Estimating the Properties of a Reservoir Using Bayesian Wavelet Regression

• Activity Number: 243
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Bruno Sanso*+ and Giselle Alvarez
• Companies: University of California Santa Cruz and Universidad Simon Bolivar

Abstract

We consider the problem of estimating the properties of an oil reservoir, where some wells have been drilled, using gamma ray logs measured from the wells as well as seismic traces around the wells.The data consist of 14 gamma ray logs and 100 km2 of 2-D seismic data recorded in the Barinas-Apure basin, in western Venezuela. The aim is to predict porosity and amount of sand in rocks. We first consider a univariate model with an isotropic spatial correlation and a regression term with one explanatory variable for each reading of the signals. We built models for each type of signal separately. Motivated by the work of Brown, Fearn and Vannucci (2001) on regression in spectroscopic calibration problems, we transformed the predictor variable by applying a discrete wavelet transform and obtained a set of wavelet coefficients. We then performed a Bayesian variable selection using a Metropolis search. A multivariate generalization was considered using convolutions of kernels with different range parameters for each component and latent variables to link the information in the seismic traces with that in the gamma ray logs.