Using direct solvers in 3D CSEM modeling and inversion

2. Using direct solvers in 3D CSEM modeling and inversion Three-dimensional modeling and inversion of controlled-source electromagnetic (CSEM) data is highly demanding on computer time and memory. Forward modeling typically proceeds by formulating the problem in terms of a linear system of equations, and solving this system using either iterative or direct solution approaches. For sufficiently small (e.g., 2D) problems, direct solvers may be preferable to iterative ones because of their efficiency for multi-source problems, and because of their ability to solve ill-conditioned problems for which iterative solvers may fail to converge (e.g., models containing strongly non-uniform meshes). With recent growth of computer power, direct solvers can now also be applied for solving 3D CSEM modeling problems of useful dimensions. In addition, matrix decompositions produced for forward modeling can be re-used in inversion for calculating Jacobians. This permits efficient implementations of Gauss-Newton type inversions within a direct-solver framework. I will present an implementation of a finite-difference frequency-domain forward modeling algorithm that makes use of the MUMPS direct solver. The modeling scheme is stabilized at low frequencies by explicitly including a divergence condition into the system of equations. The practical applicability of this algorithm is demonstrated by simulating 3D data corresponding to the survey setup of a recent land CSEM survey. Simulating this survey requires using a model volume of 14.3 x 9 x 5 km; the model contains up to 7.4 million unknowns. An additional modeling challenge is posed by the source location at the air-ground interface. In the actual survey, a new three-phase transmitter was used that was coupled to the subsurface by three grounded electrodes. First synthetic inversion studies will also be outlined, suggesting that the direct approach is becoming computationally feasible and may constitute an alternative to iterative methods in the future. Dr. Rita Streich Dr. Rita Streich is the Junior Research Group Leader for geophysical exploration within GeoEn. She is currently developing controlled-source electromagnetic methodology and instrumentation for exploration of new energy resources and monitoring of geoenergy sites. Current activities include the further development of multidimensional forward modeling and inversion schemes especially for on-shore controlled-source EM data, development of data processing tools and algorithms, and development and testing of transmitter technology. Monday, December 12, 2011 Room 90-2063 10:30 AM – 12:00 PM Host: Greg Newman, ESD Geophysics Department, GANewman@lbl.gov, 510.486.6887 Helmholtz Centre Postdam GFZ German ResearchCentre for Geosciences

4. Using direct solvers in 3D CSEM modeling and inversion December 12, 2011 Room 90-2063 10:30 AM – 12:00 PM Helmholtz Centre Postdam GFZ German ResearchCentre for Geosciences Dr. Rita Streich is the Junior Research Group Leader for geophysical exploration within GeoEn. She is currently developing controlled-source electromagnetic methodology and instrumentation for exploration of new energy resources and monitoring of geoenergy sites. Current activities include the further development of multidimensional forward modeling and inversion schemes especially for on-shore controlled-source EM data, development of data processing tools and algorithms, and development and testing of transmitter technology. Three-dimensional modeling and inversion of controlled-source electromagnetic (CSEM) data is highly demanding on computer time and memory. Forward modeling typically proceeds by formulating the problem in terms of a linear system of equations, and solving this system using either iterative or direct solution approaches. For sufficiently small (e.g., 2D) problems, direct solvers may be preferable to iterative ones because of their efficiency for multi-source problems, and because of their ability to solve ill-conditioned problems for which iterative solvers may fail to converge (e.g., models containing strongly non-uniform meshes). With recent growth of computer power, direct solvers can now also be applied for solving 3D CSEM modeling problems of useful dimensions. In addition, matrix decompositions produced for forward modeling can be re-used in inversion for calculating Jacobians. This permits efficient implementations of Gauss-Newton type inversions within a direct-solver framework. I will present an implementation of a finite-difference frequency-domain forward modeling algorithm that makes use of the MUMPS direct solver. The modeling scheme is stabilized at low frequencies by explicitly including a divergence condition into the system of equations. The practical applicability of this algorithm is demonstrated by simulating 3D data corresponding to the survey setup of a recent land CSEM survey. Simulating this survey requires using a model volume of 14.3 x 9 x 5 km; the model contains up to 7.4 million unknowns. An additional modeling challenge is posed by the source location at the air-ground interface. In the actual survey, a new three-phase transmitter was used that was coupled to the subsurface by three grounded electrodes. First synthetic inversion studies will also be outlined, suggesting that the direct approach is becoming computationally feasible and may constitute an alternative to iterative methods in the future. Host:/Contact Info: Greg Newman ESD Geophysics Department GANewman@lbl.gov 510.486.6887 Dr. Rita Streich