182 E. I. Terekhin 



recession tend to zero; except ^n_p„, which is 1 when n = Pq. Therefore 

 in this case 



1 1 



^M "^ Y ^° "^ 2" ^"^^"' 



From (') it is Icnown that 

 where k^ is the coefficient of reflection at the first boundary of separation: 



thn . 



Substituting the vakie of q ^ in expression Qj^ for -7- -> 0, we find that 



Thus, on the left part, the probe curves obtained by the apparatus at the 

 bottom have a horizontal asymptote p = — r — •, since the curves obtained 



by an apparatus at the surface would have an asymptote Qq. 

 Let us consider certain special cases of geoelectrical sections. 



(a) Under the water layer let there be an electrically homogeneous medium 

 stretching to an infinite depth. In this case />q — 1 and q^ = A;" where k 

 is the coefficient of reflection. 



The general formula for apparent resistance obtained by an apparatus 

 at the bottom of the water becomes 



(CO \ / 00 00 \ 



1 + 2 ^ kHn\ +\q, ( Zi+ Y, ^"^"-1+ Yj ^"^"+i)' 

 n=i ' ^ n=l n=l 



After certain simple conversions we finally obtain for a two -layer medium 



n = l 



In practice (from the point of view of interpreting field material) this 

 case is not of particular interest although this expression is undoubtedly 

 of theoretical interest. 



(b) In the case of a multi-layered medium, when the thickness of the 

 layer of water is a general measure of the thicknesses of the underlying 



