Fast resistivity IP inversion using a low-contrast approximation

By computing only the diagonal terms of the volume integral equation forward solution of the 3-D DC resistivity problem, we have achieved a fast forward solution accurate at low to moderate resistivity contrasts. The speed and accuracy of the solution make it practical for use in 2-D or 3-D inversion algorithms. The low-contrast approximation is particularly well-suited to the smooth nature of minimum structure inversion, since complete forward solutions may be computationally expensive. By using this approximate 3-D solution as the forward model in an inversion algorithm, and by constraining the resistivities and polarizabilities along any row of cells in the strike direction to be held constant, we effect a fast 2-D resistivity inversion that contains end corrections. Because the low-contrast solution is inaccurate for cells near the electrodes, we employ a full solution to compute the response of the near-surface when the nearsurface environment is substantially different from the host rock. This response is stored and used in the iterative resistivity inversion in conjunction with the approximate solution. Once an adequate estimated resistivity model has been found, derivatives from this model are used with Seigel's formula to compute the inverse solution to the linear polarizability problem in a single iteration.