Developing a new covariance function of Gaussian process regression for modelling marine controlled-source electromagnetic data

This work presented a study on developing new covariance function of Gaussian process (GP) regression in modelling marine controlled-source electromagnetic (CSEM) data. Processing the vast amount of marine CSEM data using computational methods proved to be very challenging. GP was employed here as an alternative method for modelling the electromagnetic (EM) responses. Simulation data with various hydrocarbon resistivities and hydrocarbon depths of 400 m and 1200 m at frequency of 0.5 Hz were utilized as the GP training set to model the estimation function, and four testing sets for each depth were computed for validation purposes. Two squared exponential (SE)-based covariance functions were developed (SE with addition operation and SE with multiplication operation), and the performance of the new SE-based GP models was compared with the ordinary SE-based GP model. Mean absolute deviation (MAD) and mean squared error (MSE) were computed to identify the deviation of the estimates with the true EM responses. The results demonstrated that new SE-based GP models produced smaller MAD and MSE compared to the ordinary SE-based model. The new SE with multiplication operation gave the best performance in modelling marine CSEM data. It implies that the developed covariance function of GP regression is able to fit the EM data very well and produce better estimation function at various unobserved input specifications.