Gaussian Process-Based Inversion: A New Approach for Estimating Hydrocarbon Parameters in Controlled-Source Electromagnetic Application

Many inversion codes in marine controlled-source electromagnetic (CSEM) inverse problems use numerical partial differential equation (PDE) solvers as the forward solutions modelers. These codes perform well only when handling limited observations, as solving the governing equations in the forward modeling is very challenging, and quantifying uncertainties is not the strength of these solvers. A Gaussian process (GP)-based inversion was proposed to allow for greater flexibility in modeling numerous forward solutions by calibrating the stochastic process with computer experiment responses to estimate hydrocarbon parameters (i.e., depth and electrical resistivity) in marine CSEM application. Here, GP was used to evaluate electromagnetic (EM) responses at untried input specifications with uncertainty quantification, and gradient decent was employed for optimization in the inversion algorithm. The developed forward and inverse models were assessed against the true values through computing deviations. Hypothesis testing was also conducted to quantify the uncertainty of the estimation function as per its corresponding estimator. This research also compared the predictive performance of the proposed inversion methodology and existing framework. The calibration enabled GP to provide numerous reliable EM responses for the inversion. All the EM responses significantly fell within the GP predictive variance at $\alpha =0.05$ . The resulting deviations and Bland-Altman plots demonstrated that GP-based inversion was capable of efficiently estimating the hydrocarbon input parameters in the marine CSEM inverse problems.