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 consi sts of dividing a volume into N small cells, equivalent to 3N dipoles. The numerical code is checked against published results obtained thro ugh algorithms that use either equivalent surface charge densities or a finite-difference approach. Good agreement is found between these me thods 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-Marqua rdt constraints formalism. We have tested two approximations: Born, an d localized non-linear (LN). The difference between resistivities calc ulated 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 c onsist of two layers (34 cells) under an overburden. It is found, in t he case of a vertical contrast, that, when a resistive feature overlay s 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 slo wer convergence rate, in the case of both vertical and lateral constra sts, the shape of the body is well resolved, even if a slight discrepa ncy in the absolute values is noticed, especially for conductive cells . Finally, the stability of the inversion is tested with noisy data.