Publications [#283814] of Qing H. Liu

Papers Published

1. Zhang, ZQ; Liu, QH, Reconstruction of axisymmetric media with an FFHT-enhanced extended born approximation, Inverse Problems, vol. 16 no. 5 (October, 2000), pp. 1281-1295, IOP Publishing [doi]
   (last updated on 2023/08/08)

   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 (FFHT) enhanced extended Born approximation (EBA). 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, FFHT-enhanced EBA. 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 FFHT algorithm, this inverse method is actually more efficient than the conventional, brute-force first-order Born approximation.