共查询到20条相似文献，搜索用时 203 毫秒
1.
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
2.
L. Klimeš 《Studia Geophysica et Geodaetica》2006,50(3):417-430
Explicit equations for the spatial derivatives and perturbation derivatives of amplitude in both isotropic and anisotropic
media are derived. The spatial and perturbation derivatives of the logarithm of amplitude can be calculated by numerical quadratures
along the rays.
The spatial derivatives of amplitude may be useful in calculating the higher-order terms in the ray series, in calculating
the higher-order amplitude coefficients of Gaussian beams, in estimating the accuracy of zero-order approximations of both
the ray method and Gaussian beams, in estimating the accuracy of the paraxial approximation of individual Gaussian beams,
or in estimating the accuracy of the asymptotic summation of paraxial Gaussian beams. The perturbation derivatives of amplitude
may be useful in perturbation expansions from elastic to viscoelastic media and in estimating the accuracy of the common-ray
approximations of the amplitude in the coupling ray theory. 相似文献
3.
In the computation of paraxial travel times and Gaussian beams, the basic role is played by the second-order derivatives of
the travel-time field at the reference ray. These derivatives can be determined by dynamic ray tracing (DRT) along the ray.
Two basic DRT systems have been broadly used in applications: the DRT system in Cartesian coordinates and the DRT system in
ray-centred coordinates. In this paper, the transformation relations between the second-order derivatives of the travel-time
field in Cartesian and ray-centred coordinates are derived. These transformation relations can be used both in isotropic and
anisotropic media, including computations of complex-valued travel times necessary for the evaluation of Gaussian beams. 相似文献
4.
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
5.
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
6.
A note on dynamic ray tracing in ray-centered coordinates in anisotropic inhomogeneous media 总被引：1，自引：0，他引：1
V. Červený 《Studia Geophysica et Geodaetica》2007,51(3):411-422
Dynamic ray tracing plays an important role in paraxial ray methods. In this paper, dynamic ray tracing systems for inhomogeneous
anisotropic media, consisting of four linear ordinary differential equations of the first order along the reference ray, are
studied. The main attention is devoted to systems expressed in a particularly simple choice of ray-centered coordinates, here
referred to as the standard ray-centered coordinates, and in wavefront orthonormal coordinates. These two systems, known from
the literature, were derived independently and were given in different forms. In this paper it is proved that both systems
are fully equivalent. Consequently, the dynamic ray tracing system, consisting of four equations in wavefront orthonormal
coordinates, can also be used if we work in ray-centered coordinates, and vice versa.
vcerveny@seis.karlov.mff.cuni.cz 相似文献
7.
Born正演是一种常用的地震波场正演模拟方法,也是线性化地震反演的理论基础.在实际应用时,Born正演通常结合常规的地震射线方法进行实现.为了克服常规地震射线方法的弊端,并且保证地震波场的模拟精度和计算效率,本文提出了一种基于高斯束的一阶散射波场Born正演方法.该方法分为两个环节:首先,我们利用高斯束的走时和振幅信息将地下散射点处的反射率映射为地表束中心位置处的局部平面波;然后,我们利用逆倾斜叠加将局部平面波转化为接收点处的时空域散射波场.在具体的实施过程中,我们提出一种以wavelet-bank方式实现的局部平面波合成方法,同现有的算法相比,可以在保持计算精度的同时,大大减少计算时间;此外,我们还利用最速下降法优化了高斯束的迭代循环过程,进一步提高了Born正演的计算效率.两个模型的应用效果证明,本文所提出的高斯束Born正演方法可以精确、高效的实现声波介质一次散射波场的正演模拟,为三维大规模地震波场的正演问题提供了一种切实可行的实现方案. 相似文献
8.
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
9.
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
10.
转换波偏移可以利用纵横波波场信息,得到高分辨率的成像结果,从而为油藏描述提供高质量的地震资料.目前的研究主要是利用纵波波场信息进行偏移成像,然而,传统的纵波方法在复杂探区成像时具有一定的局限性.为此,本文在各向异性介质声波射线追踪算法的基础上,推导出各向异性介质转换波射线追踪方程,发展了一种转换波射线追踪算法;并将研究的追踪算法应用到偏移成像中,提出了一种各向异性VTI介质角度域转换波高斯束偏移成像方法.通过各向异性VTI介质断块模型和复杂构造模型试算,说明了本文方法的正确性和有效性.模型试算的结果表明,在考虑地下各向异性时,本文研究的方法具有更好的成像效果,提取的角道集结果可以为偏移速度分析提供依据. 相似文献
11.
