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.

A Novel Methodology for Hydrocarbon Depth Prediction in Seabed Logging: Gaussian Process-Based Inverse Modeling of Electromagnetic Data

“…According to [27], the rate of detection when using GP was higher compared to other methods and the rate of false alarm was lower especially for the weak seismic signals. Researchers in [28] proved that GP was successfully capable of being exploited in processing EM responses by calibrating the stochastic and the computer experiment models for magnitude versus offset (MVO) analysis.…”

“…All the computer input properties and parameters used in the SBL modeling are indicated in Table 1. As discussed by researchers in [28], interpretation of the SBL data relies on an assumption that the normalized magnitude versus offset (MVO) between the target responses (i.e., with presence of hydrocarbon) and reference responses (i.e., without presence of hydrocarbon) can pre-identify the presence of high-resistive bodies. The idea is that the magnitudes of target response are divided by the magnitudes of reference response along the offsets (i.e., source-receiver separation distances).…”

Stochastic Process-Based Inversion of Electromagnetic Data for Hydrocarbon Resistivity Estimation in Seabed Logging

“…As discussed in Reference [40], the SBL data interpretation is based on an assumption that the existence of target bodies can be preidentified by normalizing the magnitude versus offset (MVO) between the target responses (with hydrocarbon) and the reference responses (without hydrocarbon). The normalized MVO can be calculated by dividing the target responses with the reference responses.…”