Abstract
We invert for the axisymmetric conductivity distribution fromborehole electromagnetic induction measurements using atwo-step linear inversion method based on a fast Fourier andHankel transform (FFHT) enhanced extended Born approximation (EBA).In this method, the inverse problem is first cast as anunder-determined linear least-norm problem for the inducedelectric current density; from the solution of this inducedcurrent density, the unknown conductivity distribution is thenobtained by solving an over-determined linear problem using thenewly developed, FFHT-enhanced EBA.Numerical results show that this inverse method is applicableto a very high conductivity contrast. It is a naturalextension of the original two-step linear inversion method ofTorres-Verdin and Habashy to axisymmetric media. In the firststep, the CPU time costs O(N2). In the second step, theCPU time costs O(Nlog 2N) where N is the number ofunknowns. Because of the FFHT algorithm, this inverse method isactually more efficient than the conventional, brute-forcefirst-order Born approximation.
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