Skip to main content

Advertisement

Log in

A Review of High-Performance Computational Strategies for Modeling and Imaging of Electromagnetic Induction Data

  • Published:
Surveys in Geophysics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. 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).

  2. 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

    Article  Google Scholar 

  • Alumbaugh DL, Newman GA, Prevost L, Shadid JN (1996) Three dimensional, wideband electromagnetic modeling on massively parallel computers. Radio Sci 31:1–23

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Colombo D, Keho T, McNeice G (2012) Integrated seismic-electromagnetic workflow for sub-basalt exploration in northwest Saudi Arabia. Lead Edge 31:42–52

    Article  Google Scholar 

  • Commer M, Newman GA (2008) New advances in three-dimensional controlled-source electromagnetic inversion. Geophys J Int 172:513–535

    Article  Google Scholar 

  • Commer M, Newman GA (2009) Three-dimensional controlled-source electromagnetic and magnetotelluric joint inversion. Geophys J Int 178:1305–1316

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Constable S (2006) Marine electromagnetic methods—a new tool for offshore exploration. Lead Edge 25:438–444

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Farquharson CG, Oldenburg DW (1996) Approximate sensitivities for the electromagnetic inverse problem. Geophys J Int 126:235–252

    Article  Google Scholar 

  • Fox GC (1988) Solving problems on concurrent processors. Prentice Hall, Old Tappan, NJ

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Freund R (1992) Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices. SIAM J Sci Stat Comput 13:425–448

    Article  Google Scholar 

  • Freund R, Nachtigal N (1991) QMR: a quasi-minimal residual method for non-hermitian linear systems. Numer Math 60:315–339

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Greenbaum A (1997) Iterative methods for solving linear systems. SIAM, Philadelphia, PA

    Book  Google Scholar 

  • Gribenko A, Zhdanov MS (2007) Rigorous 3D inversion of marine CSEM data based on the integral equation method. Geophysics 72:73–84

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Hestenes MR, Stiefel E (1952) Methods of conjugate directions for solving linear systems. J Res Natl Bureau Stand 49:409–435

    Article  Google Scholar 

  • Hohmann GW (1975) Three-dimensional induced polarization and electromagnetic modeling. Geophysics 40:309–324

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • Lanczos C (1952) Solution of systems of linear equations by minimized iterations. J Res Natl Bureau Stand 49:33–53

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Mackie RL, Madden TR (1993) Conjugate direction relaxation solutions for 3-D magnetotelluric modeling. Geophysics 58:1052–1057

    Article  Google Scholar 

  • Maresh J, White RS (2005) Seeing through a glass, darkly: strategies for imaging through basalt. First Break 23:27–33

    Google Scholar 

  • Moucha R, Bailey RC (2004) An accurate and robust multi-grid algorithm for 2D resistivity modeling. Geophys Prospect 52:197–212

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Newman GA, Alumbaugh DL (1997) 3-D massively parallel electromagnetic inversion—part I theory. Geophys J Int 128:345–354

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Newman GA, Commer M (2005) New advances in transient electromagnetic inversion. Geophys J Int 160:5–32

    Article  Google Scholar 

  • Newman GA, Commer M (2009) Massively parallel electrical conductivity imaging of the subsurface. J Phys Conf Ser 180:012063

    Article  Google Scholar 

  • Newman GA, Hohmann GW, Anderson WL (1986) Transient electromagnetic response of a three-dimensional body in a layered earth. Geophysics 51:1608–1627

    Article  Google Scholar 

  • Newman GA, Commer M, Carazzone JJ (2010) Imaging CSEM data in the presence of electrical anisotropy. Geophysics 75:51–61

    Article  Google Scholar 

  • Oldenburg DW, Haber E, Shekhtman R (2013) Three dimensional inversion of multisource time domain electromagnetic data. Geophysics 78:E47–E57

    Article  Google Scholar 

  • Plessix RE, Mulder WA (2008) Resistivity imaging with controlled-source electromagnetic data: depth and data weighting. Inverse Prob 24:1–22

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Schenk O, Gärtner K (2004) Solving unsymmetric sparse systems of linear equations with PARDISO. J Future Gen Comput Syst 20(3):475–487

    Article  Google Scholar 

  • Schenk O, Gärtner K (2006) On fast factorization pivoting methods for symmetric indefinite systems. Elec Trans Numer Anal 23:158–179

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Smith JT (1996b) Conservative modeling of 3-D electromagnetic fields, part II: biconjugate gradient solution and an accelerator. Geophysics 61:1319–1324

    Article  Google Scholar 

  • Smith JT, Booker JR (1991) Rapid inversion of two- and three dimensional magnetotelluric data. J Geophys Res 96:3905–3922

    Article  Google Scholar 

  • Spitzer K (1995) A 3D finite difference algorithm for DC resistivity modeling using conjugate gradient methods. Geophys J Int 123:903–914

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Torres-Verdin C, Habashy TM (1995) A two step linear inversion of two dimensional electrical conductivity. IEEE Trans Antenna Propag 43:405–415

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Wang T, Hohmann GW (1993) A finite-difference, time-domain solution for three-dimensional electromagnetic modeling. Geophysics 58:797–809

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Wannamaker PE, Hohmann GW, Ward SH (1984) Magnetotelluric responses of three-dimensional bodies in layered earths. Geophysics 49:1517–1533

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

Download references

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

Authors

Corresponding author

Correspondence to Gregory A. Newman.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10712-013-9260-0

Keywords

Navigation