Mimetic seismic wave modeling including topography on deformed staggered grids

Geophysics

Volumn 79, Issue 3, 2014, Pages T125-T141

  De la Puente, Josep ^a   Ferrer, Miguel ^a   Hanzich, Mauricio ^a   Castillo, José E ^b   Cela, José M ^a  

^a BARCELONA SUPERCOMPUTING CENTER   (Spain)

^b SAN DIEGO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISPERSION (WAVES); SEISMIC WAVES; SEISMOLOGY; SURFACE WAVES; TOPOGRAPHY; WAVE PROPAGATION;

ANALYTICAL AND NUMERICAL SOLUTIONS; FINITE DIFFERENCE SCHEME; FREE SURFACE CONDITIONS; NUMERICAL APPROACHES; NUMERICAL SCHEME; SEISMIC WAVE MODELING; SPATIAL DERIVATIVES; STAIRCASE APPROXIMATION;

FINITE DIFFERENCE METHOD;

DEFORMATION; FINITE DIFFERENCE METHOD; SEISMIC WAVE; TOPOGRAPHY; WAVE MODELING; WAVE PROPAGATION;

EID: 84903575945     PISSN: 00168033     EISSN: 19422156     Source Type: Journal    
DOI: 10.1190/GEO2013-0371.1     Document Type: Article

References (62)

