Inverse Resistivity Problems in Computational Geoscience

Alemdar Hasanov (Hasanoǧlu) () and Balgaisha Mukanova
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Alemdar Hasanov (Hasanoǧlu): Izmir University, Mathematics and Computer Science
Balgaisha Mukanova: Eurasian National University

A chapter in Handbook of Geomathematics, 2015, pp 1845-1862 from Springer

Abstract: Abstract We study coefficient inverse problems arising in modeling of resistivity prospecting problems. Numerical simulations are investigated in the cases of vertically and cylindrically layered medium. Conductivity coefficients are assumed to be sufficiently smooth 1D functions. The model leads to an inverse problem of identification of an unknown coefficient (conductivity) in an elliptic equation in R 2 inside a slab or in a cylinder. The direct problem is formulated as a mixed BVP in R 2. Measured data are assumed to be available on the upper boundary of the medium or along the axis of the well. A logarithmic transformation is applied to the unknown coefficient, and the inverse problem is studied as a minimization problem for the residual functional. A numerical method is discussed for interpreting the data of a resistivity prospecting in both considered models of layered medium. The method is implemented for realistic conductivity distributions, with both noise-free and noisy data.

Keywords: Inverse Problem; Electrical Impedance Tomography; Direct Problem; Conjugate Gradient Algorithm; Reflection Factor (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-54551-1_62

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DOI: 10.1007/978-3-642-54551-1_62

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