Gaussian Process Methodology for Multi-Frequency Marine Controlled-Source Electromagnetic Profile Estimation in Isotropic Medium

Abstract

The marine controlled-source electromagnetic (CSEM) technique is an application of electromagnetic (EM) waves to image the electrical resistivity of the subsurface underneath the seabed. The modeling of marine CSEM is a crucial and time-consuming task due to the complexity of its mathematical equations. Hence, high computational cost is incurred to solve the linear systems, especially for high-dimensional models. Addressing these problems, we propose Gaussian process (GP) calibrated with computer experiment outputs to estimate multi-frequency marine CSEM profiles at various hydrocarbon depths. This methodology utilizes prior information to provide beneficial EM profiles with uncertainty quantification in terms of variance (95% confidence interval). In this paper, prior marine CSEM information was generated through Computer Simulation Technology (CST) software at various observed hydrocarbon depths (250–2750 m with an increment of 250 m each) and different transmission frequencies (0.125, 0.25, and 0.5 Hz). A two-dimensional (2D) forward GP model was developed for every frequency by utilizing the marine CSEM information. From the results, the uncertainty measurement showed that the estimates were close to the mean. For model validation, the calculated root mean square error (RMSE) and coefficient of variation (CV) proved in good agreement between the computer output and the estimated EM profile at unobserved hydrocarbon depths.

Gauss Süreç Regresyonu ve Destek Vektör Makineleri Kullanılarak Değerlendirilen Kendiliğinden Yerleşen Beton Davranışının Deneysel Veri İle Doğrulanması

“…Sonuçları oluşturan temel işlevin, tamamen bir ortalama işlev, m(x) ve bir kovaryans işlevi, k(x,x') tarafından belirtilen stokastik bir süreç olan bir Gauss Süreci olduğu varsayımına dayanır. Gauss Sürecinin ortalama işlevi, girdi değişkenlerini çıktı değişkenlerine eşleyen herhangi bir işlev olabilirken kovaryans işlevi, işlevin düzgünlüğünü ve benzerliğini kodlar [49], [50].…”

“…burada X girdi değişkenlerinin matrisidir, Ɵ hiperparametrelerin bir vektörüdür, K, k(xi,xj) öğelerini içeren kovaryans matrisidir, σ 2 gürültü varyansıdır [50], [51]. GSR'nin amacı ise aşağıda verilen f(x) fonksiyonunu bulmaktır ki; bu fonksiyon y'nin x üzerindeki dağılımıdır [51]:…”

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

“…GP is a probabilistic and nonparametric method which capable of fitting functional forms reliant on the domain observations. According to Reference [25], this stochastic approach has a property that differs from most of the other black-box identification approaches. It searches for the correlations among the known knowledge rather than approximating the model by trying to fit the basis function parameters.…”

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

“…Studies related to the commercial SBL application can be found in [1][2][3][4][5][6][7][8][9]. Figure 1 is adopted from [10] to depict the illustration of the SBL application in the offshore environment. Numerical modeling is a crucial task in geophysics problems since it provides prior knowledge and information of the potential reservoirs.…”