## PP spherical-wave reflection coefficients
for viscoelastic media

**Vlastislav Cerveny**,
**Ivan Psencik** **&**
**Vaclav Bucha**
### Summary

Amplitudes of PP spherical waves reflected at a plane interface
between two homogeneous viscoelastic media are studied. Mostly,
the plane-wave reflection coefficients have been used in such
studies in the past. For viscoelastic media, however, the meaning of
plane-wave reflection coefficients meets some fundamental
difficulties. For this reason, the spherical-wave reflection
coefficients, corresponding to a point source, are used here.
The spherical-wave reflection coefficients were introduced
for perfectly elastic media and were evaluated by approximate
asymptotic high-frequency methods. They can be, however, also
calculated by highly accurate reflectivity method, even for
viscoelastic media. The typical feature of the amplitude of
the spherical-wave reflection coefficient is its behaviour
in the critical region, which differs significantly from
the behaviour of the amplitude of the plane-wave reflection
coefficient. Its maximum is shifted behind the critical point,
and it is followed by the amplitude oscillations in the interference
region with the head wave. The position of the maximum, its magnitude
and the oscillations are frequency-dependent. The purpose of this
study is to show that the position of the maximum of
the spherical-wave reflection coefficient depends only very weakly
on the quality factors *Q* of media above and below
the interface, and can thus hardly be used to determine *Q*
from measurements. Another purpose is to find some other simple
measurable quantities which depend on *Q* more strongly
and would be thus more convenient for the solution of inverse
problem for *Q*. It is shown that one of such quantities
could be the difference between the maximum and following minimum
of the amplitude of the spherical-wave reflection coefficient
in the oscillatory zone behind the critical point.

### Keywords

Spherical-wave reflection coefficients, critical region,
viscoelastic media, reflectivity method

### Whole paper

The paper is available in
PDF (371 kB).

In: Seismic Waves in Complex 3-D Structures, Report 23,
pp. 219-235, Dep. Geophys., Charles Univ., Prague, 2013.