all real and its eigenvectors mutually orthogonal. Eigenvectors 
give information on the various contributions of measurements to 
the determination of the profile. For instance,eigenvectors assoc- 
iated with the largest eigenvalue "sees" the dot product of the 
required profile with the average of kernels,while eigenvectors 
associated with the smallest eigenvalue "sees" the high frequency 
part of the spectrum or the finest structure in the profile and 
responds only very weakly. It could only be extracted by very 
accurate measurements. In addition,optimum selection of observat- 
ional channels(Weinreb and Crosby,1972;Kaplan,1977)-which repres- 
ent interelectrode spacing in our case- is also an important part 
of the design of the remote sensing experiment. It also requires 
eigenanalysis which is under current consideration. 
For an indication of the range of depths over which two over- 
lapping kernels may be used for profile retreival,Heintzenberg et 
a1,1981 have suggested using the ratio of kernels. This is shown 
in Fig(2) as applied to the resistivity sounding problem. In the 
depth range over which the ratio of kernels is a constant,no new 
information about the resistivity profile could be retreived from 
measurements with these two channels,since one kernel could be 
obtained from the other through multiplication by a constant. Only 
over the range of depths-indicated by arrows- for which the ratio 
between kernels is not à constant,could the resistivity profile be 
retreived using measurements corresponding to the two kernels. 
IMPLICATIONS AND CONCLUSION: 
The analogy to the atmospheric remote sensing problem 
suggests the following implications: 
1)- A small set of suitably related measurements could produce 
nearly the same resistivity profile as a larger set chosen 
without optimization,for the same allowed measurement error. 
(2)- It is possible to increase the resolution at any depth by 
inverting higher derivatives of kernels near the depth of 
interest in à way similar to that suggested by Abbas,1979. In 
addition,actual depth investigation characteristics-in the 
nonlinear resistivity profile medium- are obtained from final 
modification of the lower resolution configuration. 
(3)- Measurements using combinations of different array configura- 
tions could,therefore,be inverted to obtain resistivity 
profiles subject only to the condition that different kernels 
are suitably related. 
(4)- Bigenanalysis of actual kernels could give information concer- 
ning optimum separation of electrodes,required number of 
measurements and the range over which profiles could be ret - 
reived. 
ACKNOWLEDGEMENT: 
I would like to thank Dr.Y.Abdalla for many valuable discuss- 
ions and comments. 
  
984 
EAR RR c sme ^ sue NM