Theory And Application Of Gaussian Beam Migration

Gaussian beam migration is an elegant and efficient depth migration method between Kirchhoff integral migration and wave equation migration,which has received extensive attention in recent years.Based on Gaussian beam in local ray-centered coordinate system and global Cartesian coordinate system,this paper aims to explore the new theory and application of Gaussian beam migration,in which traditional Gaussian beam migration,reverse time migration by Gaussian beam,seismic data decomposition and reconstruction using Gaussian beam,the application of Gaussian beam migration in source and receiver ghost compensation have been studied systematically.Reverse time migration by Gaussian beam combines the high efficiency and flexibility of Gaussian beam migration with the high accuracy of wave equation reverse-time migration,which can overcome the problems of caustics,handle all arrivals,yield good images of steep flanks,and is readily extendible to target-oriented implementation.In order to realize the processing of multi-component data,multi-component Gaussian beam prestack reverse-time migration method is proposed.First,the seismic data is separated to PP and PS wave records,and then PP and PS wave Gaussian beam prestack reverse-time migration algorithms for common-shot gathers is implemented respectively.Numerical examples indicate that the proposed migration method has high accuracy.Gaussian beam in the global Cartesian coordinate system is a new mathematical approach.Compared with Gaussian beam in the local ray-centered coordinate system,it does not require coordinate conversion cumbersomely,and can be calculated in regular grids easily.By considering the smoothing and interpolation algorithm,the theory has extended to perform seismic forward modeling and migration.Numerical modeling suggests that the new method can overcome problems with caustics and simulate the wave propagation in complex media accurately.And then,the reverse time migration by Gaussian beam in the global Cartesian coordinate system is proposed,in which Green function is in terms of the Gaussian beams.Finally,the applicability of the new method has evaluated.The theory of Gaussian beam in the global Cartesian coordinate system provides a basis for the further study of Eulerian Gaussian beam.In order to test the effect of Gaussian beam method on seismic data decomposition and reconstruction,as well as analyze the impact on subsequent Gaussian beam migration,fristly plane wave decomposition filter is introduced to decompose seismic data into local plane wave.Second,the local plane wave is in term of Gaussian beam to reconstruct seismic data though iterative update to minimize the residual error.On this basis,the analysis of reconstruction results is given under the circumstances of seismic data with randomly missing traces and radom noise.After that,Gaussian beam depth migration is carried on using the reconstructed data,which indicates that the proposed approach can obtain satisfactory imaging results.Seismic data must include both precise low frequency and high frequency information in order to provide a more continuous migration profile with the lithologic information,which enhances geological interpretation.The ghosts cause angle dependent frequency and amplitude distortion of seismic record.The Gaussian beam migration algorithm of common shot gathers is proposed to compensate for the ghost effects by introducing the source and receiver ghost operators.At the same time,an appropriate algorithm is given to ensure the stability.Numerical examples show structural and resolution enhancement.