A two-step linear inversion of two-dimensional electricalconductivity |
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Authors: | Torres-Verdin C Habashy TM |
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Affiliation: | Schlumberger-Doll Res., Ridgefield, CT; |
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Abstract: | We introduce a novel approach to the inversion of two-dimensional distributions of electrical conductivity illuminated by line sources. The algorithm stems from the newly developed extended Born approximation (see J. Geophys. Res., vol.98, no.B2, p.1759, 1993), which sums in a simple analytical expression an infinitude of terms contained in the Neumann series expansion of the electric field resulting from multiple scattering. Comparisons of numerical performance against a finite-difference code show that the extended Born approximation remains accurate up to conductivity contrasts of 1:1000 with respect to a homogeneous background, even with large-size scatterers and for a wide frequency range. Moreover, the new approximation is nearly as computationally efficient as the first-order Born approximation. Most importantly, we show that the mathematical form of the extended Born approximation allows one to express the nonlinear inversion of electromagnetic fields scattered by a line source as the sequential solution of two Fredholm integral equations. We compare this procedure against a more conventional iterative approach applied to a limited-angle tomography experiment. Our numerical tests show superior CPU time performance of the two-step linear inversion process |
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