Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-14T06:44:23.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Performance Analysis of a High-Order Discontinuous Galerkin Method Application to the Reverse Time Migration

Published online by Cambridge University Press:  20 August 2015

Caroline Baldassari ,
Hélène Barucq ,
Henri Calandra ,
Bertrand Denel  and
Julien Diaz
Caroline Baldassari*
Affiliation:
INRIA Bordeaux Research Center, Project Team Magique3D, Avenue de l’université, 64013 Pau Cedex, France LMA, CNRS UMR 5142, Université de Pau, Avenue de l’université, 64013 Pau Cedex, France
Hélène Barucq*
Affiliation:
INRIA Bordeaux Research Center, Project Team Magique3D, Avenue de l’université, 64013 Pau Cedex, France LMA, CNRS UMR 5142, Université de Pau, Avenue de l’université, 64013 Pau Cedex, France
Henri Calandra*
Affiliation:
TOTAL, Avenue Larribau, 64000 Pau, France
Bertrand Denel*
Affiliation:
TOTAL, Avenue Larribau, 64000 Pau, France
Julien Diaz*
Affiliation:
INRIA Bordeaux Research Center, Project Team Magique3D, Avenue de l’université, 64013 Pau Cedex, France LMA, CNRS UMR 5142, Université de Pau, Avenue de l’université, 64013 Pau Cedex, France
*
Corresponding author.Email:caroline.baldassari@inria.fr
Email address:helene.barucq@inria.fr
Email address:henri.calandra@total.com
Email address:bertrand.denel@total.com
Email address:julien.diaz@inria.fr
Get access

Abstract

This work pertains to numerical aspects of a finite element method based discontinuous functions. Our study focuses on the Interior Penalty Discontinuous Galerkin method (IPDGM) because of its high-level of flexibility for solving the full wave equation in heterogeneous media. We assess the performance of IPDGM through a comparison study with a spectral element method (SEM). We show that IPDGM is as accurate as SEM. In addition, we illustrate the efficiency of IPDGM when employed in a seismic imaging process by considering two-dimensional problems involving the Reverse Time Migration.

Keywords

65M1265M6035L05Interior penalty discontinuous Galerkin methodspectral element methodreverse time migrationseismic imaging process
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 660 - 673
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ainsworth, M., Monk, P., and Muniz, W.. Dispersive and dissipative properties of discontinuous galerkin finite element methods for the second-order wave equation. J. Sci. Comput., 27(1-3), 2006.Google Scholar
[2]Cagniard, L.. Reflection and Refraction of Progressive Seismic Waves. McGraw-Hill, 1962.Google Scholar
[3]Ciarlet, P.G.. The Finite Element Method for Elliptic Problems. North-Holland Publishing Co., Amsterdam, 1978. Studies in Mathematics and its Applications, Vol. 4.CrossRefGoogle Scholar
[4]Claerbout, J.F.. Toward a unified theory of reflector imaging. Geophysics, 36:467–481, 1971.Google Scholar
[5]Cohen, G., Joly, P., Roberts, J.E., and Tordjman, N.. Higher order triangular finite elements with mass lumping for the wave equation. SIAM J. Numer. Anal., 38(6):2047–2078 (electronic), 2001.Google Scholar
[6]Cohen, G., Joly, P., and Tordjman, N.. Construction and analysis of higher order finite elements with mass lumping for the wave equation. In Second International Conference on Mathematical and Numerical Aspects of Wave Propagation (Newark, DE, 1993), pages 152–160. SIAM, Philadelphia, PA, 1993.Google Scholar
[7]Cohen, G., Joly, P., and Tordjman, N.. Higher-order finite elements with mass-lumping for the 1D wave equation. Finite Elem. Anal. Des., 16(3-4):329–336, 1994. ICOSAHOM ‘92 (Montpellier, 1992).CrossRefGoogle Scholar
[8]De Basabe, J. D. and Sen, M. K.. New developments in the finite-element method for seismic propagation simulation. Leading Edge, 28:562–567, 2009.CrossRefGoogle Scholar
[9]De Basabe, J. D. and Sen, M. K.. Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping. Geophys. J. Int., 181:577–590, 2010.CrossRefGoogle Scholar
[10]Hoop, A. T. de. The surface line source problem. Appl. Sci. Res. B, 8:349–356, 1959.Google Scholar
[11]Gazdag, J.. Wave equation migration with the phase-shift method. Geophysics, 43(7):1342–1351, December 1978.Google Scholar
[12]Grote, M.J., Schneebeli, A., and Schözau, D.. Discontinuous Galerkin finite element method for the wave equation. SIAM J. Numer. Anal., 44(6):2408–2431 (electronic), 2006.Google Scholar
[13]Hughes, T.J.R.. The finite element method. Prentice Hall Inc., Englewood Cliffs, NJ, 1987. Linear static and dynamic finite element analysis, With the collaboration of Ferencz, Robert M. and Raefsky, Arthur M..Google Scholar
[14]Gazdag J, J. and Sguazzero, P.. Migration of seismic data by phase shift plus interpolation. Geophysics, 49(2):124–131, February 1984.Google Scholar
[15]Komatitsch, D. and Tromp, J.. Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophys. J. Int., 139:806–822, 1999.Google Scholar
[16]Komatitsch, D., Vilotte, J-P., Vai, R., Castillo-Covarrubias, J.M., and Sanchez-Sesma, F.J.. The spectral element method for elastic wave equations: application to 2d and 3d seismic problems. Int. J. Num. Methods Engr., 45:1139–1164, 1999.3.0.CO;2-T>CrossRefGoogle Scholar
[17]Komatitsch, D. and Vilotte, J.P.. The spectral-element method: An efficient tool to simulate the seismic response of 2d and 3d geological structures. Bulletin of the Seismological Society of America, 88(2):368–392, 1998.CrossRefGoogle Scholar
[18]Stoffa, P.L., Fokkema, R.M, Freire, W.P. de Luna, and Kessinger, . Split-step fourier migration. Geophysics, 55(4):410–421, April 1990.Google Scholar