Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis （VTI media）, a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis （TTI me...Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis （VTI media）, a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis （TTI media）. This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ε. The finite difference method is used to solve the equation. In addition, a perfectly matched layer （PML） absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.展开更多
We derive an expression for phase velocity in 2D tilted transverse isotropy （TTI） media. Snapshots of phase velocity in TTI and transverse isotropy （TI） model media are simulated and analyzed using the derived exp...We derive an expression for phase velocity in 2D tilted transverse isotropy （TTI） media. Snapshots of phase velocity in TTI and transverse isotropy （TI） model media are simulated and analyzed using the derived expression. In addition, the x-component character differences between the modeled phase velocities of the two media models are compared and analyzed.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
The Tilted tilted transversely isotropic(TTI)media,a kind of anisotropic medium,widely exists within the earth.For faster calculation of travel times in the TTI anisotropic media,we modifi ed a minimum traveltime tree...The Tilted tilted transversely isotropic(TTI)media,a kind of anisotropic medium,widely exists within the earth.For faster calculation of travel times in the TTI anisotropic media,we modifi ed a minimum traveltime tree algorithm with high effi ciency by dynamical modifi cation of the secondary wave propagation region during the spread of seismic waves.To manage the wavefront points in the modified version,we used a novel minimum heap sorting technique to reduce the time spent on selecting secondary waves points.In this study,seismic group velocities were obtained from analytical solutions in terms of phase angle,and the corresponding phase angles were determined by binary search rather than approximate equations for weakly anisotropic media.For the most time-consuming part of the secondary wave traveltime calculation,the parallel computation was initially performed using multiple cores and threads.Numerical examples showed that the improved method can calculate seismic travel times and ray paths faster and accurately in a 3D TTI medium.For four cores and eight threads,the computing speed increased by six times when compared to the conventional method.展开更多
基金supported by the National Natural Science Foundation of China(No.41674118)the national science and technology major project(No.2016ZX05027-002)
文摘Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis （VTI media）, a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis （TTI media）. This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ε. The finite difference method is used to solve the equation. In addition, a perfectly matched layer （PML） absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.
文摘We derive an expression for phase velocity in 2D tilted transverse isotropy （TTI） media. Snapshots of phase velocity in TTI and transverse isotropy （TI） model media are simulated and analyzed using the derived expression. In addition, the x-component character differences between the modeled phase velocities of the two media models are compared and analyzed.
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.
基金funded by the National Key R&D Program of China (No. 2020YFA0710600)National Science Foundation of China (No. 41374098)the Special Fund of the Institute of Geophysics,China Earthquake Administration (No. DQJB19B40)
文摘The Tilted tilted transversely isotropic(TTI)media,a kind of anisotropic medium,widely exists within the earth.For faster calculation of travel times in the TTI anisotropic media,we modifi ed a minimum traveltime tree algorithm with high effi ciency by dynamical modifi cation of the secondary wave propagation region during the spread of seismic waves.To manage the wavefront points in the modified version,we used a novel minimum heap sorting technique to reduce the time spent on selecting secondary waves points.In this study,seismic group velocities were obtained from analytical solutions in terms of phase angle,and the corresponding phase angles were determined by binary search rather than approximate equations for weakly anisotropic media.For the most time-consuming part of the secondary wave traveltime calculation,the parallel computation was initially performed using multiple cores and threads.Numerical examples showed that the improved method can calculate seismic travel times and ray paths faster and accurately in a 3D TTI medium.For four cores and eight threads,the computing speed increased by six times when compared to the conventional method.
