in table 6, which consists of two parts, A and B. The pole positions given in part A are calculated by using all the data listed in table 5, including some from sites where fewer than three cores were obtained and which therefore yield data that. (110 not meet the statistical standards of data used from other sites. Part B shows pole positions calculated by using only data that meet the strictest statistical standards applied to these data. The number of specimens from which data are used in the calculations for part B of table 6 is less than half the number from which data. are used in part A, but part B shows the probably more reliable pole positions. The paleomagnertic pole positions shown in table 6, part B, for groups 1 and 2 are very close, but the poles show opposing polarity. Group 3 consists of specimens from only one site, and although the statistical parameters indicate that confidence should be placed in the results of the cal- culations, the positions calculated are so far from expected Mesozoic or Paleozoic paleopole positions DIABASE DIKES IN THE HAILE—BREWER AREA, SOUTH CAROLINA 017 TABLE 6.—Summary of magnetic data and paleomagnetic pole positions for diabase dikes and dike swarms in the Haile— Brewer area, South Carolina [Group 1, specimens from dikes A, B, D, 676, G, and I: group 2, specimens from dike C (part A) and dike swarms E (parts A & B) and H (part A); group 3, specimens from dike F. x, number of sites from which data are combined; 11, number of specimens used; Decl., mean declination; Incl., mean inclination: n95, radius of cone of confidence at 95 percent probability level; k. estimate of Fisher’s (1953) precision parameter; Lat. N. and Long. E., north latitude and east longitude of the virtual geomagnetic pole (VGP); P, polarity; N, north-seeking (reverse) polarity; S, south- seeking (normal) polarity; 5m and 6p, semiaxes of the confidence oval about the VGPJ Paleomagnetic direction Paleopole position Specimens “/1, Dec . Incl. 0195 k Lat. N. Long. E. P 6m 6p (degrees) (degrees) (degrees) (degrees) (degrees) (degrees) (degrees) Part A—all sites: Group 1 ______ 10/37 9.8 17.3 13.6 4 63 78 S 14 7 Group 2 ______ 14/37 177.1 43.4 28.0 2 30 102 N 35 22 Group 3 ______ 1/4 11 60 7 158 79 331 S 11 8 Part B—only sites yielding signficant VGP’s: Group 1 ______ 5/25 7.7 14.7 6.3 22 62 83 S 6.5 3.3 Group 2 ______ 1/3 190.4 6.7 16.6 56.3 51 82 N 16.6 8.4 Group 3 ______ 1/4 11 60 7 158 '79 331 S 11 8 that they are not paleomagnetically or geologically realistic and should probably be disregarded. CONCLUSIONS The diabase dikes in the Haile-Brewer area asso- ciated with aeromagnetic anomalies yield paleo- magnetic poles that are statistically acceptable at either 62° N., 83° E., normally polarized, or 51° N., 82° E., reversely polarized. These poles seem to be close to the mean Late Triassic paleomagnetic pole given as 68° N., 97° E. by McElhinny (1973, p. 202, table 16) and as 66° N., 95.5° E. by Beck (1972, p. 5684) for eastern North America Upper Triassic igneous rocks. The mean pole of 68.6° N., 100.9° E., calculated by Smith (1976, p. 604, table 3) for his data from diabase intrusions in Connecticut, Maryland, and southern Pennsylvania is less: than 20° from the pole positions calculated for the South Carolina dikes. The South Carolina paleomagnetic poles differ by a maximum of 225° from the 62° N., 104.5° E. pole that Beck (1972, p. 5680, and table 2) considered to be the best estimate of the Late Trias- sic geomagnetic pole derived from his samples of southeast Pennsylvania diabase intrusions. The South Carolina dikes, therefore, are likely to have been emplaced during the same time interval as these other diabase intrusions in the Late Triassic. No other group of distinctively different poles was found that might be related to the various chemical and petrographic groups recognized by Smith and others (1975) and Weigand and Ragland (1970). However, not enough dikes, sites, or cores were included in the study for us to be entirely satisfied that a group of dikes yielding some other paleomag- netic pole does not exist in the Haile—Brewer area. REFERENCES CITED Armstrong, R. L., and B‘esancon, James, 1970, A Triassic time scale dilemma; K-Ar dating of Upper Triassic mafic igneous rocks, Eastern USA. and Canada and post—Upper Triassic plutons, western Idaho, U.S.A.: Eclogae Geologicae Helvetiae, v. 63, no. 1, p. 15—28. Beck, M. E., Jr., 1972, Paleomagnetism of Upper Triassic diabase of southeastern Pennsylvania; further results: Journal of Geophysical