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

Abstract

One of the most serious problems in anisotropic velocity analysis is the trade-off between anisotropy and lateral heterogeneity, especially if velocity varies on a scale smaller than the maximum offset. We have developed a P-wave MVA (migration velocity analysis) algorithm for transversely isotropic (TI) models that include layers with small-scale lateral heterogeneity. Each layer is described by constant Thomsen parameters ε and δ and the symmetry-direction velocity V 0 that varies as a quadratic function of the distance along the layer boundaries. For tilted TI media (TTI), the symmetry axis is taken orthogonal to the reflectors. We analyzed the influence of lateral heterogeneity on image gathers obtained after prestack depth migration and found that quadratic lateral velocity variation in the overburden can significantly distort the moveout of the target reflection. Consequently, medium parameters beneath the heterogeneous layer(s) are estimated with substantial error, even when borehole information (e.g., check shots or sonic logs) is available. Because residual moveout in the image gathers is highly sensitive to lateral heterogeneity in the overburden, our algorithm simultaneously inverts for the interval parameters of all layers. Synthetic tests for models with a gently dipping overburden demonstrate that if the vertical profile of the symmetry-direction velocity V 0 is known at one location, the algorithm can reconstruct the other relevant parameters of TI models. The proposed approach helps increase the robustness of anisotropic velocity model-building and enhance image quality in the presence of small-scale lateral heterogeneity in the overburden.

Wave-equation migration velocity analysis for VTI models

“…Surface seismic data inversion for anisotropy is ill-posed and highly underdetermined due to the rapidly increasing size of the model space with the increasing complexity of the subsurface (Woodward et al, 2008;Bakulin et al, 2010b,a). To reduce the size of the model space, Sarkar andTsvankin (2003, 2004) and Takanashi and Tsvankin (2012) parametrize their model space using factorized blocks or layers, where the anisotropic parameters and δ are constant and the velocity variations are simple linear or quadratic functions of the space coordinates.…”