AMS2003-2: Spatial Estimation of Reservoir Properties Using Bayesian Wavelet Regression

Giselle Alvarez, Bruno Sanso, Reinaldo Michelena and Juan Ramon Jimenez
12/31/2003 09:00 AM
Applied Mathematics & Statistics
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 logs measured from the wells as well as seismic traces around the wells. We fit a linear regression model that accounts for the spatial correlation structure of the observations using an isotropic correlation function.

We first transform the predictor variable using discrete wavelets.

We then perform a Bayesian variable selection using a Metropolis search.

We obtain predictions of the properties over the whole reservoir providing a probabilistic quantification of their uncertainties, thanks to the Bayesian nature of our method. The cross-validated results show that a very high accuracy can be achieved even with a very small number of wavelet coefficients.