基于分数阶时间导数的黏弹性衰减VTI介质中平面波传播

目前在地震勘探频带范围内通常假设品质因子Q与频率无关,且呈衰减各向同性.事实上,相比较速度各向异性,介质的衰减各向异性同样不可忽视.本文将衰减各向异性和速度各向异性二者与常Q模型相结合,建立了黏弹性衰减VTI介质模型,并基于分数阶时间导数理论,给出了对应的本构关系和波动方程.利用均匀平面波分析和Poynting定理,推导出准压缩波qP、准剪切波qSV和纯剪切波SH的复速度、相速度、能量速度以及品质因子的解析表达式.对模型的正确性进行了数值验证,并分析了qP,qSV和SH波在介质中的传播特性.数值试验结果表明:本模型能够实现理想的恒定Q行为,表现了品质因子和速度的各向异性特征,显示出黏弹性增强将导致能量速度和相速度的频散曲线变化剧烈;速度和衰减各向异性参数与传播角度之间的耦合效应对qP,qSV和SH波的速度和能量影响明显;qP,qSV和SH波的频散曲线和波前面随着衰减各向异性强度的改变发生显著变化,其中耦合在一起的qP和qSV波变化趋势相同,而SH波与它们呈现相反的变化规律.本研究为从常Q模型角度分析地震波在衰减各向异性黏弹性介质中的传播特征奠定了理论基础.     

黏弹性VTI介质中敏感度核函数：地震波复走时关于弹性模量及Q值偏导数的计算

实际地层中地震波传播普遍存在速度和衰减各向异性现象,研究黏弹各向异性介质中高频地震波传播理论有助于揭示地震波的传播特征.本文针对黏弹性VTI介质,从Christoffel矩阵的解析特征值出发推导出qP、qSV和qSH波的复相速度和复射线速度的解析表达式,并应用实射线追踪方法确定出均匀复射线速度矢量,由此计算出实射线速度和实射线衰减以及实射线品质因子.基于非均匀复相速度和均匀复射线速度的解析表达式,推导了实射线慢度和实射线衰减关于黏弹性模量(包括弹性模量和Q值)的敏感度核函数,该敏感度核函数反映各个黏弹性模量对地震波复走时的影响程度.不同岩石样本的数值计算结果显示,实走时对弹性模量更为敏感,而射线衰减(虚走时)对弹性模量和Q值的敏感程度相当.本研究可为黏弹性VTI介质中地震射线追踪和复走时层析成像提供理论基础.     

常Q衰减介质分数阶波动方程优化有限差分模拟

本文基于Kjartansson常Q模型理论,推导了常Q衰减介质中黏声波和黏弹性波的速度-应力方程,并采用基于二项式窗函数的优化交错网格有限差分方法进行了数值模拟,同时引入不分裂的复频移卷积完全匹配层(CPML)吸收边界条件,以消除边界反射.使用基于自适应时间步长记忆方法的中心差分近似时间分数阶导数,与常用的短时记忆方法相比,提高了波动方程的离散化精度和计算效率.通过对比均匀模型下声波的数值解与解析解,验证了算法的精确性,并进一步分析了不同品质因子下地震波的频散及衰减特征.对BP盐丘模型的数值模拟结果可以较好地反映本文数值方法对复杂介质的适应性及频散压制效果.      

海底水平层状黏弹介质地震波有限差分正演模拟

地震波在海底地层的传播,有必要考虑到介质对地震波发挥的衰减和频散效应.这些效应通常可以通过品质因子Q来量化.论文讨论了水平层状黏弹介质内平面波的数值模拟,采用了一种计算垂向黏弹性介质里的平面波响应的FDTD有效算法,用来估算存在垂向速度变化模型的平面波传播参数响应值.将视品质因子Q和视速度与实测的数值对比,证实了该算法在黏弹性模拟中的精确性,证明了在10~40 Hz的相关频率范围内,即使是强衰减介质,该算法也能取得良好的计算结果.在此基础上,应用这种算法求解海底水平层状介质模型,得到了海底黏弹介质的一维地震波场响应,取得了理想效果.     

黏弹性介质中瑞雷面波正演模拟及频散特征分析

正演模拟是瑞雷面波研究的一个主要方面,目前对于瑞雷面波的正演研究大多是基于均匀层状弹性介质条件下的瑞雷面波频散曲线方程,这只适用于层状模型,无法模拟全波场,而且不考虑实际介质的黏弹效应.本文采用交错网格高阶有限差分法对黏弹性介质中的瑞雷面波进行了高精度全波场模拟,并对频散特征进行了提取与分析.其中采用属于非线性最优化的Levenberg-Marquarat方法直接计算松弛时间来拟合常Q模型,并将应力镜像法与紧致差分格式相结合来准确实施自由表面条件,在其余边界处以非分裂的多轴卷积完全匹配层为吸收边界.然后利用相移法从地震记录中提取频散剖面并对几种典型模型的面波频散特征进行了对比分析.结果表明黏弹性对面波的频散特性有显著影响,面波勘探中有必要考虑黏弹性因素.     

