Bayesian deconvolution of oil well test data using Gaussian processes
J. Andrés Christen, Bruno Sansó, Mario Santana-Cibrian, Jorge X. Velasco‐Hernández · Journal of Applied Statistics · 2015
We use Bayesian methods to infer an unobserved function that is convolved with a known kernel. Our method is based on the assumption that the function of interest is a Gaussian process and, assuming a particular correlation structure, the resulting convolution is also a Gaussian process. This fact is used to obtain inferences regarding the unobserved process, effectively providing a deconvolution method. We apply the methodology to the problem of estimating the parameters of an oil reservoir from well-test pressure data. Here, the unknown process describes the structure of the well. Applications to data from Mexican oil wells show very accurate results.