170 E. I. Terekhin 



In the article by V. V. Burgsdorf <^), a solution of the problem of distri- 

 bution of a field for the most general case, with an arbitrary placing of 

 the electrode in a horizontally stratified medium is given in an integral 

 form. 



Of practical interest for electrical prospecting at sea and in other expanses 

 of water, is the case where the source of current and the measuring apparatus 

 are placed at a certain depth within the limits of the water layer or, in a spe- 

 cial case, at the bottom of the water. 



The present paper gives a developed solution of the problem of distribu- 

 tion of the field of a point source situated within the limits of the first layer 

 of a horizontally stratified medium and, as a special case, a point source 

 situated at the lower boundary of the first layer. 



The paper gives expressions for the apparent resistance for a number of 

 instruments placed at the bottom of the water. From these formulae, calcu- 

 lations of the theoretical curve for electrical probing at sea were made. In one 

 of the sections details are given of methods of calculation used for the 

 theoretical curves of probing at sea, and also an evaluation of the accuracy 

 of the calculations. 



THE FIELD OF A POINT SOURCE AT THE BOUNDARY OF SEPARATION 

 OF THE FIRST AND SECOND LAYERS 



The main problem in electrical probing is to determine the depth of 

 various layers of the section differing in resistance. 



One of the main methods of interpreting probe curves is to compare them 

 with specially calculated theoretical curves. To calculate these curves, the 

 character of distribution of the field created by the point source of current 

 should be known. 



Let us assume a horizontally homogeneous stratified medium. Let 0, 1, 

 2, 3, ..., n be the orders of the layers (from the top downwards) Iiq, A^, 

 h^, ..., /z„_j be the thicknesses of the layers covering the supporting level 

 and Qq, q^, q^, ..., Q^ be the specific electrical resistances of the various 

 layers. 



Thus, the upper layer (in this case the water layer) has a zero number and 

 thickness Jiq and specific resistance ^q respectively. 



The current source A of strength /is placed in the upper layer at a certain 

 depth Zq < Hq from the surface. 



The potential at the point M, arbitrarily placed in the conducting semi- 

 space at a distance R from the current source, is expressed by the following 



