3D anisotropic modelling including free surface
This is an example of a 3-dimensional numerical anisotropic simulation. The table shows the modelling parameters. The animation shows a series of snapshot blocks 37.5 ms apart. The snapshots display the total particle velocity.
The material parameters are those of a transversely isotropic medium, namely Mesaverde sandstone. The axis of symmetry in this modelling example is 45 degrees tilted about a horizontal axis.
enlarged animation (~ 9.7 MB)
|c_11||31.257 * 109 N/m2|
|c_13||3.399 * 109 N/m2|
|c_33||22.487 * 109 N/m2|
|c_44||6.486 * 109 N/m2|
|c_66||8.821 * 109 N/m2|
The source is a vertical point force which lies 10 grid points below the surface. It generates qP-, qSV- and SH-waves at the same time, which have different speeds of propagation. At late times the qSV- and SH-waves are well separated. Two types of head waves can be observed in the cut of the xz-plane: A qSV type wave which is generated, were qP-wave hits the surface. A SH type wave which is generated, were qSV-wave hits the surface.
The amplitudes of the qSV- and the SH-waves are more dominant than those of the qP-wave. Since the symmetry axis is tilted the symmetry is no longer rotational.
Note also the complicated pattern of the waves at the surface (xy-plane), which exhibit a cusp with weak amplitudes.
Due to the clyclicity of the DFTs wrap-around effects can be seen at the sides. Since the modelling volume is surrounded by tapering zones waves leaving one edge are sufficiently damped when entering into the modelling grid at the opposite side.
Tessmer, E., 1995,
3-D seismic modelling of general material anisotropy in the presence of the free surface by a Chebyshev spectral method, Geophys. J. Int., 121, 557-575.