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笛卡尔坐标系中的经典程函方程在静校正、叠前偏移、走时反演、地震定位、层析成像等很多地球物理工作中都有应用,然而用其计算起伏地表的地震波走时却比较困难.本文通过把曲线坐标系中的矩形网格映射到笛卡尔坐标系的贴体网格,推导出曲线坐标中的程函方程,而后,用Lax-Friedrichs快速扫描算法求解曲线坐标系的程函方程.研究表明本文方法能有效处理地表起伏的情况,得到准确稳定的计算结果.由于地表起伏,导致与之拟合的贴体网格在空间上的展布呈各向异性,且这种各向异性的强弱对坐标变换法求解地震初至波的走时具有重要影响.本文研究表明,随着贴体网格的各向异性增强,用坐标变换法求解地表起伏区域的走时计算误差增大,且计算效率降低,这在实际应用具有指导意义. 相似文献
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地震波走时广泛应用于静校正、层析成像、Kirchhoff偏移成像、地震定位等研究.复杂地表条件是影响走时计算精度的重要因素.近年来,发展的曲线坐标系程函方程为精细刻画起伏地表条件下的地震波走时场特征提供了新的思路.然而,基于有限差分程函方程的求解方法不可避免地受到震源奇异性的影响,即震源附近波前的曲率较大,此时使用平面波近似假设的差分格式会导致较大误差.而震源误差会随着波前的传播到达整个计算区域,从而影响整个区域的求解精度.针对该问题,本文借鉴因式分解的思想,推导建立了曲线坐标系因式分解程函方程,并针对性地发展了其数值求解方法,从根源上解决了复杂模型走时计算中的震源奇异性问题.数值实例表明因式分解法能够有效降低震源误差,显著提高起伏地表走时计算的精度和效率,为起伏地表地震波走时计算提供更佳的选择,在复杂模型的地震资料处理中展现出广泛的应用前景. 相似文献
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地震波走时计算在观测系统设计、偏移成像、速度模型走时反演和地震定位等方面起到重要作用.各向异性广泛存在于地球介质中,影响地震波传播的振幅和走时,忽略各向异性的影响将对成像、反演以及地震定位等造成一定的误差.因此对于高分辨率成像和反演,走时计算中考虑各向异性十分重要.快速扫描法不需要存储和追踪波前面信息,在各向异性初至波走时计算方面应用广泛.传统的方法通过将慢度四次方程转换为走时四次方程并结合快速扫描法求解走时.该方法没有对程函方程做近似,适用于强各向异性介质,但存在计算效率低的问题.对于求解qSV波走时,本文发展了一种在局部解中将慢度四次方程简化为二次方程解析地快速求解走时的方法,极大地提高了计算效率.对于qSH波,慢度方程是二次的,可以直接解析求解.最后,本文用各向异性均匀模型和BP复杂模型进行测试,计算结果表明走时计算准确,验证了该方法的有效性. 相似文献
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快速行进法(FMM)是一种求解程函方程数值解计算网格节点走时,然后向后处理进行射线追踪的方法.为了求取任意起伏界面下高精度多震相的地震走时与相应的射线路径,本文采用任意起伏地表条件下的的三维不等距上行差分公式结合分区多步计算技术实现了三维复杂层状起伏介质中多震相(透射、反射、转换波)地震走时的计算,利用上行有限差分公式逐次进行射线路径的追踪,并且通过与较为成熟的不规则最短路径法(ISPM)对比,验证了本算法的计算精度和有效性.数值模拟实例和对比结果表明该算法具有较高的计算精度,数值计算稳健,能灵活处理含任意三维起伏界面模型中多震相地震走时及相应射线路径的追踪问题. 相似文献
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我们发展了一种模拟复杂地表下含裂缝介质地震波场的方法,这对于解释山地地区的地震资料具有重要意义。基于Coates-Schoenberg方法,把裂缝引入到有限差分法(FD)中,从而使包含裂缝的单元里的弹性介质就具有了局部的各向异性。为了模拟起伏的地表地形,我们借助于贴体网格,将笛卡尔坐标系的具有水平对称轴的横向各向同性介质(HTI)的弹性波方程和自由边界条件变换到曲线坐标系中,采用一种稳定的、显式的二阶精度的有限差分方法离散(曲线坐标系)HTI介质中的弹性波方程。数值实例充分地展现了在不规则地球表面的影响下裂缝介质中地震波传播的复杂性。合成地震记录和波场快照表明裂缝端点产生的散射波在地表处会受不规则地表地形的作用,再次被散射;同理,地表地形产生的散射波,经过裂缝端点时也会被再次散射,尤其是瑞利面波产生的散射波,因其能量很强,严重污染了地震记录,使得识别地下裂缝等产生的有效信息变得异常困难。这对山地地震勘探中资料的解释具有重要意义。 相似文献
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全球造山带及中国大陆中西部普遍具有强烈起伏的地形条件.复杂地形条件下的地壳结构成像问题像一面旗帜引领了当前矿产资源勘探和地球动力学研究的一个重要方向.深地震测深记录中反射波的有效探测深度可达全地壳乃至上地幔顶部,而初至波通常仅能探测上地壳浅部.为克服和弥补初至波探测深度的不足,本文基于前人对复杂地形条件下初至波成像的已有研究成果,采用数学变换手段将笛卡尔坐标系的不规则模型映射到曲线坐标系的规则模型,并将快速扫描方法与分区多步技术相结合,发展了反射波走时计算和射线追踪的方法.进而利用反射波走时反演,实现起伏地形下高精度的速度结构成像,从而为起伏地形下利用反射波数据高精度重建全地壳速度结构提供了一种全新方案.数值算例从正演计算精度、反演中初始模型依赖性、反演精度、纵横向分辨率以及抗噪性等方面验证了算法的正确性和可靠性. 相似文献
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在地震波正反演研究中,考虑起伏地表和地震各向异性具有非常重要的理论意义和实际应用价值.本文在前人研究的基础上,将最短路径追踪算法引入到起伏地表各向异性介质模型的地震波走时计算中.模型剖分时,整体模型划分成正方形单元,起伏边界附近以不规则网格逼近,进而采用非规则节点布置实现非规则网格处的最短路径计算.追踪计算中采用Sena群速度近似公式,得到各向异性地震波的走时,实现了复杂地表情况下各向异性介质模型中地震波的射线追踪.理论模型计算结果显示,本文方法能够可靠地应用于复杂各向异性介质模型,具有较高的计算精度. 相似文献
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地震波走时场模拟的快速推进法和快速扫描法比较研究 总被引：3，自引：0，他引：3
