2D共炮时间域高斯波束偏移

针对传统射线方法在奇异区成像精度不高,而2D频率域高斯波束叠前深度偏移需要计算成像点处每个频率的格林函数,影响计算效率的问题,本文通过使用复走时代替实走时,改变频率域下成像公式的积分顺序,给出了在时间域下进行高斯波束偏移的方法和计算公式.本文使用复杂数值模型验证了2D时间域高斯波束叠前偏移方法的正确性,并同传统射线偏移成像结果做了对比.对比结果表明时间域高斯波束偏移在成像精度上优于传统射线偏移.     

三维共偏移距叠前地震数据反假频射线束形成偏移成像

对稀疏/非规则采样或者低信噪比数据,射线束提取困难并伴随有假频产生,对叠加剖面和道集造成严重干扰.为了提升射线束偏移在稀疏和低信噪比地震数据采集中的成像效果,本文提出基于三角滤波的局部倾斜叠加波束形成偏移假频压制方法.射线束偏移首先将地震数据划分为超道集,经过部分NMO后转化为以射线束中心定义的共偏移距数据,倾斜叠加和反假频操作均在局部共中心点坐标上实现.时间域倾斜叠加是对地震数据的时移累加操作,三角低通滤波同样可以在时间域完成,在对地震数据进行因果和反因果积分后,亦为地震数据的时移累加.因此,三角低通滤波与倾斜叠加可在时间域结合同时完成,避免了频域滤波的正反傅里叶变换.本文在反假频公式中加入权重系数,用以对反假频的程度进行控制,达到分辨率和噪声压制的最佳折衷.以某海上三维实际数据为例,文中展示了反假频射线束形成对偏移叠加剖面和共成像点偏移距道集中的噪声进行了有效压制.     

复相位匹配方法及其在具有弯曲界面层状均匀结构问题中的应用（Ⅰ）——理论

本文提出了利用复射线束相位匹配原理合成地震图方法--复相位匹配方法。该方法系利用相位匹配原理把复数域中波传播方程的解和界面联系起来得到的,可解决具有任意形状、光滑曲面界面的层状均匀弹性空间波场计算问题,克服了广义射线法应用于这个问题所遇到的困难。     

TI介质射线追踪及其高斯束成像应用

射线追踪是一种高频近似前提下快速有效的波场近似计算方法,传统的基于弹性参数的各向异性介质运动学和动力学射线追踪方程,求解过程中需要处理Christoffel方程的特征值问题,因而计算效率比较低.为了解决这一问题,本文通过引入相速度和群速度,对运动学和动力学追踪方程进行修改和简化,有效地提高了各向异性介质射线追踪算法的计算效率.另外,我们将该算法应用到各向异性偏移中,实现了共炮域TI介质高斯束叠前深度偏移方法.VTI介质Hess模型和TTI介质洼陷模型的试算结果说明了该方法的正确性和有效性.     

基于成像域射线束建模的剩余静校正方法研究及应用

由信噪比极低的资料生成的剩余静校正模型,其信噪比通常也较低,导致剩余静校正效果不理想,因此提高模型的信噪比,在提高资料处理品质中有着极其重要的意义.文章提出了一种基于成像域射线束建模的剩余静校正的方法.该方法是采用成像域射线束建模对数据进行分解和重构,并且根据不同的分解级数和分解尺度,分解和重构成不同成分的数据,该方法在重构的过程中加入倾角场的约束,能有效保护高陡构造.成像域射线束建模得到的第一级分量为数据的主要成分,构造保真,信噪比高,把该分量作为外部模型,进行外部模型剩余静校正.把本文方法在低信噪比资料进行应用,提高低信噪比资料的剩余静校正效果,有效的改善了资料处理成果的品质.     

基于汉宁窗函数滤波时间域高斯束成像方法

实际地震数据中通常存在背景噪声及人为干扰信号,传统射线类方法对低信噪比数据成像适应性较差,基于此本文发展了一种适应于低信噪比数据的时间域高斯束成像方法.相比于频率域类束方法,新方法的主要优点包括:(1)频率域高斯束偏移方法需计算每个成像点处各个频率的格林函数,基于时间域高斯束偏移方法无需上述过程,大大提高了计算效率;(2)时间域高斯束公式推导中,直接对地震记录进行局部倾斜叠加并加入汉宁窗滤波处理,对低信噪比数据具有更好的适应性.在实现成像方法的基础上,本文通过对不同信噪比Marmousi炮记录进行模型试算及含噪声实际资料成像试处理表明:时间域高斯束偏移方法能够较为明显地提高低信噪比数据的偏移效果,提高成像方法对实际数据的适应性.     

