Fast mixture spatial regression: A mixture in the geographical and feature space applied to predict porosity in the post-salt

Extracting geological resources like hydrocarbon fluids requires significant investments and precise decision-making processes. To optimize the efficiency of the extraction process, researchers and industry experts have explored innovative methodologies, including the prediction of optimal drilling locations. Porosity, a key attribute of reservoir rocks, plays a crucial role in determining fluid storage capacity. Geostatistical techniques, such as kriging, have been widely used for estimating porosity by capturing spatial dependence in sampled point-referenced data. However, the reliance on geographical coordinates for determining spatial distances may present challenges in scenarios with small and widely separated samples. In this paper, we develop a mixture model that combines the covariance generated by geographical space and the covariance generated in an appropriate feature space to enhance estimation accuracy. Developed within the Bayesian framework, our approach utilizes flexible Markov Chain Monte Carlo (MCMC) methods and leverages the Nearest-Neighbor Gaussian Process (NNGP) strategy for scalability. We present a controlled empirical comparison, considering various data generation configurations, to assess the performance of the mixture model in comparison to the marginal models. Applying our models to a three-dimensional reservoir demonstrates its practical applicability and scalability. This research presents a novel approach for improved porosity estimation by integrating spatial and covariate information, offering the potential for optimizing reservoir exploration and extraction activities.