A RHEOLOGICAL MODEL FOR ANELASTIC ANISOTROPIC MEDIA WITH APPLICATIONS TO SEISMIC-WAVE PROPAGATION

This work presents a new constitutive law for linear viscoelastic and anisotropic media, to model rock behaviour and its effects on wave propagation. In areas with high dissipation properties (e.g. hydrocarbon reservoirs), the interpretation of seismic data based on the isotropic and purely elastic assumption might lead to misinterpretations or, even worse, to overlooking useful information. Thus, a proper description of wave propagation requires a rheology which accounts for the anisotropic and anelastic behaviour of rocks. The present model is based on the following mechanical interpretation; each eigenvector (eigenstrain) of the stiffness tensor of an anisotropic solid defines a fundamental deformation state of the medium. The six eigenvalues (eigenstiffnesses) represent the genuine elastic parameters. Since they are independent of the reference system, they have an intrinsic physical content. From this fact and the correspondence principle we infer that in a real medium the rheological properties depend essentially on six relaxation functions, which are the generalization of the eigenstiffnesses to the viscoelastic case. The existence of six or less complex moduli depends on the symmetry class of the medium. We probe the new stress-strain relation with homogeneous viscoelastic plane waves, and give expressions for the slowness, attenuation, phase velocity, energy velocity (wavefront) and quality factor of the different wave modes.