Jo Eidsvik

Seismic reservoir prediction using Bayesian integration of rock physics and Markov random fields A North Sea example

Quantitative interpretation of seismic data for reservoir rock and fluid properties commonly relies on deterministic rock physics relations and may often neglect statistical variability or spatial correlation. Geostatistical methods, on the other hand, take into account spatial dependence but results are often obtained without properly formalizing rock physics relations between seismic measurements and rock and fluid properties. This paper presents a strategy for integrating deterministic rock physics relations and spatial, statistical representations within a Bayesian framework.nnData from the turbidite Glitne Field in the North Sea (Figure 1) provide an example for the approach. Because the reservoir is very heterogeneous, merging statistics with rock physics is particularly worthwhile to improve seismic reservoir prediction. Figure 1. nThe location of Glitne Field in the North Sea and the top Heimdal horizon as illustrated by reflection times. Available data are AVO seismic attributes, well observations, two-way seismic traveltimes, and cap-rock properties. nnnnThe focus is on describing the spatial probability distribution of reservoir facies and fluid saturation along the seismic horizon representing the top Heimdal Formation (Figure 1), which is capped by Lista Formation at approximately 2000 m. Available data include AVO attributes (zero-offset reflectivity and AVO gradient) extracted from 3-D prestack seismic data and log-based analysis of facies and fluid saturation in four wells. Figure 2 shows zero-offset reflectivity (top, left) and AVO gradient (bottom, left) along the horizon (with the facies and fluid observations in the four wells indicated), a plot of zero-offset reflectivity versus AVO gradient (top, right), and a well log from the area (bottom, right). Two-way seismic traveltimes to the horizon of interest and cap-rock properties (density, P - and S -wave velocity) from well logs are also available (Figure 1). A 245 × 505 grid, each block being 12.5 × 12.5 m2, covers the domain of interest. This …

Directional Metropolis : Hastings Updates for Posteriors with Nonlinear Likelihoods

In this paper we consider spatial problems modeled by a Gaussian random field prior density and a nonlinear likelihood function linking the hidden variables to the observed data. We define a directional block Metropolis–Hastings algorithm to explore the posterior density. The method is applied to seismic data from the North Sea. Based on our results we believe it is important to assess the actual posterior in order to understand possible shortcomings of linear approximations.