New correction to the Born approximation

Abstract

A correction to the Born approximation for the apparent conductivity (induced voltage) in a layered medium is derived. Unlike previous corrections which rely primarily on adjusting the background conductivity artificially to fit the data, the correction in this case comes naturally out of the physics and theory of the problem. The correction involves a single constant a and is nonlinear in conductivity. An algorithm for choosing a for induction logging applications is derived. The correction is shown to be significantly more accurate than the uncorrected Born approximation at high conductivity contrasts between adjacent beds. The correction does not significantly increase the computation time or complexity of the Born approximation. Thus, it has application to the related inverse problem where the speed of computation of the forward problem is important. In typical cases studied, the correction is shown to reduce the root mean square (RMS) error of the Born approximation to no more than 5% in regions where the Born approximation without correction has a RMS error of up to 30%.