ATTENUATION AND QUALITY FACTOR SURFACES IN ANISOTROPIC-VISCOELASTIC MEDIA

We obtain expressions of the attenuation vector and quality factor of the three possible wave modes propagating in a linear anisotropic medi um. The theory assumes, in principle, a general stiffness matrix. Prob ing the medium with a time-harmonic homogeneous plane wave gives the a ttenuations and quality factors as simple forms of the propagation dir ection, complex stiffnesses and mass density. As an application, we in troduce a new constitutive relation, based on four complex moduli, for which the values of the quality factor along three preferred directio ns can be matched with experimentally pre-determined values. The rheol ogy is causal and allows an arbitrary frequency-dependence of the stif fnesses based on the generalized standard linear solid model. Two exam ples are explicitly worked out. The first is clay shale, a material of hexagonal symmetry. Since, by Neumann's principle, the attenuation sy mmetries are determined by the crystal class, the medium presents isot ropic attenuation in a plane normal to the symmetry axis. For instance , in materials with c11 > c33, it is found that the quasi-compressiona l wave attenuates more along the symmetry axis direction than in the p lane of isotropy. The second medium is tellurium dioxide, a strongly a nisotropic material of tetragonal symmetry. In this case, the diagrams show that strong attenuation is associated with high slowness values, as at around 45-degrees in the horizontal plane. Both case studies sh ow that the features of the attenuation surfaces strongly depend on th e values of the elasticities.