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1.
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
2.
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
3.
The application of Maslov asymptotic theory in a general 3-D mixed subspace of 6-D complex phase space is proposed to obtain the integral superpositions of Gaussian packets and beams. The ray method and the superposition of plane waves (Maslov method of Chapman and Drumond [7]) are special limiting cases of the above mentioned approach. The same high-frequency asymptotic expansion formulae for seismic body waves were derived previously in [8] using the Gaussian beam method. 相似文献
4.
Sensitivity of seismic waves to structure 总被引：2，自引：0，他引：2
Luděk Klime? 《Studia Geophysica et Geodaetica》2012,56(2):483-520
We study how the perturbations of a generally heterogeneous isotropic or anisotropic structure manifest themselves in the wavefield, and which perturbations can be detected within a limited aperture and a limited frequency band. A short-duration broad-band incident wavefield with a smooth frequency spectrum is considered. In-finitesimally small perturbations of elastic moduli and density are decomposed into Gabor functions. The wavefield scattered by the perturbations is then composed of waves scattered by the individual Gabor functions. The scattered waves are estimated using the first-order Born approximation with the paraxial ray approximation. For each incident wave, each Gabor function generates at most 5 scattered waves, propagating in specific directions and having specific polarisations. A Gabor function corresponding to a low wavenumber may generate a single broad-band unconverted wave scattered in forward or narrow-angle directions. A Gabor function corresponding to a high wavenumber usually generates 0 to 5 narrow-band Gaussian packets scattered in wide angles, but may also occasionally generate a narrow-band P to S or S to P converted Gaussian packet scattered in a forward direction, or a broad-band S to P (and even S to S in a strongly anisotropic background) converted wave scattered in wide angles. In this paper, we concentrate on the Gaussian packets caused by narrow-band scattering. For a particular source, each Gaussian packet scattered by a Gabor function at a given spatial location is sensitive to just a single linear combination of 22 values of the elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered wave does not fall into the aperture covered by the receivers and into the legible frequency band. 相似文献
5.
delta波包可由高斯波束经傅里叶逆变换得到,是高斯波束在时空域的表达.它最早出现在合成理论地震图的研究中,本文将其应用于偏移领域.通过delta波包叠加表达时间域格林函数,可将高斯波束偏移由频率域转换到时间域,再结合Rayleigh积分和激励时间成像条件,本文给出了基于delta波包叠加的深度偏移算法.该偏移算法可在时间域直接计算,但因包含褶积运算,成像时将耗费大量的计算时间.针对这一问题,本文提出了将褶积简化为乘积的近似公式.近似后的偏移算法,不仅保留了高斯波束偏移的优点,而且计算效率得到显著提升.文中通过两个数值算例验证了上述结论. 相似文献
6.
The procedure of choosing the shape of Gaussian beams in order to minimize a given object function of a certain kind is proposed. The general form of the object function enables both the average square of the quadratic variation of the phase and the average square of the beamwidth to be minimized along the central ray. The error of the transformation of the Gaussian beams at the structural interfaces may also be taken into account. Most of the hitherto published suggestions of how to chose the shape of Gaussian beams are special cases of the described procedure. The aim of this paper is not to propose the object function to be minimized, but only to describe the minimization of a given object function. The minimization assumes the a priori known lengths of the central rays of the Gaussian beams (i.e. the lengths of the beams are not free parameters in the minimization procedure). 相似文献
7.
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
8.
9.
Luděk Klimeš 《Studia Geophysica et Geodaetica》1994,38(2):140-156
Summary The robust nonlinear approach by Tarantola and Valette, consisting in direct evaluation of the "probability" density function,
is supplemented with the paraxial ray approximation of the travel time. A sufficiently dense 2-parametric system of rays from
each receiver is evaluated only once for all hypocentre determinations. The interpolation formulae for the travel times apply
to all travel-time branches. Their derivation is based on the summation of Gaussian packets. The proposed algorithm for determining
the hypocentre is able to find all of its possible locations. 相似文献
10.
高斯波包（Gaussian packet）传播算子可在局部时空域高效地计算局部波包的传播.高斯波包叠前深度偏移的基础是在Gabor变换域描述观测数据,再利用高斯波包传播算子计算炮点波场和检波点波场,两者相关即可得到偏移结果.利用炮道集的局部τ-p特征在Gabor变换域表达观测数据,可以仅关注部分高斯波包框架函数上的数据投影,这样既实现了波场的压缩存储,同时可利用高斯波包传播算子反传框架函数以实现整个炮道集的快速反传.这些综合了观测数据局部τ-p特征的高斯波包函数称为特征高斯波包（characteristic Gaussian packet,CGP）,相应的波场反传称为特征高斯波包反传.理论及数值分析证明了上述特征高斯波包反传方法是有效且快速的.炮点正传波场也利用高斯波包传播算子模拟.利用互相关成像条件可实现特征高斯波包叠前深度偏移（characteristic Gaussian packet pre-stack depth migration,CGPM）.由于高斯波包传播算子描述了局部方向及局部空间的波场,所以CGPM可以自然地提取角度域成像道集（ADCIG）,并易于实现面向目标叠前深度偏移,从而作为偏移引擎为偏移速度分析（MVA）服务.数值实验证明了CGPM和面向目标CGPM的有效性和实用性. 相似文献
11.
