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In the presence of anisotropy, supplementing P-wave reflection data with shear waves is often needed for estimating even the parameter set responsible for P-wave kinematics. For example, reflection moveout of P-waves in laterally homogeneous VTI media generally constrains only two parameter combinations - the zero-dip NMO velocity Vnmo, P and the anellipticity parameter η (Alkhalifah and Tsvankin, 1995). As discussed in Chapter δ, addition of reflection traveltimes of SV-waves to P-wave moveout helps resolve the vertical P- and S-wave velocities and the anisotropy parameters ε and δ, provided the reflector has a mild dip and the data are acquired for a wide range of azimuths. Moreover, joint inversion of P- and S-wave data can be effectively used in lower-symmetry orthorhombic and monoclinic media (see Chapter 6).

Therefore, finding practical ways of combining P- and S-waves is critically important for anisotropic velocity model-building. In theory, such joint processing algorithms might seem to be easy to implement because the techniques discussed in previous chapters are equally valid for both PP and SS pure-mode reflections. (Here we use the double indices “PP” and “SS” to emphasize that the downgoing and upgoing segments of ray trajectories correspond to the same wave type.) The applicability of algorithms originally designed for PP-waves to SS data is ensured by the reciprocity of pure-mode traveltimes with respect to the source and receiver positions. As a result, moveout of any pure-mode reflection in common-midpoint (CMP) gathers can be described by the traveltime series

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