Inverse problem in the conductivity model for a transversely isoropic earth

Abstract

The direct current conduction method is used in geophysical exploration to investigate the structure of the earth. It uses an apparatus which consists two pieces of electrode, a pair of electrode to measuring the difference of potential and the other as a source of current The apparent resistivity is frequently used to inter prete the potential field measurement. In mathematical modeling, the electrical potential can be represented as a partial differentia equation with conductivity or resistivity as parameters, In the relatively simpler cas where the electrical conductivity is a function of depth only, a formal solution may be obtainable through the use of an integral transform. Numerical techniques are normally required to evaluate the resulting integral. When a medium is transversely isotropic, a formal solution in closed form may still be obtainable jar special assumptions about the earth's structure, however; in general, a fully numerical technique may need to be lIsed The potential differences obtained from direct current resistivity soundings constitute a set of observed data. The problem is then to use a jinite element method to invert the set of data values to give a conductivity structures of the earth.