Multiple weights in diffraction stack migration

Decoupled elastic prestack depth migration

“…(18) is a high-frequency approximation of the back-propagated wavefield that does not require the wave-mode expansion (2) or the integration over the reflector R. Even though this equation and its time-domain counterpart (19) are still applicable to elastic wave propagation in general anisotropic media, they have the very appealing form of a multipleweighted reverse-time (back propagated) diffraction stack of the transformed data given by Eq. (20) (Tygel et al, 1993). The factor c (r) (Eq.…”

True‐amplitude weight functions in 3D limited‐aperture migration revisited

“…Thus, when P is coincident with R, the depth-migrated image given in equation (B-1) in Tygel et al (1993) is zero, independent of the weight function used. Because of this fact, at R the ratio between any two depth-migrated images has the form of 0/0.…”

“…If the seismic signal is a causal wavelet, the vector diffraction stack published in Tygel et al (1993) breaks down at an actual reflection point. Consequently, only the seismic parameters underneath the target reflector can be estimated properly.…”

“…In fact, as first shown in Bleistein (1987), applied in Geoltrain and Chovet (1991), and further developed in Tygel et al (1993), by constructing the ratio between the depth-migrated images resulting respectively from two diffraction stacks with different weight functions, one can compute several quantities related to the target reflector (seismic parameters), such as the reflection angle, the reflector dip, the velocity underneath the target reflector, and the stationary point ξ (P) st . Once the quantities are obtained, the position of the target reflector can be determined by ray tracing.…”

“…Once the quantities are obtained, the position of the target reflector can be determined by ray tracing. According to Tygel et al (1993), this type of migration scheme is called multiple-weighted or vector-weighted diffraction stack, or vector diffraction stack.…”