Chap. 11] GEOPHYSICAL WELL TESTING 845 



direction to obtain an increase in temperature of 1° C. or F. For a 

 detailed analysis of individual wells, the slope or gradient is taken over 

 limited portions of the temperature-depth curve. Areal temperature dis- 

 tribution is represented by lines of equal reciprocal gradient for a given 

 depth, or by contour lines of equal temperature. In profile view equi- 

 temperature lines or "isogeothermal surfaces" are useful for correlation 

 with regional and local dip. Temperature measurements, made in con- 

 nection with electrical logging for purposes of production engineering, are 

 represented in the form of a temperature curve, deviations from the 

 (normal or regional) gradient being shaded to indicate the anomalies. 

 Results of shallow-well investigations are plotted by showing lines of equal 

 temperature for a given depth of investigation. When temperature differ- 

 ences have been measured with two thermometers between adjacent wells, 

 temperature gradients are plotted in profile or plan view. 



B. The Universal Geothermal Gradient 



Wherever great depths have been reached, an increase of temperature 

 has been observed. In the Simplon tunnel (maximum cover under moun- 

 tain crest, 7000 feet) the highest rock temperature was 132° F. In the 

 Robinson Deep mine in the Rand of South Africa, the temperature was 

 (only) 103° F."^ at a depth of about 8500 feet. The Wasco well in the 

 San Joaquin Valley, California (15,004 feet deep), revealed a bottom 

 temperature of 268° F.,^^ which is higher than the boiling point of water. 

 Yet, the greatest depth reached to date is but a 1^ thousandth part of 

 the earth's radius. This makes any deductions in regard to the tempera- 

 ture in the earth's interior and the age of the earth highly speculative, to 

 say the least. 



Of the many approaches to the problem of temperatures in the earth's 

 interior, the so-called Kelvin theorem is probably the best known. It 

 gives the temperature at any depth as a function of an initial temperature, 

 time of eooUng and an absorption coefficient, for an infinite slab heated 

 at one face while the other is kept at 0° temperature. The solution 

 appears in the form of a probability integral^^ which, when differentiated 

 with respect to depth, gives the geothermal gradient 



'■ *^', (11-2) 



"^ Other mining districts have shown reciprocal gradients of the order of 175-375 

 feet per degree F. 



1* Probably mud temperature. Actual formation temperature was probably 

 around 300°. (Personal communication from H. Guyod.) 



" H. Cecil Spicer, Geol. Soc. Am. Bull., 48, 75-92 (1937). 



