Open AccessA support‐operator method for viscoelastic wave modelling in 3‐D heterogeneous media
Author(s) -
Ely Geoffrey P.,
Day Steven M.,
Minster JeanBernard
Publication year - 2008
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2007.03633.x
Subject(s) - hexahedron , spurious relationship , wavelength , boundary (topology) , boundary value problem , operator (biology) , polygon mesh , mathematical analysis , viscoelasticity , geometry , mathematics , computer science , physics , finite element method , optics , biochemistry , statistics , chemistry , repressor , gene , transcription factor , thermodynamics
SUMMARY We apply the method of support operators (SOM) to solve the 3‐D, viscoelastic equations of motion for use in earthquake simulations. SOM is a generalized finite‐difference method that can utilize meshes of arbitrary structure and incorporate irregular geometry. Our implementation uses a 3‐D, logically rectangular, hexahedral mesh. Calculations are second‐order in space and time. A correction term is employed for suppression of spurious zero‐energy modes (hourglass oscillations). We develop a free surface boundary condition, and an absorbing boundary condition using the method of perfectly matched layers (PML). Numerical tests using a layered material model in a highly deformed mesh show good agreement with the frequency‐wavenumber method, for resolutions greater than 10 nodes per wavelength. We also test a vertically incident P wave on a semi‐circular canyon, for which results match boundary integral solutions at resolutions greater that 20 nodes per wavelength. We also demonstrate excellent parallel scalability of our code.