171 7. Integrated seismic study the topographic variations of the floating DP. The residual time function is a long wavelength static correction which is applied on the post-stack migrated sections to compensate the long wavelength LWL static anomalies. Figure 7.5 shows the LWL static curve and the associated trend for the 2D line 07EST10. Figure 7.6 shows the 2D line 07EST10 before and after LWL static compensation. Figure 7.6 Long wavelength wave static compensation after stack. Left: seismic line before LWL static compensation. Right: seismic line after LWL static compensation. During the migration process (Robein, 2003), the data are migrated and sorted into common image gathers (CIG) to update the velocity model before stacking. Each image gather is composed of migrated seismic traces which are functions of time (time migration) and offset or angle. The offset-angle conversion can be carried out during or after the migration process by using the velocity model. The common image gathers after offset-angle conversions are used to perform Amplitude versus Angle analysis (Castagna, 1993; Walden, 1991) and elastic inversion (EI). The small angle amplitudes (near-offset or intercept) migrated stacks relate to changes in acoustic impedance (AI) and can be inverted back to AI using a post-stack inversion algorithm (acoustic inversion). The acoustic impedance is a simple function of P-wave velocity Vp and density ρ(AI = ρ.Vp). The amplitudes of angle migrated stacks relate to changes in elastic impedance EI (θ). They can be inverted back to impedances Ip (Ip = AI = ρ.Vp) and Is (Is = ρ.Vs) using a linearization of Zoeppritz equations for P-wave reflectivity R(θ). The reflectivity R(θ) is a function of the incidence angle (θ) and depends on the variations ΔVp, ΔVs, Δρ of the mechanical parameters (Vp, Vs, ρ) of the two media located on each side of the discontinuity which generates the reflection.
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