Abstract

Stochastic imaging is the process by which alternative, equiprobable images of the spatial distribution of the interest variable are generated. All such images must honour at their locations not only the principal variable but also related soft or indirect information.

Probability computation is a key component of statistical analysis on imaging structures. In the probabilistic approach to expert systems, relationships between variables are depicted as conditional probabilities. It is not an uncommon practice, before feasible computational methods were developed, to divide the image into nuclear characteristics and analyse the data as if the set of images were independently sampled. Such analysis fail to utilise part of the geophysical information provided by some interrelated variables, and hence may not be powerful enough to infer the underlying geophysical mechanism correctly. Especially, for complex structures, which are not only affected by multiple geophysical components, but may be influenced by mathematical operations factors as well.

The purpose of this research is to explore the spatial Markov Chain Monte Carlo (MCMC) method, by means of the Bayesian methodology, to provide practical geostatistics solutions on geophysical extended and complex structures. In reality, for geostatistical problems, reliable implementation of MCMC is not straightforward. The Bayes+Markov algorithm developed in [4] and presented here, allows a full updating of soft information (a priori distribution) by distinguishing the spatial structure of the soft data, it requires no more modelling effort than a traditional multiple indicator kriging. This approach allows generating a posteriori probability distribution for any unsampled value, conditional to both local hard and soft data.

A case study on a synthetic realistic data set that concatenates the joint distribution in 2D space shows that this methodology can yield excellent results.

Introduction

Methods for solving geophysical problems have been greatly influenced by modern statistics and computer methods. These new approaches and methods require few distribution assumptions and can be applied to more complicated estimators. This greatly enhances the practicality for exploring spatial data and drawing valid statistical inferences without the usual concerns for mathematical tractability.

The quality of the interpolation or spatial prediction can be measured by non-parametric assessment of local uncertainty.

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INTEGRATING PETROPHYSICAL RESERVOIR PARAMETERS BY INDIRECT SEISMIC SPATIAL INFORMATION UPDATING

A common problem in reservoir characterisation is that of spatial interpolat

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