第一章研究了一类高阶波动方程的有限差分法。
Chapter one studied the finite difference methods of a class of high-order wave equations?
高斯束是波动方程在特定射线附近的高频渐近解。
Gaussian beam is the asymptotic solution of wave equation concentred at the central ray.
波动方程方法是地震模拟和成像的基本方法之一。
Wave equation method is one of the fundamental techniques for seismic modeling and imaging.
这种方法也同样适用于求解其它非线性波动方程。
It indicates that the method is also suitable for solving other nonlinear evolution equations.
这样一来现在称为一维的波动方程就第一次出现了。
Thus what is now called the wave equation in one spatial dimension appears for the first time.
讨论了求解无限区域内波动方程的人工边界条件问题。
We consider the problem of constructing artificial boundary conditions for the wave equation.
这就是我们现在所说的连续性方程，推导波动方程的必要条件之一。
This is what we now call the equation of continuity, one of the relationships necessary for the derivation of the wave equation.
研究具非线性耗散项的强迫拟线性波动方程的初值问题。
We consider the initial value problems of forced quasilinear wave equation with nonlinear dissipation.
格点系统与非线性波动方程是两类很重要的无穷维系统。
Lattice systems and nonlinear wave equations are two kinds of very important infinite dimensional dynamical systems.
偏移的目的是要反演波动方程系数的奇性(层速度的间断面)。
The purpose of migration is to inversely solve for the singularity (interrupted surface of interval velocity) of wave equation coefficient.
共接收点倾斜叠加波动方程偏移，本质上是一种叠前偏移方法。
Wave equation migration after common receiving point slant stacks (WEMCRPSS) is essentially a prestack migration method.
本文提出一个新的坐标又换，可得到一套新的波动方程偏移算法。
A new coordinate transform is here introduced to obtain a new family of wave equation migration algorithms.
波动方程叠前深度偏移技术是复杂地表地震资料成像的有效方法。
Wave equation prestack depth migration technique is an effective method of seismic data imaginating in complicated surfaces.
结果表明该方法简单有效，并且可以应用到其它的非线性波动方程。
The results show the method is simple and effective and can be applied to other nonlinear wave equations.
另外，我们也可以利用波动方程和适当的边界条件以得出一个特解。
Alternatively, one may utilize the wave equation and appropriate boundary conditions to yield a specific solution.
利用波传播理论，建立损伤介质的一维波动方程及反问题分析理论。
Using the theory of wave propagation, one-dimensional wave equation and inverse problem of damaged medium was established and analyzed.
双平方根(dsr)方程为波动方程偏移提供了一种新的理论框架。
Double square root (DSR) equation has provided a new theoretical framework for developing wave equation migration.
提出了一套基于平面波分解的波动方程叠前地震数据深度偏移方法。
Based on plane wave decomposition, We propose a wave-equation depth migration method for pre-stack seismic data.
采用真振幅单程波动方程进行计算，补偿了几何扩散造成的能量损失；
Using true-amplitude one-way wave equation, the energy loss by geometric diffusion can be compensated.
应用现有的波动方程求解方法解决工程实际问题尚存在一定的局限性。
The known numerical methods of the wave equation have some shortcoming when applied to practical problems.
通过改变模型表面边界条件，求解波动方程实现多情景地震数值模拟。
Seismic numerical simulation in different conditions was done by solving wave equation and changing the surface border conditions.
最后给出了构造的单程波动方程在开发常规WIMIG偏移模块中的应用。
The application of such one-way wave equation to exploiting WIMIG module for migration is described finally.
高斯射线束方法是将波动方程和射线理论相结合的一种地震正演模型方法。
Gaussian beam method is essentially a seismic forward modeling method that combines wave equation and ray theory.
从近轴波动方程出发推导了窄带和宽带双曲正割脉冲光束的解析传输公式。
Starting from paraxial wave equation, analytical propagation expressions of hyperbolic secant pulsed beams with narrowband and broadband are derived.
本文利用能量扰动法得到具边界记忆项波动方程初边值问题解的指数衰减性。
The exponent decay of solution of wave equation with boundary memory is obtained by the energy method.
在波动方程有限差分数值模拟基础上，用波形记录残差平方并建立目标函数。
The objective function can be built based on the finite difference modeling for the wave equation.
复杂介质中地震波的传播多是通过求取单程或双程波动方程的数值解进行模拟的。
Propagation of seismic wave in complex medium is mostly simulated by numeric solution of oneway or two-way wave equation.
本文通过引入一个与波的入射角度有关的参量，给出一种单程波动方程的构造方法。
We present a method for constructing one-way wave equation with the use of a parameter that is related to the Angle of wave incidence.
本文通过引入一个与波的入射角度有关的参量，给出一种单程波动方程的构造方法。
We present a method for constructing one-way wave equation with the use of a parameter that is related to the Angle of wave incidence.
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