Attenuation vector in heterogeneous, weakly dissipative, anisotropic media

Vlastislav Cerveny, Ludek Klimes and Ivan Psencik


Attenuation vector A plays an important role in the investigation of waves propagating in dissipative, isotropic or anisotropic media. It is defined as the imaginary part of the complex-valued slowness vector p=P+iA. In this paper, simple expressions for the attenuation vector A are derived for seismic body waves propagating in heterogeneous, weakly dissipative, anisotropic media. Ray-theory perturbation method is used, in which the dissipative medium is considered to be a small perturbation of perfectly elastic medium. The general perturbation procedure proposed by Klimes (2002) is very suitable for this purpose, as it does not require to perform ray tracing in dissipative media; the computation of rays in the background perfectly elastic medium, followed by quadratures along them, is quite sufficient. It is shown that the waves propagating in a heterogeneous, weakly dissipative, anisotropic or isotropic medium are, in general, inhomogeneous. This means that their attenuation vector A is not parallel to the propagation vector P. This holds also for waves generated by a point source, propagating in homogeneous anisotropic dissipative media. Exception is a wave generated by a point source in a homogeneous isotropic dissipative medium, where the generated wave is homogeneous. Thus, the commonly used concept of homogeneous waves, used often in isotropic dissipative media, cannot be used in anisotropic dissipative media. The situation is different for plane waves propagating in homogeneous dissipative isotropic or anisotropic media. In this case, the homogeneity or inhomogeneity of the plane wave depends on initial conditions, which may be chosen freely. It is also shown that the intrinsic attenuation factor Ain, defined as twice the projection of A into the direction of the reference ray, does not depend on the weak inhomogeneity of the wave, and represents a convenient measure of material dissipation. The intrinsic attenuation factor is used to determine the position and direction dependent quality factor Q for heterogeneous anisotropic weakly dissipative media.


Anisotropy, attenuation, attenuation vector, inhomogeneous waves, perturbation ray theory, viscoelasticity.

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In: Seismic Waves in Complex 3-D Structures, Report 17, pp. 195-212, Dep. Geophys., Charles Univ., Prague, 2007.
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