Beamlet migration based on local perturbation theory

Abstract

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.

High Resolution/High Fidelity Seismic Imaging and Parameter Estimation for Geological Structure and Material Characterization

“…However, the inability to provide localized-angle information prevented them from being utilized for illumination calculation. Recently developed techniques, such as LSS (e.g., Xie and Wu, 2002) and beamlet decomposition (e.g., Wu et al, 2000), can decompose the wavefield into local plane waves, which are mixed domain wavefields simultaneously localized in space and direction. These methods are independent on the extrapolator and coordinate system for extrapolation.…”

“…Beamlet decomposition (e.g., Wu et al, 2000) can also decompose the wavefield into local plane waves. The propagation and imaging methods based on beamlet decomposition proposed by Wu et al (2000) have been developed using the GDF Wu and Chen, 2001;, LCB (local cosine basis) Wang and Wu, 2002;Luo and Wu, 2003;Wang et al, 2003;Wu et al, 2008), and LHB (local harmonic basis) .…”

“…The beamlet decomposition (e.g., Steinberg, 1993;Wu et al, 2000;Wu and Chen, 2001;Mao and Wu, 2007) provides a basis to simultaneously localize the wavefield in space and wavenumber domain. The frequency-space domain wavefield ( , ) u x  at depth level z for frequency  , obtained from any extrapolator, can be decomposed into beamlets, ( , ) ( , , ) ( ) The beamlet used to obtain the LAD image and image amplitude correction factor must have uniquely defined local direction information.…”

“…The propagation and imaging methods based on beamlet decomposition proposed by Wu et al (2000) have been developed using the GDF Wu and Chen, 2001;, LCB (local cosine basis) Wang and Wu, 2002;Luo and Wu, 2003;Wang et al, 2003;Wu et al, 2008), and LHB (local harmonic basis) . The GDF beamlets have uniquely defined local direction information available during the propagation process so that angle-domain imaging (Wu and Chen, 2002;2003;Chen et al, 2006) and other angle-related operations can be easily incorporated into the migration process, but the GDF beamlet propagator is computationally more expensive than the LCB propagator due to the redundancy in its representation.…”

Seismic Illumination Analysis with One-Way Wave Propagators Coupled with Reflection/Transmission Coefficients in 3D Complex Media

“…Recently, One-way wave propagators have been widely used to seismic modelling and migration for its huge memory-saving and high computational efficiency. Localized illumination methods based on the Gabor-Daubechies frame decomposition or the local slant stack have been presented, which can give local information both in space and direction (e.g., Xie and Wu, 2002;Wu et al, 2000;Xie et al, 2003;Wu & Chen, 2006;Mao & Wu, 2007;Cao & Wu, 2008). However, its computational burden is still unacceptable due to the wavefield decomposition in every spatial point.…”