Abstract
Many geoscientific applications exploit electrostatic and electromagnetic fields to interrogate and map subsurface electrical resistivity—an important geophysical attribute for characterizing mineral, energy, and water resources. In complex three-dimensional geologies, where many of these resources remain to be found, resistivity mapping requires large-scale modeling and imaging capabilities, as well as the ability to treat significant data volumes, which can easily overwhelm single-core and modest multicore computing hardware. To treat such problems requires large-scale parallel computational resources, necessary for reducing the time to solution to a time frame acceptable to the exploration process. The recognition that significant parallel computing processes must be brought to bear on these problems gives rise to choices that must be made in parallel computing hardware and software. In this review, some of these choices are presented, along with the resulting trade-offs. We also discuss future trends in high-performance computing and the anticipated impact on electromagnetic (EM) geophysics. Topics discussed in this review article include a survey of parallel computing platforms, graphics processing units to multicore CPUs with a fast interconnect, along with effective parallel solvers and associated solver libraries effective for inductive EM modeling and imaging.
Similar content being viewed by others
Notes
I consider the beginning of the HPC era circa 1988, with the development of multiple instructions multiple data (MIMD) asynchronous computing architectures (cf. Fox 1988).
One petaflop is equivalent to 1015 operations per second.
References
Alumbaugh DL, Newman GA (1997) 3-D massively parallel electromagnetic inversion—part II. Anal Crosswell Exp Geophys J Int 128:355–363
Alumbaugh DL, Newman GA, Prevost L, Shadid JN (1996) Three dimensional, wideband electromagnetic modeling on massively parallel computers. Radio Sci 31:1–23
Amestoy PR, Duff IS, Koster J, L’Excellent JY (2001) A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J Matrix Anal Appl 23(1):15–41
Amestoy PR, Guermouche A, L’Excellent JY, Pralet S (2006) Hybrid scheduling for the parallel solution of linear systems. Parallel Comput 32(2):136–156
Balay S, Brown J, Buschelman K, Eijkhout V, Gropp WD, Kaushik D, Knepley MG, McInnes LC, Smith BF, Zhang H (2010) PETSc users manual. Tech. Rep. Number ANL-95/11—revision 3.1, Argonne National Laboratory
Börner R-U, Ernst OG, Spitzer K (2008) Fast 3-D simulation of transient electromagnetic fields by model reduction in the frequency domain using Krylov subspace projection. Geophys J Int 173:766–780. doi:10.1111/j.1365-246x.2008.03750.x
Carazzone JJ, Burtz OM, Green KE, Pavlov DA, Xia C (2005) Three-dimensional imaging of marine CSEM data. In: 75th Annual international meeting, SEG, expanded abstracts, pp 575–578
Carazzone JJ, Dickens TA, Green KE, Jing C, Wahrmund LA, Willen DE, Commer M, Newman GA (2008) Inversion study of a large marine CSEM survey. In: 78th Annual international meeting, SEG, expanded abstracts, pp 644–647
Chen J, Dickens T (2009) Effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled-source electromagnetics data. Geophys Prospect 57:61–74
Chen J, Hoversten GM, Vasco D, Rubin Y, Zhou Z (2007) A Bayesian model for gas saturation estimation using marine seismic AVA and CSEM data. Geophysics 72:WA85–WA95
Chen J, Tompkins M, Zhang P, Wilt M, Mackie R (2012) Frequency-domain EM modeling of 3D anisotropic magnetic permeability and analytical analysis. In: 82nd Annual international meeting, SEG extended abstracts, pp 1–5. doi:10.1190/segam2012-0308.1
Chen J, Hoversten GM, Key K, Nordquest G, Cumming W (2012b) Stochastic inversion of magnetotelluric data using a sharp boundary parameterization and application to a geothermal site. Geophysics 77(4):E265–E279. doi:10.1190/geo2011-0430.1
Colombo D, Keho T, McNeice G (2012) Integrated seismic-electromagnetic workflow for sub-basalt exploration in northwest Saudi Arabia. Lead Edge 31:42–52
Commer M, Newman GA (2008) New advances in three-dimensional controlled-source electromagnetic inversion. Geophys J Int 172:513–535
Commer M, Newman GA (2009) Three-dimensional controlled-source electromagnetic and magnetotelluric joint inversion. Geophys J Int 178:1305–1316
Commer M, Newman GA, Carazzone JJ, Dickens TA, Green KE, Wahrmund LA, Willen DE, Shiu J (2008) Massively parallel electrical-conductivity imaging of hydrocarbons using the IBM Blue Gene/L supercomputer. IBM J Res Dev 52(½):93–103
