A quick 2-D geoelectric inversion method using series expansion

This paper presents the principles of a new inversion method used for determining 2-D geological structures. The basis of the method is that horizontal changes in layer-thicknesses and resistivities of the geological structure are discretized in the form of series expansion. The unknown expansion coefficients are determined by linearized iterative least-squares (LSQ) inversion of data provided by surface geoelectric measurements. The discretization of the 2-D model by means of series expansion gives the possibility to reduce the number of model parameters. Thus, the resulting inverse problem becomes overdetermined and can be solved without the application of additional regularization, e.g., by smoothness constraints, which is usually required for traditional 2-D/3-D inversion. By knowing the expansion coefficients, the local layer parameters are calculated along the profile, point by point. In conformity with the complexity of the model, 1-D forward modeling is applied in the initial iteration steps, then as a continuation the direct problem is handled as a real 2-D problem by means of a finite difference (FD) procedure—i.e., the forward modeling is combined, whereas the unknowns (the expansion coefficients) are the same. This combination of the 1-D and 2-D forward modeling procedures makes it possible to analyze quickly the geological models having considerable lateral variation.