Numerical Investigations of Electrical Resistivity Tomography using Lattice Boltzmann Modeling and Adjoint-State Method
Abstract
Numerical studies have been conducted to initiate and explore electrical resistivity tomography (ERT) to better understand subsurface heterogeneity and characterization of heterogeneous porous media. ERT is a geophysical method which calculates the electrical resistivity distribution in the subsurface environment from a large number of electrical potential measurements made from electrodes. In this study, the electrostatic model is solved by a lattice Boltzmann method (LBM) to investigate its application to ERT and parameterization of electrical resistivity. The LBM is an alternative numerical modeling technique originally created to solve the Navier-Stokes equation. Recently the LBM has been applied for solutions to various diffusion-type differential equations, e.g., potential-resistivity model. In this study, the ERT is formulated as a regularized least-squares (RLS) problem. The inversion of electrical resistivity is conducted through an efficient adjoint-state method, where the Jacobian matrix is not necessary. At each optimization step we only need to solve the electrostatic model and the adjoint state model once to evaluate the gradients of RLS with respect to the unknown resistivity regardless of the dimensions of parameterization. The LBM is also applied to the solution of the adjoint-state equation. We numerically demonstrate the applicability of LBM in a two- dimensional ERT problem.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2006
- Bibcode:
- 2006AGUFM.H31B1417T
- Keywords:
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- 1835 Hydrogeophysics;
- 1894 Instruments and techniques: modeling;
- 3260 Inverse theory