Acoustic Wave Field Simulation In Anisotropic Medium

We mainly use the finite difference method to study the anisotropic acoustic wave field simulation in this paper.It is usually to set the structure of the medium and the various parameters of the opposite sex,and then study the propagation of seismic waves in it.The ups and downs of the surface and complex interfaces are common conditions for land exploration and seabed exploration.In addition,the development of oil and gas resources to the mountainous areas and other complex structures will give full consideration to the anisotropy and undulate surface and complex interface of the formation medium,which is necessary for the numerical simulation of seismic exploration.On the basis of previous studies,this paper derives the wave equation of pure acoustic wave in anisotropic medium.For the anisotropic elastic wave equation,the anisotropic pure acoustic wave equation avoids the various anisotropic parameters of the elastic wave.However,the anisotropic pure acoustic equation contains time four derivative and spatial mixed four order derivative,which will cause large memory demand and long time consuming in the process of forward modeling,which is unfavorable for subsequent inversion and migration.In order to avoid these problems,the phase velocity formula of anisotropic medium is derived,and the pseudo acoustic wave equation of anisotropic medium is derived based on phase velocity.Considering the calculation of artificial boundary reflection,considering the computation and computation time and the absorption effect,the mixed absorbing boundary condition is adopted,and the corner is optimized,and a good absorption effect is obtained.When the terrain is hilly or irregular interface even rough sea surface,the numerical simulation in the Descartes coordinate system will not be able to accurately depict the solving region,in view of this,on the basis of previous research,chose to portray the undulating surface grid and irregular interface,and can use the traditional finite difference simulation in anisotropic medium acoustic wave field division method.In addition,in order to avoid the instability of numerical simulation caused by the dramatic change of physical parameters,SBP finite difference algorithm is applied to solve the anisotropic pseudo acoustic equation in numerical simulation.After that,we also studied the adaptability of the algorithm to the grid angle and the rate of grid change,and realized the numerical simulation of three-dimensional undulating surface,which laid a good foundation for follow-up work.