Borehole Wave Propagation In Isotropic And Anisotropic Media I: Finite Difference Method
In this paper we developed a 3-D finite difference method to simulate wave propagations in an isotropic medium. The wave equation is formulated into the first-order hyperbolic equations by using velocity and stress and then discretizing it on a staggered grid. The 3-D time domain finite differenc...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Technical Report |
| Published: |
Massachusetts Institute of Technology. Earth Resources Laboratory
2012
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| Online Access: | http://hdl.handle.net/1721.1/75224 |
| Summary: | In this paper we developed a 3-D finite difference method to simulate wave propagations
in an isotropic medium. The wave equation is formulated into the first-order hyperbolic
equations by using velocity and stress and then discretizing it on a staggered grid. The
3-D time domain finite difference scheme is second order accurate in time and fourth
order accurate in space. The grid dispersion and anisotropy are analyzed and the stable
condition of the scheme is obtained. Higdon's absorbing boundary condition is discussed
and generalized to the anisotropic medium. The scheme can provide realistic 3-D wave
propagation simulation by the use of a parallel computer.
The scheme is tested in the homogeneous medium. The finite difference results
agree excellently with the analytic solutions of a point explosion source in the acoustic
medium and a point force source in the elastic medium. The finite difference method
accurately models not only the far field P and S waves, but also the near field term. It
demonstrates that the second-order Higdon's absorbing boundary condition works very
well in an acoustic and elastic medium. |
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