地震波走时信息在叠前偏移、叠前速度分析、地震层析成像、走时反演及地震定位等中都有重要应用.快速推进法因其理论完善、精确灵活,无条件稳定,近年来已在走时计算领域得到广泛应用.快速扫描法作为求解一阶非线性双曲型偏微分方程的高效方法,已在图像处理、计算机视图、控制论等领域得到有效应用,且在走时计算方面有所应用且展现了广泛的应用前景.本文介绍了两种方法的基本原理且(通过均匀介质模型、局部低速体模型和Marmousi模型)把两种方法做了详细对比.研究结果表明:1)基于逆风差分格式的快速推进法和快速扫描法对纵横向速度变化很大的不均匀介质依然有很好的稳定性和适用性,均可以准确地计算地震波初至走时;2)对于相同的模型和在相同的计算条件下,两种方法的精度相当,但快速扫描法所耗的CPU时间较快速推进法明显减少,效率显著提高. 相似文献
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三维复杂山地条件下的各种地震波型的走时计算技术,可以直接用于复杂山地区域地震波运动学特性的分析、地震数据采集观测系统的设计以及直接基于三维复杂地表的地震数据处理技术的研发.为了在三维复杂地表条件下准确、灵活且稳定地计算各种地震波型的走时,提出一种多级次群推进迎风混合法.该算法利用不等距迎风差分法简洁稳定地处理三维复杂地表及附近的局部走时计算问题,利用计算精度不错的迎风双线性插值法处理绝大部分均匀正方体网格中的局部走时计算问题,利用群推进法模拟三维复杂地表条件下地震波前的扩展问题,利用多级次算法处理各种类型的地震波的走时计算问题.算法分析和计算实例表明:新方法具有很好的计算精度与效率,且能灵活稳定地处理三维复杂地表复杂介质条件下的多波型走时计算问题. 相似文献
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A Fast Sweeping Scheme for Calculating P Wave First-Arrival Travel Times in Transversely Isotropic Media with an Irregular Surface 总被引：2，自引：0，他引：2
Seismic wave propagation shows anisotropic characteristics in many sedimentary rocks. Modern seismic exploration in mountainous areas makes it important to calculate P wave travel times in anisotropic media with irregular surfaces. The challenges in this context are mainly from two aspects. First is how to tackle the irregular surface in a Cartesian coordinate system, and the other lies in solving the anisotropic eikonal equation. Since for anisotropic media the ray (group) velocity direction is not the same as the direction of the travel-time gradient, the travel-time gradient no longer serves as an indicator of the group velocity direction in extrapolating the travel-time field. Recently, a topography-dependent eikonal equation formulated in a curvilinear coordinate system has been established, which is effective for calculating first-arrival travel times in an isotropic model with an irregular surface. Here, we extend the above equation from isotropy to transverse isotropy (TI) by formulating a topography-dependent eikonal equation in TI media in the curvilinear coordinate system, and then use a fast sweeping scheme to solve the topography-dependent anisotropic eikonal equation in the curvilinear coordinate system. Numerical experiments demonstrate the feasibility and accuracy of the scheme in calculating P wave travel times in TI models with an irregular surface. 相似文献
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An upwind fast sweeping scheme for calculating seismic wave first‐arrival travel times for models with an irregular free surface 
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下载免费PDF全文 The topography‐dependent eikonal equation formulated in a curvilinear coordinate system has recently been established and revealed as being effective in calculating first‐arrival travel times of seismic waves in an Earth model with an irregular free surface. The Lax–Friedrichs sweeping scheme, widely used in previous studies as for approximating the topography‐dependent eikonal equation viscosity solutions, is more dissipative and needs a much higher number of iterations to converge. Furthermore, the required number of iterations grows with the grid refinement and results in heavy