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.
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