384 



MAGNETIC METHOD 



[Chap. 8 



zontal intensity anomalies is | the depth. This obtains for the single 

 pole only. 



2. Vertical magnetic doublets (magnets) must be assumed in place of 

 single poles if the depth extent of geologic bodies as described on page 381 

 is small, that is, if a negative anomaly surrounds the area of positive 

 anomaly. If the negative anomaly does not surround the positive anomaly 

 completely, the doublet is inclined and relations shown in the next para- 

 graph are applied. The field of a vertical magnetic doublet follows from 

 an addition of the fields of two poles at different depths. If di is the 

 depth and n the distance from P to the upper (positive) pole, di the 

 depth and r,2 the distance to the lower (negative) pole, 



and 



(8-53) 



Thal^n has given two depth rules for the magnetic doublet which apply 

 when its pole distance 21 is greater than three times the depth to the 

 upper pole, d\ : 



(a) A line connecting a point of zero vertical intensity (abscissa Co) 

 with tne center of the magnet makes an angle of 54.75° with its axis, so 

 that cot 54° = (di + l)/eo • This depth rule is not very reliable. If it 

 is applied to Nippofdt's figure 19, the formula gives a depth of 17 instead 

 of 20; in his figure 22 it gives 13.3 instead of 15. 



(b) The distance between the maximum and minimum in AH is approxi- 

 mately equal to the depth to the center of the magnet. (This rule is still 

 less reliable; it gives a depth of 14 instead of 20 for Nippoldt's figure 19, 

 and 14 instead of 15 for his figure 22.) 



3. For a dipping magnetic doublet, the fields of the upper and lower pole 

 are again added (see Fig. 8-46) so that by substitution of ^2 = 21 cos i 

 and di = di -{- 21 sin i, 



AH = 



=4 



— ei , ei — 21 cos i 



+ 



^2 



•] 



and 



AZ 





di + 21 sin i 



(8-54) 



" A. Nippoldt, Magnetische Mutung, pp. 68-70. 



