Bayesian Wavelet Regression for Spatial Estimation

We consider the problem of estimating the properties of an oil reservoir, like porosity and sand thickness, in an exploration scenario where only a few wells have been drilled. We use gamma ray records measured directly from the wells as well as seismic traces recorded around the wells. To model the association between the soil properties and the signals, we fit a linear regression model. Additionally we account for the spatial correlation structure of the observations using a correlation function that depends on the distance between two points. We transform the predictor variable using discrete wavelets and then perform a Bayesian variable selection using a Metropolis search. We obtain predictions of the properties ∗Tel.+34 91 488 8322, Fax: +34 91 488 7626, e-mail: [email protected] †Phone: +1 831 459-1484, Fax: +1 831 459-4829, e-mail:[email protected]