Three-dimensonal Forward Modeling And Inversion Of Frequency-domain CSEM Data

Controlled-source electromagnetic (CSEM) method in frequency domain, as an established geophysical technique, has been widely used for mineral resources prospecting and offshore hydrocarbon reservoir exploration. CSEM method often has the advantages of larger exploration depths, higher lateral and vertical resolution, and better data quality over other EM techniques. An increasing trend is to carry out three-dimensional (3D) CSEM surveys as the EM explorations now increasingly occur in complex geological environments, thus improving the spatial resolution of conductivity structure.Quantitative interpretation of large-scale CSEM data requires efficient and stable 3D forward modeling and inversion codes. The main objective of this thesis is to develop efficient and accurate 3D inversion schemes used for both land and marine CSEM surveys, integrating fresh programming language for scientific computing and advanced numerical algorithms for solving large scale linear equations.Inverse modeling plays a central role in the interpretation of any EM data. From a numerical point of view, inverse modeling can be regarded as an optimization process which heavily relies on the underlying forward modeling engine. So the overarching issue for any efficient inversion scheme is to develop a fast and accurate forward modeling routine. Mimetic finite volume method (FVM) is used to discretized the forward governing equation considering its ability for natural discretization of highly heterogeneous and anisotropic conductivity media. Stable and accurate solution of large linear system resulting from discretization of governing equation will provide solid basis for efficient 3D forward modeling. Two different forward modeling schemes are implemented:one is based on electromagnetic governing equation, the other on vector and scalar potential governing equation in terms of computational cost and memory storage. For both schemes, source singularities are eliminated by a scattering-field approach, in which the total field is split into primary field, which can be computed analytically for a homogeneous or 1D layered media, and secondary field due to the presence of anomalous conductivities deviated from background model. In the first scheme, the system arising from FV discretization of the Helmholtz equation of secondary electric fields is solved using MUMPS direct solver, whereas BiCGSTAB iterative solver is applied to solve the system arising from FV discretization of secondary potential governing equation. Compared to direct solvers, iterative solvers generally required less memory because only matrix-vector products are computed and stored. However, they become expensive for the multi-source problems due to independence of computation over sources, and the performance of iterative solvers are closed related to the conditioning of the system equation. On the other hand, direct solvers involve a resource-demanding (in terms of memory and computational time) matrix factorization step following by inexpensive forward-backward substitution steps for many right hand sides, which are well suitable for multi-source CSEM surveys. Moreover, direct solvers are less affected by ill-conditioning of matrices, providing more stable solutions than iterative ones. A series of numerical experiments have been carried out to test the correctness of 3D forward modeling codes on synthetic 1D layered models for marine- and land-based CSEM surveys. Numerical solutions by our 3D codes demonstrate excellent agreement with quasi-analytic solutions.The EM response of the Earth in a typical CSEM survey involves the combination of three distinct mechanisms:geometric spreading, galvanic effect and inductive effect, among which the later two mechanisms are closely related to the subsurface conductivity structure. In the modeling scheme based on potential governing equation, it is generally considered that the components of the electric field associated with the vector and scalar potentials correspond to the inductive and galvanic contributions to the electric response respectively. Atypical 3D offshore reservoir model is used to investigate the contributions of galvanic and inductive effect to the electric field for marine CSEM method. The results provide important insights into survey design and data interpretation for offshore CSEM surveys in complex geological environments.Gradient-based optimization techniques are extensively used for large scale optimization, several key components of these inverse schemes including computation of sensitivity matrix, selection and update of regularization parameter, and line search strategies for model update have been thoroughly investigated. Two different optimization schemes are implemented corresponding to differing forward modeling routines in order to obtain optimal inversion performance in terms of computational cost and storage requirement. In the first inverse scheme, L-BFGS optimization technique is used in combination with iterative solver for underlying forward engine based on potential governing equation. L-BFGS algorithm only requires sparse approximate of the inverse of Hessian, making it favorable for large scale inverse problem where computational resources are limited. The other one is a GN-based inverse scheme where direct solver is used for the forward problem. Preconditioned conjugate gradient (PCG) algorithm is used to solve the normal equation resulting from linearization at each GN iteration so as to avoid computing and storing sensitivity matrix explicitly. This scheme only requires matrix-vector products of Jocabian and its transpose with vectors, which are equivalent to one forward and one adjoint problem. Therefore the matrix factorization obtained by solving forward problem can be used in subsequent PCG iteration, which dramatically speeds up the computation and reduces the cost.A fresh programming language for scientific computing Julia is used to implement 3D inverse schemes proposed in this thesis. In addition, parallel computation based on frequency- and source- partitioning schemes is developed to speed up the inversion process considering the independence of computations over frequencies and transmitter locations. A suite of numerical experiments are performed on synthetic 3D data from both marine and land CSEM surveys, demonstrating the efficiency and robustness of the newly developed 3D modeling and inversion codes.