Bayesian Kriging for Seismic Depth Conversion of a Multi-Layer Reservoir

Abstract

A stochastic model for a petroleum reservoir with L seismic subsurfaces is presented. The seismic velocities within each layer is described by linear regression models and Gaussian random fields. Seismic interpretation errors are modeled as Gaussian random fields. Intercorrelations between all subsurfaces and all velocity fields are taken into consideration. This simplifies the handling of deviating wells and ensures consistent prediction and prediction variances for all L subsurfaces and L velocity fields. Bayesian kriging is used for prediction of subsurfaces and velocity fields.

In the limit corresponding to exact prior knowledge, the Bayesian method is equivalent to cokriging with 2L covariables. In the limit corresponding to no prior knowledge, the method is equivalent to a combination of universal kriging and cokriging with 2L dependent regression models and 2L covariables.