Bayesian Inversion in Hidden Markov Models with Varying Marginal Proportions

Knowledge of the sub-surface characteristics is crucial in many engineering activities. Sub-surface soil classes must, for example, be predicted from indirect measurements in narrow drill holes and geological experience. In this study, the inversion is made in a Bayesian framework by defining a hidden Markov chain. The likelihood model for the observations is assumed to be in factorial form. The new feature is the specification of the prior Markov model as containing vertical class proportion profiles and one reference class transition matrix. A criterion for selection of the associated non-stationary prior Markov model is introduced, and an algorithm for assessing the set of class transition matrices is defined. The methodology is demonstrated on one synthetic example and on one case study for offshore foundation of windmills. It is concluded that important experience from the geologist can be captured by the new prior model and that the associated posterior model is, therefore, improved.