Mathematics (Dec 2022)
Revisited Bayesian Sequential Indicator Simulation: Using a Log-Linear Pooling Approach
Abstract
It has been more than a decade since sequential indicator simulation was proposed to model geological features. Due to its simplicity and easiness of implementation, the algorithm attracts the practitioner’s attention and is rapidly becoming available through commercial software programs for modeling mineral deposits, oil reservoirs, and groundwater resources. However, when the algorithm only uses hard conditioning data, its inadequacy to model the long-range geological features has always been a research debate in geostatistical contexts. To circumvent this difficulty, one or several pieces of soft information can be introduced into the simulation process to assist in reproducing such large-scale settings. An alternative format of Bayesian sequential indicator simulation is developed in this work that integrates a log-linear pooling approach by using the aggregation of probabilities that are reported by two sources of information, hard and soft data. The novelty of this revisited Bayesian technique is that it allows the incorporation of several influences of hard and soft data in the simulation process by assigning the weights to their probabilities. In this procedure, the conditional probability of soft data can be directly estimated from hard conditioning data and then be employed with its corresponding weight of influence to update the weighted conditional portability that is simulated from the same hard conditioning and previously simulated data in a sequential manner. To test the algorithm, a 2D synthetic case study is presented. The findings showed that the resulting maps obtained from the proposed revisited Bayesian sequential indicator simulation approach outperform other techniques in terms of reproduction of long-range geological features while keeping its consistency with other expected local and global statistical measures.
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