This paper presents the principles of a new inversion method used for the determination of 3D geological structures. The horizontal variations of the layer parameters i.e. layer thicknesses and resistivities are discretized in the form of series expansion. The unknown coefficients of the series expansion are determined by an iterative linearized inversion method using weights specified by the Most Frequent Value Method (MFV). The result of the inversion is estimated from the data of the bi-directional VES (Vertical Electric Sounding) measurements with Schlumberger array in each profile and in multiple profiles. A 3D Finite Difference method was applied to forward modelling, however, the structure is approximated along the profile with a 2D model discretized by single-variable series expansion. The 3D forward modeling procedure gives the opportunity to calculate data measured in two or multiple directions. The suggested interpretation method gives an approximate solution. Proceeding more accurate 3D inversion will be provided by the binary series expansion.
Authors:D. Drahos, Á. Gyulai, T. Ormos, and M. Dobróka
A new L2 norm joint inversion technique is presented and combined with the series expansion inversion method applied for different simulated erroneous Vertical Electric Sounding (VES) data sets over a complicated two dimensional structure. The applied joint inversion technique takes into consideration the complete form of the likelihood function. As a result there is no need to apply input weights to the individual objective functions. The model consists of three layers with homogeneous resistivities. The first layer boundary is a horizontal plane, the other is a two dimensional laterally varying surface. For the VES inversion the exact data sets were calculated by finite difference method, one in strike direction and the other in dip direction. These data sets were contaminated with normally distributed random errors. During inversion the second layer boundary function was determined. For comparison individual and joint inversion examples were calculated for the two data sets. The best model parameter estimate result was produced by the method of automated weighting.