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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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笛卡尔坐标系中经典的程函方程在静校正、叠前偏移、走时反演、地震定位、层析成像等许多地球物理工作都有应用,然而用其计算起伏地表的地震波走时时却比较困难.我们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了曲线坐标中的程函方程,此时,曲线坐标系的程函方程呈现为各向异性的程函方程(尽管在笛卡尔坐标系中介质是各向同同性的).然后尝试用求解各向同性程函方程的快速推进法和Lax-Friedrichs快速扫描算法来分别求解该方程.数值试验表明未加考虑各向异性程函方程与各向同性程函方程的差别而把求解各向同性程函方程的快速推进法直接拓展到曲线坐标中的程函方程的做法是错误的,而Lax-Friedrichs快速扫描算法总能稳定地求解曲线坐标系的程函方程,进而有效地处理了地表起伏的情况,得到稳定准确的计算结果. 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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多个震源组合激发通过改变激发延时,可以得到沿某方向传播的地震波场,即定向地震波场激发技术,它可用于特定目标体的照明与探测之中.本文以水平地表的组合震源定向激发原理为基础,推导了倾斜地表情况下的组合震源定向激发公式,并计算绘制了其理论方向图.另外本文将组合震源波场定向方法推广至任意起伏地表,根据惠更斯菲涅尔原理,提出了旋转坐标方法,即将水平坐标旋转至定向波场传播方向法向的倾斜坐标,可方便地计算震源传播至定向波场波前面的走时,作为组合震源的激发延时.根据本文提出的方法,我们分别计算了倾斜地表条件与复杂地表条件定向地震波场的组合震源延时参数,通过波动方程数值模拟技术得到的波场快照验证了本文方法的有效性. 相似文献
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走时计算广泛应用于地震数据处理中,其中对复杂地表地形的处理一直是走时计算的关键和难点.相比于传统的规则网格,贴体网格的建模方式可以完美地刻画地表的起伏形态.然而,目前常用的方法在利用贴体网格变换解决复杂地形问题的同时,需要针对性地发展适应贴体网格的特殊求解方法,这导致算法复杂且在网格扭曲较大的地方易造成精度损失.基于物理信息约束的神经网络是一种无网格方法,它对程函方程的求解不受具体网格形态的限制.为此,本文中我们将基于物理信息约束的神经网络和贴体网格结合,提出一种有效计算复杂模型中地震波走时的方法;用贴体网格构建任意复杂地质体,然后用基于物理信息约束的神经网络求解该复杂地质体上的地震波传播的走时.另外,我们使用残差神经网络替换了原有的神经网络架构,这在一定程度上提高了神经网络的学习能力.我们利用三组模型的数值模拟结果来验证方法的有效性和高精度;同时讨论了训练替代模型和迁移学习等神经网络技术在复杂模型中计算走时的应用,这极大地加速了实际问题的求解过程,有望在具体问题的求解中得到广泛应用. 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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三维起伏地表条件下的地震波走时计算技术是研究三维起伏地表地区很多地震数据处理技术的基础性工具.为了获得适应于任意三维起伏地表且计算精度高的走时算法,提出三维不等距迎风差分法.该方法采用不等距网格剖分三维起伏地表模型,通过在迎风差分格式中引入不等距差分格式、Huygens原理及Fermat原理来建立地表附近的局部走时计算公式,并通过在窄带技术中设定新的网格节点类型来获得三维起伏地表条件下算法的整体实现步骤.精度及算例分析表明:三维不等距迎风差分法具有很高的计算精度且能够适应于任意三维起伏地表模型. 相似文献
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三维复杂黄土塬区初至走时计算与特征分析,对于分析复杂黄土塬区地震波运动学特征、观测系统设计、初至拾取及层析反演等均具有重要意义.针对该问题：首先,采用三维分区局部变加密不等距网格剖分复杂黄土塬速度模型;然后,建立基于费马原理和迎风格式的双线性插值局部走时算法,采用修正后的群推进法作为波前扩展方式;最后,以理论模型考察了算法的精度与效率、分析了三维复杂黄土塬区地震初至波的走时特征.结果表明：变加密网格策略能在增加很少计算量的情况下,大幅降低因震源奇异性引起的计算误差问题,同时还能无条件稳定且灵活的适应三维复杂黄土塬区的复杂地震地质条件;和层状均匀模型相比,黄土塬区地震初至波的走时场和时距曲线较为复杂. 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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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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Hui Sun Jian-Guo Sun Zhang-Qing Sun Fu-Xing Han Zhi-Qiang Liu Ming-Chen Liu Zheng-Hui Gao Xiu-Lin Shi 《应用地球物理》2017,14(1):56-63
3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method (FMM) is useful for calculating 3D traveltime and has proven to be efficient and stable. However, it has low calculation accuracy near the source, which thus gives it low overall accuracy. This paper proposes a joint traveltime calculation method to solve this problem. The method firstly employs the wavefront construction method (WFC), which has a higher calculation accuracy than FMM in calculating traveltime in the small area near the source, and secondly adopts FMM to calculate traveltime for the remaining grid nodes. Due to the increase in calculation precision of grid nodes near the source, this new algorithm is shown to have good calculation precision while maintaining the high calculation efficiency of FMM, which is employed in most of the computational area. Results are verified using various numerical models. 相似文献
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射线追踪是地震波走时层析成像的基础,射线空间位置的准确性及射线走时的精度决定了层析成像的可靠性.本文根据哈密尔顿系统可以有效提高程函方程解稳定性的特性,采用辛几何算法（SAM-Symplectic Algorithm Method）及二维三次卷积插值技术进行地震波射线追踪.由于采用了SAM算法,保证了地震波波前精度,提高了射线空间位置的准确性.数值模拟结果表明SAM既能保证哈密尔顿系统的稳定性又具有运算速度快的特点,提高了射线追踪的计算精度. 相似文献