Forward And Inverse Resistivity Modelling On Complex Three Dimensional Structures Using The Finite Element Method

Abstract

The finite element method has been used by several authors in the context of direct current forward and inverse modelling. This versatile numerical method is particularly useful for engineering applications in which very varied structures (e.g. walls, dams, concrete piles) can be modelled for nondestructive investigations. Nevertheless, there is currently a need in developing forward and inverse resistivity modelling codes that are better suited for imaging structures with complex geometries. Therefore, various original approaches must be used to create a well-adapted program. This paper presents the adaptation and the use of the CESAR-LCPC finite element code for the forward and inverse modelling of 3D resistivity data. Firstly, the forward modelling code uses an electrode-independent mesh that allows to place the electrodes at their exact locations and to use a coarse mesh at the same time. To calculate apparent resistivity values, a normalisation approach is used that gives significantly better results than the use of the geometrical factor and allows the modelling of any kind of complex 3D structure. An inversion code was also implemented for the processing of resistivity tomographies on complex 3D structures using any electrode arrangement. This algorithm uses an original strategy to avoid high-computation costs since it does not involve the explicit calculation of a sensitivity (Jacobian) matrix. Synthetic results are presented to illustrate the efficiency of these forward and inverse modelling codes.