Multiscale Data Integration Using Markov Random Fields Conference Paper uri icon


  • Abstract We propose a hierarchical approach to spatial modeling based on Markov Random Fields (MRF) and multi-resolution algorithms in image analysis. Unlike their geostatistical counterparts that simultaneously specify distributions across the entire field, MRFs are based on a collection of full conditional distributions that rely on local neighborhood of each element. This critical focus on local specification provides several advantages:MRFs are computationally tractable and are ideally suited to simulation-based computation such as MCMC (Markov Chain Monte Carlo) methods, andmodel extensions to account for non-stationarity, discontinuity and varying spatial properties at various scales of resolution are easily accessible in the MRF framework. Our proposed method is computationally efficient and well suited to reconstruct fine scale spatial fields from coarser, multi-scale samples (e.g., based on seismic and production data) and sparse fine scale conditioning data (e.g., well data). It is easy to implement and can account for the complex, non-linear interactions between different scales as well as precision of the data at various scales in a consistent fashion. We illustrate our method using a variety of examples that demonstrate the power and versatility of the proposed approach. Finally, a comparison with Sequential Gaussian Simulation with Block Kriging (SGSBK) indicates similar performance with less restrictive assumptions. Introduction A persistent problem in petroleum reservoir characterization is to build a model for flow simulations based on incomplete information. Because of the limited spatial information, any conceptual reservoir model to describe heterogeneities will necessarily have large uncertainty. Such uncertainties can be significantly reduced by integrating multiple data sources into the reservoir model.1 In general, we have hard data such as well logs, cores and soft data such as seismic traces, production history, conceptual depositional model, regional geological analyses etc. Integrating information from these wide variety of sources into the reservoir model is a non-trivial task. This is because different data sources scan different length scales of heterogeneity and can have different degrees of precision.2 Reconciling multi-scale data for spatial modeling of reservoir properties is important because different data types provide different information about the reservoir architecture and heterogeneity. It is essential that reservoir models preserve small scale property variations observed in well logs and core measurements and capture the large-scale structure and continuity observed in global measures such as seismic and production data. A hierarchical model is particularly well-suited to address the multi-scaled nature of spatial fields, match available data at various levels of resolution and to account for uncertainties inherent in the information.1–7 Several methods to combine multiscale data have been introduced in the literature with a primary focus on integrating seismic and well data.7–14 These include conventional techniques such as cokriging and its variations7–11, Sequential Gaussian Simulation with Block Kriging (SGSBK)12 and Bayesian updating of point kriging13,14. Most kriging-based methods are restricted to multi-Gaussian and stationary random fields.7–14 They, therefore, require data transformation and variogram construction. In practice, variogram modeling with a limited data set can be difficult and strongly user dependent. Improper variograms can lead to errors and inaccuracies in the estimation. Thus, one might also need to consider the uncertainty in variogram models during estimation.15 However, conventional geostatistical methods do not provide an effective framework to take into account the uncertainty of the variogram. Furthermore, most of the multiscale integration algorithms assume a linear relationship between the scales.

author list (cited authors)

  • Lee, S. H., Malallah, A., Datta-Gupta, A., & Higdon, D.

citation count

  • 4

publication date

  • January 2000


  • SPE  Publisher