Commun. Comput. Phys., 5 (2009), pp. 84-107.

A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces

Daniel Appelo 1*, N. Anders Petersson 2

1 Department of Mechanical Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
2 Center for Applied and Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

Received 3 January 2008; Accepted (in revised version) 6 May 2008
Available online 15 July 2008


A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented. The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface, Dirichlet and periodic boundary conditions. The fully discrete version of the method conserves a discrete energy to machine precision.

AMS subject classifications: 65M06, 74B05, 86A15

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Key words: Elastic wave equation, curvilinear grids, finite differences, stability, energy estimate, seismic wave propagation.

*Corresponding author.
Email: (D. Appelo), (N. A. Petersson)

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