Forward Modeling And Inverse Time Migration Analysis Of Elastic Wave Field In VTI Medium

Seismic wave numerical simulation and migration imaging belong to the basic contents of geophysics.The two belong to seismic forward and inversion sections respectively.Numerical simulation of seismic waves plays an important role in understanding the propagation law of seismic waves in complex media.Compared with the one-way wave equation which only considers the single direction propagation,the reverse time migration based on the two-way wave equation can have a good effect on the complex model imaging.In this paper,the forward modeling and inverse time migration imaging technology of elastic wave equations are studied.After studying the numerical simulation of wave equation and the related principles of post stack and prestack reverse time migration imaging,this paper studies the homogeneous VTI medium,Kelvin viscoelastic VTI medium,non-uniform Biot dual phase isotropic medium and uniform Biot dual phase VTI medium,starting with the constitutive equation,geometric equation and differential equation of motion.The first order velocity stress wave equation is derived,and then the staggered grid difference scheme of 2N order on the 2 order space of time is derived.The above mentioned media are numerically simulated,and the propagation rules and wave field characteristics of seismic waves in the above mentioned media are analyzed.At the same time,some difficulties in forward modeling such as differential structure,boundary problem,stability problem and numerical dispersion are discussed.The staggered grid finite difference technique is widely used in seismic wave field numerical simulation because of its high simulation precision,fast calculation efficiency and small amount of memory.However,this method can not be correctly simulated when the accuracy of the wave field is obviously reduced and the amplitude appears abnormal when the numerical simulation of the heterogeneous medium containing geological anomalies is numerically simulated.The propagation of seismic wave fields.On the basis of the traditional staggered grid finite difference technique,the rotating staggered grid finite difference technique is adopted.In the subsequent non uniform biphasic isotropic medium simulation example,it is proved that the rotation staggered grid is better than the traditional staggered grid when the medium is strong in the medium inhomogeneity,and it can also be better to be true.Wave field characteristics is a practical numerical simulation method for seismic wave field.Finally,the inverse time migration technique is studied,and the post stack reverse time migration imaging condition is studied.Then the high order sound wave equation is applied to the post stack inverse time migration,and the reverse time migration imaging is carried out for the depression and graben combination model,the fault model and the eroded Qianshan model.The migration imaging results verify the correctness of the algorithm.And practicality.