Wave-equation Migration Velocity Analysis With The Time-shift Imaging Condition

The technique of pre-stack migration is now developing fast along with the development of oil and gas exploration and the transition of seismic exploration objects from the oil and gas resources of structural type to lithological type. Because of the restriction of the theory, Kirchhoff integral type pre-stack depth migration(PSDM) could not solve the problems of caustic phenomena and multi-path phenomena in areas of acute lateral velocity variation. While, PSDM method, which is the unique among all the imaging methods, can accurately depict the propagation of seismic waves in complex subsurface situation and also image the complex subsurface structure of acute lateral velocity variation. Then, PSDM is widely used.The uncertainty of the velocity and depth makes it difficult of PSDM method to have a best imaging section because of the sensitivity of PSDM method to velocity. Therefore, we can construct velocity model by means of PSDM method and the optimization of imaging result should be the criterion to judge the validity of migration velocity. We put these methods collectively known as the migration velocity analysis(MVA).According to the different imaging conditions, we were able to get the different characteristics of the common imaging gathers by PSDM method. In this article, I conducted a brief overview of several gathers such as ray parameter domain CIGs(PhCIGs), angle-domain CIGs(ADCIGs), offset-domain CIGs(ODCIGs) and time-shift CIGs(TSCIGs) and discuss their application and extraction methods in terms of migration velocity analysis. Focusing on the principle and the extraction method of TSCIGs, I can know time-shift imaging is cheaper to apply, and thus it might alleviate some of the difficulties posed by costly crosscorrelations in 3D imaging condition.Subsequently, we detail the wave-equation migration velocity analysis(WEMVA) theories. WEMVA is a velocity estimation technique to obtain velocity information by migrated images and can appropriate in steep or under illumination events. Through the first-order Born approximation,a linear relationship between image perturbation and velocity perturbation is established. Then, velocity perturbation are inversed with image perturbation. Based on previous theory, we achieve its basic processes and computational experiments using a synthetic data set from a model demonstrate the feasibility of the method.A key step in implementing WEMVA is to design an appropriate procedure for constructing image perturbation. In this paper, we propose a new methodology for constructing image perturbations based on the time-shift imaging condition. This alternative approach avoids the cycle skipping problem and can easily compute image perturbation. Meanwhile, we illustrate the practicality and accuracy of our approach by testing the method on simple and complex synthetic data sets.