Simulating propagation of separated wave modes in general anisotropic media, Part II: qS-wave propagators |
Shear-wave modeling is complicated by the presence of the shear-wave singularities. As investigated by Crampin and Yedlin (1981), a TI material only has line and kiss singularities, while other anisotropic materials excluding those with triclinic symmetry (e.g., orthorhombic and monoclinic anisotropic materials) have point singularities in many propagation directions. Line singularities occur only at a fixed angle from the symmetry axis and cause no distortion of phase velocity surfaces or polarization phenomena. For kiss singularities (along the direction of symmetry axis), qS-wave polarizations vary rapidly in their vicinity but are well-behaved because there is no distortion in phase-velocity surfaces. These features facilitate the derivations of pseudo-pure-mode qSV-wave and pure-mode SH-wave equations for TI media. For directions near point singularities, however, the polarization of plane qS-waves changes very rapidly, and amplitudes and polarizations of qS-waves with curved wavefronts behave quite anomalously. Therefore, although pseudo-pure-mode qP-wave equations exist for general anisotropic media, it may be more confusing than helpful to extend the proposed pseudo-pure-mode qS-wave equations to symmetry systems lower than TI.
polar3dvtiS1,polar3dvtiS2
Figure 8. Polarization vectors of 3D qS-waves in a VTI material (Mesaverde shale): (a) qS1-wave; (b) qS2-wave. |
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polar3dortS1,polar3dortS2
Figure 9. Polarization vectors of 3D qS-waves in an orthorhombic anisotropic material: (a) qS1-wave; (b) qS2-wave. |
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Simulating propagation of separated wave modes in general anisotropic media, Part II: qS-wave propagators |