3-D INVERSION IN SUBSURFACE ELECTRICAL SURVEYING .1. THEORY

The problem of 3-D inverse modelling in Direct Current (DC) surveys is addressed in this paper. First, forward modelling of the response of 3-D bodies in DC surveys is carried out by the moment method. It consists of dividing a volume into N small cells, equivalent to 3N dipoles. The numerical code is checked against published results obtained through algorithms that use either equivalent surface charge densities or a finite-difference approach. Good agreement is found between these methods and a maximum discrepancy of 3 per cent is computed on a widely published test model. Secondly, inverse modelling is carried out by a classical least-squares (LS) scheme that includes the Levenberg-Marquardt constraints formalism. We have tested two approximations: Born, and localized non-linear (LN). The difference between resistivities calculated with and without these approximations is found to be too large for inverse modelling, especially in the case of conductive bodies. We use this inversion scheme for different theoretical 3-D models that consist of two layers (34 cells) under an overburden. It is found, in the case of a vertical contrast, that, when a resistive feature overlays a conductive one, resistivities are resolved very accurately, with a low number of iterations and with a better accuracy than in the case where the conductive feature overlays the resistive one. Despite a slower convergence rate, in the case of both vertical and lateral constrasts, the shape of the body is well resolved, even if a slight discrepancy in the absolute values is noticed, especially for conductive cells. Finally, the stability of the inversion is tested with noisy data.