3-D inversion of induced polarization data

Abstract

We present an algorithm for inverting induced polarization (IP) data acquired in a 3-D environment. The algorithm is based upon the linearized equation for the IP response, and the inverse problem is solved by minimizing an objective function of the chargeability model subject to data and bound constraints. The minimization is carried out using an interior‐point method in which the bounds are incorporated by using a logarithmic barrier and the solution of the linear equations is accelerated using wavelet transforms. Inversion of IP data requires knowledge of the background conductivity. We study the effect of different approximations to the background conductivity by comparing IP inversions performed using different conductivity models, including a uniform half‐space and conductivities recovered from one‐pass 3-D inversions, composite 2-D inversions, limited AIM updates, and full 3-D nonlinear inversions of the dc resistivity data. We demonstrate that, when the background conductivity is simple, reasonable IP results are obtainable without using the best conductivity estimate derived from full 3-D inversion of the dc resistivity data. As a final area of investigation, we study the joint use of surface and borehole data to improve the resolution of the recovered chargeability models. We demonstrate that the joint inversion of surface and crosshole data produces chargeability models superior to those obtained from inversions of individual data sets.