Finite Difference Inverse Modeling of VLF and VLF-R data over 2-D Earth- A Development and Comparison

Abstract:

We present 2-D joint inversion code incorporating smoothness constrained least-squares approach for very low frequency (VLF) data (the real and imaginary anomalies) and VLF-R data (the apparent resistivity and phase) using finite difference modus operandi. To increase the efficiency of forward solver 1) A new technique to compute coefficient matrix from discrete equation implicitly and 2) Comparison of different method with preconditioners for best invert matrix solver have been incorporated. To check the efficiency of present inversion algorithm, First 2D forward modeling algorithm has been compared with Wannamaker code on various two dimensional synthetic geological structures Second, joint inversion has been performed for both VLF and VLF-R data. A model obtained by individual inversion of VLF data (either real or imaginary anomaly) would not fit both observations. However, a model obtained by the joint inversion of the real and imaginary data sets fits both observations. The models obtained by joint inversion of VLF data do not show good agreement with the VLF-R observations. Conversely, the joint inversion of the apparent resistivity and phase data yields models which give good agreement with the real and imaginary anomalies. Individual inversion of any response cannot yield a reliable subsurface structure no matter how well a particular observed response is fitted by the computed responses. To check the efficiency of present work on field data, two profiles providing different geological structures were also inverted to demonstrate the efficacy of the approach for delineating the geometry and properties of 2-D structures in which The VLF-R inversions invariably give better results in comparison with the VLF inversions.