330 EXPLORATION GEOPHYSICS 



The value of «•» = ^^i -r n2 -|- na ^ From the first three readings this balance is 93.9 

 and is entered in the n'o column opposite orientation position 2. 



The next »» value, 93.6 is ^ "^ — and is entered opposite position 3, the tti 



being the check reading for orientation 1 or the 4th dot on the plate for balance /.. The 



third tVo value used ( ^ ' "^ J in a similar manner and equals 93.3. The change in 



the Uo values is largely due to temperature. This method of handling the fio partly 

 compensates for temperature change. 



A/ = Hi — Uo, Aa = ni — Ho, As = iii — Uo, as indicated by Equation 87. A check 

 is obtained on the accuracy of a station, as the sum of Ai + A2 + A3 should equal zero. 



Forming A' and B' and A" and B", and determining their sums and differences 

 carries out the operations indicated in Equation 88. (Note that Aj and Aj only are 

 used). The instrument constants O, P, -Q and -R appear in the form. S and T are 

 omitted. 



The observed results of the 4 gravity components, shown in the lower left of the 

 plate form above, represent uncorrected values. In order to obtain gravity values more 

 closely related to subsurface conditions, these values must be corrected for the "normal 

 value" of the gradient and curvature (planetary correction) and for the irregularities 

 of the terrain surrounding the station. These matters will be considered in detail. 



Reduction of Observations. — The gradient and differential curva- 

 ture values given by the torsion balance are the vector sums of the effects 

 of all the irregular mass distributions in the vicinity of the instrument which 

 are sufficiently large to affect it. t These effects may be classified into three 

 types : geologic, topographic and latitude. The geologic effects are those 

 due to structural anomalies. The latitude effects are produced by the normal 

 variation of gravity with latitude. The topographic effects, which are fre- 

 quently of the same order of magnitude as the structural effects, are 

 produced by irregularities in the distribution of mass due to hills and valleys 

 and smaller mounds and depressions in the vicinity of the torsion balance. 



Hence, before structural anomalies can be deduced from the torsion 

 balance data, it is necessary to correct the values observed at each station 

 for topographic and latitude effects. 



Latitude or Planetary Corrections 



The variation of gravity with latitude is given by Equation 3. That is 



g = 978.039 (1 + 0.0053 sin2 cf> - 0.000007 sin^ 2«^) (20) 



The variation of the gravity gradient with latitude can be obtained by dif- 

 ferentiating Equation 20 with respect to x and y respectively. 



Because the parallels of latitude are circles, gravity does not vary from 



east to west. That is, — = Uyz — 0. Also, — ^ = Uxz is approximately 



oy 0-1' 



equal to - — where is the latitude of the area under investigation and 



t D. C. Barton, "Eotvos Torsion Balance Method of Mapping Geologic Structure," A.I.M.E. 

 Geophysical Prospecting, 1939, pp. 431-433. 



