Realizing Of Generalized Diffraction Stack Migration

Seismic migration is a seismic data processing technique based on the wave equation.Its basic purpose is to map the events on the seismic section to the correct locations in the underground space.According to the mathematical theory of seismic migration,the early seismic migration methods can be divided into three types,namely wave equation migration,F-K migration,and Kirchhoff migration.Among these three methods,Kirchhoff migration has the advantages of flexibility,high efficiency,and adaptability to various data styles.It was once a mainstream method in industrial applications and still plays an important role.Generalized diffraction stack migration is an extension of the classical Kirchhoff migration.Its basic purpose is to overcome the main disadvantages of Kirchhoff migration and the limitations of using only primary reflection imaging.The core technique is to use numerical Green's function instead of the ray Green's function.Therefore,the migration operator not only includes the primary reflection information but also includes multiple reflection and diffraction information.Therefore,generalized diffraction stack migration can not only use primary reflection imaging,but also utilize multiple reflection and diffraction imaging.In addition,due to the use of numerical Green's function,the intrinsic caustic region failure problem of the ray Green function is completely overcome.However,since the Green's function has a Dirac pulse as the field source,it has an infinite bandwidth,making it difficult to implement a finite difference approximation.To solve this problem,the source of the wave equation is decomposed and the numerical Green's function with limited bandwidth is used to replace the exact infinite Green's function.In order to obtain the limited bandwidth Green function at the receiver point,a reciprocity theorem was used.The migration operator is obtained by the combination of the above two limited bandwidth Green functions.Further,the Hessian matrix is calculated by using the Green Band function with limited bandwidth,and a illumination compensation scheme based on the point-source limited bandwidth Green function is established.Due to the extreme amplitude distortion in the shallow layer due to reverse time migration,the illumination compensation term is introduced into the reverse time migration.Numerical examples show that the illumination compensation method can solve the problem of reflective seismic imaging under complex geological conditions.