## Vector wavefields for weakly attenuating anisotropic
media by the ray method

**Dirk Gajewski** ** & **
**Ivan Psencik**
### Summary

The ray method is used to compute high-frequency
seismic vector wavefields in weakly attenuating layered
anisotropic structures. The attenuating effects are
introduced by substituting the real elastic parameters
for perfectly elastic media by complex frequency
dependent elastic parameters with small imaginary
parts. The imaginary parts are formally considered to
be of the order of *omega*^{-1}
for *omega* --> +*infinity*. Under this
assumption, it is possible to work with real rays, only
the eikonal is complex. The approximate computations
based on this algorithm are only a few percent
slower than those for perfectly elastic anisotropic
media. The range of applicability of the weak attenuation
concept is investigated by comparison of ray
computations with results of the reflectivity method
for an isotropic, constant gradient model. The study
indicates that the region of applicability of the weak
attenuation concept may be broader than expected. The
combined effects of anisotropy and attenuation on the
propagation of seismic waves in a three-dimensional
model of the uppermost crust with an anisotropic attenuating
layer are then studied. The anisotropy as well as
the attenuation are supposed to be caused by aligned
partially liquid-filled cracks. Hudson's formulas to compute
complex effective elastic parameters are used.
Frequency responses and VSP synthetic seismograms
for different degrees of viscosity of the liquid, and, thus,
different degree of attenuation, show the effects of attenuation
on the propagating waves. Nine-component VSP
vector wavefields are computed for two different source-borehole
directions along the strike of the cracks and 45
degrees off the strike of the cracks. The seismograms for
the attenuating model are compared with seismograms
for the corresponding perfectly elastic model.

### Whole paper

The reprint is available in
PDF (1215 kB !).

*Geophysics*, **57** (1992), 27-38.

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