Research, v. 77, no. 29, p. 5673— 5687. Bell, Henry, III, and Popenoe, Peter, 1976, Gravity studies in the Carolina slate belt near the Haile and Brewer mines, north-central South Carolina: US. Geological Sur— vey Journal of Research, v. 4, no. 6, p. 667—682. Chalcraft, R. G., 1976, The petrology of Mesozoic dolerite dikes in South Carolina: South Carolina Division of Geology Geologic Notes, v. 20, no. 2, p. 52—61. Conley, J. F., and Bain, G. L., 1965, Geology of the Carolina slate belt west of the Deep River—Wadesboro Triassic basin, North Carolina: Southeastern Geology, v. 6, no. 3, p. 117—138. deBoer, Jelle, 1967, Paleomagnetic—tectonic study of Mesozoic dike swarms in the Appalachians: Journal of Geophysical Research, v. 72, no. 8, p. 2237—2250. 1968, Paleomagnetic differentiation and correlation of the Late Triassic volcanic rocks in the central Appala- chians (with special reference to the Connecticut Val- ley) : Geological Society of America Bulletin, v. 79, no. 5, p. 609—626. Doell, R. R., and Cox, Allan, 1965, Measurement of the rema- nent magnetization of igneous rocks: US. Geological Survey Bulletin 1203—A, p. A1—A32. Fisher, R. A., 1953, Dispersion on a sphere: Royal Society [London] Proceedings, Series A, v. 217, no. 1130, p. 295— 305. Fullagar, P. D., 1971, Age and origin of plutonic intrusions in the Piedmont of the southeastern Appalachians: Geo- logical Society of America Bulletin, v. 82, no. 10, p. 2845—2862. Kane, M. R., Harwood, D. S., and Hatch, N. L., Jr., 1971, Continuous magnetic profiles near ground level as a means of discriminating and correlating rock units: Geo- C18 logical Society of America Bulletin, v. 82, no. 9, p. 2449— 2456. King, P. B., 1961, Systematic pattern of Triassic dikes in the Appalachian region: U.S. Geological Survey Professional Paper 424—B, p. B93—B95. 1971, Systematic pattern of Triassic dikes in the Ap- palachian region—second report: U.S. Geological Survey Professional Paper 750~D, p. D84—D88. McElhinny, M. W., 1973, Paleomagnetism and plate tectonics: London, Cambridge University Press, 357 p. McSWeen, H. Y., Jr., 1972, An investigation of the Dutch- mans Creek Gabbro, Fairfleld County, South Carolina: South Carolina Division of Geology Geologic Notes, v. 16, no. 2, p. 19—42. May, P. R., 1971, Pattern of Triassic-Jurassic diabase dikes around the North Atlantic in the context of predrift position of the continents: Geological Society of America Bulletin, v. 82, no. 5, p. 1285—1291. Nystrom, P. G., Jr., 1972, Geology of the Catarrah NW (Jef— ferson) quadrangle: Columbia, SC, University of South Carolina, unpublished M.S. dissertation, 49 p. Overstreet, W. C., and Bell, Henry, III, 1965a, The crystalline rocks of South Carolina: U.S. Geological Survey Bul— letin 1183, 126 p. 1965b, Geologic map of the crystalline rocks of South Carolina: U.S. Geological Survey Miscellaneous Geo- logic Investigations Map I—413, scale 1:250,000. Popenoe, Peter, and Bell, Henry III, 1975, Simple Bouguer gravity map of part of the Carolina slate belt including the. Haile and Brewer mine areas, north-central South Carolina: U.S. Geological Survey Geophysical Investiga- tions Map GP—904, scale 1:125,000. Popenoe, Peter, and Zietz, Isidore, 1977, The nature of the geophysical basement beneath the Coastal Plain of South Carolina and northeastern Georgia: U.S. Geological Sur- vey Professional Paper 1028—I, p. 118—137. Ragland, P. C., Rogers, J. J. W., and Justus, P. S., 1968, Origin and differentiation of Triassic dolerite magmas, North Carolina, USA: Contributions to Mineralogy and Petrology, v. 20, no. 1, p. 57—80. Randazzo, A. F., Swe, Win, and Wheeler, W. H., 1970, A study of tectonic influence on Triassic sedimentation— SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 the Wadesboro basin, central Piedmont: Journal of Sedi— mentary Petrology, v. 40, no. 3, p. 998—1006. Randazzo, A. F., and Copeland, R. E., 1976, The geology of the northern portion of the Wadesboro Triassic basin, North Carolina: Southeastern Geology, v. 17, no. 3, p. 115—138. Rothe, G. H., and Long, L. T., 1975, Geophysical investiga- tion of a diabase dike swarm in west-central Georgia: Southeastern Geology, v. 17, no. 2, p. 67-79. Secor, D. T., Jr., and Wagener, H. D., 1968, Stratigraphy, structure, and petrology of the Piedmont in central South Carolina—Carolina Geological Society Field Trip, Oct. 18—20, 1968: South Carolina Division of Geology Geo- logic Notes, v. 12, no. 4, p. 67—84. Smith, R. C., II, Rose, A. W., and Lanning, R. M., 1975, Geology and