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REMOTE SOUNDING OF THE EARTH'S 
RESISTIVITY-DEPTH PROFILE 
M.EL-RAEY ; 
Department of Physics and Advanced Research Center 
University of Alexandria,Alexandria,Egypt. 
  
ABSTRACT 
The analogy of the inverse problem of underground resistivity 
sounding by two current electrodes and two colinear potential 
electrodes,to the general remote sensing integral equation of 
radiative transfer,has been demonstrated. Kernels of resistivity 
sounding have been shown to have maxima at depths determined by 
interelectrode spacing,as well as by the resistivity profile it- 
self. Chahine's nonlinear relaxation technique have been suggested 
to retrieve resistivity profiles to depths determined by maximum 
current penetration. Optimum interelectrode Spacing-required to 
reduce the number of surface measurements-have been determined by 
suitable choice of kernels. A technique is suggested-in which a 
uniform resistivity-depth profile is used to calculate initial 
kernels. Implications are drawn by analogy to the atmospheric 
sensing problem:(1) A small-suitably chosen- set of surface meas- 
urements could produce nearly the same resistivity profile as any 
other larger set;(2) measurements using combinations of array 
configurations could be inverted,subject only to the suitable 
choice of kernels;(3)it is possible to increase the resolution at 
any depth by inverting higher derivatives of kernels near this 
depth. 
INTRODUCTION: 
A variety of methods have been developed to solve the 
general problem of determining underground resistivity - depth 
profile, from surface measurements using two current electrodes 
and two colinear potential electrodes(Ghosh,1971;Parker,1971;Inman 
et al,1973;Inman 1975;Koefeod,1979). Nevertheless,problems assoc- 
iated with measurement errors,nonlinearities and nonuniqueness 
were not completely resolved. Recently,a method of interpretation 
of direct current resistivity measurements using linearized Backus 
and Gilbert technique,has been advanced by Oldenburg,1978. In his 
method ,the resistivity is assumed to be a continuous function of 
depth,and iterative technique is used to construct a resistivity 
model whose calculated responses agree with observations within a 
prescribed error range. The nonuniqueness of the problem was 
resolved by determining only averages of resistivity at various 
depths. However,even in this method, the nonlinearity of the prob- 
lem prohibited definitive statements about advantages and disadva- 
ntages of any particular electrode configuration until a large 
variety of resistivity structures have been considered. 
The purpose of this article,is to make use of the analogy 
of the four electrode resistivity sounding to the general problem 
of remote sensing of the atmosphere,to suggest & nonlinear relax- 
ation technique that takes into account the continuous structure 
of he ‘earth. The applicability of remote sensing technique makes 
it possible to draw implications by analogy,concerning appropriate 
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