基于双线性插值的三维横向各向同性介质初至波射线追踪

给出了基于旅行时双线性插值(LTI)的三维横向各向同性(VTI)介质中的地震初至波旅行时计算及射线追踪方法,通过三维均匀及水平层状VTI介质模型的试算,证实了该方法的准确性及适应性.该方法可用于三维VTI介质中的深度偏移及层析成像.     

一种线性走时插值射线追踪改进算法

针对线性走时插值算法(LTI)不能正确追踪逆向传播射线的问题, 目前已提出多种改进算法, 如扩张收缩LTI算法、 循环计算LTI算法、 动态网络最短路径射线追踪算法等, 但这些算法的计算效率普遍偏低. 在分析各种改进LTI算法的优劣后, 本文提出了改进动态网络最短路径射线追踪算法. 该改进算法依据波的传播规律以及LTI算法的基本方程, 排除动态网络最短路径射线追踪算法中大量冗余节点计算, 并采用传统的二叉树堆排序算法对波前阵列节点进行管理. 数值算例表明, 本文提出的改进算法具有较高的计算效率, 其计算效率是动态网络最短路径射线追踪算法的4.5—30倍, 是原始LTI算法的2—6.5倍; 当动态网络最短路径射线追踪算法采用堆排序算法时, 改进算法的计算效率是其3.5—15倍.      

最短路径射线追踪方法及其改进

综述了用网络最短路径算法求解地震射线追踪问题的原理、方法技术以及存在问题和改进措施。特别介绍了作者在最短路径算法基础上，提出的动态网络最短路径地震射线追踪方法。该方法先采集从炮点到整个模型所有节点上的初至旅行时，其中，在一个单元内，对相邻每对已计算出最小旅行时的节点进行线性插值，并利用Fermat原理计算未知节点的最小旅行时；然后，利用同样的方法，从接收点开始，反向追踪炮点到接收点的射线路径、该方法能适于各种复杂的非均匀介质，极大地提高了射线追踪的精度。     

基于LTI和网格界面剖分的三维地震射线追踪算法

将二维线性走时插值射线追踪算法(LTI)推广应用至三维模型,并结合网格界面剖分方式,提出了一种三维射线追踪算法．该算法既可获得高精度的全局最小走时和射线路径,又具有快速稳定的特点．三维模型计算结果表明,在模型参数包括网格密度完全相同情况下,本文算法较传统的三维最短路径算法在计算效率、走时和射线的计算精度上均有明显改进．     

非线性插值地震射线追踪方法

针对走时线性插值法(LTI)的计算精度问题,利用非线性插值替代传统的线性插值。该方法利用边界上多个节点的走时,使得插值误差减小,从而提高整体边界网格离散点走时精度,同时保留LTI所具有快速、全局性的优点。数值模拟结果表明,非线性插值算法比LTI算法精度高,可以追踪包括直达波、折射波、透射波等多种射线路径,适合速度突变模型。     

基于波前面三角形网格剖分的波前重建法三维射线追踪

在许多地震反演和偏移成像方法中,都要涉及到射线路径和旅行时的计算.本文将波前面三角形网格剖分和三维波前重建法射线追踪技术结合使用,实现了射线路径和旅行时的准确快速计算.三维波前重建法射线追踪过程中可以保证稳定合理的射线密度,克服了常规射线追踪方法存在阴影区的问题.波前面三角形网格剖分在描述和拆分波前面时更加准确有效,而且不需太多的网格数目,从而提高了射线追踪的精度和效率.该方法在三维复杂构造成像方面有独特的优势,目前在实际的Kirchhoff 偏移中的已经有相关应用.     

初至波走时层析速度建模方法研究

层析反演的核心是敏感核函数的求取和旅行时反演方程的建立.在射线理论下,射线追踪技术是计算敏感核函数和旅行时的主要方法,因此初至层析的实现需要有一种可以准确追踪初至波路径的射线追踪方法.本文推导了抛物旅行时插值射线追踪公式,提出了基于抛物旅行时插值的最短路径射线追踪方法.理论模型和实际资料处理结果表明,利用该方法实现初至层析速度建模可行.     