geochemistry of Triassic diabase in Penn- sylvania: Geological Society of America Bulletin, v. 86, no. 7, p. 943—955. Smith, T. E., 1976, Paleomagnetic study of lower Mesozoic diabase dikes and sills of Connecticut and Maryland: Canadian Journal of Earth Science, v. 13, no. 4, p. 597—609. Steele, K. F., Jr., 1971, Chemical variations parallel and per— pendicular to strike in two Mesozoic dolerite dikes, North Carolina and South Carolina: Chapel Hill, N.C., Uni- versity of North Carolina Ph.D. dissertation, 213 p. Stuckey, J. L., 1958, Geologic map of North Carolina: Raleigh, North Carolina Division of Mineral Resources, scale 1 : 500,000. U.S. Geological Survey, 1970, Aeromagnetic map of the Cam- den-Kershaw area, north-central South Carolina: U.S. Geological Survey open-file map, scale 1:24,000. Waskom, J. D., and Butler, J. R., 1971, Geology and gravity of the Lilesville Granite batholith, North Carolina: Geo- logical Society of America Bulletin, v. 82, no. 10, p. 2827—2844. Wiegand, P. W., and Ragland, P. C., 1970, Geochemistry of Mesozoic dolerite dikes from eastern North America: Contributions to Mineralogy and Petrology, v. 29, no. 3, p. 195—214. Zablocki, C. J., 1967, Results of some geophysical investiga- tions in the Wood Hills area of northeastern Nevada: U.S. Geological Survey Professional Paper 575—3, p. Bl45—B154. Aerial Gamma-Ray Survey in Duval, MeMullen, Live Oak, and Webb Counties, Texas By JOSEPH S. DUVAL and KAREN A. SCHULZ SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 GEOLOGICAL SURVEY PROFESSIONAL PAPER 1123-1) A presentation of aerial gamma-ray data as apparent surface concentrations of potassium, equivalent uranium, and equivalent thorium FIGURE 1. 2. TABLE 3. 4. I“ CONTENTS Page Abstract _________________________________________________________________ D1 Introduction ______________________________________________________________ 1 Survey description ________________________________________________________ 1 Geology of the surveyed area ______________________________________________ 3 Expected radiometric signatures ___________________________________________ 3 Presentation of the data __________________________________________________ 5 Discussion of the data ____________________________________________________ 8 Conclusions ______________________________________________________________ 9 References cited __________________________________________________________ 11 ILLUSTRATIONS Page Geologic map of the area covered by the aerial survey near Freer, Tex _______________________________ D2 Contour maps of the apparent surface concentrations of potassium, equivalent uranium, and equivalent thorium ______________________________________________________________________________________ 4 Contour maps of the total count data, eU/eTh, eU/K, and eTh/K __________________________________ 6 Graph showing frequency distributions of the radioelement concentrations for the Oakville Sandstone ____ 8 Anomaly map of ‘eU and eU/eTh anomalies where the values exceed the expected ranges ______________ 10 TABLES Page List of the energy windows used in the measurement of the radiometric data __________________________ D3 Average values and indicated range of expected values of the radiometric data for the mapped geologic units ________________________________________________________________________________________ 9 III SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 AERIAL GAMMA-RAY'SURVEY IN DUVAL, MCMULLEN, LIVE OAK, AND WEBB COUNTIES, TEXAS By JOSEPH S. DUVAL and KAREN A. SCHULZ ABSTRACT High-sensitivity gamma—ray data have been obtained for an area of about 3300 km2 in Duval, McMullen, Live Oak, and Webb Counties, Tex. Contour maps of the aerial gamma- ray data show the apparent surface concentrations of the radioelements potassium, uranium, and thorium. The dif- ferent geologic units within the survey area have the fol- lowing average values: 1.2 percent K, 1.8 ppm (parts per million) eU (equivalent uranium), and 5.6 ppm eTh (equiva- lent thorium) for the Goliad Sand; 1.5 percent K, 1.9 ppm eU, and 6.5 ppm eTh for the Oakville Sandstone; 1.5 percent K, 2.3 ppm eU, and 9.7 ppm eTh for the undivided Catahoula Tufl‘; 1.9 percent K, 2.9 ppm eU, and 9.9 ppm eTh for the Frio Clay; 1.5 percent K, 2.8 ppm eU, and 9.7 ppm eTh for the Jackson Group. A comparison of anomalies defined on the map of eU with those defined on the map of eU/eTh indi- cates that the ratio is the more effective function for locating areas where known mineralization occurs. INTRODUCTION