Stochastic imaging is the process by which alternative<br>and equiprobable images of the spatial distribution of<br>the interest variable are generated. All such images<br>must honor at their locations not only the principal<br>variable but also the related indirect information.<br>Probability computation is a key component of<br>statistical analysis on imaging structures. In the<br>probabilistic approach to expert systems, relationships<br>between variables are depicted as conditional<br>probabilities. It is not an uncommon practice, before<br>feasible computational methods were developed, to<br>divide the image into nuclear characteristics and<br>analyze the data as if the set of images were<br>independently sampled. Such analysis fail to utilize<br>part of the geophysical information provided by some<br>interrelated variables, and hence may not be powerful<br>enough to infer the underlying geophysical<br>mechanism correctly.<br>The purpose of this research is to explore the spatial<br>Markov Chain Monte Carlo (MCMC) method, by<br>means of the Bayesian methodology, to provide<br>practical geostatistics solutions on geophysical<br>extended and complex structures. In reality, for<br>geostatistical problems, reliable implementation of<br>MCMC is not straightforward. The Bayes+Markov<br>algorithm proposed in [4] and developed here, allows<br>a full updating of soft information (a priori<br>distribution) by distinguishing the spatial structure of<br>the soft data and it requires no more modelling effort<br>than a traditional multiple indicator kriging. This<br>approach allows generating a posteriori probability<br>distribution for any unsampled value, conditional to<br>both local hard and soft data.<br>A case study on a synthetic realistic data set that<br>concatenates the joint distribution in 2D space shows<br>that this methodology can yield excellent results.<br>Keywords: Amplitude; Bayesian Modeling; Geostatistics; Impedance;<br>Markovian Calibration.


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