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Anisotropic Attenuation and Material Symmetry

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The internal structure of a material (as, e.g., expressed by the stiffnesses) dictates the dependence of the quality factor Q on direction. Therefore, the attenuation should have at least the symmetry of the crystallographic form of the material. To investigate this property, we compare three different constitutive equations for modeling anisotropic attenuation of wave propagation in rocks. The present analysis considers media with symmetries ranging from orthorhombic to transversely isotropic with the anelasticity described by a relaxation model.

The first stress-strain relation is based on Backus's averaging theory, which provides the best model for laminated media. The other two constitutive laws are not restricted to stratified media and can be tested with the first model. The second constitutive law is based on the following mechanical interpretation: Each eigenvector (called eigenstrain) of the stiffness tensor of an anisotropic solid defines a fundamental deformation state of the medium. The six eigenvalues (called eigenstiffnesses) represent the genuine elastic parameters, which generalize to relaxation functions in the anelastic case. The third constitutive equation satisfies the condition that the mean stress depends only on the dilatational relaxation function in any coordinate system (the trace of the stress tensor is invariant under coordinate transformations). Moreover, the deviatoric stresses solely depend on the shear relaxation function.

The last two constitutive relations yield similar results when modeling a laminated medium, but they differ for an orthorhombic medium. Tests on available experimental data indicate that the second model provides the best fitting.
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Document Type: Research Article

Publication date: May 1, 1998

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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