Exact formulas for qP, qSV, and SH group velocities in VTI media

Joe Wong


For analyzing traveltimes of qP and qS arrivals propagating through media with transversely isotropic or VTI symmetry, geophysicists often use the Thomsen linearized formulas for phase velocities to approximate group velocities. However, the Thomsen approximations are suitable only for weak anisotropy and for small angles relative to the VTI symmetry axis. When the anisotropy is strong and for larger angles, exact expressions for group velocity may be more appropriate. The exact group velocity formulas are not widely familiar to most applied geophysicists. This report summarizes the derivation of these exact formulas using the method of characteristics, and presents them in forms that facilitate calculation of traveltimes relevant to all the common acquisition geometries (surface reflection, VSP, and crosswell).

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