Novel inverse algorithm for borehole induction measurements using a spectral hybrid EBA forward method

Qing Huo Liu; Zhong Qing Zhang

doi:10.1117/12.390641

6 July 2000 Novel inverse algorithm for borehole induction measurements using a spectral hybrid EBA forward method

Qing Huo Liu, Zhong Qing Zhang

Proceedings Volume 4129, Subsurface Sensing Technologies and Applications II; (2000) https://doi.org/10.1117/12.390641
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

We invert for the axisymmetric conductivity distribution from borehole electromagnetic induction measurements using a two-step linear inversion method based on a fast Fourier and Hankel transform enhanced extended Born approximation. In this method, the inverse problem is first cast as an under- determined linear least-norm problem for the induced electric current density; from the solution of this induced current density, the unknown conductivity distribution is then obtained by solving an over-determined linear problem using the newly developed, fast Fourier and Hankel transform enhanced extended Born approximation. Numerical results show that this inverse method is applicable to a very high conductivity contrast. It is a natural extension of the original two-step linear inversion method of Torres-Verdin and Habashy to axisymmetric media. In the first step, the CPU time costs O(N²). In the second step, the CPU time costs O(N log₂ N) where N is the number of unknowns. Because of the fast Fourier and Hankel transform algorithm, this inverse method is actually more efficient than the conventional, brute-force first-order Born approximation.

Citation Download Citation

Qing Huo Liu and Zhong Qing Zhang "Novel inverse algorithm for borehole induction measurements using a spectral hybrid EBA forward method", Proc. SPIE 4129, Subsurface Sensing Technologies and Applications II, (6 July 2000); https://doi.org/10.1117/12.390641

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