从TTI介质一阶应力—速度方程出发,利用旋转交错网格高阶有限差分方法,将非分裂完全匹配层(Non-spliting Perfect Match Layer,简称NPML)边界吸收条件和自由边界条件相结合形成组合边界条件,进行了二维三分量TTI介质弹性波场数值模拟。...从TTI介质一阶应力—速度方程出发,利用旋转交错网格高阶有限差分方法,将非分裂完全匹配层(Non-spliting Perfect Match Layer,简称NPML)边界吸收条件和自由边界条件相结合形成组合边界条件,进行了二维三分量TTI介质弹性波场数值模拟。波场快照和炮记录表明:①采用非分裂式边界条件能较好地消除近地表大角度入射波和瞬逝波;②组合边界条件与NPML边界吸收条件相比,不仅有效地压制了边界反射,同时实现了对自由地表的模拟,获得了丰富的全波场信息,其中在地表产生的PS转换横波作为一种特殊的横波现象,可为近地表结构调查以及多波波场分析等提供有益信息;③自由地表引起的面波以及多次波对偏移结果有着重要影响,因此在实际地震资料处理中应当充分考虑自由地表条件对波场的影响效应。数值模拟结果证实了组合边界条件下二维三分量TTI介质波场数值模拟方法的可行性和正确性。展开更多
A rotated staggered grid finite-difference (FD) method with a perfectly matched layer (PML) method is proposed for numerically solving elastic wave equations in inhomogeneous elastic and poroe- lastic media. Compared ...A rotated staggered grid finite-difference (FD) method with a perfectly matched layer (PML) method is proposed for numerically solving elastic wave equations in inhomogeneous elastic and poroe- lastic media. Compared with a standard staggered- grid FD, the former has the advantage over the latter in that its physical variables need only to be defined at two locations. In the rotated staggered grid, stress and strain components (or particle velocity and dis- placement components) are defined at elementary cell centers, and the velocity or displacement com- ponents (or the stress and strain components) are defined at vertexes. In this way, no elastic moduli need to be interpolated or averaged. Numerical re- sults from the proposed method have been compared with the standard staggered FD method. The results are in good agreement with each other. Our numeri- cal results show that the proposed algorithm can handle much stronger impedance contrast. This is especially true when simulating fractured medium filled with fluids such as water or gas without giving special treatment. On the other hand, the imple- mented PML absorbing boundary condition works well in efficiently reducing reflected waves from the artificial interfaces. It generates almost no reflection at artificial interfaces with a boundary of PML thick- ness of half a wavelength. Our theoretical analysis and numerical tests proved that the PML absorbing algorithm in the rotated staggered grid is almost identical to those in the standard staggered grid. In this paper, we also presented all of the formulations of the PML implementation and modeling examples展开更多
Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to ...Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme（RSG） is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme（CSG） is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme（RSGC）. The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.展开更多
文摘从TTI介质一阶应力—速度方程出发,利用旋转交错网格高阶有限差分方法,将非分裂完全匹配层(Non-spliting Perfect Match Layer,简称NPML)边界吸收条件和自由边界条件相结合形成组合边界条件,进行了二维三分量TTI介质弹性波场数值模拟。波场快照和炮记录表明:①采用非分裂式边界条件能较好地消除近地表大角度入射波和瞬逝波;②组合边界条件与NPML边界吸收条件相比,不仅有效地压制了边界反射,同时实现了对自由地表的模拟,获得了丰富的全波场信息,其中在地表产生的PS转换横波作为一种特殊的横波现象,可为近地表结构调查以及多波波场分析等提供有益信息;③自由地表引起的面波以及多次波对偏移结果有着重要影响,因此在实际地震资料处理中应当充分考虑自由地表条件对波场的影响效应。数值模拟结果证实了组合边界条件下二维三分量TTI介质波场数值模拟方法的可行性和正确性。
文摘A rotated staggered grid finite-difference (FD) method with a perfectly matched layer (PML) method is proposed for numerically solving elastic wave equations in inhomogeneous elastic and poroe- lastic media. Compared with a standard staggered- grid FD, the former has the advantage over the latter in that its physical variables need only to be defined at two locations. In the rotated staggered grid, stress and strain components (or particle velocity and dis- placement components) are defined at elementary cell centers, and the velocity or displacement com- ponents (or the stress and strain components) are defined at vertexes. In this way, no elastic moduli need to be interpolated or averaged. Numerical re- sults from the proposed method have been compared with the standard staggered FD method. The results are in good agreement with each other. Our numeri- cal results show that the proposed algorithm can handle much stronger impedance contrast. This is especially true when simulating fractured medium filled with fluids such as water or gas without giving special treatment. On the other hand, the imple- mented PML absorbing boundary condition works well in efficiently reducing reflected waves from the artificial interfaces. It generates almost no reflection at artificial interfaces with a boundary of PML thick- ness of half a wavelength. Our theoretical analysis and numerical tests proved that the PML absorbing algorithm in the rotated staggered grid is almost identical to those in the standard staggered grid. In this paper, we also presented all of the formulations of the PML implementation and modeling examples
文摘Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme（RSG） is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme（CSG） is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme（RSGC）. The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.
