Uncertainty analysis for the integration of seismic and CSEM data

Abstract

Geophysical inverse problems consist of three stages: the forward problem, optimization, and appraisal. We study the appraisal problem for the joint inversion of seismic and controlled source electro‐magnetic (CSEM) data and utilize rock‐physics models to integrate these two disparate data sets. The appraisal problem is solved by adopting a Bayesian model, and we incorporate four representative sources of uncertainty. These are uncertainties in (1) seismic wave velocity, (2) electric conductivity, (3) seismic data, and (4) CSEM data. Uncertainties in porosity and water saturation are quantified by a posterior random sampling in the model space of porosity and water saturation of a marine one‐dimensional structure. We study the relative contributions from four individual sources of uncertainty by performing several statistical experiments. Uncertainties in the seismic wave velocity and electric conductivity play a more significant role on the variation of posterior uncertainty than do uncertainties in the seismic and CSEM data noise. Numerical simulations also show that the assessment of porosity is most affected by uncertainty in seismic wave velocity and the assessment of water saturation is most influenced by uncertainty in electric conductivity. The framework of the uncertainty analysis presented in this study can be utilized to effectively reduce uncertainty of porosity and water saturation derived from integration of seismic and CSEM data.