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Based on beamlet decomposition of wave field and Green's function, we formulated an amplitude correction method in angle domain. The formulation relates the local image matrix (LIM), which bears the footprints of the acquisition aperture and propagation path effects, and the local scattering matrix (LSM), which is directly related to the medium property. From the formulation, two types of amplitude correction are proposed: one is the correction for common reflection-angle image for AVA analysis. The other is the correction for total strength image. From the imaging results of the four-layer model and the SEG/EAGE model, we see significant improvement in amplitude fidelity and image quality.

Beamlet migration based on local perturbation theory is proposed. The method is formulated with a l o c a l bac kground velocity and local perturbations for each window of the wave eld decomposition using Gabor-Daubechies frame and local cosine basis. The propagators and phase-correction operators are obtained analytically for the G-D tight-frame, and numerically for the local cosine basis. The numerical test using the SEG-EAEG salt model poststac k data demonstrates the great potential of this approach.

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S U M M A R YThe scattering features of elastic waves in media with geometrically anisotropic heterogeneities are investigated in terms of scattering attenuation, coda level and scattering directivity. The theoretical variation of scattering attenuation with normalized wavenumber (ka) is formulated using the multiple forward scattering and single backscattering approximation. Estimates obtained from numerical simulations agree with the theoretical predictions well. The level of scattering is influenced by the anisotropy (aspect ratio, direction) and the wave incidence direction. The scattering level is not sensitive to the scale variation in the wave incidence direction, but is highly sensitive to the scale variation in the tangential direction. Forward scattering is dominant when waves are incident along the major direction of geometrically anisotropic heterogeneity, and backward scattering is dominant when the waves are incident in the minor direction. The scattered energy is not distributed isotropically in media with anisotropic heterogeneity, and the level of early coda varies with the wave incidence angle. The late coda is composed of multiscattered and multipathing waves, and displays a stochastically stable energy level. The incidence angle of waves is a key parameter in the early coda variation, and an approach with classified seismic data for incidence angle is desired in the study of anisotropic heterogeneity in Earth's deep interior from seismic coda and precursor.

In this paper. we first give a brief summary of the formulation for calculating reflections from a 3D elastic structure based on a complex-screen method. The incident wave and reflected wave are propagated by using a complexscreen propagator. The reflections are calculated based on local Born approximation. When using a small angle approximation, the backscattering can also be formulated into a screen reflection which has a high computation efficiency and needs relatively small computer memory. As expected from the scattering theory. the forward transmitted waves, like P to P or to are controlled by the Pand S-wave velocity perturbations, while the reflections are controlled by the impedance perturbations. The converted waves are mainly controlled by the density and shear module perturbations. Numerical examples are given to show the accuracy of the method. For two special cases, the synthetic seismograms obtained with this method are compared with that calculated by elastic finite-difference method. The results show general consistency.