Impedance Transmission Conditions for the Electric Potential across a Highly Conductive Casing

Hélène Barucq 1, 2 Aralar Erdozain 1 Victor Péron 1, 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : Borehole resistivity measurements are a common procedure when trying to obtain a better characterization of the Earth's subsurface. The use of a casing surrounding the borehole highly complicates the numerical simulations due to a large contrast between the conductivities of the casing and the rock formations. In this work, we consider the casing to be a thin layer of uniform thickness and motivated by realistic scenarios, we assume that the conductivity of such casing is proportional to the thickness of the casing to the power of -3. We derive Impedance Transmission Conditions (ITCs) for the static (zero frequency) electric potential for a 2D configuration. Then, we analyse these models by proving stability and convergence results. Next, we asses the numerical performance of these models by employing a Finite Element Method. Finally we present present asymptotic models for similar configurations including the time-harmonic configuration and a 3D axisymmetric scenario.
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Hélène Barucq, Aralar Erdozain, Victor Péron. Impedance Transmission Conditions for the Electric Potential across a Highly Conductive Casing. [Research Report] RR-8998, Inria Bordeaux Sud-Ouest. 2016. ⟨hal-01412369⟩

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