复杂介质中地震波前及射线追踪综述

本文较为系统综述了国内外在不均匀介质中各种主要和实用的射线追踪方法,例如:基于射线理论的打靶法、弯曲法(伪弯曲法)、高斯射线束算法等;基于网格单元扩展的有限差分解程函方程法(FD)、最短路径算法(SPM);以及结合射线和网格单元扩展的波前构造法等.同时对目前出现的多次波射线追踪技术、以及多值波前追踪技术(如:相空间算法、水平集算法)也进行了分析讨论.同时对基于网格单元扩展算法的优缺点进行了评述,其基本结论是:基于单元模型的SPM要优于FD算法,而基于网格的SPM算法则次之.就传统的射线追踪算法(如:打靶法和弯曲法)而言,其未来的发展方向是实现完全非线性的相应算法,而基于网格单元的算法则主要是扩展功能(如:后续波、多值波前的追踪).射线追踪方法技术未来需要解决的问题主要有:块状模型中多次波的追踪;多值波前及多值射线追踪;走时与振幅的同时追踪计算;以及其它领域新方法的引入.     

基于分区多步快速行进法下3D起伏层状介质中多震相射线追踪

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.     

一种改进的线性走时插值射线追踪算法

线性走时插值法（LTI）在走时的计算中,由于射线方向考虑不全,计算得到的节点走时不一定最小,导致追踪的射线路径无法满足最小走时.针对这一问题,本文提出了一种改进的射线追踪算法,通过采用多方向的循环计算,得到所有计算节点的最小走时,使追踪到的射线路径能真正满足最小走时,以确保射线追踪的精度.模拟实验结果表明,在介质速度变化剧烈的结构中,该算法与传统的LTI算法相比,有效地提高了射线追踪的精度.     

SEISMIC RAY TRACING USING LINEAR TRAVELTIME INTERPOLATION1

A new ray-tracing method called linear traveltime interpolation (LTI) is proposed. This method computes traveltimes and raypaths in a 2D velocity structure more rapidly and accurately than other conventional methods. The LTI method is formulated for a 2D cell model, and calculations of traveltimes and raypaths are carried out only on cell boundaries. Therefore a raypath is considered to be always straight in a cell with uniform velocity. This approach is suitable to tomography analysis. The algorithm of LTI consists of two separate steps: step 1 calculates traveltimes on all cell boundaries; step 2 traces raypaths for all pairs of receivers and the shot. A traveltime at an arbitrary point on a cell boundary is assumed to be linearly interpolated between traveltimes at the adjacent discrete points at which we calculate traveltimes. Fermat's principle is used as the criterion for choosing the correct traveltimes and raypaths from several candidates routinely. The LTI method has been compared numerically with the shooting method and the finite-difference method (FDM) of the eikonal equation. The results show that the LTI method has great advantages of high speed and high accuracy in the calculation of both traveltimes and raypaths. The LTI method can be regarded as an advanced version of the conventional FDM of the eikonal equation because the formulae of FDM are independently derived from LTI. In the process of derivation, it is shown theoretically that LTI is more accurate than FDM. Moreover in the LTI method, we can avoid the numerical instability that occurs in Vidale's method where the velocity changes abruptly.     

中国地震台网初至P波区域三维走时表的建立

基于LLNL-G3Dv3全球P波三维速度模型,应用FMM软件包计算并建立了中国地震台网990个台站的初至P波区域三维走时表．该走时表覆盖了以台站为中心的水平向20°×20°、 垂直向-5.1—80 km （向下为正）的三维空间. 其水平向间隔为0.2°,垂直向间隔为5 km．这样对于任一深度小于80 km的震源,均可以应用此三维走时表计算其到周围10°范围内台站的走时．中国地震台网初至P波区域三维走时表的建立,对于改善区域初至P波走时预测,提高地震定位精度有一定现实意义．      

基于局部一维模型与走时标定的区域 三维速度模型构建技术研究

构建区域介质三维速度模型并以之获得准确的区域震相走时, 是提高区域地震定位精度的重要手段之一. 为充分利用已有的一维模型、 GT事件、 地质资料等实现三维模型构建, 尝试基于目标区域内已有的部分局部一维模型, 通过克里金空间插值建立初始三维模型, 然后利用GT事件走时数据并参考其它地震地质资料对其不断进行修正, 使得其走时偏差图与GT事件走时偏差图一致, 进而获得能够提高区域地震定位精度的三维模型. 使用不同模型进行的地震定位实验表明, 以此方法建立的三维模型的定位偏差较初始模型减少约20%, 较好地起到了减小区域震相走时残差, 提高区域地震定位精度的作用.      