1. Alterman, Z., and F. C. Karal, 1968, Propagation of elastic waves in layered media by finite difference methods: Bulletin of the Seismological Society of America, 58, 367-398.
2. Andrews, D. J., 1976, Rupture propagation with finite stress in antiplane strain: Journal of Geophysical Research, 81, 3575-3582, doi: 10.1029/JB081i020p03575.
3. Appelö, D., and N. A. Petersson, 2009, A stable finite difference method for the elastic wave equation on complex geometries with free surfaces: Communications in Computational Physics, 5, 84-107.
4. Berg, P., F. If, P. Nielsen, and O. Skovgaard, 1994, Analytical reference solutions, in K. Helbig, ed., Modeling the earth for oil exploration: Pergamon Press.
5. Bernth, H., and C. Chapman, 2011, A comparison of the dispersion relations for anisotropic elastodynamic finite-difference grids: Geophysics, 76, no. 3, WA43-WA50, doi: 10.1190/1.3555530.
6. Campman, X., and C. D. Riyanti, 2007, Non-linear inversion of scattered seismic surface waves: Geophysical Journal International, 171, 1118-1125, doi: 10.1111/j.1365-246X.2007.03557.x.
7. Castillo, J., and R. Grone, 2003, A matrix analysis approach to higher-order approximations for divergence and gradients satisfying a global conservation law: SIAM Journal on Matrix Analysis and Applications, 25, 128-142, doi: 10.1137/S0895479801398025.
8. Castillo, J., J. Hyman, M. Shashkov, and S. Steinberg, 2001, Fourth- and sixth-order conservative finite difference approximations of the divergence and gradient: Applied Numerical Mathematics, 37, 171-187, doi: 10.1016/S0168-9274(00)00033-7.
9. Castillo, J. E., and G. F. Miranda, 2013, Mimetic discretization methods: CRC Press
10. Cerjan, C., D. Kosloff, R. Kosloff, and M. Reshed, 1985, A nonreflecting boundary condition for discrete acoustic and elastic wave equations: Geophysics, 50, 705-708, doi: 10.1190/1.1441945.
11. Chaljub, E., P. Moczo, S. Tsuno, P.-Y. Bard, J. Kristek, M. Käser, M. Stupazzini, and M. Kristekova, 2010, Quantitative comparison of four numerical predictions of 3D ground motion in the Grenoble valley, France: Bulletin of the Seismological Society of America, 100, 1427-1455, doi: 10.1785/0120090052.
12. Cruz-Atienza, V. M., and J. Virieux, 2004, Dynamic rupture simulation of non-planar faults with a finite-difference approach: Geophysical Journal International, 158, 939-954, doi: 10.1111/j.1365-246X.2004.02291.x.
13. Davydycheva, S., V. Druskin, and T. Habashy, 2003, An efficient finitedifference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media: Geophysics, 68, 1525-1536, doi: 10.1190/1.1620626.
14. de Hoop, A., 1960, A modification of Cagniard's method for solving seismic pulse problems: Applied Scientific Research, B8, 349-356.
15. de la Puente, J., 2008, Seismic wave propagation for complex rheologies: VDM Verlag, Dr. Müller.
16. Dumbser, M., and M. Käser, 2006, An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes II: The three-dimensional case: Geophysical Journal International, 167, 319-336, doi: 10.1111/j.1365-246X.2006.03120.x.
17. Ely, G. P., S. M. Day, and J.-B. Minster, 2008, A support-operator method for viscoelastic wave modelling in 3-D heterogeneous media: Geophysical Journal International, 172, 331-344, doi: 10.1111/j.1365-246X.2007.03633.x.
18. Fornberg, B., 1988a, Generation of finite difference formulas on arbitrary spaced grids: Mathematics of Computation, 51, 699-706, doi: 10.1090/S0025-5718-1988-0935077-0.
19. Fornberg, B., 1988b, The pseudospectral method; accurate representation of interfaces in elastic wave calculations: Geophysics, 53, 625-637, doi: 10.1190/1.1442497.
20. Garvin,W., 1956, Exact transient solution of the buried line source problem: Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 234, 528-541, doi: 10.1098/rspa.1956.0055.
21. Gibou, F., and R. Fedkiw, 2005, A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem: Journal of Computational Physics, 202, 577-601, doi: 10.1016/j.jcp.2004.07.018.
22. Gottschämmer, E., and K. B. Olsen, 2001, Accuracy of the explicit planar free-surface boundary condition implemented in a fourth-order staggered-grid velocity-stress finite-difference scheme: Bulletin of the Seismological Society of America, 91, 617-623, doi: 10.1785/0120000244.
23. Graves, R. W., 1996, Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences: Bulletin of the Seismological Society of America, 86, no. 4, 1091-1106.
24. Hestholm, S., 1999, Three-dimensional finite difference viscoelastic wave modelling including surface topography: Geophysical Journal International, 139, 852-878, doi: 10.1046/j.1365-246x.1999.00994.x.
25. Hestholm, S., M. Moran, S. Ketcham, T. Anderson, M. Dillen, and G. McMechan, 2006, Effects of free-surface topography on movingseismic-source modeling: Geophysics, 71, no. 6, T159-T166, doi: 10.1190/1.2356258.
26. Hestholm, S., and B. Ruud, 2002, 3D free-boundary conditions for coordinate- transform finite-difference seismic modelling: Geophysical Prospecting, 50, 463-474, doi: 10.1046/j.1365-2478.2002.00327.x.
27. Igel, H., P. Mora, and B. Riollet, 1995, Anisotropic wave propagation through finite-difference grids.: Geophysics, 60, 1203-1216, doi: 10.1190/1.1443849.
28. Käser, M., and M. Dumbser, 2006, An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes I: The twodimensional isotropic case with external source terms: Geophysical Journal International, 166, 855-877, doi: 10.1111/j.1365-246X.2006.03051.x.
29. Käser, M., V. Hermann, and J. de la Puente, 2008, Quantitative accuracy analysis of the discontinuous Galerkin method for seismic wave propagation: Geophysical Journal International, 173, 990-999, doi: 10.1111/j.1365-246X.2008.03781.x.
30. Komatitsch, D., and J. P. Vilotte, 1998, The spectral-element method: Anefficient tool to simulate the seismic response of 2D and 3D geological structures: Bulletin of the Seismological Society of America, 88, 368-392.
31. Kristek, J., P. Moczo, and R. J. Archuleta, 2002, Efficient methods to simulate planar free surface in the 3D 4th-order staggered-grid finitedifference schemes: Studia Geophysica et Geodaetica, 46, 355-381. 10.1023/A:1019866422821.
