Fast resistivity/IP inversion using a low-contrast approximation
Society of Exploration Geophysicists, Geophysics Vol. 61, No. 1 (Jan.-Feb. 1996); p. 169-179.
Les P. Beard *, Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee;
Gerald W. Hohmannt, formerly Dept. of Geology and Geophysics, University of Utah;
Alan C. Tripp, Dept. of Geology and Geophysics, University of Utah, Salt Lake City, Utah
Paper – [pdf] Fast_IP_inversion_LPB_1995
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 approxi-mation is particularly well-suited to the smooth nature of minimum structure inversion, since complete forward solutions may be computa-tionally 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 near-surface 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.
In this paper, we present a fast, flexible resistivity/IP inversion algorithm that can produce a 2-D image of geoelectric structures in only a few minutes on modest workstations. The inversion algorithm employs a fast and simple low-contrast resistivity approximation in its volume integral equation forward solution that allows 3-D models consisting of thousands of cells to be computed in a few seconds on modest workstations. Since electric field measurements are strongly affected by the volume of earth near the electrodes, we designed the algorithm so that additional
knowledge of the near-surface geoelectric structure can be incorporated. By taking the near-surface response into account, we are able to better image deeper structures. Since strike length dimensions that permit an accurate 2-D approximation are the exception rather than the rule in many areas, we have chosen to use a 3-D forward solution in our inversion to better simulate the edge effects of 3-D bodies. The inversion itself is 2-D in the sense that we constrain the resistivity of any row of cells in the strike direction.