One of the biggest challenges in assessing the long-term stability of the geological environment is modelling the development of faulting (e.g. Plate 1, below) in regions where faults or fractures zones are not known to exist or are very sparse. Moreover, the existence of faults beneath the surface may not be known due to being obscured by sediments or volcanic products. In such cases it is virtually impossible to make spatial and/or spatio-temporal estimates deterministically. Probabilistic approaches on the other hand offer one way of making future and/or current snap-shot estimates, quantifying uncertainties and degrees of conservatism. In particular for regions with few or no faults, it is necessary to include some other dataset or information. One powerful tool that can be used in such circumstances is Bayesian inference. This method, first thought up by the Rev. Thomas Bayes in 1763, essentially involves combining one or more sets of information to a priori knowledge yielding a posteriori probabilities.
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| Plate 1: Outcrop of the Itoigawa-Shizuoka Tectonic Line (ISTL), central Japan. | Figure 1: Probability of a new active fault (>100m length) developing in NE Japan, conditioned on shallow crustal low P wave velocity perturbation. |
At Quintessa, we have developed a probabilistic methodology based on the Bayesian paradigm for making spatial and/or spatio-temporal predictions of faulting/fracturing for both regional and local (URL/repository) scales. The underlying concept involves modelling spatial patterns of known faulting/fracturing through point process models (e.g., nearest-neighbours, kernel functions) and/or extreme value statistics, and incorporating this through the Bayesian concept to a geological or geophysical model. For example, Figure 1 (above) shows the probability of one or more active faults (>100m in length) forming on a regional scale in 100,000 years using Bayesian inference. Here probability estimates of active faulting were made using only one geophysical dataset (in this case shallow depth P-wave velocity perturbation) and known locations of active faults (black diamonds). The real strength of the method lies in the fact that as additional information (e.g., recent shallow earthquakes, GPS data, uplift etc) become available, such datasets can be readily incorporated into the model.