Three-Dimensional Complex Resistivity Tomography

A new three-dimensional (3-D) complex-resistivity forward-modeling and inversion<br>program has been developed. Complex finite-difference equations were solved using either biconjugate<br>gradient (Bi-CG) method or quasi-minimal residual (QMR) method. A symmetric<br>successive over-relaxation (SSOR) preconditioner was implemented for both solvers. A secondorder<br>Laplacian roughness operator was employed for the regularization of the 3-D<br>underdetermined inverse problem. The linearized inversion requires the solution of a complex<br>Hermitian system of equations. The solution of this system uses an efficient complex-conjugate<br>gradient algorithm with a diagonal preconditioner to obtain the parameter change vector. This<br>program was implemented in FORTRAN 90 with the dynamic memory allocation for an<br>efficient memory usage. Synthetic data tests showed that our forward solutions were accurate<br>and the inverse algorithm was able to reconstruct the synthetic model.<br>The analysis of complex resistivity data offers important additional information that<br>could be useful in discrimination of aquitards, saline zones or presence of non-aqueous phase<br>liquids (NAPLs). An example is shown using the algorithm for the inversion of scale model<br>results. Additional phase data helped distinguish different targets.