PP spherical-wave reflection coefficients for viscoelastic media

Vlastislav Cerveny, Ivan Psencik & Vaclav Bucha


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.


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

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