If research is to be done to improve the interpre— tation and understanding of aerial gamma-ray data, high-quality data must be obtained over an area where the surface geology and mineralization occur- rences are known and also where surface dis~ turbances due to man’s activities are minimal. The U.S. Geological Survey has obtained such data for an area of about 3300 km2 in south Texas. This paper presents those data in terms of appar- ent surface concentrations of the radioelements‘ po- tassium, uranium, and thorium, and the data are discussed relative to the known lithology. Use of the data to detect areas of known mineralization is also discussed. SURVEY DESCRIPTION The data presented are from a survey flown for the U.S. Geological Survey by Geodata International, 1 Any use of trade names in this publication is for descriptive purposes only and does not constitute endorsement by the U.S. Geological Survey. Inc], in Duval, McMullen, Live Oak, and Webb Counties, Tex., near Freer, Tex. (fig. 1). High-sensitivity aeroradiometric data were ob- tained continuously along flight lines spaced at 1.6-km intervals. The flight lineswere oriented north- west-southeast at an angle of about 34° west of north. Fifty-two lines each 40 km long were flown,‘ resulting in 2,080 line-kilometers of data. The nomi- nal altitude of the aircraft during the: survey was 120 m above the ground surface. The radiometric data were measured using eight NaI(Tl) (thallium-activated sodium iodide) detec- tors. The detectors were right cylinders 29.2 cm in diameter and 10.2 cm thick, and the total detector volume was 54.4 L. An additional NaI(TI) detector (with the same dimensions as the other eight detec- tors) was shielded from the ground radiation by about 10 cm of lead. This detector was used to monitor Bi214 in the atmosphere. A radar altimeter was used to measure the altitude of the aircraft above the ground surface. The aircraft location was determined from the output of a doppler radar navi- gation system, and a cross check was provided by a 35-mm film with pictures of the ground below the aircraft. One picture was taken every 3 seconds, and at the nominal airspeed of 192 km/h, each picture had a 15 to 20 percent overlap of both the previous and succeeding pictures. Various corrections were applied to the data. Background counts due to cosmic rays, aircraft con- tamination, and airborne Bi2M were subtracted from the observed radiometric count rates. The counts due to cosmic rays were determined by monitoring the gamma-ray spectrum from 3.0 MeV (million electron volts) to 6.0 MeV. The aircraft contamination was measured by flying at altitudes higher than 1,000 m, where radiation from the ground is negligible. The D1 D2 20 Kl LOMETE RS SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 EXPLANATION QUATERNARY ALLUVIUM TERRACE DEPOSITS TERTIARY GOLIAD SAND (PLIOCENE) OAKVILLE SANDSTONE (MIOCENE) CATAHOULA TUFF, UNDIVIDED (MIOCENE) Chusa Member Soledad Member Fant Member FRIO CLAY (OLIGOCENE?) JACKSON GROUP (EOCENE) Known uranium mineralization Fault LA SALLE Aerial survey area FIGURE 1.—Geologic map of the area covered by the aerial survey near Freer, Tex. airborne Bi214 was measured by the shielded detector. The radiometric data were also adjusted to a com- mon altitude of 122 m using a standard equation for the exponential attenuation of gamma rays. The corrections for Compton scattered gamma rays in the potassium and equivalent uranium (eU) energy windows were the final corrections applied to the radiometric data. Table 1 lists the radioelements (potassium, equivalent uranium, and equivalent thorium) and the energy windows that were used to obtain the count rates that are proportional to the concentrations of the elements. Two energy windows were used to measure eU. The second, lower, energy window, which includes the 1.12 MeV gamma ray of Bi“, increases the net eU count rate by a factor approximately equal to 2.8 times the count rate ob- tained with the higher energy window alone. The total count Window is also listed in table 1. AERIAL GAMMA-RAY SURVEY; DUVAL, MCMULLEN, LIVE OAK, WEBB COUNTIES, TEXAS TABLE 1.