Adjoint-based formulation for computing derivatives with respect to bed boundary positions in resistivity Geophysics - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Computational Geosciences Year : 2019

Adjoint-based formulation for computing derivatives with respect to bed boundary positions in resistivity Geophysics

Abstract

In inverse geophysical resistivity problems, it is common to optimize for certain re-sistivity values and bed boundary positions, as needed, for example, in geosteering applications. When using gradient-based inversion methods such as Gauss-Newton, we need to estimate the derivatives of the recorded measurement with respect to the inversion parameters. In this article, we describe an adjoint-based formulation for computing the derivatives of the electric potential and electromagnetic fields with respect to the bed boundary positions. The key idea to obtain this adjoint-based formulation is to separate the tangential and normal components of the field, and treat them differently. We then apply this method to a 1.5D borehole resistivity problem. We illustrate its accuracy and some of its convergence properties via numerical experimentation by comparing those results vs. both the analytical results when available and a finite differences approximation of the derivative.
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Dates and versions

hal-01790697 , version 1 (13-05-2018)

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Théophile Chaumont-Frelet, M Shahrari, D Pardo. Adjoint-based formulation for computing derivatives with respect to bed boundary positions in resistivity Geophysics. Computational Geosciences, 2019, ⟨10.1007/s10596-019-9808-2⟩. ⟨hal-01790697⟩

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