Commer M, Maia FRN, Newman GA (2011) Iterative Krylov solution methods for geophysical electromagnetic simulations on throughput-oriented processing units. Int J High Perform Comput Appl 26(4):378–385. doi:10.1177/1094342011428145
Constable S (2006) Marine electromagnetic methods—a new tool for offshore exploration. Lead Edge 25:438–444
Druskin V, Knizhnerman L (1994) Spectral approach to solving three-dimensional Maxwell’s diffusion equations in the time and frequency domains. Radio Sci 29(4):937–953
Druskin V, Knizhnerman LA, Ping L (1999) New spectral Lanczos decomposition method for induction modeling in arbitrary 3-D geometry. Geophysics 64(3):701–706
Eidesmo T, Ellingsrud S, MacGregor LM, Constable S, Sinha MC, Johansen S, Kong S, Westerdahl FN (2002) Sea Bed Logging (SBL), a new method for remote and direct identification of hydrocarbon filled layers in deepwater areas. First Break 20(3):144–152
Ellingsrud S, Eidesmo T, Johansen S, Sinha MC, MacGregor LM, Constable S (2002) Remote sensing of hydrocarbon layers by seabed logging (SBL): results from a cruise offshore Angola. Lead Edge 21:972–982
Farquharson CG, Oldenburg DW (1996) Approximate sensitivities for the electromagnetic inverse problem. Geophys J Int 126:235–252
Fox GC (1988) Solving problems on concurrent processors. Prentice Hall, Old Tappan, NJ
Franke A, Börner R-U, Spitzer K (2007) Adaptive unstructured grid finite element simulation of two-dimensional magnetotelluric fields for arbitrary surface and seafloor topography. Geophys J Int 171:71–86
Freund R (1992) Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices. SIAM J Sci Stat Comput 13:425–448
Freund R, Nachtigal N (1991) QMR: a quasi-minimal residual method for non-hermitian linear systems. Numer Math 60:315–339
Grayver AV, Streich R, Ritter O (2013) Three-dimensional parallel distributed inversion of CSEM data using a direct forward solver. Geophys J Int 193(3):1432–1446. doi:10.1093/gji/ggt055
Greenbaum A (1997) Iterative methods for solving linear systems. SIAM, Philadelphia, PA
Gribenko A, Zhdanov MS (2007) Rigorous 3D inversion of marine CSEM data based on the integral equation method. Geophysics 72:73–84
Gropp W, Lusk E, Doss N, Skjellum A (1996) A high-performance, portable implementation of the MPI message passing interface standard. Parallel Comput 22:789–828
Habashy TM, Groom RW, Spies BR (1993) Beyond the Born and Rytov approximations: a nonlinear approach to electromagnetic scattering. J Geophy Res 98:1759–1775. doi:10.1029/92JB02324
Heroux MA, Willenbring JM, Heaphy R (2003) Trilinos developers guide part II: ASCI software quality engineering practices version 1.0. Tech. Rep. SAND2003-1899, Sandia National Laboratories
Heroux MA, Salinger AG, Bartlett RA, Thornquist HK, Howle VE, Tuminaro RS, Hoekstra RJ, Willenbring JM, Hu JJ, Willina SA, Kolda T, Lehoucq RB, Long KR, Pawlowski RP, Philipps ET, Stanley KS (2005) An overview of the Trilinos project. ACM Trans Math Softw 31:397–423
Hestenes MR, Stiefel E (1952) Methods of conjugate directions for solving linear systems. J Res Natl Bureau Stand 49:409–435
Hohmann GW (1975) Three-dimensional induced polarization and electromagnetic modeling. Geophysics 40:309–324
Hoversten G, Constable S, Morrison H (2000) Marine magnetotellurics for base-of-salt mapping: Gulf of Mexico field test at the Gemini structure. Geophysics 65:1476–1488
Jegen MD, Hobbs R, Tarits P, Chave A (2009) Joint inversion of marine magnetotelluric and gravity data incorporating seismic constraints: preliminary results of sub-basalt imaging off the Faroe Shelf. Earth Planet Sci Lett 282:47–55
Key K, Ovall J (2011) A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modeling. Geophys J Int 186(1):137–154. doi:10.1111/j.1365-246X2011.05025.x
Krylov A (1931) On the numerical solution of the equation by which in technical questions frequencies of small oscillations of material systems are determined. Izv. Akad. Nauk SSSR 7:491–539 (in Russian)
Lanczos C (1952) Solution of systems of linear equations by minimized iterations. J Res Natl Bureau Stand 49:33–53
Lawlor OS (2009) Message passing for GPGPU clusters. In: CudaMPI: IEEE international conference on cluster computing and workshops, 2009. CLUSTER ‘09, pp 1–8
Li XS, Demmel JW (2003) SuperLU_DIST: a scalable distributed-memory sparse direct solver for unsymmetric linear systems. ACM Trans Math Softw 29(2):110–140
