3D inversion of frequency-domain CSEM data based on Gauss-Newton optimization
PENG Rong-Hua;HU Xiang-Yun;HAN Bo;Institute of Geophysics and Geomatics,China University of Geosciences;Department of Earth,Ocean and Atmospheric Sciences,University of British Columbia;College of Marine Geosciences,Ocean University of China;
The Controlled-source electromagnetic(CSEM)method in the frequency domain has evolved into an established technique for mineral resources prospecting and hydrocarbon exploration.An increasing trend is to carry out three-dimensional(3D)CSEM surveys as EM explorations now are increasingly conducted in complex geological environments in order to improve the spatial resolution of subsurface conductivity structure.Quantitative interpretation of large-scale CSEM data in the frequency domain requires efficient and stable 3Dforward modeling and inversion codes.Considerable efforts have been contributed to developing numerical algorithms concerning 3Dinversion of CSEM data that can accurately and efficiently recover subsurface electrical structure over last decade.Most existing3 Dinversion algorithms employ Krylov subspace iterative methods as their forward solvers.Iterative techniques usually need little memory due to only matrix-vector products storagerequired,and they are fast for computation of single field solution.However,there are two main issues when using iterative solvers for 3D CSEM problems:(1)The ill-conditioning of linear systems arising from discretization of Helmholtz equation can lead to poor behavior of iterative solvers and even divergence in some cases.(2)Iterative solvers are very time-consuming for multi-source problems.These difficulties become major impediments when solving large-scale multi-source CSEM problems using iterative solvers.Given the availability of more powerful workstations or computer clusters,direct methods have been increasingly used for solving 3D CSEM problems.Compared to iterative methods,direct solvers have several distinct advantages:(1)They provide more accurate solutions.(2)They are less prone to ill-conditioning of matrix, making them more robust for highly heterogeneous models or non-uniform grids.And(3)they separate the solving of linear system into an expensive matrix factorization and comparably inexpensive forward-backward substitution steps,which make them more suitable for multi-source CSEM surveying.In this paper,we present an efficient inversion algorithm for 3Dinversion of multi-frequency and multi-source CSEM data,which is based on a direct solver for solving the forward problem.The Gauss-Newton(GN)optimization algorithm is applied considering its high convergence rate,thus limiting the number of expensive matrix factorization required when using a direct solver.A preconditioned conjugate gradient solver(PCG)is used to solve the normal equation resulted from linearization at each GN iterate,in order 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.In addition,the matrix factorization obtained when solving forward problem can be used in subsequent PCG iterates,which dramatically speeds up PCG iteration and reduces computational costs. Numerical experiments on synthetic data from land and marine CSEM surveys show that our inversion algorithm has an excellent convergence rate and only tens to several tens of iterates are needed to reach desired misfit,demonstrating its efficiency and stability.
【Fund】： 国家自然科学基金(41274077 41474055);; 国家重点基础研究发展计划项目(2013CB733200);; 国家留学基金委(201406410020);; 湖北省自然科学基金(2015CFA019)联合资助
【CateGory Index】： P631.325
【CateGory Index】： P631.325