Time-averaged and time-dependent energy-related quantities of waves propagating in inhomogeneous viscoelastic anisotropic media

Vlastislav Cerveny & Ivan Psencik


The energy-flux vector plays an important role in various wave propagation problems. In acoustics and seismology, the main attention has been devoted to the time-averaged energy flux of time-harmonic wave fields propagating in non-dissipative, isotropic and anisotropic media. In this paper, we investigate the energy-flux vector and other energy-related quantities of wave fields propagating in inhomogeneous anisotropic viscoelastic media. These quantities satisfy energy-balance equations, which have, as we show, formally different forms for real-valued wave fields with arbitrary time dependence and for time-harmonic wave fields. In case of time-harmonic wave fields, we do not study only time-averaged, but also time-dependent constituents of the energy-related quantities. We show that the energy-balance equations for time-harmonic wave fields can be obtained in two different ways. First, using real-valued wave fields in the real-valued equation motion and stress-strain relation. Second, using complex-valued wave fields in the complex-valued equation motion and stress-strain relation. Both approaches, when used for the Kelvin-Voigt viscoelastic model, yield the same expressions for the time-averaged and time-dependent constituents of all energy-related quantities and the same energy-balance equations. The latter approach is more powerful, as it can be applied to media of unrestricted anisotropy and viscoelasticity.


Viscoelastic anisotropic media, energy-flux vector, time-averaged energy-related quantities, time-dependent energy-related quantities.

Whole paper

The image of the paper in GIF 150dpi (742 kB) is designed for an instant screen preview.

The paper is available in PostScript (294 kB) and GZIPped PostScript (125 kB).

In: Seismic Waves in Complex 3-D Structures, Report 16, pp. 179-195, Dep. Geophys., Charles Univ., Prague, 2006.
SW3D - main page of consortium Seismic Waves in Complex 3-D Structures .