Chap. 8] MAGNETIC METHOD 395 



susceptibility difference of the geologic body against the adjacent rock.*^ 

 The torsion balance furnishes the gravity gradients d^U/dx'dz and 

 d^U/dy'dz, and the curvature values d^U/dyl - d^U/dxl and d^U/dy'dx'. 

 For two-dimensional bodies d^U /dy^ = d^U /dxdy = d^U /dydz = 0, which 

 leaves the gradient d^U /dxdz = Uxz and the curvature value d^U/dx^ = Uxx 

 in the profile direction. Since —d IJ jdz = d^U/dx^, 



AH = ,- . (Ho sin aU^x + Zo f/„) 



AZ = -^ . (Ho sin aUxz - Zo Uxx). 



► (8-60e) 



In the derivation of these equations uniform magnetization is assumed 

 and demagnetization is disregarded. 



3. Magnetic anomalies of two-dimensional bodies have been calculated for 

 faults, slabs, vertical and inclined dikes, anticlines, and synclines from the 

 corresponding torsion balance anomalies derived in Chapter 7 on pages 

 258-65. Angles and distances in the following formulas correspond to the 

 notation used in Fig. 8-52; statements concerning maxima and minima 

 apply mostly to high magnetic latitudes. 



For a vertical fault (step, cliff, vertical edge of subsurface erosional 

 feature, flank of an intrusion, and the like), the magnetic anomalies are, 

 when both horizontal and vertical magnetizations are considered, 



AH = 2/c Ho sin a(<p2 — <pi) + Zo loge - 

 AZ = 2k Ho sin a loge - — Zo((^ — v'l) • 



(8-61a) 



For N-S strike of the fault the horizontal anomaly is proportional to the 

 gravity gradient and shows a maximum over the fault. The vertical in- 

 tensity is proportional to the negative curvature value and has a mini- 

 mum to the south. It is zero over the fault and has a maximum toward 

 north. 



*8 At this point of the theory it would be possible to introduce the demagnetiza- 

 tion by a substitution of apparent for true susceptibility (see p. 390, eq. [8-58c]. 

 The demagnetization factor is different for the transverse and the vertical magnetiza- 

 tion and depends on the dip. The component magnetizing the body in its longitud- 

 inal direction has the smaller demagnetizing factor. For steeply dipping, strongly 

 magnetic bodies, the transverse apparent susceptibility may thus be but a fraction 

 of the actual rock susceptibility. This fact is additional justification for neglecting 

 the transverse horizontal compared with the vertical longitudinal magnetization 

 (see p. 396). 