computation in dense grids, which hampers the application of the Lax–Friedrichs sweeping scheme to seismic wave travel‐time calculation and high‐resolution imaging. In this paper, we introduce a new upwind fast sweeping solver by discretising the Legendre transform of the numerical Hamiltonian of the topography‐dependent eikonal equation using an explicit formula. The minimisation related to the Legendre transform in the sweeping scheme is solved analytically, which proved to be much more efficient than the Lax–Friedrichs algorithm in solving the topography‐dependent eikonal equation. Several numerical experiments demonstrate that the new upwind fast sweeping method converges and achieves much better accuracy after a finite number of iterations, independently of the mesh size, which makes it an efficient and robust tool for calculating travel times in the presence of a non‐flat free surface. 相似文献
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The complex‐valued first‐arrival traveltime can be used to describe the properties of both velocity and attenuation as seismic waves propagate in attenuative elastic media. The real part of the complex‐valued traveltime corresponds to phase arrival and the imaginary part is associated with the amplitude decay due to energy absorption. The eikonal equation for attenuative vertical transversely isotropic media discretized with rectangular grids has been proven effective and precise to calculate the complex‐valued traveltime, but less accurate and efficient for irregular models. By using the perturbation method, the complex‐valued eikonal equation can be decomposed into two real‐valued equations, namely the zeroth‐ and first‐order traveltime governing equations. Here, we first present the topography‐dependent zeroth‐ and first‐order governing equations for attenuative VTI media, which are obtained by using the coordinate transformation from the Cartesian coordinates to the curvilinear coordinates. Then, we apply the Lax–Friedrichs sweeping method for solving the topography‐dependent traveltime governing equations in order to approximate the viscosity solutions, namely the real and imaginary parts of the complex‐valued traveltime. Several numerical tests demonstrate that the proposed scheme is efficient and accurate in calculating the complex‐valued P‐wave first‐arrival traveltime in attenuative VTI media with an irregular surface. 相似文献
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3D P‐wave traveltime computation in transversely isotropic media using layer‐by‐layer wavefront marching 下载免费PDF全文
下载免费PDF全文 Jiangtao Hu Junxing Cao Huazhong Wang Xingjian Wang Renfei Tian 《Geophysical Prospecting》2018,66(7):1303-1314
