RESINVM3D: A 3D resistivity inversion package

Abstract

We have developed an open source 3D, MATLAB based, resistivity inversion package. The forward solution to the governing partial differential equation is efficiently computed using a second-order finite volume discretization coupled with a preconditioned, biconjugate, stabilized gradient algorithm. Using the analytical solution to a potential field in a homogeneous half space, we evaluate the accuracy of our numerical forward solution and, subsequently, develop a source correction factor that reduces forward modeling errors associated with boundary effects and source electrode singularities. For the inversion algorithm we have implemented an inexact Gauss-Newton solver, with the model update being calculated using a preconditioned conjugate gradient algorithm. The inversion uses a combination of zero and first order Tikhonov regularization. Two synthetic examples demonstrate the usefulness of this code. The first example considers a surface resistivity survey with 3813 measurements. The discretized model space contains 19,040 cells. For this example, the inversion package converges in approximately [Formula: see text] on a [Formula: see text] Pentium 4, with [Formula: see text] of RAM. The second example considers the case of borehole based data acquisition. For this example there were 4704 measurements and 13,200 model cells. The inversion for this example requires [Formula: see text] of computational time.