共查询到20条相似文献，搜索用时 46 毫秒
1.
The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams
diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which
reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method,
which deals with the abridged parabolic equation and describes diffraction of the Gaussian beams; (ii) complex form of the
dynamic ray tracing method, which generalizes paraxial ray approximation on Gaussian beams and (iii) paraxial WKB approximation
by Pereverzev, which gives the results, quite close to those of Babich’s method. For Gaussian beams all the methods under
consideration lead to the similar ordinary differential equations, which are complex-valued nonlinear Riccati equation and
related system of complex-valued linear equations of paraxial ray approximation. It is pointed out that Babich’s method provides
diffraction substantiation both for the paraxial CGO and for complex-valued dynamic ray tracing method. It is emphasized also
that the latter two methods are conceptually equivalent to each other, operate with the equivalent equations and in fact are
twins, though they differ by names.
The paper illustrates abilities of the paraxial CGO method by two available analytical solutions: Gaussian beam diffraction
in the homogeneous and in the lens-like media, and by the numerical example: Gaussian beam reflection from a plane-layered
medium. 相似文献
2.
Expansion of a plane wave into Gaussian beams 总被引：1，自引：0，他引：1
Summary An integral expansion which expresses a plane monochromatic wave as a superposition of Gaussian beams is found. The expansion can be used to solve many wave propagation problems in complicated structures, including laterally inhomogeneous media with curved interfaces. 相似文献
3.
R. L. Nowack 《Pure and Applied Geophysics》2003,160(3-4):487-507
— In this paper, an overview of the calculation of synthetic seismograms using the Gaussian beam method is presented accompanied by some representative applications and new extensions of the method. Since caustics are a frequent occurrence in seismic wave propagation, modifications to ray theory are often necessary. In the Gaussian beam method, a summation of paraxial Gaussian beams is used to describe the propagation of high-frequency wave fields in smoothly varying inhomogeneous media. Since the beam components are always nonsingular, the method provides stable results over a range of beam parameters. The method has been shown, however, to perform better for some problems when different combinations of beam parameters are used. Nonetheless, with a better understanding of the method as well as new extensions, the summation of Gaussian beams will continue to be a useful tool for the modeling of high-frequency seismic waves in heterogeneous media. 相似文献
4.
Optimization of the shape of Gaussian beams 总被引：1，自引：0，他引：1
K. Žáček 《Studia Geophysica et Geodaetica》2006,50(3):349-366
The applicability and accuracy of the Gaussian beam method depend on the proper choice of the shape of beams. Gaussian beams
become inaccurate solutions of the elastodynamic equation if the velocity field changes considerably within the beam width.
We present a procedure of determining the optimum initial shape of Gaussian beams based on minimizing the average squared
widths of Gaussian beams and smoothing the distribution of the optimum parameters of Gaussian beams on the Hamiltonian hypersurface
in the phase-space. The original method of smoothing represents an essential part of the algorithm, which is designed particularly
for the optimization of the shape of Gaussian beams for Gaussian beam or packet migrations. 相似文献
5.
《Journal of Atmospheric and Solar》2008,70(7):980-990
In this paper, the propagation of two initially (z=0) parallel Gaussian electromagnetic beams, propagating in the z-direction in ionosphere, has been investigated. The nonlinearity in the dielectric function, responsible for the interaction between the beams arises from the redistribution of the electron density, caused by the nonuniform distribution of electron temperature determined by the Ohmic heating of the electrons and the energy loss of electrons on account of collisions. The wave frequencies have been assumed to be much larger than the electron collision frequency and gyrofrequency. A self-consistent solution of the electromagnetic wave equation and energy balance equation (considering the solar radiation) has been obtained in the paraxial approximation. Second-order coupled ordinary differential equations have been obtained for the distance between the centers of the beams and the beam widths in the x and y directions as a function of the distance of propagation along the z-axis. Using the available database for the mid-latitude daytime ionosphere, the equations have been solved numerically for a range of parameters and a discussion of the results has been presented. The physical basis for the fact that the beams move towards each other, when the resulting irradiance distribution of the two beams has a maximum in the space between the two beams, has been highlighted. 相似文献
6.
高斯束逆时偏移是一种兼具计算效率和成像精度的深度域成像方法,能够面向目标成像.地下介质中黏滞性普遍存在,利用传统各向同性或完全弹性的成像方法处理黏滞性探区的数据会降低分辨率,并导致成像位置不准确和振幅欠估计等问题.本文在高斯束逆时偏移的基础上,通过对震源点和检波点处的波场进行衰减补偿,并结合高斯束求解时的角度信息,实现了黏声介质角度域高斯束逆时偏移方法.最后通过模型和实际资料试算对本文方法的正确性和适用性进行了验证.试算结果表明:相比于声波高斯束逆时偏移,本文方法能够对黏滞性引起的吸收衰减进行有效补偿,同时提取的角度域共成像点道集(ADCIGs)不仅可以用于分角度叠加成像压制成像噪声,而且能够为后续的偏移速度分析提供支撑. 相似文献
7.
