196 



EXPLORATION GEOPHYSICS 



It is evident that AZ does not depend on I^ but does depend on the 

 layer thickness d. If the overlying formation consisted of a number of 



layers having different values of 

 k, the effects would still cancel 

 out. Figure 87 illustrates the ver- 

 tical anomaly profiles for the case 

 that 1 2 is much greater than 7i. t 



Anomaly Due to Horizontal 

 Component of Induction 

 If, as is generally the case, the 

 earth's field is not vertical, the pheno- 

 menon would be the same as though 

 two fields were present, i.e., a vertical 

 field equal to the vertical component Z 

 and a horizontal field equal to the hori- 

 zontal component H. The calculations 

 just made may be used to give the ef- 



FiG. 87.-Anomaly due to buried contact of two ^^"^^ ^^ ^^e vertical field. The horizontal 

 thick layers. (Equation 83.) component, however, would produce an 



additional distribution of magnetism 

 along the plane AB. (The eflfects produced by such a distribution will be considered 

 in a later section.) 



Thin Layer Terminating at a Distance d Below the Surface. — In 



this case there are two kinds of effects to be taken into account : the effect 

 due to the end of the layer and the effect due to 

 magnetization at right angles to the plane of 

 the layer. (Figure 88.) We shall consider the 

 end effect first. If /i is the intensity of mag- 

 netization parallel to the plane of the paper 

 and normal to the end of the layer and t the 

 thickness of the layer, the pole strength per 

 unit length of the end of the layer is tli. If 

 the layer is thin, the end effect is the same as 

 that produced by a linear distribution of mag- 

 netic poles oriented at right angles to the plane 

 of the paper. The potential due to such a dis- 

 tribution is given by Equation 79 ; that is, 



_ Fig. 88. — Sketch showing quan- 

 tities which enter into the calcu- 

 lation of the potential due to mag- 

 netization at right angles to the 

 surface of the layer. 



Vi = 2th log ro = 2tli log (rf2 + p^ 

 The vertical component of the anomaly at P is : 



dVi 2thd 



% 



dd 



d^ + P 



(84)^ 



t See also L. B. Slichter, A.I.M.E. Geophysical Prospecting, 1929, p. 240. 



* The field is expressed as the positive derivative of V in order to avoid carrying 

 negative signs. Actually, the sign of the anomaly depends on the sign of / and this in 

 turn depends on the orientation of the magnetic layer with respect to the earth's field. 



