Inversion of TEM sounding data using the steepest descent and the conjugate gradients methods

Abstract

In this study, the inversion of TEM sounding is investigated. I solved the over-determined and the under-determined inversion problems using the steepest descent and the conjugate gradients methods. The study depends on results from the inversion of synthetic responses generated by synthetic test models. In the over-determined problem, the inversion of layer conductivities and thicknesses are solved separately for few-layer Earth models. Out of 468 inversion runs, the results showed that the conjugate gradients method demands less calculation than the steepest descent method. The final model error and misfit values are generally better for the conjugate gradients. Although the Inversion for layer conductivities proved to be impractical in the over-determined problem, the inversion for layer thicknesses proved to be very reliable. I suggested a strategy to use both inversion types in mapping horizontal layers. The under-determined problem was solved by a regularized inversion. A total of 48 inversion runs of five synthetic responses and one real data set have been performed. The steepest descent and the conjugate gradients methods showed a comparable performance. The regularized under-determined inversion proved to be more satisfactory in constructing the original test models than the over-determined problem, in consistency with previous works. The inversion of real data from a geologically 1-D site in Central Texas resulted in final models consistent with prior geological information about the site.