基于τ-p域动态聚焦控制束偏移方法

地震资料数据处理中,高斯束偏移方法不仅拥有射线类方法高效性,还具有波动方程类方法的高质量成像精度．但高斯束偏移受其初始波束参数影响较大,选定的初始宽度大小,直接影响近地表区域成像精度好坏,而将动态聚焦射线束引入到高斯束偏移中,在射线追踪过程中采用变化而非固定的初始宽度参数,合理控制射线束的传播范围,解决了高斯束束宽随传播距离增加发散过快的问题,且针对低信噪比的地震数据的问题,无法得到高信噪比的成像精度．本文从高斯束理论出发,采用τ-p域阈值控制和动态聚焦初始波束方法策略,发展了一种基于τ-p域动态聚焦控制束偏移方法．有效压制了噪声数据干扰,削弱了初始波束对射线传播范围影响,充分的改善了复杂构造区域的成像质量,并通过了水平层状模型和Marmousi模型,以及胜利油田东部某探区的实际资料进行了测试来验证了我们方法的正确性和有效性．     

二维各向异性多波高斯束叠前深度偏移

基于多分量地震资料的深度偏移能够更加充分的利用地震记录上的多波信息,而且地下介质中广泛的存在各向异性,本文提出了一种有效的适用于二维各向异性介质的多波高斯束叠前深度偏移方法.首先基于各向异性射线追踪理论,导出了适用于二维各向异性介质的射线追踪方程组,实现了二维各向异性介质中P波和S波的射线追踪.其次将各向异性射线追踪理论引入到高斯束偏移方法中,分别给出适用于二维各向异性介质的PP波和PS波高斯束叠前深度偏移成像方法.本文成像方法充分考虑各向异性因素对地震波场的影响,能够对存在各向异性介质的地下构造准确偏移归位.通过对不同各向异性介质的数值模型进行PP波和PS波高斯束叠前深度偏移成像测试分析表明,本文方法是一种准确有效的适应于各向异性介质条件的多波叠前深度偏移成像算法.     

基于高斯束传播算子的成像域走时层析成像方法

层析反演是速度建模中最重要的方法之一,结合偏移成像在成像域进行走时层析速度反演是当前比较成熟有效且广泛应用的技术.本文从高斯束偏移成像条件出发,在波动方程的一阶Born近似和Rytov近似下,推导了成像域走时扰动与速度扰动的线性关系,建立了成像域走时层析方程及其显式表达的层析核函数.该核函数的本质是有限频层析核函数,利用该核函数替换常规射线层析核函数可以明显提高层析反演精度.该核函数的计算关键是背景波场格林函数的计算,本文利用高斯束传播算子计算格林函数进而得到走时层析核函数,实现方式灵活高效且计算精度较高.基于高斯束传播算子的偏移成像与层析成像相结合进行深度域建模迭代,体现了速度建模与偏移成像一体化的思想.数值计算及实际数据应用证明了基于高斯束传播算子的成像域走时层析方法的有效性.     

基于有效邻域波场近似的起伏地表保幅高斯束偏移

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.     

散射问题中柱面坐标波函数的全域变换公式

为满足偏心源和多体散射理论研究发展的需求,阐明了柱面坐标下波函数变换的基本类型,指出了现有变换公式的局限性,提出了全域变换公式,给出了应用实例并讨论了应用前景。研究表明,不同柱面坐标下波函数变换可以分为内域和外域两种基本类型,现有Graf加法公式仅适用于内域变换问题。提出的新公式突破了现有公式的限制,可完成弹性波散射问题中不同圆柱坐标系下波函数全空间域上的变换。应用新公式,构造了圆形空穴的外线源散射和内线源散射的解答,通过实例与大圆弧近似方法进行了对比,表明了新公式的优势和有效性。波函数变换基本类型的划分、全域变换概念的引入和公式构建的原理具有普适性,可以推广到其它坐标系下波函数的坐标变换公式的建立中。     

A whole-space transform formula of cylindrical wave functions for scattering problems

The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.     

地震波场的复射线展开

利用复射线理论将惠更斯原理推广到复空间,发展出一种简便的波场计算方法.本文以均匀柱面波在平界面上的反射场为例,用复射线展开法计算了时谐地震波及瞬变地震波在部分反射、全反射和临界角过渡区的场分布,并与平面波谱积分结果进行了比较.结果表明,用复射线展开法可以自动平滑过渡区反射场的奇异性,因而该方法可直接处理焦点、焦散线和全反射过渡区等复杂的波场分析与综合问题,并可简化数值计算过程.     

