On the inversion of potential field data : physical property estimations and model geometry changes

Inversion tools for potential field data are especially important for multi-method or integrated modeling approaches. Computational developments and the increasing amount of, e.g. gravity gradient data from satellite missions, also lead to increasingly complex models. Furthermore, forward modeling of gradient data is rather non-intuitive and inverse methods are preferable. This thesis focuses on the development of inversion tools for potential field data, aiming at the inversion of physical properties and the optimization of model geometries, that are applicable to models of varying geometric representations. The first part regards the estimation of physical properties of subsurface models that are built of voxels or have a fixed geometry based on polyhedral model bodies. This inversion task allows the application of a linear method: The Minimum Mean Square Error(MMSE) method utilizes the mean square approach and Gaussian random variables within a statistical framework. A previous implementation of the method is extended and new features include inversion of all gravity tensor components, combined inversion of all available data sets, correlations between voxels and exact calculation of the potential fields in contrast to mass point approximation. The application of the tool in different case studies is shown: The tests involve a conceptional salt structure in voxel representation and two polyhedron-based models from the North German Basin for synthetic applications. A fourth model, describing the Capel and Faust Basins offshore Queensland, Australia, is given in both geometric representations and allows a comparative method assessment. Results show that the voxel tool performs well when the inversion is constrained by additional information, guiding the estimations and reducing ambiguity. The polyhedron tool is quite fast and provides improvements for the model densities. To evaluate the results, anomaly sensitivities towards model bodies are calculated and discussed. In some cases the property estimation alone is not sufficient to achieve a satisfying interpretation of the subsurface. Therefore, the second part of the thesis deals with automated geometry modifications and anomaly fitting. When addressing model geometries, the inverse problem becomes non-linear and can no longer be solved with the previous method. An optimization tool was designed which modifies vertex-based model geometries by applying spatial operators to the model that use an adaptive, on-the-fly model discretization. These operators deform the existing model via vertex-dragging and their defining parameters are subject to the optimization process. This parametrization causes a strong reduction of unknowns (dimensionality of the search space), allows a variety of possible modifications and ensures that geometries are not destroyed by crossing polygon lines or punctured planes. A Particle Swarm Optimization (PSO) is implemented as a global searcher with restart option for the task of finding optimal operator parameters. The tool estimates an ensemble of model solutions which allows a selection and geologically reasonable interpretations. Although designed for 3D applications, the novel approach is implemented here in 2D and two case studies are shown: One model is a synthetic salt structure in a horizontally layered background model. Expected geometry modifications are considerably small and localized and the initial models contain rather little structural information. The Capel and Faust Basins model from the first part of the thesis provides the large scale example for the second study. With the aim to evaluate the seismically derived model, large scale operators are applied that mainly cause depth adjustments to the model horizons. In these case studies, that are used to test the parametrization and the performance of the optimization with varying set-ups, the developed tool performs well which is promising for future applications. Both presented tools and examples show the usefulness of potential field inversion and should be implemented in a multi-method workflow.