HR: 0800h
AN: S31B-1056    [Abstracts]
TI: Numerical Demonstration of A New Method of Computing Wave Fields as A Realization of An Isolated Linear Dynamic System Excited Periodically
AU: * Nagai, T
EM: nagai@itc.nagoya-u.ac.jp
AF: Information Technology Center, Nagoya University, Chikusa, Nagoya, 464-8601 Japan
AU: Ishii, K
EM: ishii@itc.nagoya-u.ac.jp
AF: Information Technology Center, Nagoya University, Chikusa, Nagoya, 464-8601 Japan
AU: Kumazawa, M
EM: mkumazawa@eps.nagoya-u.ac.jp
AF: School of Envronmental Science, Nagoya University, Chikusa, Nagoya, 464-8601 Japan
AU: Kumazawa, M
EM: mkumazawa@eps.nagoya-u.ac.jp
AF: Tono Geoscience Center, Akeyo-cho, Mizunami, 509-6132 Japan
AB: A strong demand exists for the computation code of wave field in an arbitrary medium excited by a sinusoidal force for the system designing in ACROSS technology and also for the data analysis. Numerical examination is made on the new method of wave field computation proposed by Kumazawa et al., (2003). The theory is expected to be applied commonly to both elastic and electromagnetic waves in any heterogeneous medium with anisotropy and frequency dependent property. Wave field $w(t,x)$ is described by an inhomogeneous differential equation of the second order with respect to time and space, $DW = e$, where $D$ ($= p_1(\partial /\partial t)^2+\nabla (p_2 \nabla)$ ) is a dynamic operator ($p_1$ & $p_2$: two material parameters, $\nabla$: nabla) and $e$ is an excitation as an inhomogeneous term. Whereas the spatial discontinuity in $p_1$ & $p_2$ does not allow the space-differentiation in ordinary sense, we do differentiate all parameters and variables in wave equation by introducing hyper-function in their description in space. Then we can rewrite the wave equation in a local form of $D(\omega , \kappa, x)w(x)=e(x)$, where both $\omega$ and $\kappa$ originate from time and space derivatives, respectively. The consequence is the derivation of a set of two linear dynamic system equations of global nature; $D(\omega , \kappa',\kappa)w(\omega ,\kappa)$ = $e(\omega , \kappa')$ and $w(\omega , \kappa ) = R(\omega , \kappa ,\kappa') e(\omega , \kappa')$, which are mutually inverse with $DR=1$ at a specified frequency $\omega$, where $\kappa$ and $\kappa'$ are wavenumber vectors of wave field and excitation, respectively. The $R(\omega , \kappa ,\kappa')$ is the `frequency-wavenumber response characteristics', relating the wavenumber spectrum of excitation $e(\omega , \kappa')$ to that of the wave field $w(\omega , \kappa)$ linearly. Validity of this theory is numerically demonstrated with a simple model in 1D medium. There are two paths to derive $R(\omega , \kappa ,\kappa')$ numerically from $D(\omega , \kappa , x)$ : Path-1 via $D(\omega , \kappa',\kappa)$ involving large matrix inverse leads to more accurate result, whereas path-2 via $1/D(\omega , \kappa , x)$ without large computational load gives only approximate solution to data.
DE: 7223 Seismic hazard assessment and prediction
DE: 7260 Theory and modeling
DE: 7200 SEISMOLOGY
SC: Seismology [S]
MN: 2004 AGU Fall Meeting