Wave Propagation In Beamlet Domain Based On Local Cosine Base

The traditional method of wave field propagation,such as high-frequency wave equation Kirchhoff approximation solution method,frequency-wavenumber domain phase shift method,etc.,are a set of basic functions with global characteristics of the wave field decomposition,which makes the plane wave global the basic function of occupying the entire space,point source excitation wave field full of all directions.They spread in an inhomogeneous space will become very complicated,the need to address the whole problem space wave field to wave equation solver,can not well reflect local characteristics heterogeneous media.Therefore,based on the wave field propagation using local spatial decomposition of localized operator overrides the global spread of the operator,in order to improve the accuracy of wave field propagation with frequency-domain forward modeling,seismic wave propagation provides a new field ideas.This article described local application of methods which transform the acoustic equation to the frequency domain,so localized in the spatial domain decomposition,then spread in the frequency domain wave field and use of the localized space,the application localized wave field propagator of seismic wave field numerical simulation.First,from the physical point of view,the choice of local cosine wave field decomposition group as a window function,derivation of orthogonal characteristic local cosine base,and on its basis in the establishment of a space sparse characteristic localization propagator.Secondly,based on global wave field propagation methods,using local cosine transform wave field data and propagator small beamspace decomposition,were small wave field reconstruction completed beamspace wave field propagation in the corresponding medium.This article is the acoustic wave field beamlet domain was simulated by a uniform medium,transverse inhomogeneous media,vertical and inclined inhomogeneous wave field simulation model,validated application localization methods,as well as draw a small beam spread has a dual local spatial and wave number.