A new correction to the Born approximation

A correction to the Born approximation for the apparent conductivity (induced voltage) in a layered medium is derived. 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%.<
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