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Bayesian deconvolution of oil well test data using Gaussian processes

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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.
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Keywords: 35R30; 62-07; 62F15; 62M09; 62M10; 62P30; Bayesian inference; Gaussian processes; deconvolution; inverse problems; oil well test data; simulation

Document Type: Research Article

Affiliations: 1: Centro de Investigación en Matemáticas, Guanajuato, Mexico 2: Applied Mathematics and Statistics, University of California, Santa Cruz, CA, USA 3: Centro de Innovación Matemática, UNAM, Querétaro, Mexico

Publication date: March 11, 2016

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