Electric resistivity tomography for geophysical inverse problems

A new method for electric resistivity tomography (ERT) is developed for geophysical inverse problems by adapting sensitivity analysis. The outputs of potential electrodes are computed using the two dimensional finite element method in wave number space by Fourier transforming the governing equations. The resistance distribution in the region of interest, which makes the computed potential distribution coincide with the measured potential, is found by minimizing the objective function using an optimization method. In this process sensitivity analysis is introduced in order to compute the derivatives of the objective function. And an adjoint variable method is used to save the computational efforts for the sensitivity coefficients.