Pre-stack Depth Migration Based On G-D Frame Wave Field Decomposition

Pre-stack wave equation depth migration is the most effective technique for complex structure imaging. The problem of steep-dip reflecting layer imaging, wave propagation and imaging in lateral velocity medium can also be solved. Extrapolate imaging is carried on shot-by-shot traditionally, so to achieve better imaging, many shots offset stacking and large computation are needed because of a single shot's migration aperture restriction. In addition, during the wave propagation process, common shot gathers data pre-stack depth migration is lack of directivity as ray method's. With the seismic data analysis and processing technology developing steadily, fine target structure imaging is being paid more attention to. And to get a more specific goal-oriented acquisition and imaging, analysis of the impact of these imaging factors comes into focus.In this paper, based on split-step Fourier propagator, frame expansion method is applied to the phase-shift operator of split-step Fourier transmission. After that the spatial overall phase-shift operator transformed into a local phase-shift operator. At the same time, a window-shift operator is introduced, so a partial split-step Fourier propagator can be obtained. Deficiencies of split-step Fourier propagator are overcome by partial split-step Fourier propagator. Calculation precision has been improved in strong lateral velocity variation medium. The characteristics of high computational efficiency are maintained. This propagator is composed by phase shift operator and window-shift operator, the former is from phase space-frequency domain, while the latter is from space-frequency domain. Compared with space global phase-shift operator, which is from wave number-frequency domain, phase-shift operator has good spatial locality.G-D frame wave field decomposition is extended, point source can be decomposed into plane-wave. Wave field plane-wave decomposition can be completed by a linear time correction and stacking along the offset axis. In order to generate slant stacking gathers, slant stacking for different p values is needed. In mathematics, this process can be called linear Radon transformation. Plane-wave migration can be described as a decomposition of a list of single-shot record spherical waves into a series of plane-wave with different ray propagation parameters. Its wave field depth extrapolation operator and imaging conditions are the same as single-shot migration's. Plane-wave has the overall directivity and high computational efficiency, its migration imaging result can be comparable to shot-by-shot migration's. Common image gathers, generated spontaneously in ray parameter angle domain, can be used for migration velocity updating or provide reliable research data for AVA / AVO analysis, can be naturally generated in plane-wave imaging process.