-—List of the energy windows used in the meas- urement of the radiometric data Element Energy window (MeV) K —————————— 1.34—1.65 eU —————————— 1.07—1.33 eU —————————— 1.66—2.42 eTh —————————— 2.44—2.81 Total count —————— .40—3 GEOLOGY OF THE SURVEYED AREA The survey was flown over the surface exposures of a sequence of Texas Gulf Coast Tertiary rocks ranging from the Pliocene Goliad Sand to the Eocene Jackson Group. The stratigraphy from youngest to oldest, as given by Eargle, Dickinson, and Davis (1975), is as follows: Pliocene: Goliad Sand: Sandstone, light-gray, calichified, fine- to medium-grained in upper part, medium- to coarse-grained near base; and pink, calcare- ous clay. Miocene: Fleming Formation: Claystone and minor sandstone, gray, pink, red, and light-brown; red color increases upward in unit. Oakville Sandstone: Sandstone, gray to light-reddish-brown, fine- to coarse-grained; contains clay pebbles, silt, clay, and calcite cement. Catahoula Tuff : Chusa Member: Claystone, pink, calcareous, tuffaceous, mont- morillonitic; and a basal sandy conglom- erate containing pebbles of volcanic rock, siliceous limestone, and sandstone. Soledad Member: Conglomerate, sandy volcanic; contains boulders of amygdaloidal rhyolite, trachyte, and trachyandesite as large as 30 cm in diameter. Fant Member: Tuff, white to light-gray, zeolitic, mont- morillonitic; and interbedded sandstone. D3 Oligocene ( ?) : Frio Clay: Clay, light-gray to green, montmorilllonitic, zeo- litic, tuffaceous; and channel-sandstone beds. Eocene (upper) : Whitsett Formation (of Jackson Group) : Fashing Clay Member: Clay and tufl‘, gray, calcareous, montmoril- lonitic, zeolitic, fossiliferous; and some beds of lignite, coquina, and sandstone. Callihan Sandstone Member (Ataslosa County) and its approximate equivalent the Tordill'a Sandstone Member of the Whitsett in Karnes County: Sandstone, yellowish-gray, fine-grained, arkosic, tuffaceous, fossiliferous. Dubose Member: Clay and siltstone, gray, montmorillonitic, tuffaceous; and minor amounts of sand- stone and lignite. Deweesville Sandstone Member: Sandstone, gray, fine-grained, arkosic, cross- bedded; contains burrows of Ophiomorpha sp. and root impressions and a few beds of fossiliferous siltstone and Claystone. Conquista Clay Member: Mudstone, gray, tuifaceous, montmorillonitic, fossiliferous, opalitic, zeolitic, carbonace- ous; and a few thin beds of fine-grained arkosic sandstone. Dilworth Sandstone Member: Sandstone, light-gray, very fine to medium- grained, arkosic, criossbedded to weakly laminated; contains burrows of Ophiomor- pha sp. and root impressions. The geologic map shown on figure 1 was adapted from the Laredo and Crystal City Atlas Sheets of the Texas Bureau of Economic Geology, Austin, Tex. (1976). If the Fleming Formation is present in the survey area, it has not been recognized as a separate unit on the Atlas Sheets. EXPECTED RADIOMETRIC SIGNATURES Because lithologically different materials have both physical and chemical differences, prediction of the relative radioactivity levels and the expected concentrations of potassium, uranium, and thorium should be possible, given typical values for rocks hav- ing similar lithologies. Duex (1971) gives average values for the exposed Catahoula Tufi' as 1.1 percent K, 3.1 ppm (parts per million) eU, and 9.4 ppm eTh D4 SHORTER CONTRIBUTIONS T0 GEOPHYSICS, 1979 A 0 10 20 KILOMETERS l_—__l____| Contour interval 0.2 percent Apparent surface concentration of K, in percent. 20 Kl LOMETE RS 3. 2 Apparent surface concentration of eU, in ppm. Contour interval 0.4 ppm FIGURE 2.—Contour maps of the apparent surface concentrations of A, potassium; B, Equivalent uranium; C, Equivalent thorium. (equivalent thorium). Duval and others (1972) give concentrations of 0.6 percent K, 1.1 ppm eU, and 2.9 ppm eTh for a sandstone in the area of the Llano Uplift in central Texas. Because the Friuo Clay, the ‘Catahoula Tufi‘ (ex- cepting the Soledad Member), and the upper mem- bers of the Whitsett Formation are lithologically similar, in that they are of volcanic origin and are tufl’aceous, they can be expected to have similar radiometric signatures. Inherent in the preceding statement are the assumptions that the original aver- age concentrations of the: radioelements in the sedi- ments did not differ by more than a few parts per million and that all the sedimentary rocks have undergone similar weathering. In the Soledad Mem- ber, the concentrations of potassium and uranium should be higher than those in the other volcanic sedimentary rocks, because weathering processes AERIAL GAMMA-RAY SURVEY; DUVAL, MCMULLEN, LIVE OAK, WEBB COUNTIES, TEXAS “39° {9. (W _ .. fl ' .m- . _ \. 9.0 Contour interval 1.8 ppm D5 EXPLANATION GOLIAD SAND (PLIOCENE) OAKVI LLE SANDSTONE (MIOCENE) CATAHOULA TUFF, UNDIVIDED (MIOCENE) Chusa Member Soledad Member Fant Member FRIO CLAY (OLIGOCENE?) JACKSON GROUP (EOCENE) , Geologic contact. Dashed where approximate Fault Known uranium mineralization 20 KILOMETERS Apparent surface concentration of eTh, in ppm. FIGURE 2.