Subsurface rocks (e.g. shale) may induce seismic anisotropy, such as transverse isotropy. Traveltime computation is an essential component of depth imaging and tomography in transversely isotropic media. It is natural to compute the traveltime using the wavefront marching method. However, tracking the 3D wavefront is expensive, especially in anisotropic media. Besides, the wavefront marching method usually computes the traveltime using the eikonal equation. However, the anisotropic eikonal equation is highly non‐linear and it is challenging to solve. To address these issues, we present a layer‐by‐layer wavefront marching method to compute the P‐wave traveltime in 3D transversely isotropic media. To simplify the wavefront tracking, it uses the traveltime of the previous depth as the boundary condition to compute that of the next depth based on the wavefront marching. A strategy of traveltime computation is designed to guarantee the causality of wave propagation. To avoid solving the non‐linear eikonal equation, it updates traveltime along the expanding wavefront by Fermat's principle. To compute the traveltime using Fermat's principle, an approximate group velocity with high accuracy in transversely isotropic media is adopted to describe the ray propagation. Numerical examples on 3D vertical transverse isotropy and tilted transverse isotropy models show that the proposed method computes the traveltime with high accuracy. It can find applications in modelling and depth migration. 相似文献
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Tariq Alkhalifah 《Geophysical Prospecting》2002,50(4):373-382
A linearized eikonal equation is developed for transversely isotropic (TI) media with a vertical symmetry axis (VTI). It is linear with respect to perturbations in the horizontal velocity or the anisotropy parameter η. An iterative linearization of the eikonal equation is used as the basis for an algorithm of finite-difference traveltime computations. A practical implementation of this iterative technique is to start with a background model that consists of an elliptically anisotropic, inhomogeneous medium, since traveltimes for this type of medium can be calculated efficiently using eikonal solvers, such as the fast marching method. This constrains the perturbation to changes in the anisotropy parameter η (the parameter most responsible for imaging improvements in anisotropic media). The iterative implementation includes repetitive calculation of η from traveltimes, which is then used to evaluate the perturbation needed for the next round of traveltime calculations using the linearized eikonal equation. Unlike isotropic media, interpolation is needed to estimate η in areas where the traveltime field is independent of η, such as areas where the wave propagates vertically.
Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach. 相似文献
Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach. 相似文献
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本文以基于改进BISQ模型的二维双相各向同性介质一阶速度-应力方程为基础，推导出了曲线坐标系下对应的方程，然后采用低频散、低耗散的同位网格MacCormack有限差分法来离散方程，并采用紧致的单边MacCormack差分格式结合牵引力镜像法来施加自由地表边界条件，实现了地震波场数值模拟.曲线网格有限差分法采用贴体网格来描述自由表面，地表的网格线紧贴地形，避免了台阶近似造成的数值散射.数值模拟结果表明，在双相介质起伏自由地表和分界面处，各类波型复杂的反射透射规律可以清晰展现，曲线网格有限差分法可以精确地解决地震波在含起伏地表的双相各向同性介质中的传播问题. 相似文献
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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