268 



GRAVITATIONAL METHODS 



[Chap. 7 



constant which, however, necessitates a replotting of the geologic section 

 to that scale. A limited strike extent proportional to depth (as in salt 

 domes and anticlines) may be introduced as shown in Figs. 7-lOlc, d, e, 

 and/. Calculations of the anomalies are then based on formulas (7-92c?). 

 4. Planimeter and integraph methods may be used for the calculation 

 of torsion balance anomalies from known or assumed outlines of a geologic 

 body. Since, according to eq. (7-9 Ic), the action of a two-dimensional 

 feature depends not only on area but also on distance and vertical angle, 

 the area to be evaluated must be replotted to suitable scale before a regular 



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Fig. 7-102a. Scale distortion in Below-Jung planimeter interpretation method for 

 two-dimensional bodies (after Jung). 



planimeter can be applied to give the torsion balance anomaly (Below 

 method,^^^ see eq. [7-446] and Figs. 7-46 and 7-47). To convert the 

 double integral in eq. (7-9 Ic) into a surface integral independent of azi- 

 muth and distance, the substitutions R for v'2 loge p, $ for \ sin 2^, and 

 \ cos 2(p, respectively, are necessary so that the gradients and curvatures 

 are proportional // R d^ dR after the scale distortion has been accom- 

 plished, as shown in Fig. 7-102a. 



A direct evaluation of gravity integrals without scale distortion is pos- 



ies Jung, Ze.it. Geophys., 6(2), 114-122 (1930). 



