Model Calibration of Stochastic Process and Computer Experiment for MVO Analysis of Multi-Low-Frequency Electromagnetic Data

Abstract

An electromagnetic (EM) technique is employed in seabed logging (SBL) to detect offshore hydrocarbon-saturated reservoirs. In risk analysis for hydrocarbon exploration, computer simulation for subsurface modelling is a crucial task. It can be expensive and time-consuming due to its complicated mathematical equations, and only a few realizations of input-output pairs can be generated after a very lengthy computational time. Understanding the unknown functions without any uncertainty measurement could be very challenging as well. We proposed model calibration between a stochastic process and computer experiment for magnitude versus offset (MVO) analysis. Two-dimensional (2D) Gaussian process (GP) models were developed for low-frequencies of 0.0625–0.5 Hz at different hydrocarbon depths to estimate EM responses at untried observations with less time consumption. The calculated error measurements revealed that the estimates were well-matched with the computer simulation technology (CST) outputs. Then, GP was fitted in the MVO plots to provide uncertainty quantification. Based on the confidence intervals, hydrocarbons were difficult to determine especially when their depth was 3000 m from the seabed. The normalized magnitudes for other frequencies also agreed with the resulting predictive variance. Thus, the model resolution for EM data decreases as the hydrocarbon depth increases even though multi-low frequencies were exercised in the SBL application.