KLAUS HELBIG 《Geophysical Prospecting》1990,38(2):189-220
Wavefront charts in anisotropic gradient media are a useful tool in ray geometric constructions, particular in shear-wave exploration. They can be constructed by: (i) a family of wavefronts that contains a vertical plane as member - it is convenient to choose constant time increments; (ii) tracing one ray that makes everywhere the angle with the normal to the wavefront that is required by the anisotropy of the medium; (iii) scaling this ray to obtain a set of rays with different ray parameters; (iv) shifting these rays (with wavefront elements attached) so that they pass through a common source point; (v) interpolating the wavefronts between the elements. The construction is particularly simple in linear-gradient media, since here all members of the family of wavefronts are planes. Since the ray makes everywhere the angle prescribed by the anisotropy with the normal of the (plane) wavefronts, the ray has the shape of the slowness curve rotated by ?π/2. For isotropic media the slowness curve is a circle, and thus rays are circular arcs. The circles themselves intersect in the source point and in a second point above the surface of the earth. This provides a simple proof that wavefronts emanating from a point source in an isotropic linear-gradient medium are spheres: inversion of the set of circular rays with the source as centre maps the pencil of circular rays into a pencil of straight lines passing through a point. A pencil of concentric spheres around this point is perpendicular to the pencil of straight lines. On inverting back the pencil of spheres is mapped into another pencil of spheres that is perpendicular to the circular rays. 相似文献
12.
We introduce a new method for prestack depth migration of seismic common-shot gathers. The computational procedure follows
standard steps of the reverse-time migration, i.e., downward continuation of the source and the receiver wavefields, followed
by application of an imaging condition (e.g. zero-lag cross-correlation of these fields). In our method we first find a sparse
data representation with a small number of Gaussian wave packets. We then approximate the downward wavefield propagation (for
the source and the receiver fields) by a rigid flow of these wave packets along seismic rays. In this case, the wave packets
are simply translated and rotated according to the ray geometry. One advantage of using Gaussian wave packets is that analytic
formulas can be used for translation, rotation, and the application of the cross-correlation imaging condition. Moreover,
they allow more sparse representations than competing methods. Finally we formulate a computationally and memory efficient
migration procedure, as only few rays have to be traced, and since it is cheap to compute the cross-correlation for the intersecting
rays. 相似文献
13.
14.
通过对太阳风-磁层-电离层系统的全球MHD模拟,研究地球弓激波相对日地连线的旋转非对称性．模拟限于太阳风速度沿日地连线、地球磁偶极矩和行星际磁场（IMF）与日地连线垂直的简单情况．模拟结果表明,即便对于IMF强度为零的情况,弓激波相对日地连线也不具备旋转对称性质：终端面（晨昏子午面）及其向阳侧的弓激波截线的东西宽度大于南北宽度（约9%~11％）,终端面尾侧的弓激波截线东西宽度小于南北宽度（约8％）．在存在IMF的情况下,弓激波的位形同时受到磁层顶的形状和快磁声波速度各向异性的影响．磁层顶向外扩张并沿IMF方向拉伸,且其扩张和拉伸程度随IMF由北转南而增强．在磁鞘中,垂直于磁场方向的快磁声波速度高于平行方向．因此,磁层顶拉伸方向与快磁声波速度最大方向垂直,它们对弓激波位置的效应恰好相反;弓激波的最终形状取决于何种效应占据主导地位．对于终端面尾侧,快磁声波速度的各向异性起主导作用,弓激波截线沿IMF垂直方向的宽度大于平行方向．对于终端面及其向阳侧,弓激波截线的形状与IMF取向有关：在准北向或晨昏向IMF情况下,弓激波截线沿IMF垂直方向的宽度仍大于平行方向;在准南向IMF情况下,弓激波截线沿IMF垂直方向的宽度小于平行方向的．鉴于弓激波形状同IMF取向之间的密切关系,我们提议以IMF为基准方向,提取弓激波截线的平行半宽度Rb∥和垂直半宽度Rb⊥作为尺度参数．这些尺度参数和通常引入的弓激波截线的东西半宽度yb和南北半宽度zb相比,更为合理地表征了弓激波的几何性质．模拟结果表明,在终端面上,yb/zb和Rb∥/Rb⊥在IMF各向同性取向下的统计平均值均低于1,与观测得到的结论一致. 相似文献
15.
