Anisotropy influences many aspects of seismic wave propagation and, therefore, has implications for conventional processing schemes. It also holds information about the nature of the medium. To estimate anisotropy, we need both forward modeling and inversion tools. Forward modeling in anisotropic media is generally done by ray tracing. We present a new and fast method using the τ-p transform to calculate exact reflection-moveout curves in stratified, laterally homogeneous, anisotropic media for all pure-mode and converted phases which requires no conventional ray tracing. Moreover, we obtain the common conversion points for both P-SV and P-SH converted waves. Results are exact for arbitrary strength of anisotropy in both HTI and VTI media (transverse isotropy with a horizontal or vertical symmetry axis, respectively). Since inversion for anisotropic parameters is a highly nonunique problem, we also develop expressions describing the phase velocities that require only a reduced number of parameters for both types of anisotropy. Nevertheless, resulting predictions for traveltimes and conversion points are generally more accurate than those obtained using the conventional Taylor-series expansions. In addition, the reduced-parameter expressions are also able to handle kinks or cusps in the SV traveltime curves for either VTI or HTI symmetry.

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