172 Seismic Imaging Shuey (1985) proposes the following approximation between the reflectivity R(θ), the elastic impedance EI(θ) and the mechanical parameters: R A B θ θ θ θ ( ) = ( ) ( ) = + ( ) 1 2 2 ∆EI EI sin with A= = + 1 2 1 2 ∆ ∆ ∆ Ip Ip Vp Vp ρ ρ (7.1) The coefficient B is called the gradient and can be approximated by: B = − − 1 2 2 ∆ ∆ ∆ Vp Vp Vs Vs ρ ρ (7.2) The parameter A in equation (7.1) represents the seismic trace as a compressional wave associated with acoustic impedance contrast Ip. The parameters A and B represent the seismic trace as a shear wave associated with acoustic impedance Is contrasts. If the incidence angle equals 0 (θ=0), the elastic impedance EI(θ) is the acoustic impedance Ip. Equations (7.1) and (7.2) show that the elastic impedance EI(θ) is a function of P-wave velocity Vp, S-wave velocity Vs, and density ρ. Connolly (1999) shows that the elastic impedance EI(θ) can be written as follows: EI Vp Vs tan sin sin θ ρ θ θ θ ( ) = + ( ) − − ( ) 1 8 1 4 2 2 2 K K with K = Vs Vp 2 2 (7.3) Such processing is referred to elastic inversion (Shuey, 1985; Connolly, 1999; Whitecombe et al., 2002). A model-based elastic inversion (a priori impedance model obtained from well data), applied to the angle migrated stacks, provides impedance sections (Ip and Is sections). In our field case, three angle migrated stacks have been generated (0-14°, 14-28°, 28-42°) to perform the elastic inversion to compute Ip and Is – sections. Figure 7.7 Ip and Is sections for the 07EST10 profile.
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