Moveout analysis of wide-azimuth data in the presence of lateral velocity variation

Abstract

Moveout analysis of wide-azimuth reflection data seldom takes into account lateral velocity variations on the scale of spreadlength. However, velocity lenses (such as channels and reefs) in the overburden can cause significant, laterally varying errors in the moveout parameters and distortions in data interpretation. Here, we present an analytic expression for the normal-moveout (NMO) ellipse in stratified media with lateral velocity variation. The contribution of lateral heterogeneity (LH) is controlled by the second derivatives of the interval vertical traveltime with respect to the horizontal coordinates, along with the depth and thickness of the LH layer. This equation provides a quick estimate of the influence of velocity lenses and can be used to substantially mitigate the lens-induced distortions in the effective and interval NMO ellipses. To account for velocity lenses in nonhyperbolic moveout inversion of wide-azimuth data, we propose a prestack correction algorithm that involves computation of the lens-induced traveltime distortion for each recorded trace. The overburden is assumed to be composed of horizontal layers (one of which contains the lens), but the target interval can be laterally heterogeneous with dipping or curved interfaces. Synthetic tests for horizontally layered models confirm that our algorithm accurately removes lens-related azimuthally varying traveltime shifts and errors in the moveout parameters. The developed methods should increase the robustness of seismic processing of wide-azimuth surveys, especially those acquired for fracture-characterization purposes.

Migration Velocity Analysis for TI Media in the Presence of Quadratic Lateral Velocity Variation

“…Likewise, a highvelocity lens can be characterized by a negative k x2 . Takanashi and Tsvankin (2012) discuss the influence of thin laterally heterogeneous (LH) layers on the reflection moveout from deeper interfaces. They show that the distortion of the NMO velocity or ellipse depends on the curvature (second spatial derivatives) of the vertical interval traveltime surface and increases with the distance between the LH layer and the target.…”

“…They show that the distortion of the NMO velocity or ellipse depends on the curvature (second spatial derivatives) of the vertical interval traveltime surface and increases with the distance between the LH layer and the target. Although Takanashi and Tsvankin (2012) present general 3D moveout equations for wide-azimuth data, here we use their results for 2D geometry (i.e., the acquisition line coincides with a vertical symmetry plane). It is also assumed that each layer has a horizontal symmetry plane (e.g., VTI) and both anisotropy and lateral heterogeneity are weak.…”

“…It is also assumed that each layer has a horizontal symmetry plane (e.g., VTI) and both anisotropy and lateral heterogeneity are weak. In the special case of a medium composed of three horizontal layers with lateral heterogeneity confined to the second layer, the NMO velocity from the bottom of the model is given by (Takanashi and Tsvankin, 2012…”

“…As discussed in Takanashi and Tsvankin (2012), equation 9 can be extended to models with an arbitrary number of LH layers. V NMO;het is responsible for conventional-spread moveout and usually can be estimated from migration velocity analysis (unless there are abrupt lateral velocity changes caused, for example, by salt domes).…”

“…The k x2 -related error in the effective NMO velocity increases with target depth because both τ 0 and D become larger (Takanashi and Tsvankin, 2012). Thus, the moveout in image gathers for deep reflectors is highly sensitive to the error in k x2 (i.e., to the difference k x2;M − k x2;T ) in the overburden.…”