Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of p...Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.展开更多
A staggered-grid finite difference method is used to model seismic wave records in a coal bearing, porous medium. The variables analyzed include the order of the difference calculations, the use of a perfect match lay...A staggered-grid finite difference method is used to model seismic wave records in a coal bearing, porous medium. The variables analyzed include the order of the difference calculations, the use of a perfect match layer to provide absorbing boundary conditions, the source location, the stability conditions, and dispersion in the medium. The results show that the location of the first derivative of the dynamic variable with respect to space is coincident with the location of the first derivative of the kinematic varable with respect to time. Outgoing waves are effectively absorbed and reflection at the boundary is very weak when more than 20 perfect match layer cells are used. Blot theory considers the liquid phase to be homogeneous so the ratio of liquid to solid exposure of the seismic source depends upon the medium porosity. Numerical dispersion and generation of false frequencies is reduced by increasing the accuracy of the difference calculations and by reducing the grid size and time step. Temporal second order accuracy, a tenth order spatial accuracy, and a wavelength over more than ten grid points gave acceptable numerical results. Larger grid step sizes in the lateral direction and smaller grid sizes in the vertical direction allow control of dispersion when the medium is a low speed body. This provides a useful way to simulate seismic waves in a porous coal bearing medium.展开更多
文摘Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.
基金supported by the National Basic Research Program of China (Nos.2009CB219603 and 2006CB202209)the National Natural Science Foundation of Special Equipment (No. 50727401)the National Science & Technology Pillar Program in the Eleventh Five-Year PlanPeriod (No. 2007BAK28B03)
文摘A staggered-grid finite difference method is used to model seismic wave records in a coal bearing, porous medium. The variables analyzed include the order of the difference calculations, the use of a perfect match layer to provide absorbing boundary conditions, the source location, the stability conditions, and dispersion in the medium. The results show that the location of the first derivative of the dynamic variable with respect to space is coincident with the location of the first derivative of the kinematic varable with respect to time. Outgoing waves are effectively absorbed and reflection at the boundary is very weak when more than 20 perfect match layer cells are used. Blot theory considers the liquid phase to be homogeneous so the ratio of liquid to solid exposure of the seismic source depends upon the medium porosity. Numerical dispersion and generation of false frequencies is reduced by increasing the accuracy of the difference calculations and by reducing the grid size and time step. Temporal second order accuracy, a tenth order spatial accuracy, and a wavelength over more than ten grid points gave acceptable numerical results. Larger grid step sizes in the lateral direction and smaller grid sizes in the vertical direction allow control of dispersion when the medium is a low speed body. This provides a useful way to simulate seismic waves in a porous coal bearing medium.
