A Bayesian Framework of Uncertainties Integration in 3D Geological Model

3D geological model can describe complicated geological phenomena in an intuitive way while its application may be limited by uncertain factors. Great progress has been made over the years, lots of studies decompose the uncertainties of geological model to analyze separately, while ignored the comprehensive impacts of multi-source uncertainties. Great progress has been made over the years, while lots of studies ignored the comprehensive impacts of multi-source uncertainties when analyzed them item by item from each source. To evaluate the synthetical uncertainty, we choose probability distribution to quantify uncertainty, and propose a bayesian framework of uncertainties integration. With this framework, we integrated data errors, spatial randomness, and cognitive information into posterior distribution to evaluate synthetical uncertainty of geological model. Uncertainties propagate and cumulate in modeling process, the gradual integration of multi-source uncertainty is a kind of simulation of the uncertainty propagation. Bayesian inference accomplishes uncertainty updating in modeling process. Maximum entropy principle makes a good effect on estimating prior probability distribution, which ensures the prior probability distribution subjecting to constraints supplied by the given information with minimum prejudice. In the end, we obtained a posterior distribution to evaluate synthetical uncertainty of geological model. This posterior distribution represents the synthetical impact of all the uncertain factors on the spatial structure of geological model. The framework provides a solution to evaluate synthetical impact on geological model of multi-source uncertainties and a thought to study uncertainty propagation mechanism in geological modeling.