Gaussian Processes for Hydrocarbon Depth Estimation in Forward Modeling of Seabed Logging

摘要

Seabed logging (SBL) is an application of the marine controlled-source electromagnetic (CSEM) technique to discover offshore hydrocarbon reservoirs underneath the seabed. This application is based on electrical resistivity contrast between hydrocarbon and its surroundings. In this paper, simulation and forward modeling were performed to estimate the hydrocarbon depths in one-dimensional (1-D) SBL data. 1-D data, consisted offset distance (input) and magnitude of electric field (output), were acquired from SBL models developed using computer simulation technology (CST) software. The computer simulated outputs were observed at various depths of hydrocarbon reservoir (250 m-2,750 m with an increment of 250 m) with frequency of 0.125 Hz. Gaussian processes (GP) was employed in the forward modeling by utilizing prior information which is electric field (E-field) at all observed inputs to provide Efield profile at unobserved/untried inputs with uncertainty quantification in terms of variance. The concept was extended for two-dimensional (2-D) model. All observations of E-field were then investigated with the 2-D forward GP model. Root mean square error (RMSE) and coefficient of variation (CV) were utilized to compare the acquired and modeled data at random untried hydrocarbon depths at 400 m, 950 m, 1,450 m, 2,100 m and 2,600 m. Small RMSE and CV values have indicated that developed model can fit well the SBL data at untried hydrocarbon depths. The measured variances of the untried inputs revealed that the data points (true values) were very close to the estimated values, which was 0.003 (in average). RMSEs obtained were very small as an average of 0.049, and CVs found as very reliable percentages, an average of 0.914%, which implied well fitting of the GP model. Hence, the 2-D forward GP model is believed to be capable of predicting unobserved hydrocarbon depths.