《Journal of Atmospheric and Solar》2000,62(7):541-552
The purpose of this paper is to discuss the properties of electron beams formed by cyclotron interactions between radiation belt electrons and a quasi-monochromatic whistler wave packet from a ground-based VLF transmitter. The beams are formed due to trapping of the electrons at the forward edge of the wave packet, their acceleration inside the wave packet, the escape of the accelerated electrons from the moving backward edge of the wave packet, and their following free motion in an inhomogeneous magnetic field. A combination of these processes provides the main features of the spatial-temporal evolution of the beams which are investigated both analytically and numerically. It is shown that one or two beams can appear at one point at the same time, and that the density of the beams increases during their expansion. Motion of the pumping wave packet in the inhomogeneous magnetic field provides the variations of the initial velocity and position of the beam injection which change the spatial and temporal gradients of the parallel velocity of the beam, in contrast with the case of the pure adiabatic motion of an individual electron. Such a behaviour can be significant for the generation of secondary emissions. Numerical calculations demonstrate a wide variety of the spatio–temporal patterns of the beam parallel velocity depending on the plasma and wave packet parameters. It is shown that the most significant parameters which determine the beam characteristics are the wave packet length about the equator, its group velocity, and the initial energy and pitch angle of the electrons. 相似文献
8.
On the basis of the model of the three-dimensional (3D) generalized Kadomtsev-Petviashvili equation for magnetic field h = B ~/B the formation, stability, and dynamics of 3D soliton-like structures, such as the beams of fast magnetosonic (FMS) waves generated in ionospheric and magnetospheric plasma at a low-frequency branch of oscillations when β = 4πnT/B 2 ? 1 and β > 1, are studied. The study takes into account the highest dispersion correction determined by values of the plasma parameters and the angle θ = (B, k), which plays a key role in the FMS beam propagation at those angles to the magnetic field that are close to π/2. The stability of multidimensional solutions is studied by an investigation of the Hamiltonian boundness under its deformations on the basis of solving of the corresponding variational problem. The evolution and dynamics of the 3D FMS wave beam are studied by the numerical integration of equations with the use of specially developed methods. The results can be interpreted in terms of the self-focusing phenomenon, as the formation of a stationary beam and the scattering and self-focusing of the solitary beam of FMS waves. These cases were studied with a detailed investigation of all evolutionary stages of the 3D FMS wave beams in the ionospheric and magnetospheric plasma. 相似文献
9.
Gaussian beam summation method is used for numerical modelling of seismic wave fields in several simple types of models of media. Main attention is paid to the waves reflected from a plane interface, namely from the vicinity of a critical point. Comparison with exact solutions shows that the Gaussian beam summation method yields sufficiently accurate results even in the singular region of the critical point. By summation of Gaussian beams of waves reflected in the overcritical region even head waves are obtained. In the second part of this work, we shall investigate sensitivity of the results to various parameters, for example, to the initial width of a Gaussian beam, to the parameters of the summation of Gaussian beams, etc. 相似文献
10.
Prestack depth migration is a key technology for imaging complex reservoirs in media with strong lateral velocity variations. Prestack migrations are broadly separated into ray-based and wave-equation-based methods. Because of its efficiency and flexibility, ray-based Kirchhoff migration is popular in the industry. However, it has difficulties in dealing with the multi-arrivals, caustics and shadow zones. On the other hand, wave-equation-based methods produce images superior to that of the ray-based methods, but they are expensive numerically, especially methods based on two-way propagators in imaging large regions. Therefore, reverse time migration algorithms with Gaussian beams have recently been proposed to reduce the cost, as they combine the high computational efficiency of Gaussian beam migration and the high accuracy of reverse time migration. However, this method was based on the assumption that the subsurface is isotropic. As the acquired azimuth and maximum offsets increase, taking into account the influence of anisotropy on seismic migration is becoming more and more crucial. Using anisotropic ray tracing systems in terms of phase velocity, we proposed an anisotropic reverse time migration using the Gaussian beams method. We consider the influence of anisotropy on the propagation direction and calculate the amplitude of Gaussian beams with optimized correlation coefficients in dynamic ray tracing, which simplifies the calculations and improves the applicability of the proposed method. Numerical tests on anisotropic models demonstrate the efficiency and accuracy of the proposed method, which can be used to image complex structures in the presence of anisotropy in the overburden. 相似文献
11.
Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss–Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach. 相似文献
12.
在给出真实模型和相应光滑背景模型的情况下,如何计算扰动模型(散射体)产生的散射波场是一个有实际意义的正演问题.在Gabor变换域描述散射体,且入射波场为短时宽带信号时,散射波场可以在频率域用高斯束或时间域用高斯波包描述.相对于波动方程方法,高斯束和高斯波包的计算效率更高;背景模型光滑时,高斯束和高斯波包方法的精度也接近波动方程方法.文中导出了声波假设下应用高斯束和高斯波包计算散射波的方法.测试分析了高斯波包的计算精度.给出了一般散射体的散射波模拟策略.同时针对一个理论模型完成了本文方法计算散射波的实验,实验结果表明高斯波包散射波计算方法是有效可行的. 相似文献
13.
Robert L. Nowack Wang-Ping Chen Ulrich Kruse Saptarshi Dasgupta 《Pure and Applied Geophysics》2007,164(10):1921-1936
We carry out a sequence of numerical tests to understand conditions under which rapid changes in crustal thickness can be
reliably imaged by teleseismic body waves. Using the finite-difference method over a 2-D grid, we compute synthetic seismograms
resulting from a planar P-wavefield incident below the grid. We then image the Moho using a migration scheme based on the Gaussian beam representation
of the wavefield. The use of Gaussian beams for the downward propagation of the wavefield is particularly advantageous in
certain geologically critical cases such as overthrusting of continental lithosphere, resulting in the juxtaposition of high-velocity
mantle material over crustal rocks. In contrast to ray-based methods, Gaussian beam migration requires no special treatment
to handle such heterogeneities. Our results suggest that with adequate station spacing and signal-to-noise ratios, offsets
of the Moho, on the order of 10 km in height, can be reliably imaged beneath thickened crust at depths of about 50 km. Furthermore,
even sharp corners and edges are faithfully imaged when precise values of seismic wave speeds are available. Our tests also
demonstrate that flexibility in choices of different types of seismic phases is important, because any single phase has trade-offs
in issues such as spatial resolution, array aperture, and amplitude of signals. 相似文献
14.
自相似扩展拟合法(Self-Similar Expansion,SSE)假设日冕物质抛射(CME)具有恒定角宽度、沿径向向外传播的、自相似扩展的球形前沿,由日心出发的、与这个球形前沿相切的圆锥的圆锥角就是通常所说的CME角宽度,半角宽度取值范围是[0°,90°],固定Φ角拟合法(Fixed-Φ,FΦ)和调和均值拟合法(Harmonic-mean,HM)分别对应SSE模型的半角宽度为0°和90°的特殊情况.本文中修改后的自相似扩展拟合法(MSSE)假设CME具有自相似扩展的半球形前沿,能够提取的CME参数包括由日心出发的、圆锥截面过球心的圆锥的半圆锥角和CME的主传播方向、传播速度,其中半圆锥角取值范围是[0°,90°],FΦ和HM分别对应MSSE模型的半圆锥角为0°和45°的特殊情况,半圆锥角为90°时,CME前沿是以日心为圆心的半圆.MSSE拟合法扩大了SSE模型对CME前沿形态的描述范围,将半圆锥角作为判断CME是否能够到达、何时到达某颗卫星的重要参数.基于单颗STEREO卫星日球层成像仪(Heliospheric Imager,HI)图像,结合STEREO和ACE卫星的太阳风实地观测数据,本文深入分析了2010年23个CME事件,结果发现:在用于预报CME事件是否能到达某颗卫星、何时到达时,MSSE拟合法相比FΦ、HM和SSE拟合法,不但可以更准确地拟合CME主传播方向和传播速度,也可以缩小预计到达时间和到达速度的误差. 相似文献
15.
各向异性射线理论基础上的局部角度域叠前深度偏移方法能够为深度域构造成像与基于角道集的层析反演提供有力支撑,但是对于复杂地质构造而言,高斯度叠前深度偏移在不失高效、灵活等特点的情况下,具有明显的精度优势.为此,本文研究局部角度域理论框架下的高斯束叠前深度偏移方法.为提高算法效率与实用性,文中讨论了一种从经典弹性参数表征的各向异性介质运动学和动力学射线方程演变而来的由相速度表征的简便形式,并提出了一种比较经济的各向异性高斯束近似合成方案.结合地震波局部角度域成像原理,讨论一种适合高斯束偏移的角度参数计算方法.国际上通用的理论模型合成数据试验表明：相比局部角度域Kirchhoff叠前深度偏移成像方法,本文方法具有更高的成像精度与抗噪能力,既适用于复杂构造成像,也可为TI介质深度域偏移速度分析与模型建立提供高效的偏移引擎. 相似文献
16.
