800 



ELECTRICAL METHODS 



[Chap. 10 



Fig. 10-115 shows in double logarithmic scale a diagram for the calculation 

 of the function of eq. (10-64). 



(/) Model experiments. In the interpretation of field data obtained by 

 horizontal loops, experiments with small-scale models play an important 

 part. They are applicable to both mining (ore bodies) and oil exploration 

 problems (stratified ground). To obtain perfect similitude, it is necessary 

 to change the physical properties of the materials as well as the frequenc5^^^ 

 If the fields are expressed in terms of primary current and the model scale 

 is reduced n times, it is necessary to increase both frequency and conduc- 

 tivity n times. If the conductivity cannot be increased n times, it is 

 necessary to increase the frequency n^ times. 



<^a.f, 



^w/"<?» 



a/ 



ai 



10 



m 



4. -^ 



Fig. 10-115. Diagram for the calculation of apparent conductivity as a function 

 of conductivity contrast on the n th layer, and of the ratio of loop radius (= R) and 

 layer depth (= d„) (after Stefanescu). (Note: for i„, read r-n.) 



Extensive experiments with model ore bodies have been made by Lund- 

 berg, Sundberg, Hedstrom, and their associates. Some of the results are 

 reproduced in Figs. 10-116 to 10-118. Fig. 10-1 16a represents the dis- 

 tribution of the vertical primary field inside the loop as well as the vertical 

 and horizontal components of the (combined primary and secondary) fields 

 without regard to phase, for a vertical ore body. The anomalies are sym- 

 metrical, the vertical intensity having a maximum over the center of the 

 body, the horizontal intensity two maxima over the edges. When the ore 

 body is dipping (Fig. 10-1166), the maximum in vertical intensity over the 

 up-dip edge of the ore body is greater than the anomaly over the down-dip 

 edge. A clearer picture of conditions is obtained when the field vectors 

 are split up into their in-phase (P) and quadrature (Q) components 



s^ Sundberg, Beitr. angew. Geophys., 1(3), 334 (1931). 

 Geophys. Pros., 446 (1934). 



L. B. Slichter, A.I.M.E. 



