Evaluating the Stolt-stretch parameter

Stolt stretch for anisotropic media

As follows from the analysis of the reflection moveout in a vertically heterogeneous transversely isotropic medium (Fomel and Grechka, 1996), expression (17) for the Stolt stretch parameter will remain valid in this case if the values of $v_{rms}$ and $S$ are computed according to equations

$$v_{rms}^2\left(t_v\right) = {1 \over t_v}\,\int_{0}^{t_v} v^2(t) \left(1 + 2\,\delta(t)\right)\,dt\;,$$ (21)

$$S\left(t_v\right) = {1 \over{v_{rms}^4 t_v}}\,\int_{0}^{t_v} v^4(t) \, \left(1 + 2\,\delta(t)\right)^4\,\left(1 + 8\,\eta(t)\right) \,dt\;,$$ (22)

where $\delta$ and $\eta$ are the conventional anisotropic parameters (Thomsen, 1986; Alkhalifah and Tsvankin, 1995), which may vary with depth.

As we demonstrate in the next section, the method of cascaded migrations (Larner and Beasley, 1987) can improve the performance of Stolt migration in the case of variable velocity (Beasley et al., 1988). However, this method affects only the isotropic part of the model and cannot change the contribution of the anisotropic parameters. Therefore, in the anisotropic case, it is important to incorporate anisotropic parameters into the Stolt stretch correction.

Evaluating the Stolt-stretch parameter