Improving local mean stress estimation using Bayesian hierarchical modelling

Local mean stress state is an important parameter to many rock mechanics and geomechanics applications, yet its estimation may be subject to large uncertainty owning mainly to the usual limited number of high-quality stress data and the potentially significant natural variability of stresses in a rock volume. Hence, it is essential to quantify and reduce uncertainty in local mean stress estimation. This paper proposes a novel Bayesian hierarchical model that both probabilistically quantifies uncertainty in local mean stress estimation and allows logical borrowing of information across stress data from nearby locations. By application to both real-world and simulated stress data, our results show that the hierarchical model can improve local mean stress estimation simultaneously at each location in terms of uncertainty reduction in comparison to the customary approach. This improved probabilistic estimation has further benefits in that it not only allows for probabilistic implementation of further analyses in other applications involving mean stresses, but also gives more accurate analysis results.