Topics: I am interested in how to combine information is a consistent way such that decision makers can take decisions on an as informed base as possible. On example is the integration of strcutural geological infomation with geophysical information.
Ideally any decision related to the subsurface needs to be taken on an as informed base as possible. Consider the question: “What is the probability that the pollution at location A is connected through a high permeable path to location B?”. This question cannot be answered directly from a resistivity model obtained inversion of e.g. geophysical data. One need also to know something about the relation between resistivity and permeability, and other available information. Traditionally different types of information are combined in a sequential workflow, where 1) geophysical data are inverted to a resistivity model, 2) which is converted into a conceptual geological model, 3) which is converted into a model of permeability, 4) …
It is difficult, if not in practice impossible, to maintain a full model of uncertainty and consistency with all types of information. The probabilistic approach to inverse problems offers an intriguing alternative in which all information is combined into one consistent ‘a posteriori’ probability density. This is especially appealing to decision makers, as they do not need to be experts with respect to the different types of information available. It is enough that they can ask the correct question, such as the one given above.
Current state of the art geostatistical simulation methods and sampling algorithms allow to, in principle, combine very complex structural geological information with dense geophysical atasets, using sampling methods. In practice however, the computational requirements can be huge. A key challenge is how one can reduce the computational requirements, while still providing decision makers a useful tool. The following three topics will be considered in this respect.
A key problem is how to obtain a computationally tractable problem, while at the same time solving the original problem without adding any bias to the solution (the posterior probability density). These challenges will be addressed and illuminated by cases related to