Rapid frequency domain three-dimensional electromagnetic forward modeling and inversion

The future perspective in electromagnetic (EM) geophysical methods lies in the development of multitransmitter and multireceiver methods. Interpretation of massive electromagnetic data sets is impossible without efficient computerized modeling and inversion capable of handling inhomogeneous three dimensional geological structures. The mathematical complexity and computational cost of the three-dimensional (3-D) EM problems currently prevents extensive use of these methods. The goal of this dissertation is to develop rapid integral-based forward modeling and inversion algorithms to produce geologically meaningful models using limited computer resources.; First, I consider quick, reasonably accurate integral approximations for the solution of the EM forward problem. A new family of approximations based on the quasi-analytical (QA) technique are proposed as a combination of existing approximations, providing not only a fast forward modeling tool, but also a rapid inversion scheme as well.; Accurate EM forward modeling is one of the most difficult and time consuming problems in computational geophysics. In Chapter 3, the solution of the electromagnetic integral equation using iterative schemes is discussed. I introduce the contraction integral equation method, which leads to a new set of diagonal preconditioners. These preconditioners speed up the solution many fold.; The ultimate goal in exploration geophysics is the reconstruction of underground geological structures by inversion of the measured data. In Chapter 4 the aspects of 3-D electromagnetic inversion based on the diagonalized quasi-analytical (DQA) method are studied. The DQA approach provides an extremely fast algorithm enabling practitioners with no supercomputer access to perform inversions on large models and data sets almost interactively. The DQA approach is applied to the inversion of massive synthetic and real data sets. The inversion results show that the method is fast and efficient.