—(For caption, see facing page.) should be less effective in leaching potassium and uranium from the conglomerate than from the tuffaceous sedimentary rocks. Because the Oakville Sandstone and the Goliad Sand are sandstones of continental origin, they might be expected to have radioelement concentra- tions similar to those of sandstone of continental origin stuied by Duval and others (1972). If the source rocks for the sandstones are very different or if differences in weathering exist, this assumption Will not hold true. The Oakville and Goliad should have similar radioelement concentrations, and they should have lower concentrations than any of the volcanic sedimentary rocks. PRESENTATION OF THE DATA The data from the aerial survey are presented in the form of contour maps in figures 2 and 3. These D6 20 Kl LOMETE RS Total count. Contour interval 1.8 ur SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 20 Kl LOMETERS 0.33 eU/eTh. Contour interval 0.056(ppm eU/ppm eTh) FIGURE 3.——Contour maps of A, The total count data; B, eU/eTh; C, eU/K; D, eTh,/K. maps were adapted from maps produced by an auto~ matic contouring computer program. The fully cor- rected count-rate data Were converted to represent the apparent surface concentrations of K, in percent, eU, in parts per million, and eTh, in parts per mil- lion (fig. 2), using the calibration constants given by Duval, Schultz, and Pitkin (1977). The units used for the total-count map (fig. 3A) are defined such that 1 ur (radioelement unit, International Atomic Energy Agency, 1976) is equal to the total count that would be measured by a detector being carried at an altitude of 122 m over a broad source of gamma rays that has an apparent surface concen— tration of 1 ppm eU but lacks potassium. and thor- ium. The value of 1 ur=55 cps (counts per second) adopted for this aerial survey was determined by using a linear regression fit to establish the relation- ship between the total count and the radioelemen-t concentrations. AERIAL GAMMA-RAY SURVEY; DUVAL, MCMULLEN, LIVE OAK, WEBB COUNTIES, TEXAS D7 C 0 10 20 KILOMETEHS D O 10 20 KILOMETERS |—%l l—L_W_____J eTh/K. Contour interval 0.9(ppm eTh/ percent K) eU/K. Contour interval 0.4(ppm eU/percent K‘ 5.4 EXPLANATION 2.0 FRIO CLAY (OLIGOCENE ?) JACKSON GROUP (EOCENE) GOLIAD SAND (PLIOCENE) OAKVILLE SANDSTONE (MIOCENE) CATAHOULA TUFF, UNDIVIDED (MIOCENE) Chusa Member Soledad Member »r—~-—v~-»—---~- Contact—Dashed where approximate Fault n Mem . . . . Fa t her 0 Known uranium mmeraluzatlon FIGURE 3,—(For caption, see facing page.) D8 DISCUSSION OF THE DATA Before the data can be discussed relative to the mapped geology, the normal or expected values for each geologic unit must be determined. Because geologic formations are not necessarily uniform in radioactivity, calculations of mean values and of standard deviations can be in error. A better method to determine the average value for a unit is to plot a frequency distribution of the number of data points with a. given value versus the value. Figure 4 shows the frequency distributions of the radioelement con- centrations for the Oakville Sandstone. Once the frequency distributions have been plotted, the expected values for each geologic unit can be defined either by fitting a mathematical func- tion, such as a normal distribution, to the curves or by visual inspection. Table 2 lists the average values of the radiometric data for each geologic unit plus or minus a value representative of the normal range of values. The average values were determined by inspection of the frequency distribution curves. The plus or minus deviation from the mean value was defined as 0.75 times the full width of the curve at SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 one-half of the peak number of data points. The values given for the Oakville Sandstone are shown in figure 4. As expected, the radioactive characteristics (par- ticularly eU, eTh, and eTh/K of fig. 3D) of the Goliad and the Oakville are significantly different from those of the more tuifaceous sediments; how- ever, the concentrations given by Duval and others (1972) for the sandstone in central Texas are also significantly different. This difference suggests that care must be taken to avoid classifying geologic units on the basis of such physical parameters as grain size when the purpose of the classification is to predict expected radioelement concentrations. The differences between the Goliad and the Oak- ville are subtle, and the values given in table 2 could not be used to distinguish them. However, the con- tour maps indicate that some of the mapped Goliad has lower values for K, eTh, and total count. This fact could provide aid for geologic mapping. The differences among the Catahoula, Frio, and Jackson sedimentary rocks are also subtle; the great- est differences are in eTh, total count, and eU/eITh. 50° I I I I u l I I I I I 1 I I I «2400— H ’— E o O. < .