Secondary sources and linearization in geoelectric problems

Geoelectric problems involve a basic (horizontally layered) model and a bas ic (quasi-stationary, purely electrodynamic) process. In this situation, th e known integral representations of any variable and distributed source are solvable. The numerical treatment of the basic problem has been comprehens ively developed and provides a basis for the interpretation process. Any de viation from the basic problem (e.g., increased dimensionality) can be repr esented as the same basic problem with an additional (secondary) distribute d source, which allows a formal representation of the solution in terms of integral equations. It is shown in this paper, however, that such a represe ntation of the solution can yield a number of very useful consequences, suc h as an integral representation of derivatives with respect to the paramete rs of the basic model, a response in the form of contributions from individ ual layers, an approximate incorporation of displacement currents in transi ent processes, and a fast method for calculating the effect of multidimensi onal conductivity disturbances (Born linear approximation).