层状介质中轴对称柱面瑞利面波频散函数的计算

本采用层状、均匀、各向同性和完全弹性模型，在柱坐标系下，利用位移应力在各界面处连续及自由表面边界条件和无穷远处的辐射条件，得出了层状介质中轴对称柱面瑞利面波的频散函数，并进行了数值计算，取得了好的效果。对瑞利面波在工程中的应用有一定的理论指导作用。     

Scattering and refracting of plane strain wave by a cylindrical inclusion in fluid-saturated soils

The problems involving scattering and refracting of plane strain wave by a cylinder in fluid-saturated soils are studied in this paper. The theoretical solutions for the amplitudes of scattering and refracting are derived on the basis of modified Biot’s theory for two-phase medium in engineering, in which the compressibility of soil grains and the viscous coupling effect between the skeletal frame and the pore fluid are taken into account. Moreover, the amplitude equations of potential function are presented when the fluid-saturated soil cylindrical inclusion is degenerated into cylindrical cavity, rigid cylinder, single phase elastic cylinder and single phase fluid cylinder.     

General velocity formula of boundary layer above mobile sediment bed induced by asymmetric waves

Sediment movement in the wave boundary layer above a mobile sediment bed is complex.A velocity formula for the boundary layer is proposed for sheet flow induced by asymmetric waves above a mobile sediment bed.The formula consists of a free stream velocity and a defect function which contains a phase-lead,boundary layer thickness and mobile sediment bed.Phase-lag of sediment movement is considered in the formula for the mobile sediment bed.The formula needs six dependent variables about asymmetric wave and sediment characteristics.Asymmetry effects on parameters(orbital amplitude,roughness height,bed shear stress,and boundary layer thickness)are properly considered such that the formula can yield velocity differences among onshore,offshore,acceleration,and deceleration stages.The formula estimates the net boundary layer velocity resulting from the mobile sediment bed and asymmetric boundary layer thickness.In addition,a non-constant phase-lead also contributes to the net boundary layer velocity in asymmetric oscillatory sheet flow.Results of the formula are as good as that of a two-phase numerical model.Sheet flow transport induced by asymmetric waves,and the offshore net sediment transport rate with a large phase-lag under velocity-skewed waves,can be adequately estimated by the formula with a power sediment concentration function.     

横向各向同性地层斜井中正交偶极子激发声场的数值模拟

本文采用三维应力-速度有限差分(SV-FD)方法,数值模拟了横向各向同性(TI)地层对称主轴与井轴斜交情况下正交偶极子声源激发的井孔声场.主要解决了与倾斜角有关的三维空间弹性模量矩阵的推导,柱坐标系下应力-速度有限差分方程组的建立,井轴上场点奇异性与内边界处理等几个关键问题,提高了计算精度.在横向各向同性地层对称主轴与井轴平行的情况下,与实轴积分法所得结果进行了对比,验证了本文方法的正确性.计算了不同倾角情况下xx和yy两分量的弯曲波,并用频域加权相似法提取了弯曲波频散曲线,结果显示了横向各向同性介质中不同方向偏振的弯曲波传播的分裂现象,其频散曲线在低频段分裂,随频率增大而逐渐重合.弯曲波低频截止频率处速度与理论公式得到的横波速度基本符合.     

Scattering of SH waves induced by a symmetrical V-shaped canyon: a unified analytical solution

This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.     

沉积盆地中地震波速度与地层年龄有关吗？

通过分析沉积盆地中地震波速度与地层年龄的关系,指出地震波速度与地层年龄没有内在的、成因上的联系. 由于沉降速度的大小、沉积成岩后期热液活动、沉积间断所造成的不整合面、盆地地质构造复杂等因素,使这种关系通常有不确定性.文献\[1\]给出的地震波速度与地层年龄的关系式所计算的地层年龄、盆地基底年龄与实测年龄之间有很大的误差,这种计算方法缺乏科学性,没有任何地质意义.     

On the Seddon speed formula

Abstract

The Seddon speed formula expressed mathematically as c = dQ/dA (or alternatively, as c = (1 + m)u_o; where Q is the discharge, A is the area of cross-section, c is the wave speed, u_o is the normal flow velocity, and m is a dimensionless parameter) is revisited in the context of elasticity and thermodynamics. Its link with the linearized solution of St Venant's equations for wave celerity, which does not appear to have been reported in the hydrological literature, is established. The rating exponent m is shown to be equivalent to the dimensionless relative celerity and is found to be the ratio of two specific heats, viz. c_p and c_v which are the specific heats at constant pressure and volume, respectively. The use of the parameter m as a complex variable helps describe shallow wave characteristics, the damping capacity of a wave, and the mechanism of occurrence of the hysteretic phenomenon. The damping capacity is found to describe the magnitude of wave subsidence, whereas the hysteresis also describes the speed of subsidence.