Solutions of the inherent problem of the equivalence in direct current resistivity and electromagnetic methods through global optimization and joint inversion by successive refinement of model space

摘要

The problem of equivalence in direct current (DC) resistivity and electromagnetic methods for a thin resistive and conducting layer is well-known. Attempts have been made in the past to resolve this problem through joint inversion. However, equivalence still remains an unresolved problem. In the present study, an effort is made to reduce non-uniqueness due to equivalence using global optimization and joint inversion by successive refinement of the model space. A number of solutions derived for DC resistivity data using very fast simulated annealing global inversion that fits the observations equally well, follow the equivalence principle and show a definite trend. For a thin conductive layer, the quotient between resistivity and thickness is constant, while for a resistive one, the product between these magnitudes is constant. Three approaches to obtain very fast simulated annealing solutions are tested. In the first one, layer resistivities and thicknesses are optimized in a linear domain. In the second, layer resistivities are optimized in the logarithmic domain and thicknesses in the linear domain. Lastly, both layer resistivities and thicknesses are optimized in the logarithmic domain. Only model data from the mean models, corresponding to very fast simulated annealing solutions obtained for approach three, always fit the observations.