Inversion of Induction Tool Measurements Using the Distorted Born Iterative Method and CG-FFHT

Weng Cho Chew, Qing Huo Liu

Research output: Contribution to journalArticlepeer-review


The inversion of induction tool measurements using the distorted Born iterative method (DBIM) and the conjugate gradient-fast Fourier-Hankel transform (CG-FFHT) is described. The inverse problem is formulated in terms of an integral equation of scattering where the unknown to be sought is the conductivity in the rock formation, when tHe measurements along a boreHole axis are performed. The nonlinear problem is linearized at each stage using the distorted Born approximation. The inhomogeneous medium Green's function in the distorted Born approximation is found by solving a volume integral equation using the CG-FFBT method, which allows a rapid solution to a large problem with reduced computational complexity and memory requirement. In this manner, the inverse problem is solved with a computational complexity proportional to NtlN log N where Ntl is the number of transmitter locations used in the data collection and N is the total number of pixels used to model the unknown formation. The memory requirement is of order NNtl.

Original languageEnglish (US)
Pages (from-to)878-884
Number of pages7
JournalIEEE Transactions on Geoscience and Remote Sensing
Issue number4
StatePublished - Jul 1994

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Earth and Planetary Sciences(all)


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