— < o » _ IL 0 a: ”J m 3 Z200— — I——O——I o l I I I I 1.0 1.2 1.4 1.6 1.8 2.0 2.21.3 1.5 1.7 1.9 2.1 2.3 2.5 2.74.0 5.0 6.0 7.0 8.0 9.0 10.0 K, IN PERCENT eU, IN PARTS PER MILLION eTh, IN PARTS PER MILLION FIGURE 4.—Frequency distributions of the radioelement concentrations for the Oakville Sandstone. The mean value is rep- resented by the open circle; the expected range of values, by the bar. AERIAL GAMMA-RAY SURVEY; DUVAL, MCMULLEN, LIVE OAK, WEBB COUNTIES, TEXAS D9 TABLE 2.—A11e7‘age values and indicated range of expected values of the radiometric data for the mapped geologic units Geologic unit K eU eTh Total eU/eTh eU/K eTh/K (percent) (ppm) (ppm) count (ur) Goliad Sand -—— 1.2103, 1.8+o.4 5.6+1.7 32.8+6.8 0.31+o.09 1.4+o.5 3.3+O.8 Oakville _. _- —- _- _- _ Sandstone ——— 1-5i0-3 1.9:0.4 6.5:l.2 35.4:2.7 0.27io.07 1.2103 3.3:O.8 Catahoula Tuff (undivided) — 1-5i0-4 2.3:0.8 9.7:3.o 28.2:6.8 0.23:0.06 l.4+0.6 4.9+1.3 Chusal ———————— 2-0i0-3 2.7:o.9 11.9:2.7 45514.1 0.22:0.07 1410.4 4.6:0.8 Soledadl —————— 1-2i0-5 2.8:0.6 12.8:1.9 47-3i4-1 0.22:0.09 1.3£0.3 4.05.3 Fantl ————————— 2.0:o.3 3.3:0.6 11.7:2.7 38.2:6.4 0.25:0.10 1.5:o.5 4.1+1.0 Frio Clay ————— 1.9:O.6 2.9:0.7 9.9:2.7 35-5i7-0 0.28i0.08 1.4+O.6 4.010.7 Jackson Group — l-5i0-7 2.8:O.9 9.7:2.4 30.0:8.9 0.28:0.07 1.7£0.8 4.7522 1Member of Catahoula Tuff. The Catahoula in the northeastern part of the survey area, where it is undivided, has values of K, eU, eTh, and total count that are significantly lower than the values of the divided members of the Catahoula in the southwestern part of the survey area. Also, the undivided Catahoula can be more readily distin- guished from the divided Catahoula than can either the Frio or the Jackson. This difference within the Catahoula suggests a facies change, and such a change would reflect a difference in the depositional environment. Galloway and others (1977) show a channel facies that correlates at least in part with the area of the divided Catahoula and a floodplain facies that correlates with the undivided Catahoula. Another difference between the Catahoula and the other sedimentary rocks is that the eU/eTh is sig- nificantly lower in the Catahoula (fig. 3B). The lower eU/eTh could be indicative of a greater rela- tive leaching of uranium from the Catahoula. Mox- ham (1964) and Duex (1971) suggest that uranium has been leached from the Catahoula sedimentary rocks, and Galloway and others (1977) have analyti- cal data that support a hypothesis that extensive leaching of the uranium occurred soon after the sedi- ments were deposited. Although the differences among the radiometric characteristics are interesting and useful for geoh logic mapping, they do not provide any direct indi- cators for specific areas of uranium mineralization. The values in table 2 can, however, be used to define anomalous radiometric values. Figure 5 shows eU and eU/eTh anomalies mapped as areas where the measured values exceed the maximum expected values, as given in table 2. Figure 5 also shows gen- eralized locations of known uranium mineralization. An examination of figure 5 shows that most of the known mineralized areas occur Within 10 km of a eU/eTh anomaly. The mineralized areas coincide reasonably well with eU anomalies within the Cata- houla; however, there are no eU anomalies Within the Oakville. CONCLUSIONS Relative radioactivity levels for a sequence of sedi- ments can be predicted using the lithologic descrip— tions; however, the absolute concentration levels cannot be accurately estimated at present. More ac- curate estimates o-f the concentration levels would require knowledge of the mineral assemblage in the sediment and better information on known concen- trations in similar sediments. In order to establish a table of known concentrations in similar sedi- ments, a classification scheme will be necessary. Such a classification scheme should only use character- istics that are directly related to chemical or miner- alogical