This paster was presented at AGU 2001 Fall Meeting, December 10-14, 2001, San Francisco, USA, section S32C-0652 .  

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Efficient 3D Hybrid Ray-Fd Modeling For Elastic Media With Locally Complex Structures

I. Oprsal (1), J. Brokesova (2), D. Giardini (1),

Swiss Seismological Service,
ETH-Hoenggerberg/HPP, CH-8093 Zuerich, Switzerland.
FAX: +41-1-6331065,
Phone: +41-1-6332602,

Department of Geophysics, Charles University,
Ke Karlovu 3, 121 16, Prague, Czech Republic,


A new hybrid ray-FD method combines the ray and the 2nd order finite-difference (FD) approaches. It was designed for computations in large (compared to the wavelength) 3D elastic models containing a complex local (inner) structure embedded in a considerably simpler medium (outer structure).

The hybrid method is based on two successive steps. In the first step, the wavefield propagating in the outer structure is calculated by the ray method. It is incident at the points along a two-fold formal boundary (excitation box, EB) surrounding the inner structure. This provides the input for the second step consisting in calculating the wavefield by the FD method. The FD computational domain contains the EB and its close vicinity. The EB remains fully permeable for all waves propagating within the FD domain.

Asymptotic high frequency solution makes the approach very efficient despite of the two-point ray tracing that is required to connect the source point with the excitation gridpoints. 3D rays are necessary due to arbitrary source-EB configuration, even in case the outer structure is less dimensional (2D, 1D, homogeneous). However, it is still much faster than the whole FD modeling (retaining the advantages of the FD solution) provided the outer structure does not contain too many layers. Then this approach benefits from the efficiency of the ray method in the outer structure while exploiting the wavefield completeness of the FD method.

The hybrid method is applied for models in which the locally complex structure is adjacent to the earth surface and includes topography. The wavefield is due to a double-couple source buried in the outer structure. The outer structure is 1D or 2D containing vertical as well as lateral gradients of medium parameters. The former case allows the results to be compared with DWN-FD hybrid approach replacing the ray method in the first step by discrete wavenumber (DWN) method.

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