Liu B, Li SC, Nie LC, Wang J, Nie LC, Wang J, Zhang QS (2012) 3D resistivity inversion using an improved Genetic Algorithm based on control method of mutation direction. J Appl Geophys 87:1–8. doi:10.1016/j.jappgeo.2012.08.002
Lu JJ, Wu XP, Spitzer K (2010) Algebraic multigrid methods for 3D DC resistivity modeling. Chin J Geophys. Special issue of the 19th international workshop on electromagnetic induction in the Earth, Beijing, Oct 23–29, 2008, vol 53, pp 700–707
MacGregor L, Andeis D, Tomlinson T, Barker N (2006) Controlled-source electromagnetic imaging of the Nuggets-1 reservoir. Lead Edge 25:984–992
Mackie RL, Madden TR (1993) Conjugate direction relaxation solutions for 3-D magnetotelluric modeling. Geophysics 58:1052–1057
Maresh J, White RS (2005) Seeing through a glass, darkly: strategies for imaging through basalt. First Break 23:27–33
Moucha R, Bailey RC (2004) An accurate and robust multi-grid algorithm for 2D resistivity modeling. Geophys Prospect 52:197–212
Mudge JC, Heinson GS, Thiel S (2011) Evolving inversion methods in geophysics with cloud computing—a case study of an eScience collaboration. In: Proceedings of IEEE eScience, pp 119–125
Newman GA, Alumbaugh DL (1995) Frequency domain modeling of airborne electromagnetic responses using staggered finite differences. Geophys Prospect 43:1021–1042
Newman GA, Alumbaugh DL (1997) 3-D massively parallel electromagnetic inversion—part I theory. Geophys J Int 128:345–354
Newman GA, Alumbaugh DL (1999) 3-D electromagnetic modeling and inversion on massively parallel computers. In: Oristaglio MN, Spies BR (eds) Three-dimensional electromagnetics. Society of exploration geophysicists, Geophysical Developments No. 7, Tulsa OK, pp 299–321
Newman GA, Alumbaugh DL (2000) Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophys J Int 140:410–424
Newman GA, Commer M (2005) New advances in transient electromagnetic inversion. Geophys J Int 160:5–32
Newman GA, Commer M (2009) Massively parallel electrical conductivity imaging of the subsurface. J Phys Conf Ser 180:012063
Newman GA, Hohmann GW, Anderson WL (1986) Transient electromagnetic response of a three-dimensional body in a layered earth. Geophysics 51:1608–1627
Newman GA, Commer M, Carazzone JJ (2010) Imaging CSEM data in the presence of electrical anisotropy. Geophysics 75:51–61
Oldenburg DW, Haber E, Shekhtman R (2013) Three dimensional inversion of multisource time domain electromagnetic data. Geophysics 78:E47–E57
Plessix RE, Mulder WA (2008) Resistivity imaging with controlled-source electromagnetic data: depth and data weighting. Inverse Prob 24:1–22
Plessix RE, van der Sman P (2007) 3D CSEM modeling and inversion in complex geological settings. In: 77th Annual international meeting, SEG, expanded abstracts, pp 589–593
Plessix RE, van der Sman P (2008) Regularized and blocky 3D controlled source electromagnetic inversion. In: 24th Progress in electromagnetic research symposium, abstracts, pp 755–760
Puzyrev V, Koldan J, de la Puente J, Houzeaux G, Vazquez M, Cele J (2013) A parallel finite-element method for 3D controlled-source electromagnetic forward modeling. Geophys J Int 193:678–693. doi:10.1093/gji/ggt027
Schenk O, Gärtner K (2004) Solving unsymmetric sparse systems of linear equations with PARDISO. J Future Gen Comput Syst 20(3):475–487
Schenk O, Gärtner K (2006) On fast factorization pivoting methods for symmetric indefinite systems. Elec Trans Numer Anal 23:158–179
Schwarzbach C, Haber E (2013) Finite-element based inversion for time-harmonic electromagnetic problems. Geophys J Int 193:615–634. doi:10.1093/gji/ggt006
Schwarzbach C, Börner R-U, Spitzer K (2005) 2D inversion of direct current resistivity data using a parallel, multi-objective genetic algorithm. Geophys J Int 162:685–695
Schwarzbach C, Börner R-U, Spitzer K (2011) Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics—a marine CSEM example. Geophys J Int 187:63–74
Smith JT (1992) Conservative modeling of 3-D electromagnetic fields. Paper presented at the 11th workshop on electromagnetic induction in the earth. International association of geomagnetism and aeronomy. Wellington, New Zealand, Aug 26–Sept 2
Smith JT (1996a) Conservative modeling of 3-D electromagnetic fields, part I: properties and error analysis. Geophysics 61:1308–1318
Smith JT (1996b) Conservative modeling of 3-D electromagnetic fields, part II: biconjugate gradient solution and an accelerator. Geophysics 61:1319–1324
