Three-Dimensional Parallel Forward Modeling And Inversion Of Frequency-Domain CSEM Data

Frequency-domain controlled-source electromagnetic (CSEM) methods have long been used for mineral resources exploration, and have also become an established technique for offshore hydrocarbon exploration in addition to traditional seismic methods. To provide sufficiently realistic representations of the subsurface, three-dimensional imaging techniques are required. Inversion is a key step in the CSEM data processing and interpretation. CSEM inversion techniques have been transformed from 1D into 2D, or even 3D currently.The main goal of this thesis is to develop a fast and accurate 3D inverse modeling tool for both land and marine CSEM surveys.Forward modeling is the engine of inverse modeling. Three-dimensional modeling of electromagnetic data is a computationally demanding problem. For frequently-used numerical techniques such as finite-element and finite-difference methods, solving the large linear systems arising from the discretization of Maxwell’s equations is a key step which has a major impact on the applicability of the solution, and it has always been a topic for research that how to solve the linear equations efficiently, robustly and accurately. A 3D modeling scheme based on Cholesky decomposition of the system matrix is presented for CSEM simulating in the frequency domain. The Helmholtz equation in terms of secondary electric fields is discretized using a finite-volume (FV) method over a staggered grid. The resulting linear system of FV equations is solved directly using the massively parallel solver MUMPS. Compared with the most commonly used linear solvers, i.e. Krylov subspace iterative techniques, direct solvers have two major advantages, one is their high accuracy and stability in solving ill-conditioned linear systems, the other is that once the matrix factorization is accomplished, multiple solutions for multi right hand sides can be obtained very quickly. To evaluate the computational performance of the direct solver, a suite of numerical tests on synthetic 1D and 3D models is conducted. The modeling results demonstrate the capability and benefits of the presented scheme.In controlled-source electromagnetic (CSEM) surveys which utilize electric dipole sources, observations can be greatly influenced by the orientation, the length as well as the shape of the source. Nevertheless, most of the presented 3-D CSEM modeling algorithms do not take all these factors into account, and many are only able to deal with very simple source geometries such as a point dipole with a fixed orientation, which may cause significant inaccuracies in the modeling result. Our 3D forward modeling code is capable of simulating complex source geometries, such as arbitrarily orientated finite-length straight/bent wire sources. Since the primary/secondary field approach is employed, the primary fields calculation is the only part of the 3D modeling that source geometries need to be considered. We demonstrate the validity of the 3D code for 1D synthetic models with complex source geometries by comparisons against analytic solutions. Further, we run a suite of 3D forward modeling tests based on 3D models to investigate influences of source geometries.The Jacobian of the forward operator is a key component in all gradient-based inversion methods, including variants on Gauss-Newton and non-linear conjugate gradients. We exhaustively show how to calculate sensitivity via solving quasi-forward problems, including the computation of the full sensitivity and the product of it with any vector. Based on the open-source ModEM (the Modular system for Electromagnetic inversion) system, we developed a code for frequency-domain CSEM 3-D inversion. By doing some numerical experiments on synthetic models, we demonstrate the effectiveness of the code applied to synthetic data.