32. Kristeková, M., J. Kristek, P. Moczo, and S. Day, 2006, Misfit criteria for quantitative comparison of seismograms: Bulletin of the Seismological Society of America, 96, no. 5, 1836-1850, doi: 10.1785/0120060012.
33. Lebedev, V., 1964, Difference analogues of orthogonal decompositions, basic differential operators and some boundary value problems: USSR Computational Mathematics and Mathematical Physics, 4, 449-465.
34. Lee, S.-J., Y.-C. Chan, D. Komatitsch, B.-S. Huang, and J. Tromp, 2009, Effects of realistic surface topography on seismic ground motion in the Yangminshan region of Taiwan based upon the spectral-element method and LiDAR DTM: Bulletin of the Seismological Society of America, 99, 681-693, doi: 10.1785/0120080264.
35. Levander, A. R., 1988, Fourth-order finite difference P-SV seismograms: Geophysics, 53, 1425-1436, doi: 10.1190/1.1442422.
36. Lisitsa, V., and D. Vishnevskiy, 2010, Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity: Geophysical Prospecting, 58, 619-635, doi: 10.1111/j.1365-2478.2009.00862.x.
37. Lisitsa, V., and D. Vishnevsky, 2011, On specific features of the Lebedev scheme in simulating elastic wave propagation in anisotropic media: Numerical Analysis and Applications, 4, 125-135, doi: 10.1134/S1995423911020042.
38. Lombard, B., J. Piraux, C. Gélis, and J. Virieux, 2008, Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves: Geophysical Journal International, 172, 252-261, doi: 10.1111/j.1365-246X.2007.03620.x.
39. Ma, S., R. J. Archuleta, and P. Liu, 2004, Hybrid modeling of elastic P-SV wave motion: A combined finite-element and staggered-grid finitedifference approach: Bulletin of the Seismological Society of America, 94, 1557-1563, doi: 10.1785/012003087.
40. Marfurt, K., 1984, Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations: Geophysics, 49, 533-549, doi: 10.1190/1.1441689.
41. Moczo, P., E. Bystricky, J. Kristek, J. Carcione, and M. Bouchon, 1997, Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures: Bulletin of the Seismological Society of America, 87, 1305-1323.
42. Moczo, P., J. Kristek, M. Galis, E. Chaljub, and V. Etienne, 2011, 3-D finitedifference, finite-element, discontinuous-Galerkin and spectral-element schemes analysed for their accuracy with respect to P-wave to S-wave speed ratio: Geophysical Journal International, 187, 1645-1667, doi: 10.1111/j.1365-246X.2011.05221.x.
43. Moczo, P., J. Kristek, M. Galis, P. Pazak, and M. Balazovjech, 2007, The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion: Acta Physica Slovaca, 57, 177-406, doi: 10.2478/v10155-010-0084-x.
44. Moczo, P., J. Kristek, V. Vavrycuk, R. J. Archuleta, and L. Halada, 2002, 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities: Bulletin of the Seismological Society of America, 92, 3042-3066, doi: 10.1785/0120010167.
45. Molinari, I., 2011, Modeling theEuropeancrust for seismicwave propagation: Ph.D. thesis, Alma Mater Studiorum-Universita degli Studi di Bologna.
46. Nye, J., 2003, An introduction to seismology, earthquakes, and earth structure: Blackwell Publishing.
47. Ohminato, T., and B. A. Chouet, 1997, A free-surface boundary condition for including 3D topography in the finite-difference method: Bulletin of the Seismological Society of America, 87, 494-515.
48. Park, C., R. Miller, and J. Xia, 1999, Multichannel analysis of surface waves: Geophysics, 64, 800-808, doi: 10.1190/1.1444590.
49. Robertsson, J. O. A., 1996, A numerical free-surface condition for elastic/ viscoelastic finite-difference modeling in the presence of topography: Geophysics, 61, 1921-1934, doi: 10.1190/1.1444107.
50. Rojas, O., 2007, Mimetic finite difference modeling of 2D elastic P-SV wave propagation: Qualifying exam report, San Diego State University, Computational Science Research Center.
51. Rojas, O., S. Day, J. Castillo, and L. A. Dalguer, 2008, Modelling of rupture propagation using high-order mimetic finite differences: Geophysical Journal International, 172, 631-650, doi: 10.1111/j.1365-246X.2007.03651.x.
52. Rubio, F., M. Hanzich, A. Farrés, J. de la Puente, M. Ferrer, and J. M. Cela, 2012, Generalized elastic staggered grids on multi-GPU platforms: 82nd Annual International Meeting, SEG, Expanded Abstracts, doi: 10.1190/segam2012-1108.1.
53. Saenger, E. H., N. Gold, and S. A. Shapiro, 2000, Modeling the propagation of elastic waves using a modified finite-difference grid:Wave Motion, 31, 77-92, doi: 10.1016/S0165-2125(99)00023-2.
54. Tarrass, I., L. Giraud, and P. Thore, 2011, New curvilinear scheme for elastic wave propagation in presence of curved topography: Geophysical Prospecting, 59, 889-906.
55. Tessmer, E., D. Kosloff, and A. Behle, 1992, Elastic wave propagation simulation in the presence of surface topography: Geophysical Journal International, 108, 621-632, doi: 10.1111/j.1365-246X.1992.tb04641.x.
56. Virieux, J., 1984, SH-wave propagation in heterogeneous media: Velocitystress finite-difference method: Geophysics, 49, 1933-1942, doi: 10.1190/1.1441605.
57. Virieux, J., 1986, P-SV wave propagation in heterogeneous media: Velocitystress finite-difference method: Geophysics, 51, 889-901, doi: 10.1190/1.1442147.
58. Yee, K., 1966, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media: IEEE Transactions on Antennas and Propagation, P14, 302-307.
59. Zeng, C., J. Xia, R. D. Miller, and G. P. Tsoflias, 2012, An improved vacuum formulation for 2D finite-difference modeling of Rayleigh waves including surface topography and internal discontinuities: Geophysics, 77, no. 1, T1-T9, doi: 10.1190/geo2011-0067.1.
60. Zhang, J., 1997, Quadrangle-grid velocity-stress finite-difference method for elastic-wave propagation simulation: Geophysical Journal International, 131, 127-134, doi: 10.1111/j.1365-246X.1997.tb00599.x.
61. Zhang, W., and X. Chen, 2006, Traction image method for irregular free surface boundaries in finite difference seismic wave simulation: Geophysical Journal International, 167, 337-353, doi: 10.1111/j.1365-246X.2006.03113.x.
62. Zhang, W., Z. Zhang, and X. Chen, 2012, Three-dimensional elastic wave numerical modelling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids: Geophysical Journal International, 190, 358-378, doi: 10.1111/j.1365-246X.2012.05472.x.