Seismic velocity anisotropy in mica-rich rocks: an inclusion model

Abstract

We calculated seismic wave velocity anisotropy caused by the preferred orientation of mica minerals by using the differential effective medium method (DEM). Spheroidal biotite crystals with their c‐axes coinciding with the symmetry axis of the spheroid are embedded in an isotropic matrix up to a volume ratio of 30 per cent. All crystals are aligned with their c‐axes parallel to the symmetry axis of the effective homogeneous medium, which shows transverse isotropy. The effect of crystal shape on anisotropy was studied by changing the aspect ratio (the ratio between the minor axis and the major axis of the spheroid) from 0.01 (flat spheroid) to 1 (sphere). The S‐velocity anisotropy becomes large as the crystal shape becomes flat, whereas the P‐velocity anisotropy shows only small changes with changes of the crystal shape. In particular, biotite generates large S‐wave anisotropy, and the anisotropy becomes stronger as the aspect ratio of the biotite crystal becomes smaller. When the volume ratio of the mica mineral is large, the P‐wave phase velocity surface shows considerable deviation from the ellipse, and the SV‐wave phase velocity surface forms a large bulge and crosses the SH‐wave phase velocity surface (singularity) in the plane including the symmetry axis. These results show an interesting contrast when compared with the effect of crack or pore shape on seismic velocity anisotropy: crack (or pore) shape affects the P velocity more than the S velocity. We also calculated Thomsen's anisotropic parameters, ε, γ and δ as functions of the crystal aspect ratio and the mica volume ratio.