Towards Combining Probabilistic, Interval, Fuzzy Uncertainty, and Constraints: An Example Using the Inverse Problem in Geophysics

Combining uncertainty models within cyberinfrastructure is a challenging problem. The main objective of cyberinfrastructure is to be able to seamlessly move data between different databases (where this data is stored in different formats), to feed the combined data into a remotely located program (which may require yet another data format), and to return the result to the user. It is also important to gauge the quality and accuracy of this result. We may have different models for describing uncertainty of different databases and programs; it is therefore important to be able to combine different uncertainty models. A case study: The seismic inverse problem. The existing techniques for solving the seismic inverse problem, such as Hole's tomographic inversion code [2], only take into account the measurement results. Expert geophysicists also have some prior knowledge about the structure of the region. If we could take this prior knowledge into account when processing the geophysical measurements, this would greatly improve the accuracy of the geophysical structures uncovered by solving the inverse problem and also aid the inversion to converge. Probabilistic prior knowledge. Measurement results often come with probabilistic uncertainty (i.e., we know the probabilities of different values of measurement errors). As a result o