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
16.
针对提高磁异常化磁极的质量问题,提出基于离散余弦变换(DCT)的化磁极方法.以位场余弦变换谱分析为基础,从理论上推导了基于DCT的二度和三度体总场磁异常化磁极转换公式.在倾斜板状体模型实验中,化磁极误差小于0.001 nT,具有较高的精度;在单球体及多球体模型实验中,采用基于DCT的化磁极方法在5.倾斜磁化时就可以取得较好的化磁极结果,15°时化磁极的效果更加明显,其等值线的形态、幅值以及所反映的磁性体的水平位置都得到较好的恢复,这说明,采用本文方法进行化磁极时,可以取得较好的效果. 相似文献
17.
引言新丰江水库自蓄水后,发生了一系列地震。区内存在三件基本事实:一、河源断裂近期具左旋错动;二、地震主要沿水库狭谷区呈北西西向分布,河源断裂本身很少地震活动;三、震源机制解表明,主张应力轴(T)稳定于北北东向,近于水平,主压应力轴(P)则在垂 相似文献
18.
Ray-tracing techniques are used to computationally investigate the propagation of gravity waves through the middle atmosphere, as characterized by the vertically varying CIRA-86 wind and temperature models, plus a tidal wind model that varies temporally as well as vertically. For the wave parameters studied here, the background wind variation has a much stronger influence on the ray path and changes in wave characteristics than does the temperature variation. The temporal variation of the tidal component of the wind changes the observed frequency, sometimes substantially, while leaving the intrinsic frequency unaltered. It also renders temporary any critical levels that occur in the tidal region. Different starting times for the rays relative to the tidal phase provide different propagation environments, so that the temporary critical levels appear at different heights. The lateral component of the tidal wind is shown to advect propagating wave packets; the maximum lateral displacement of a packet varies inversely with its vertical group velocity. Time-dependent effects are more pronounced in local winter than in summer. 相似文献
19.
Fritz Gassmann 《Pure and Applied Geophysics》1964,58(1):63-112
Summary Section 1 (and 11) develops the concepts of the front velocity, the front gradient, the travel time in space and on seismometric profiles, the profile velocity and the profile gradient in connection with the propagation of the fronts of elastic waves in solid isotropic and anisotropic media. The sectional velocity and the sectional gradient are defined in terms of the motion of the curve of intersection of a front with a fixed surface. Section 2 (and 12) relates the coefficients of elasticity of the medium, the front types, and their respective rays. In section 12, the theory of fronts of arbitrary shape and of the corresponding rays for any anisotropic, homogeneous or inhomogeneous solid medium is summarized. In section 3 (and 13), the law of reflection and refraction of fronts on surfaces of discontinuity of arbitrary shape is presented. Sections 4 to 6 (and 14 to 16) treat some elementary applications of seismic travel time methods to homogeneous, uniaxially anisotropic media (=transverse isotropy) in greater detail. In section 4 (and 14), the travel time of a direct front generated by a point source is considered and it is shown how the coefficients of elasticity of the medium can be found based on travel time measurements. The seismic prospection of a plane reflector and of a reflecting boundary of arbitrary shape and position are discussed in section 5 (and 15). In section 6 (and 16), the seismic refraction method is used to locate a plane boundary between a homogeneous, uniaxially anisotropic and a homogeneous isotropic medium, where the boundary is perpendicular or at an arbitrary angle to the direction of anisotropy. 相似文献
20.
扰动高斯波包理论指出,在Gabor域描述模型的扰动成分,且入射波场为短时宽带信号时,扰动波场可在时间域通过高斯波包算子描述.在此基础上通过拟合反射波的走时,提出一种速度反演方法.反射波走时残差利用地震道局部波形的互相关函数表示,以走时残差的二范数作为目标函数,优化目标函数实现对速度场的反演.基于一阶Born近似,利用扰动高斯波包理论推导出目标函数对速度场的梯度是本文理论部分的核心内容.梯度包括两部分:正传的背景波场与反传的扰动高斯波包之间的互相关,反传的背景波场和正传的扰动高斯波包之间的互相关.梯度表达式中背景波场和扰动波场均利用高斯波包算子模拟.计算梯度的具体算法中,如何模拟扰动波场,以及如何计算反射波的走时残差是两个要点,文中对此做了详细的讨论.数值实验进一步阐述了反演的实现策略,实验结果表明高斯波包反射走时速度反演方法和实现策略有效可行,并得到了理想的反演结果. 相似文献