measuring configurations,optimum electrode separations,and condit- 
ions of existance and uniqueness of solution. In addition investi- 
gations of kernels permits extraction of information content on 
the number of appropriate measuring channels and the possible 
range of depths over which the resistivity profile is retreivable. 
The technique makes use of the property that the variation with 
depth,of the contribution made by a thin horizontal layer of ground 
to the measured signal,is nonlinear and exhibits a maximum. at a 
certain depth called the depth investigation characteristic( Roy 
and Apparao,1971) The main advantage of the proposed technique is 
that vertical resolution is determined based on actual resistivity 
profiles and not on model profiles. In addition,better stability 
to measurement errors than that of the linear technique is also 
expected. The underlying physics of this new approach may help to 
obtain new valuable information on profiles under consideration. 
THEORY: 
According to Oldenburg,1978;for a uniformly conducting half 
space, the measurable change of electric field at the surface $E(r) 
where r is half the separation between electrodes,resulting from 
a change Sm(z) of the dimensionless resistivity parameter m(z), 
where z is the depth,are related thruogh the weighting functions 
or kernels G(r,z),by 
&E(r) = f 9,2 Sm(z) dz (1) 
where o 
G(r,z)-g(r,y, z)-8(r,q,2)-grgy 2) *& rg, 2) (2) 
ana gr,z)e(22/rY /r? (1492/7)? 9/? (3) 
A,B are current electrode positions and M,N are potential electrale 
positions. The amplitude normalized kernels G(r,z)-shown in Fig(1)- 
determine both the characteristic depth of investigation and the 
possible resolution obtainable. The depth investigation character- 
istic is a curve which shows the variation with depth,of the 
contribution made by a thin horizontal layer of ground to the 
measured potential. Narrower peaked depth investigation curves or 
kernels result in a better resolvable variations of resistivity 
depth profile. Since these kernels are expected to change in the 
presence of a continuously varying resistivity function with depth 
we may write equation(1) in the generalized form: 
$E(r) + €(r) = f G(r,z,n(z)) $n(z)az (4) 
0 
The resistivity is related to the parameter $m(z) through f(z)= 
perl), P=(10.,m) ‚and Em(z)=m(z)-m, (z), where m, (3) is the mean 
value of m(z). 6m(z) represents the sought perturbation, which 
when added to the present estimate of uer Droduces a model that 
reduces discrepancies between calculated responses and observations. 
In other words,our problem can be defined as: given a small set of 
surface potential measurements SE(r.) with errors E.,we wish to 
infer the resistivity profile f(z) Àt all values of/z down to a 
depth determined by the information content of the kernels. 
Equation(4) ‘is a generalized nonlinear remote sounding 
integral equation of Fredholm type of the first kind. Its solution 
982 
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