Efficient computation of the ERT sensitivity matrix via a semi-analytical approach

The partial derivative of data with respect to model parameters also known as the Jacobian or sensitivity matrix plays a significant role in electrical resistivity tomography inversion by which the influence of a differential model parameter change on individual measurements is denoted. Hence, providing the sensitivity matrix is a crucial step in the ۲D/۳D electrical resistivity tomography inversion process. While the sensitivity matrix is extensive, calculating each individual sensitivity associated with every cell (or model parameter) is computationally expensive which may not feasible in the case of large model space. There is always a challenge in keeping the accuracy of the analytical method while reaching a reasonable computing time. This paper proposed a semi-analytical method to reduce the sensitivity matrix calculation time compared to the conventional method. The integration over the signal contribution which is the most time-consuming part of the sensitivity calculation, was solved using the Modified Gauss–Legendre quadrature (MGLQ) method. To verify the functionality of the proposed approach, the sensitivity distribution of an isotropic and homogeneous model was displayed for three common electrode configurations, i.e., pole-pole, dipole-dipole, and Wenner arrays. Our investigation demonstrate that the sensitivity values vary spatially depending on the type of electrode positions. Furthermore, when employing a semi-analytic scheme, the proposed algorithm delivers a substantial reduction in computation time while maintaining acceptable accuracy in the calculated values. The presented method can be readily extended to other electrode configurations with arbitrary subsurface conductivity distribution.

کلیدواژه ها:

ERT ، Gaussian quadrature ، Modified gauss&ndash ، legendre quadrature ، Sensitivity matrix.