Study And Application Of Nearly Perfectly Matched Layers Method For Seismic Wave Propagation

It is necessary to introduce the absorbing boundary to eliminate false reflection while simulating infinite area with finite computational domain.The perfect matching layer is the best and most widely used boundary condition for the current absorption effect,and it develops rapidly.There are three kinds of problems in perfectly matched layers(PML)introduced in the seismic wave field simulation,one is how to reduce the extra storage capacity in practical boundary application and enhance the computing speed;the second is how to absorb incident wave more quickly and make the absorption better,the last is how to improve the stability of the perfect matching layer.The first problem has been resolved well with the development of many advanced non-split perfectly matched layer technologies.The nearly perfectly matched layer we adopted obtained by transforming the wavefield directly has no change of the wavefield form and convolution.However,the NPML suffers from large spurious reflections at grazing incidence and evanescent wave.There has not been much progress on how to enhance the absorption of the boundary further because of the complexity of the discrepancy caused by discretization.Currently,we decrease the discretization discrepancy by adding the number of layers.At the same time,there is a certain instability in the perfectly matched layer.NPML will produce low-frequency singular values.Even if the complex frequency shift is used,it is still instability.In this paper we observed instability when simulating wave seismic wave propagation for various media.Instability was observed.In this paper,For the purpose of reducing false reflections caused by discrete differences without increasing the number of matching layers and without reducing the theoretical error,we analyze the property of damping term and design a new attenuation function which can improve the absorption effect further.The function could weaken the amplitude value of reflected wave by 20%—60% when the numbers of layers is 5-10 compared with traditional attenuation function.For the problem that NPML is difficult to absorb at large angle and could generate the low frequency singular value.After introducing the complex frequency shift technique,we proposed the CFS-NPML to realize the absorption of the large angle incident wave and the very low frequency wave.In terms of the stability of NPML,this paper introduced a new section perpendicular to the original attenuation profile in the boundary,and proposed MCFS-NPML.The MCFS-NPML introduces the attenuation factor,frequency shift factor,scale factor and stability factor to the original wave equation.Whereafter,we study and analyze the stability and absorption effect by numerical modeling and matrix eigenvalues.The result demonstrated the MCFS-NPML not only has the advantages of NPML but also can absorb the wave at any incidence more effectively and is more stable.In order to meet the needs of forward and inversion development,this paper also applied MCFS-NPML to different media simulations.Including elastic media,anisotropic media and dual-phase anisotropic media.