Inversion methods and resolution analysis for the 2D/3D reconstruction of resistivity structures from DC measurements

TLDR: In this article, the authors dealt with the multi-dimensional reconstruction of the earth's conductivity distribution based on DC resistivity data, which represents a nonlinear and ill-posed minimization problem with many degrees of freedom.

Abstract: The presented thesis deals with the multi-dimensional reconstruction of the earth’s conductivity distribution based on DC resistivity data. This task represents a nonlinear and ill-posed minimization problem with many degrees of freedom. In this work, techniques for regularization and controlling of this problem are depicted and classified. Particularly, it is concentrated on explicit regularization types, which impose constraints onto the model. The system of equations as resulting from the application of the Gauss-Newton minimization can be solved efficiently. Furthermore, it is shown how the regularization strength can be controlled. The method of non-linear resolution analysis plays a central role in the thesis. It represents a powerful tool to estimate the quality of inversion results. Furthermore, the derived resolution measures provide the basis for the optimization of experimental design concerning information content and efficiency. Methods of error estimation, forward modeling and the calculation of the Jacobian matrix for DC resistivity data are developed. Procedures for appropriate parameterization and inversion control are pointed out by studies of synthetic models. Different inversion and regularization methods are examined in detail. A linearized study is used to compare different data sets considering their efficiency. Moreover, a triplegrid-technique for the incorporation of topography into three-dimensional inversion is presented. Finally the inversion methods are applied to field data. The depicted optimization strategies are realized in practice, which increases the economic relevance of threedimensional data acquisition. The structure of the subsurface is imaged in detail for several applications in the fields of cavity detection, archaeology and the investigation of ground falls. The resolution analysis is successfully established to appraise the obtained results.