properties. Almost all sedimentary rocks, particularly those fluvial in origin, have facies changes along strike that can have distinctive radiometric characteristics, as is true of the differences between the channel facies and the floodplain facies in the Catahoula Tufl". The possibility that similar differences may occur within other sedimentary rocks raises doubt D10 SHORTER CONTRIBUTIONS TO GEOPHYSICS, 1979 EXPLANATION GOLIAD SAND (PLIOCENE) OAKVILLE SANDSTONE (MIOCENE) CATAHOULA TUFF, UNDIVIDED (MIOCENE) Chusa Member SoIedad Member Fant Member FRIO CLAY (OLIGOCENE .7) JACKSON GROUP (EOCENE) Geologic contact. Dashed where approximate Fault Location of known uranium mineralization eU anomaly eU/eTh anomaly 20 Kl LOMETE RS FIGURE 5.—eU and eU/eTh anomalies where the values exceed the expected ranges. concerning the validity of expressing radiometric characteristics in terms of mapped geologic formations. One approach that would eliminate the limitations imposed by displaying the data in terms of mapped geology is to define radiometric map units. A radi- ometric unit should have relatively homogeneous radioactive characteristics and be geographically continuous. Duval (1976) presents a method utiliz- ing factor analysis that might be used to define radiometric uni-ts, and Duval, Pitkin, and Macke (1977) present a method using color images, which also might be used. However, both of the cited methods appear to require further development, and such questions as the definition of relative homo- geneity must be resolved. If the concept of radiometric anomalies is to be applied to aerial gamma-ray data, normal expected values should be defined using frequency histograms of the values measured «over mapped geologic units AERIAL GAMMA-RAY SURVEY; DUVAL, MCMULLEN, LIVE OAK, WEBB COUNTIES, TEXAS or radiometric units. The application of the anomaly concept to the eU and eU/eTh (fig. 30) data pre— sented here indicates that within the Catahoula Tuif, both eU and eU/eTh are useful as indicators of uranium mineralization; however, within the Oak- ville Sandstone only eU/eTh provides some indica- tion of uranium mineralization. REFERENCES CITED Duex, T. W., 1971, K/Ar age dates and U, K geochemistry of the Gueydan (Catahoula) formation of south Texas, Final Report: U.S. Atomic Energy Commission research contract AT(O5—1)—935, p. 101—145. Duval, J. S., 1976, Statistical interpretation of airborne gamma-ray spectrometric data using factor analysis, in International Atomic Energy Agency, Exploration for uranium ore deposits—a symposium: International Atomic Energy Agency, IAEA—SM—208, p. 71—80. Duval, J. S., Pitkin, J. A., and Macke, D. L., 1977, Composite images of radiometric data from south Texas and Wyom- ing, in U.S. Geological Survey, Short papers of the U.S. Geological Survey uranium—thorium symposium: U.S. Geological Survey Circular 753, p. 21—22. Duval, J. S., Schulz, K. A., and Pitkin, J. A., 1977, Calibra- tion constants for the Geodata International, Inc., and Texas Instruments, Inc., high sensitivity systems used for D11 the ERDA aerial gamma-ray surveys: U.S. Geological Survey Open—File Report 77—159, 15 p. Duval, J. S., Worden, J. M., Clark, R. B., and Adams, J. A. S., 1972, Experimental comparison of NaI(Tl) and solid organic scintillation detectors for use in remote sensing of terrestrial gamma rays: Geophysics, v. 37, no. 5, p. 879—888. Eargle, D. H., Dickerson, K. A., and Davis, B. 0., 1975, South Texas uranium deposits: American Association of Pe- troleum Geologists Bulletin, v. 59, no. 5, p. 766—779. Galloway, W. E., Murphy, T. D., Belcher, R. C., Johnson, B. D., and Sutton, S., 1977, Catahoula Formation of the Texas coastal plain; depositional systems, composition, structural development, ground—water flow history, and uranium distribution: Texas University Bureau of Eco- nomic Geology Report of Investigations 87, 63 p. International Atomic Energy Agency, 1976, Radiometric re- porting methods and calibration in uranium exploration: International Atomic Energy Agency Technical Report Series 174, 57 p. Moxham, R. M., 1964, Radioelement dispersion in a sedi- mentary environment and its effect on uranium explora- tion: Economic Geology, v. 59, no. 2, p. 309—321. Texas University Bureau of Economic Geology, 1976, Crystal City-Eagle Pass Sheet: Geologic Atlas of Texas, scale 1:250,000. 1976, Laredo Sheet: Geologic Atlas of Texas, scale 1:250,000. fir U.S. GOVERNMENT PRINTING OFF|CEz I980 O— 3ll-344/ll RETURN EAnmsaEN'ces LIBRARY Wrth Scienres Bldg. 647-9007 ,. x 2075765