3-D inversion of induced polarization data

We present an algorithm for inverting induced polarization (IP) data acquir ed in a 3-D environment. The algorithm is based upon the linearized equatio n for the IP response, and the inverse problem is solved by minimizing an o bjective function of the chargeability model subject to data and bound cons traints. The minimization is carried out using an interior-point method in which the bounds are incorporated by using a logarithmic barrier and the so lution of the linear equations is accelerated using wavelet transforms. Inv ersion of TP data requires knowledge of the background conductivity. We stu dy the effect of different approximations to the background conductivity by comparing IP inversions performed using different conductivity models, inc luding a uniform half-space and conductivities recovered from one-pass 3-D inversions, composite 2-D inversions, limited AIM updates, and full 3-D non linear inversions of the de resistivity data. We demonstrate that, when the background conductivity is simple, reasonable IP results are obtainable wi thout using the best conductivity estimate derived from full 3-D inversion of the de resistivity data. As a final area of investigation, we study the joint use of surface and borehole data to improve the resolution of the rec overed chargeability models, We demonstrate that the joint inversion of sur face and crosshole data produces chargeability models superior to those obt ained from inversions of individual data sets.