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