P-and S-wavefield simulations using both the firstand second-order separated wave equations through a high-order staggered grid finite-difference method

In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations： the first-order （velocity-stress） and the second- order （displacement-stress） separate elastic wave equa- tions, with the first-order （velocity-stress） and the second- order （displacement-stress） full （or mixed） elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.

Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo＇s amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^（3＋）：YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp（α＇L）,which is previously employed to describe the relationship between echo＇s efficiency and thickness,should be modified as 1.3 · 0.09 exp（2.4 ·α＇L） with the propagation of echo considered.

一般正交曲线坐标系中的WEFDTD

相对于时域有限差分法,波动方程时域有限差分法(WEFDTD)具有程序简单、节约内存和机时等优势,但目前WEFDTD的应用还局限于直角坐标系,计算精度也只有二阶。为了把WEFDTD推广到一般正交曲线坐标系(GOC),在GOC中用中心差分离散波动方程,得到了GOC中具有二阶精度的WEFDTD迭代公式。为了提高计算精度,用泰勒公式和波动方程把对时间的导数转化为对空间的导数,用具有高阶精度的导数近似公式替代泰勒公式和波动方程中对空间的导数,实现了GOC中的WEFDTD的高阶算法。相对于具有二阶精度的算法,高阶算法没有增加存储量。数值实验证实了方法的有效性。

WEFDTD的一种新激励源

研究了"总场-散射场源"在波动方程时域有限差分法(WEFDTD)中的应用方法,这一问题的难点是如何把基本差分格式应用于总场区和散射场区的分界面。具体做法是将激励源设置在两区域的分界面上,并基于总场-散射场原理对基本差分格式加以修正,使得用其刷新某一网格点的总场值或散射场值时,该点周围四个网格点能同时提供总场值或散射场值。这一技术有效地克服了WEFDTD的已有激励源的不足。使用这一技术数值模拟了简谐波和高斯脉冲的传播过程,发现计算结果和解析解符合得很好。

WEFDTD(2M,2N)的一种实现方法

采用高阶差分格式能有效地减小波动方程时域有限差分法(WEFDTD)的数值色散和计算误差。文章提出了WEFDTD(2M,2N)的一种实现方法,把对时间的高阶差分转化为对空间的差分,相对于WEFDTD(2,2),并不增加存储量。数值实验证实了这一方法的有效性。

Propagation characteristics of oblique incidence terahertz wave through non-uniform plasma

The propagation characteristics of oblique incidence terahertz(THz) waves through non-uniform plasma are investigated by the shift-operator finite-difference time-domain(SO-FDTD) method combined with the phase matching condition.The electron density distribution of the non-uniform plasma is assumed to be in a Gaussian profile. Validation of the present method is performed by comparing the results with those obtained by an analytical method for a homogeneous plasma slab.Then the effects of parameters of THz wave and plasma layer on the propagation properties are analyzed. It is found that the transmission coefficients greatly depend on the incident angle as well as on the thickness of the plasma, while the polarization of the incident wave has little influence on the propagation process in the range of frequency considered in this paper. The results confirm that the THz wave can pass through the plasma sheath effectively under certain conditions,which makes it a potential candidate to overcome the ionization blackout problem.

用指数差分实现有耗介质的WEFDTD方法

提出了有耗介质下的波动方程时域有限差分法(WEFDTD),并应用得到其指数差分的差分格式。与传统的FDTD和采用普通差分的WEFDTD相比,提高了计算精度,且不增加存储量。同时,将这一差分方法推广得到其高阶形式。数值实验证明了这一方法的有效性。

A Revised Piecewise Linear Recursive Convolution FDTD Method for Magnetized Plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method improves accuracy over the original recursive convolution （RC） FDTD approach and current density convolution （JEC） but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method.

Splitting Finite Difference Methods on Staggered Grids for the Three-Dimensional Time-Dependent Maxwell Equations

In this paper,we study splitting numerical methods for the three-dimensional Maxwell equations in the time domain.We propose a new kind of splitting finitedifference time-domain schemes on a staggered grid,which consists of only two stages for each time step.It is proved by the energy method that the splitting scheme is unconditionally stable and convergent for problems with perfectly conducting boundary conditions.Both numerical dispersion analysis and numerical experiments are also presented to illustrate the efficiency of the proposed schemes.

“总场-散射场源”在波动方程时域有限差分法中的应用研究

研究了"总场-散射场源"在波动方程时域有限差分法(WEFDTD)中的应用方法,这一问题的难点是如何把基本差分格式应用于总场区和散射场区的分界面。具体做法是将激励源设置在两区域的分界面上,并基于总场-散射场原理对基本差分格式加以修正,使得用其刷新某一网格点的总场值或散射场值时,该点周围四个网格点能同时提供总场值或散射场值。这一技术有效地克服了WEFDTD的已有激励源的不足。使用这一技术,数值模拟了简谐波和高斯脉冲的传播过程,发现计算结果和解析解符合得很好。

Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium

This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L2 and H1 norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L2 and H1 norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.

Optimal error estimates and modified energy conservation identities of the ADI-FDTD scheme on staggered grids for 3D Maxwell's equations

This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain （ADI-FDTD） method which is a popular scheme for solving the 3D Maxwell＇s equations. Precisely, for the case with a perfectly electric conducting （PEC） boundary condition we establish the optimal second-order error estimates in both space and time in the discrete Hi-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell＇s equations introduced in this paper. ~rthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.

SO-FDTD Analysis of the Plasma Reflectance of Epstein Distribution

The analysis of electromagnetic propagation in a dispersive medium is complicated in the time-domain because its dielectric constant is frequency-dependent. In this paper, the dielectric constant of the dispersive medium is written as a rational polynomial function, and the relationship between D and E is derived in the time-domain. It is referred to as the shift operator finite-different time-domain （SO-FDTD） method. Compared to an analytical solution and a piecewise linear current density recursive convolution （PLJERC） solution, the high accuracy and efl%iency of this method is verified by calculating the reflectance of the electromagnetic wave through a cold plasma slab. As the electron density in plasma is distributed as the Epstein formula, the effect of distribution grads and electron collision frequency on the reflectance is calculated by using the SO-FDTD method. The result shows that the increase in the distribution grads coefficient affects the reflectance sharply. When it comes to a smaller distribution grads coelBcient, the increase of the collision frequency showed a significant effect on the reflectance, but on the contrary, there is actually less and less effect till it disappears.