on calculation of eri sensitivity matrix

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 2d/3d electrical resistivity imaging (eri) inversion process. sensitivity patterns are also a criterion to assess the reliability of the inverted models and to design optimum resistivity surveys. in this study, a numerical approach based on the forward matrix calculation in the frame work of the 2.5d finite difference electrical resistivity forward modeling is presented. first, using the potential distribution in the fourier space obtained from the forward calculation and the derivatives of the coupling coefficients with respect to the conductivity distribution, the sensitivity values in the wavenumber domain are computed. then, these values are transformed into the space domain using an inverse fourier technique. to verify and analyze the proposed numerical method, the sensitivity distributions assuming homogeneous and inhomogeneous media for commonly used electrical resistivity tomography configurations (e.g. pole-pole, pole-dipole, dipole-dipole, and the wenner arrays) are computed. the numerical experiments reveal that the sensitivity patterns vary spatially throughout the model depending not only on the resistivity distribution but also on the electrode configuration. it is also concluded that the sensitivity analysis can be used as a supplementary tool for any optimum electrical tomography survey design.