高斯束偏移虽然克服了Kirchhoff偏移不能处理多波至和单程波动方程偏移不能对陡倾构造准确成像的问题,但在复杂地表条件下其偏移精度取决于所选择的初始束宽度,即当初始宽度较小时,近地表成像精度较高,但此时中深层成像质量较差;反之当初始宽度较大时,中深层成像质量提高,但近地表成像精度降低.针对高斯束偏移中深层和浅层成像精度的矛盾,本文发展了一种适用于陆地复杂地表条件的叠前菲涅尔束偏移方法.基于惠更斯-菲涅尔原理,本文首先给出了菲涅尔束的概念及其表征的格林函数,并采用有效邻域波场近似理论和反褶积成像条件,导出了复杂地表条件下叠前保幅深度偏移公式.最后,针对常规旁轴射线追踪中的数值噪音,给出了一种压制策略.同高斯束偏移相比,本文方法不仅解决了中深层和浅层成像精度的矛盾,而且提高了复杂地表条件下平面波的分解精度,使得偏移结果更加准确可靠.典型的模型算例验证了本文方法的有效性和稳健性. 相似文献
12.
13.
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
14.
We present a Gaussian packet migration method based on Gabor frame decomposition and asymptotic propagation of Gaussian packets. A Gaussian packet has both Gaussian‐shaped time–frequency localization and space–direction localization. Its evolution can be obtained by ray tracing and dynamic ray tracing. In this paper, we first briefly review the concept of Gaussian packets. After discussing how initial parameters affect the shape of a Gaussian packet, we then propose two Gabor‐frame‐based Gaussian packet decomposition methods that can sparsely and accurately represent seismic data. One method is the dreamlet–Gaussian packet method. Dreamlets are physical wavelets defined on an observation plane and can represent seismic data efficiently in the local time–frequency space–wavenumber domain. After decomposition, dreamlet coefficients can be easily converted to the corresponding Gaussian packet coefficients. The other method is the Gabor‐frame Gaussian beam method. In this method, a local slant stack, which is widely used in Gaussian beam migration, is combined with the Gabor frame decomposition to obtain uniform sampled horizontal slowness for each local frequency. Based on these decomposition methods, we derive a poststack depth migration method through the summation of the backpropagated Gaussian packets and the application of the imaging condition. To demonstrate the Gaussian packet evolution and migration/imaging in complex models, we show several numerical examples. We first use the evolution of a single Gaussian packet in media with different complexities to show the accuracy of Gaussian packet propagation. Then we test the point source responses in smoothed varying velocity models to show the accuracy of Gaussian packet summation. Finally, using poststack synthetic data sets of a four‐layer model and the two‐dimensional SEG/EAGE model, we demonstrate the validity and accuracy of the migration method. Compared with the more accurate but more time‐consuming one‐way wave‐equation‐based migration, such as beamlet migration, the Gaussian packet method proposed in this paper can correctly image the major structures of the complex model, especially in subsalt areas, with much higher efficiency. This shows the application potential of Gaussian packet migration in complicated areas. 相似文献
15.
Vlastislav Červený 《Studia Geophysica et Geodaetica》2013,57(2):267-275
Recently, several expressions for the two-point paraxial travel time in laterally varying, isotropic or anisotropic layered media were derived. The two-point paraxial travel time gives the travel time from point S′ to point R′, both these points being situated close to a known reference ray Ω, along which the ray-propagator matrix was calculated by dynamic ray tracing. The reference ray and the position of points S′ and R′ are specified in Cartesian coordinates. Two such expressions for the two-point paraxial travel time play an important role. The first is based on the 4 × 4 ray propagator matrix, computed by dynamic ray tracing along the reference ray in ray-centred coordinates. The second requires the knowledge of the 6 × 6 ray propagator matrix computed by dynamic ray tracing along the reference ray in Cartesian coordinates. Both expressions were derived fully independently, using different methods, and are expressed in quite different forms. In this paper we prove that the two expressions are fully equivalent and can be transformed into each other. 相似文献
16.
Paraxial ray methods have found broad applications in the seismic ray method and in numerical modelling and interpretation
of high-frequency seismic wave fields propagating in inhomogeneous, isotropic or anisotropic structures. The basic procedure
in paraxial ray methods consists in dynamic ray tracing. We derive the initial conditions for dynamic ray equations in Cartesian
coordinates, for rays initiated at three types of initial manifolds given in a three-dimensional medium: 1) curved surfaces
(surface source), 2) isolated points (point source), and 3) curved, planar and non-planar lines (line source). These initial
conditions are very general, valid for homogeneous or inhomogeneous, isotropic or anisotropic media, and for both a constant
and a variable initial travel time along the initial manifold. The results presented in the paper considerably extend the
possible applications of the paraxial ray method. 相似文献
17.
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
18.
《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
19.
基于Born散射理论的二维黏声介质高斯波束正演 总被引：1，自引：0，他引：1
Born散射理论可以通过省略高阶项实现针对一次散射波场的模拟.在这一理论的基础上,本文提出了一种针对二维黏声介质的一次散射波场高斯束Born正演方法.在该方法中,格林函数通过一系列不同初射方向的高斯波束累加获得,可以计算多至走时波场,保证了正演算法的计算精度.同时为了提高计算效率,正演方法使用了wavelet-bank方式合成局部平面波.区别于针对声波介质正演的wavelet-bank使用方法,文中将介质黏滞性信息融入了局部平面波的wavelet-bank合成方法中,以此实现针对黏声介质的快速一次散射波场模拟.两个模型的计算结果表明:本文提出的黏声介质高斯波束正演方法具有良好的计算精度以及较高的计算效率. 相似文献
20.
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