Elastic Wave Field Forward Modeling And Reverse Time Migration For The Inhomogeneous Media

Forward modeling and offset imaging have been an important research field in the field of seismic exploration.Seismic wave forward modeling is an important means to study the characteristics of seismic wave propagation.The reverse-time migration of two-way wave is extrapolated in the time direction,The complex model with large lateral and lateral velocity can also have better imaging effect.In this paper,forward modeling and inverse migration imaging of elastic wave equation are studied.After studying the theory of wave equation,on the basis of constitutive equation?geometric equation and differential equation of motion,the first order velocity-stress elastic wave equation are derived in isotropic medium,VTI medium,Kelvin viscoelastic medium and Biot two phase medium respectively and staggered grid difference scheme in time on the second order space even are obtained.And the ways of the source loading,boundary conditions,stability conditions and numerical dispersion are systematically discussed.Secondly,based on staggered grid,high-order finite difference scheme of acoustic wave equation is derived.And the two layers model and the step model are used to simulate the calculation.After verifying the correctness of the algorithm,the seismic wave simulation is carried out for the above media.Meanwhile,the propagation law and wave field characteristics of seismic wave are analyzed.Lastly,the theory of reverse time migration is analyzed.Using staggered grid highorder difference scheme of the acoustic wave equation,the post stack reverse time migration is achieved.The calculation of reverse time migration imaging of the graben model,the correctness and practicability of the algorithm are verified by the offset imaging results.