为研究地震产生的应力波在断续节理岩体中的传播规律和应力分布趋势,首先,采用数值模拟方法分析应力波通过贯通节理的传播规律,并与已有理论研究结果进行对比,验证数值分析的准确性和适用性;然后,对应力波在断续节理岩体中的传播进行数值模拟,分析透射系数在水平方向的分布趋势以及不同节理连续性对波传播的影响,并结合波的衍射原理,给出定性的理论解释。结果表明:应力波通过断续节理时,节理的透射作用会使应力波振幅减小,引起波的衰减,岩桥的衍射作用则会使波阵面由平面变为曲面,波的传播方向发生改变,从而导致应力波振幅在水平方向的分布发生变化;应力波通过断续节理的透射系数与岩桥尺寸Lr和衍射角μ相关,当衍射角比较小时,透射系数主要受岩桥尺寸Lr的影响,当衍射角较大时,岩桥尺寸Lr和衍射角μ共同影响应力波在岩体中的传播。 相似文献
17.
An Erratum has been published for this article in Earthquake Engineering & Structural Dynamics 33(6) 2004, 793. The dynamic stiffness of a foundation embedded in a multiple‐layered halfspace is calculated postulating one‐dimensional wave propagation in cone segments. In this strength‐of‐materials approach the sectional property of the cone segment increases in the direction of wave propagation. Reflections and refractions with waves propagating in corresponding cone segments occur at layer interfaces. Compared to rigorous procedures the novel method based on cone segments is easy to apply, provides conceptual clarity and physical insight in the wave propagation mechanisms. This method postulating one‐dimensional wave propagation in cone segments with reflections and refractions at layer interfaces is evaluated, calculating the dynamic stiffness of a foundation embedded in a multiple‐layered halfspace. For sites resting on a flexible halfspace and fixed at the base, engineering accuracy (deviation of ±20%) is achieved for all degrees of freedom with a vast parameter variation. The behaviour below the cut‐off frequency in an undamped site fixed at its base is also reliably predicted. The accuracy is, in general, better than for the method based on cone frustums, which can lead to negative damping. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
18.
随着我国陆上地震勘探向复杂地表探区的转移,高精度、适应性强的地震成像方法在地震资料的处理、解释及后续属性分析、储层预测中具有重要意义.本文基于有效邻域波场近似理论发展了一种成像精度更高且适用于复杂起伏地表条件的叠前保幅高斯束偏移方法.在传统水平地表高斯束偏移的基础上,本文根据中心射线附近有效邻域内高斯束表征的近似波场,导出了起伏地表条件下具有相对振幅保持的高斯束偏移公式,并给出了一种精度更高的旁轴射线传播角度计算方法.同现有的高斯束偏移方法相比,本文方法不仅考虑了起伏地表对高斯束走时的线性影响,而且首次引入了由地表高程差异和近地表速度变化引起的二次时差校正项和振幅校正项,使得成像结果更加准确可靠.两个典型模型算例验证了本文方法的正确性和有效性. 相似文献
19.
地震波在热弹性介质中的衰减性质及其相应Q值的计算方法 总被引：1，自引：1，他引：0
该文得出热弹性介质中波的基本形式有准弹性纵波、横波和具有有限传播速度的温度波,并指出横波在传播过程中同其在完全弹性介质中一样是不衰减的,而准弹性纵波和温度波是相互伴随的、衰减的。其次,给出了具有两种不同传播速度的准弹性纵波的基本形式。最后,将地震P波看作由初始位移扰动的准弹性纵波,就固定频率和固定波长两种情况分别给出了相应Qr值的计算公式和近似公式。通常人们是利用多台的地震波资料在空间域中计算Qr值,而本文得到的时间域中Qr值的近似公式,为利用单台地震P波资料计算Qr值提供了一种方法。 相似文献
20.
利用二维全隐欧拉格式对重力波在可压、非等温大气中的非线性传播过程进行了数值模拟和分析.分析结果表明，从对流层顶激发的重力波能稳定地经平流层传到中层顶，从而将能量和动量从一个区域带到另一个区域；在向上传播过程中，重力波经历了发展、位温翻转、对流直至最终破碎的演变；重力波的破碎是对流和小尺度波动的重要的源，对流不稳定和翻转是非线性现象的一个基本特征.计算还显示，扰动源的大小直接影响着重力波的非线性传播过程，当扰动源足够小时，重力波能稳定传播，而大振幅扰动可以加速重力波的破碎. 相似文献