 |
| Titel |
Structure-preserving spectral element method in attenuating seismic wave
modeling |
| VerfasserIn |
Wenjun Cai, Huai Zhang |
| Konferenz |
EGU General Assembly 2016
|
| Medientyp |
Artikel
|
| Sprache |
en
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 18 (2016) |
| Datensatznummer |
250122283
|
| Publikation (Nr.) |
 EGU/EGU2016-1280.pdf |
|
|
|
|
|
| Zusammenfassung |
| This work describes the extension of the conformal symplectic method to solve the
damped acoustic wave equation and the elastic wave equations in the framework of
the spectral element method. The conformal symplectic method is a variation of
conventional symplectic methods to treat non-conservative time evolution problems
which has superior behaviors in long-time stability and dissipation preservation.
To construct the conformal symplectic method, we first reformulate the damped
acoustic wave equation and the elastic wave equations in their equivalent conformal
multi-symplectic structures, which naturally reveal the intrinsic properties of the original
systems, especially, the dissipation laws. We thereafter separate each structures into
a conservative Hamiltonian system and a purely dissipative ordinary differential
equation system. Based on the splitting methodology, we solve the two subsystems
respectively. The dissipative one is cheaply solved by its analytic solution. While for
the conservative system, we combine a fourth-order symplectic Nyström method
in time and the spectral element method in space to cover the circumstances in
realistic geological structures involving complex free-surface topography. The Strang
composition method is adopted thereby to concatenate the corresponding two parts of
solutions and generate the completed numerical scheme, which is conformal symplectic
and can therefore guarantee the numerical stability and dissipation preservation
after a large time modeling. Additionally, a relative larger Courant number than
that of the traditional Newmark scheme is found in the numerical experiments in
conjunction with a spatial sampling of approximately 5 points per wavelength. A
benchmark test for the damped acoustic wave equation validates the effectiveness of our
proposed method in precisely capturing dissipation rate. The classical Lamb problem is
used to demonstrate the ability of modeling Rayleigh-wave propagation. More
comprehensive numerical experiments are presented to investigate the long-time
simulation, low dispersion and energy conservation properties of the conformal
symplectic method in both the attenuating homogeneous and heterogeneous mediums. |
|
|
|
|
|
|