Numerical Algorithms for Cooperative Imaging of Complex Geological Regions

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Many different types of data are collected in order to image the subsoil. Corresponding modeling techniques are used, generally independently, to represent different geological features and calculate model responses. Our aim is to develop a methodology to make of this a cooperative enterprise. The principal investigator has already developed seismic inversion techniques, with fairly sophisticated three dimensional modeling of material interfaces. He is nor achieving similar capabilities for other methods, including magnetotelluric inversion. Multiobjective optimization is the mathematical technique on which we are basing our approach. It provides a natural setting for the cooperative fitting of multiple models to corresponding data sets, when the models have coupling unknown parameters. Usually, when run independently, these different techniques will produce conflicting results. Our multiobjective algorithm employs quadratic programming to calculate weights that scalarize the vector of misfit functionals, while trying to model the user's preferences with respect to a set of proposed parameter vectors. The algorithm attempts to generate Pareto optimal parameter vectors for the user's consideration.