400 MAGNETIC METHOD [Chap. 8 



For symmetrical and asymmetrical anticlines and synclines the analytical 

 expressions become too complicated even if the transverse magnetization 

 is neglected, and it is simpler to operate with the graphical methods dis- 

 cussed in the next paragraph. 



4. The magnetic anomalies of irregular, features may be calculated by 

 evaluating first their torsion-balance anomalies with graticules, interpreta- 

 tion diagrams, or integraphs, as discussed in detail in Chapter 7, on pages 

 265-70. If the number of elements comprised by the outline of a geologic 

 body is i in a curvature diagram, and n in a gradient diagram, the gravi- 

 tational anomalies are Uxz = C'hn and Uxx = Chi, where C is the con- 

 stant effect of each mass element in E.U. The magnetic anomalies follow 

 by substitution of these expressions in eq. (8-60e) : f or 6 = 1 and C'/k = C 



AH = CK(Hosina.i + Zo-n) ] 



\ (8-62a) 

 AZ = Ck(Ho sin a-n — Zo-i). j 



If the unit effect in the torsion-balance diagrams is 1/10 E.U., the con- 

 stant C in eq. (8-62a) is I5O7. Diagrams for the direct calculation of 

 magnetic anomalies may be constructed by introducing some simplifica- 

 tions in the last formula. 



As shown in Chapter 7, gravitational anomalies may be calculated 

 mechanically with special integraphs. The*magnetic anomalies then follow 

 from the surface integrals of the section of subsurface bodies so that, by 

 combination with eq. (8-60e), the horizontal and vertical intensity 

 anomalies 



AH = 2kV If sin ^ cos (<p - I') ^ 



s 



AZ = 2/cT' J J cos (p cos {<p - I') 



dp 

 P 



} (8-626) 



where I' and T' are the apparent total intensity and inclination and p 

 and (p the polar coordinates of the elements in the section at right angles 

 to the strike. Gamburzeff has constructed single integraphs for calcu- 

 lations of intensities at one station, and multiple integraphs for simulta- 

 neous indication of the surface integral at ten stations. 



E. Interpretation Theory Based on Both Permanent and 

 Induced Magnetization 



While the induction theory gives fairly accurate results for formations 

 of low or intermediate susceptibility and furnishes at least the shape of 



»2 J. Pirson, A.I.M.E. Contr., 91 (Nov., 1935). 



" G. A. Gamburzeff, Gerl. Beitr., 24(2/3), 83-93 (1929). 



