Two unconventional approaches to electromagnetic inversion: hierarchical Bayesian inversion and inverse scattering series

Abstract

Electromagnetic methods are effective complementary tools, when combined with seismic exploration, for the delineation of a hydrocarbon reservoir, because electromagnetic methods provide extra information about, for example, electric conductivity, which is an important property for the economic evaluation of reservoirs. In this study, we analyze unconventional approaches of electromagnetic inversion: hierarchical Bayesian inversion and inverse scattering series. We apply the hierarchical Bayesian inversion to the uncertainty analysis for the joint inversion and utilize rock-physics models to integrate these two disparate data sets. The study shows that the uncertainties in the seismic wave velocity and electric conductivity play a more significant role in the variation of posterior uncertainty than do the seismic and CSEM data noise. The numerical simulations also show that the uncertainty in porosity is most affected by the uncertainty in seismic wave velocity and that the uncertainty in water saturation is most influenced by the uncertainty in electric conductivity. The framework of the uncertainty analysis presented in this study can be utilized to effectively reduce the uncertainty of the porosity and water saturation derived from integration of seismic and CSEM data. We also study the feasibility of the inverse scattering series, which can effectively resolve the nonlinearity of an inverse problem, for the interpretation of electromagnetic data. The application of the inverse scattering series has been limited because the series converges when the reference model sufficiently close to the true model. This study quantifies convergence conditions of the inverse scattering series and suggests a different approach of the inverse series, the modified inverse scattering series, which guarantees the convergence of the series and facilitates the choice of a reference model.