Item

Abstract

The main goals of this thesis are: (i) developing a 3D inversion scheme for controlled-source electromagnetic (CSEM) data in frequency-domain using modern computational concepts; (ii) creating a methodology to invert real datasets including those collected using a three-phase transmitter configuration developed within the research group I have been working with. Three-dimensional inversion of non-stationary electromagnetic fields is a challenging task that, given problems of practical interest, can only be handled through using massively parallel platforms. Therefore, I developed a parallel distributed inversion scheme that runs on modern supercomputers and clusters. Since memory that is required to store vectors, matrices and arrays, as well as workload are distributed evenly among processes, good scalability of the numerical scheme is achieved. A number of technical and numerical challenges were addressed in the implementation. First, I use a direct solver for 3D forward modeling. Since direct solvers have not been widely used for 3D inversions, analysis of advantages and drawbacks of this decision from both technical and numerical points of view is presented. Second, in inversion I calculate and store the Jacobian matrix explicitly. Analysis of memory and time complexities shows that, if a direct solver is used for forward modeling, the calculation of the full Jacobian is feasible for a large amount of practical cases. Advantages of this approach are demonstrated in the following chapters. For the first time in 3D CSEM inversion I study the implicit regularization effect resulting from incomplete solutions of linear least-squares problems using Krylov subspace techniques. This study gives an insight into sources of inverse problem instability. Moreover, several explicit stabilizing functionals have been implemented. In addition to well-known smoothing regularization, this work includes minimum-norm and focusing stabilizers. The application of different regularization techniques helps explore the model space and estimate the bias of individual regularization techniques. Finally, the algorithm developed is applied to the land-based CSEM data collected across the Ketzin CO$_2$ storage formation. I start with data preparation and aim to extract a representable subset of data that permits many inversion runs within reasonable computational time and effectively contains most of subsurface information. Then, the design of inversion and forward modeling grids is presented. A proper discretization of the domain has to (i) minimize negative boundary effects, (ii) provide accurate model responses and (iii) be able to adequately capture subsurface structures resolved during inversion. Different regularization techniques, starting models and several approaches to avoid numerical singularities arising in land-based CSEM studies are studied and compared. The preferred model is selected based on overall misfit. I provide the analysis of data fit, resolution and depth penetration for the preferred model. Finally, it is compared with a regional geological model and shows a good agreement with respect to both structure and lithology. The methodology devised in this work can be generally followed when dealing with real CSEM datasets.