Smith JT, Booker JR (1991) Rapid inversion of two- and three dimensional magnetotelluric data. J Geophys Res 96:3905–3922
Spitzer K (1995) A 3D finite difference algorithm for DC resistivity modeling using conjugate gradient methods. Geophys J Int 123:903–914
Spitzer K, Wurmstich B (1999) Speed and accuracy in 3D resistivity modeling. In: Oristaglio ML, Spies BR (eds) Three-dimensional electromagnetics, SEG book series “Geophysical Developments”, No. 7, Society of exploration geophysicists, pp 161–176, Tulsa, OK
Streich R (2009) 3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: direct solution and optimization for high accuracy. Geophysics 74(5):F95–F105. doi:10.1190/1.3196241
Stuart JA, Owens JD (2009) Message passing on data-parallel architectures. In: Proceedings of the 23rd IEEE international parallel and distributed processing symposium
Torres-Verdin C, Habashy TM (1994) Rapid 2.5-dimensional forward modeling and inversion via a new nonlinear scattering approximation. Radio Sci 29:1051–1079
Torres-Verdin C, Habashy TM (1995) A two step linear inversion of two dimensional electrical conductivity. IEEE Trans Antenna Propag 43:405–415
Tuminaro RS, Heroux M, Hutchinson SA, Shadid JN (1999) Official Aztec user’s guide: version 2.1, sand report SAND99-8801J, Sandia National Laboratories
Um E, Harris JM, Alumbaugh DL (2010) 3D time-domain simulation of electromagnetic diffusion phenomena: a finite-element electric-field approach. Geophysics 75:115–126
Um E, Commer M, Newman GA (2013) Efficient pre-conditioned iterative solution strategies for the electromagnetic diffusion in the Earth: finite-element frequency-domain approach. Geophys J Int. doi: 10.1093/gji/ggt071
van der Vorst H (1992) Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J Sci Statist Comput 13:631–644
Vieira da Silva N, Morgan JV, Macgregor L, Warner M (2012) A finite element multifrontal method for 3D CSEM modeling in the frequency domain. Geophysics 77:101–115
Wang T, Hohmann GW (1993) A finite-difference, time-domain solution for three-dimensional electromagnetic modeling. Geophysics 58:797–809
Wang S, de Hoop MV, Xia J (1011) 2011, On 3D modeling of seismic wave propagation via a structured parallel multifrontal direct Helmholtz solver. Geophys Prospect 59:857–873. doi:11/j.1365-2478.2011.00982.x
Wang S, de Hoop MV, Xia J, Li XS (2012) Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3-D anisotropic media. Geophys J Int 191(1):346–366. doi:10.1111/j.1365.246X.2012.05634.x
Wannamaker PE, Hohmann GW, Ward SH (1984) Magnetotelluric responses of three-dimensional bodies in layered earths. Geophysics 49:1517–1533
Weiss CJ, Schultz A (2011) An evaluation of parallelization strategies for low-frequency electromagnetic induction simulators using staggered grid discretizations. In: American geophysical union fall meeting conference proceedings, informatics session, San Francisco
Yang C, Huang C, Lin C (2011) Hybrid CUDA, OpenMP, and MPI parallel programming on multicore GPU clusters. Comput Phys Commun 182(1):266–269
Zach JJ, Bjørke AK, Støren T, Maaø F (2008) 3D inversion of marine CSEM data using a fast finite-difference time-domain forward code and approximate Hessian-based optimization. In: 78th Annual international meeting, SEG, expanded abstracts, pp 614–618
Zhdanov MS, Fang S (1999) 3D electromagnetic inversion based on the quasi-linear approximation. In: Three-dimensional electromagnetics, SEG book series “Geophysical Developments”, No. 7, Society of exploration geophysicist, pp 233–255. Society of Exploration Geophysicists, Tulsa, OK
Acknowledgments
I wish to thank Yasuo Ogawa, Graham Heinson, and other members of the 21st EM Workshop Program Committee for the invitation and opportunity to write this review article. Input from the two referees, Klaus Spitzer and Chester Weiss, also improved the content of the review. Finally, I also wish to acknowledge my employer, Lawrence Berkeley Laboratory, and the U.S. Department of Energy Office of Science for funding, under contract number DE-AC02-05CH11231.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Newman, G.A. A Review of High-Performance Computational Strategies for Modeling and Imaging of Electromagnetic Induction Data. Surv Geophys 35, 85–100 (2014). https://doi.org/10.1007/s10712-013-9260-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10712-013-9260-0