Interferometric interpolation of sparse marine data

We present the theory and numerical results for interferometrically interpolating 2D and 3D marine surface seismic profiles data. For the interpolation of seismic data we use the combination of a recorded Green's function and a model‐based Green's function for a water‐layer model. Synthetic (2D and 3D) and field (2D) results show that the seismic data with sparse receiver intervals can be accurately interpolated to smaller intervals using multiples in the data. An up‐ and downgoing separation of both recorded and model‐based Green's functions can help in minimizing artefacts in a virtual shot gather. If the up‐ and downgoing separation is not possible, noticeable artefacts will be generated in the virtual shot gather. As a partial remedy we iteratively use a non‐stationary 1D multi‐channel matching filter with the interpolated data. Results suggest that a sparse marine seismic survey can yield more information about reflectors if traces are interpolated by interferometry. Comparing our results to those of f‐k interpolation shows that the synthetic example gives comparable results while the field example shows better interpolation quality for the interferometric method.     

A new 3-D ray tracing method based on LTI using successive partitioning of cell interfaces and traveltime gradients

We present a new method of three-dimensional (3-D) seismic ray tracing, based on an improvement to the linear traveltime interpolation (LTI) ray tracing algorithm. This new technique involves two separate steps. The first involves a forward calculation based on the LTI method and the dynamic successive partitioning scheme, which is applied to calculate traveltimes on cell boundaries and assumes a wavefront that expands from the source to all grid nodes in the computational domain. We locate several dynamic successive partition points on a cell's surface, the traveltimes of which can be calculated by linear interpolation between the vertices of the cell's boundary. The second is a backward step that uses Fermat's principle and the fact that the ray path is always perpendicular to the wavefront and follows the negative traveltime gradient. In this process, the first-arriving ray path can be traced from the receiver to the source along the negative traveltime gradient, which can be calculated by reconstructing the continuous traveltime field with cubic B-spline interpolation. This new 3-D ray tracing method is compared with the LTI method and the shortest path method (SPM) through a number of numerical experiments. These comparisons show obvious improvements to computed traveltimes and ray paths, both in precision and computational efficiency.     

高斯波包反射走时速度反演方法

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.     

Reconstruction of the near‐offset gap in marine seismic data using seismic interferometric interpolation

In conventional seismic exploration, especially in marine seismic exploration, shot gathers with missing near‐offset traces are common. Interferometric interpolation methods are one of a range of different methods that have been developed to solve this problem. Interferometric interpolation methods differ from conventional interpolation methods as they utilise information from multiples in the interpolation process. In this study, we apply both conventional interferometric interpolation (shot domain) and multi‐domain interferometric interpolation (shot and receiver domain) to a synthetic and a real‐towed marine dataset from the Baltic Sea with the primary aim of improving the image of the seabed by extrapolation of a near‐offset gap. We utilise a matching filter after interferometric interpolation to partially mitigate artefacts and coherent noise associated with the far‐field approximation and a limited recording aperture size. The results show that an improved image of the seabed is obtained after performing interferometric interpolation. In most cases, the results from multi‐domain interferometric interpolation are similar to those from conventional interferometric interpolation. However, when the source–receiver aperture is limited, the multi‐domain method performs better. A quantitative analysis for assessing the performance of interferometric interpolation shows that multi‐domain interferometric interpolation typically performs better than conventional interferometric interpolation. We also benchmark the interpolated results generated by interferometric interpolation against those obtained using sparse recovery interpolation.     

Fresnel zone inversion for lateral heterogeneities in the earth

We propose a different kind of seismic inversion from travel-time or waveform inversion for lateral heterogeneities in the earth: Fresnel zone inversion. Amplitude and phase delay of data in several frequency ranges are inverted for model space around ray paths with a width corresponding to the considered frequency so that primary effect of finiteness of wavelength be included. For vertically heterogeneous media, Fréchet derivatives for inversion are obtained very efficiently using the paraxial ray approximation, with nearly similar amounts of computation compared to travel-time inversion. As an example, Fréchet derivatives are computed for a teleseismic observation system for a three-dimensional structure in the lithosphere beneath an array of seismic stations. Even if the used frequency is around 2 Hz, the width of Fréchet derivatives cannot be neglected, particularly near the bottom of the lithosphere. Sensitivity of model parameters to observations is, moreover, different in our approach from conventional travel-time inversion: it is zero along ray paths but large slightly away from them. Some model calculations show that travel-time inversion, particularly with models divided into very fine meshes or blocks, might give misleading results. An example of inversion for a simple Camembert model, in the event that travel-time inversion gives no reliable results, shows how this technique works with much smaller data sets and computation than waveform inversions.