An efficient regularized inversion approach for self-potential data interpretation of ore exploration using a mix of logarithmic and non-logarithmic model parameters

A very fast and efficient approach to self-potential (SP) data inversion for ore exploration has been developed. This approach is based on Tikhonov regularization and the conjugate gradient method, and simultaneously inverts for the depth (z), electric dipole moment (k), and angle of polarization (θ) of a buried anomalous body from SP data measured along a profile. This inversion algorithm works iteratively, and solves for z and k in the logarithmic-space (log(z) and log(k)), and solves for θ in the linear-space (non-logarithmic). It is found that the original inversion formulation that uses the model parameters themselves (z, k and θ) is unstable and divergent. It is also found that the inversion formulation that uses the logarithm of the model parameters (log(z), log(k) and log(θ)) is unstable and divergent. Rather, the new inversion scheme that is based on the aforementioned mixed log-linear combination of the model parameters (log(z), log(k), and θ) overcomes and eliminates the mentioned instability and divergence problems. The sensitivity analysis and numerical experiments investigated have indicated that the new approach has a far better and far more optimized minimization search direction. This proposed technique fits the observed data by some geometrically simple body in the restricted class of vertical cylinder, horizontal cylinder, and sphere models. The applicability of the algorithm has been demonstrated on various reliable synthetic data sets with and without noise. The algorithm has been carefully and successfully applied to six real data examples, with ore bodies buried in different complex geologic settings and at various depths in the subsurface. The method is shown to be highly applicable for mineral exploration, and is of particular value in cases where the SP observed data is due to ore body embedded in the subsurface. On average, it took about 40 s of computation (not CPU) time on a 1 GHz PC.