Abstract:

For avoiding the problems caused by solving large linear equation systems numerically, we introduce the basic concept of the electrical reflectivity tensor and the basic idea of the quasi-analytical approximation into D.C. electrical potential field, and define three auxiliary functions, namely the volume potential reflection function, the surface potential reflection function, and the surface charge density reflection function. Also, we give the quasi-analytical approximations to the reflection functions for general cases and the analytical solutions of the reflection function in simple situations, i.e. a uniform or a point current source background electrical field and uniform cylinders and spheres as the anomalous body. Simple comparison shows that the surface charge density reflection function is a function of the free surface charge density on the surface of the anomalous body under consideration. In simple situations described above, the function reduces into a simple proportional relationship. The same is true for the surface potential reflection function in simple cases. However, in general cases it is difficult to establish an explicit relationship between the surface reflection function and the free surface charge density.

Key words: geophysical prospecting-electrical, D. C. electrical potential field, quasi-analytical approximation, reflection function, physical meaning