The most critical step in extending seismic inversion and processing to anisotropic media is to identify the medium parameters responsible for measured reflection signatures. In chapter 1 it was demonstrated that Thomsen notation makes it possible to reduce the number of parameters that govern P-wave kinematics in VTI media from four to three (V_P0, ∈, and δ). Therefore, if amplitude preservation is not an issue, for purposes of P-wave depth imaging (e.g., prestack depth migration) one needs to reconstruct the spatial distributions of those three parameters.

The subject of this chapter is time-domain P-wave processing, which includes normal-moveout (NMO) and dip-moveout (DMO) corrections, prestack and post-stack time migration. As shown here, for laterally homogeneous VTI models above a horizontal or a dipping target reflector, P-wave time-domain signatures depend on the interval values of just two combinations of (V_P0, ∈, and δ). Furthermore, both “time-processing” parameters can be recovered from P-wave reflection moveout alone, without using borehole information or multicomponent (S or PS) data.

According to the results of chapter 4, long-spread P-wave moveout in a horizontal VTI layer is controlled by the vertical traveltime (t_P0) and two medium parameters, one of which is the NMO velocity commonly measured in seismic processing:

The other parameter is the anisotropy coefficient η, which quantifies the anellipticity of the medium [equation (4.14)]:

Whereas V_nmo²(0) is responsible for the initial slope of the t²(x²)-curve, η determines the deviation of the traveltime function from a hyperbola. If the medium is elliptical (∈ = δ, η = 0),