黏弹性与弹性介质中Rayleigh面波特性对比研究

Rayleigh面波的频散特性可以用来研究地表浅层结构. 本文使用时域有限差分法来模拟复杂黏弹性介质中的Rayleigh面波,研究了Q值对面波频散特性的影响.文中采用旋转交错网格有限差分,以非分裂卷积形式的完全匹配层为吸收边界,推出了求解二阶位移-应力各向同性黏弹性波动方程的数值方法.为了检验数值解的精度,首先将简单模型的正演结果与解析解对比,验证了方法的正确性;然后模拟了横向缓变层状介质和含有洞穴的介质中的面波,对弹性和黏弹性介质中的面波的频散特性进行对比分析.模拟结果表明浅层Q值对面波的频散特性有显著的影响;强吸收情况下,高阶面波的能量相对低阶面波能量显著增强.     

VTI地层井孔模式波理论频散计算时伪极点的影响

波的频散特征在声波测井中有着十分关键的作用.VTI地层下井孔模式波的理论频散曲线可根据频散方程求解.本文首先采用常用的耦合位移势函数对应的频散方程进行了VTI地层斯通利波理论频散曲线的求解.结果发现,在一定各向异性强度范围内,会得到两种计算结果:一条常规斯通利波频散曲线和一条非频散曲线.这是频散矩阵行列式在该模型下存在两个零点导致的.进一步采用一种对称形式的位移势函数推导的对称频散矩阵时分析发现,非频散曲线对应的零点k~2-q~2_p=0为频率—波数响应函数的一个伪极点.经分析,在横波速度范围内,满足伪极点存在的Thomsen参数γ有一定范围,通常在弱各向异性地层中存在.且满足伪极点存在的Thomsen参数γ范围与地层泊松比成负相关,泊松比越小,满足伪极点存在的γ范围越大.在计算理论频散曲线时应消除k~2-q■这一公因式的影响,避免得到错误的计算结果,进而影响各向异性反演等计算结果.     

黏弹性介质瑞雷波有限差分模拟与特性分析

本文通过数值模拟研究了介质黏弹性对瑞雷波传播的影响.模拟采用结合了交错Adams-Bashforth时间积分法、应力镜像法和多轴完美匹配层的标准交错网格高阶有限差分方案.通过模拟结果和理论结果对比,测试了方法的精度,验证了结果的正确性.在均匀半空间模型中,分别从波场快照、波形曲线及频散能量图三个角度,对黏弹性介质瑞雷波衰减和频散特性进行了详细分析.两层速度递增模型被用于进一步分析瑞雷波在黏弹性层状介质中的特性.结果表明：由于介质的黏弹性,瑞雷波振幅发生衰减,高频成分比低频成分衰减更剧烈,衰减程度随偏移距增大而增强;瑞雷波相速度发生频散,且随频率增大而增大,频散能量的分辨率有所降低;黏弹性波动方程中的参考频率,不会影响瑞雷波振幅衰减和相速度频散的程度,但决定了黏弹性和弹性介质瑞雷波相速度相等的频率位置.本研究有助于人们更好地理解地球介质中瑞雷波的行为,并为瑞雷波勘探的应用和研究提供了科学和有价值的参考.     

含孔隙、裂隙地层随钻多极子声波测井理论

储层岩石中普遍存在孔隙与裂隙,对钻井中的测井声波产生重要影响.基于孔、裂隙介质弹性波理论,导出了随钻声波测井的井孔声场表达式.据此考察了地层裂隙密度与含气饱和度的变化时井孔内随钻多极子模式波（斯通利波、弯曲波和螺旋波）的速度、衰减与灵敏度以及地层纵、横波的响应特征.裂隙密度与含气饱和度对模式波的速度频散与衰减都有影响,且两参数的值越大,影响越大.具体来说,速度对裂隙密度更敏感,而衰减对含气饱和度更敏感.具有"艾里相"特征的随钻偶极和四极子波在地层含气时产生强烈衰减,可以作为判断地层含气的一个明显指示.理论模拟与实际测井数据分析结果符合较好.     

面波频散曲线提取方法对比分析

高频面波方法是以瑞雷波和勒夫波为研究对象,在水文、工程和环境研究中具有广泛的应用,其主要思想是利用面波的频散特性来反映浅层地质问题,提取高质量的频散曲线成了面波勘探中的一个重要步骤.本文通过对理论模型研究说明,利用τ-p变换与F-K变换两种方法均能有效地进行频散能量成像,其效果在高频范围差别不大,在低频范围F-K变换提取频散曲线更为精确;与瑞雷波记录相比,勒夫波记录信噪比较高,通过对同一地区采集的瑞雷波和勒夫波进行频散分析可知,瑞雷波记录频散能量成像效果差,频散能量出现间断、跳跃的现象,而勒夫波记录频散能量连续、集中,相速度分辨率较高,提取频散曲线简单清晰,可为反演地表横波精细速度结构提供更好的频散曲线数据.     

Propagation of guided waves in a fluid layer bounded by two viscoelastic transversely isotropic solids

The analysis of Stoneley wave propagation in a fracture is essential for the identification and evaluation of fracture parameters from the borehole Stoneley wave. Also, it is important for many geophysics considerations, e.g. for tremor and long-period events observed in volcanoes and geothermal areas. In this paper, we investigate the guided waves propagation in a fluid layer lying between two viscoelastic vertically transversely isotropic media. The viscoelastic mechanism models the attenuation due to the presence of fluid saturation in the rock. A model based on the superposition of three inhomogeneous partial plane waves: one in the fluid and two heterogeneous waves in the solid is developed. The dispersion equation is obtained for this case. A numerical solution is carried out to obtain the guided wave velocity and attenuation coefficient. The results of this investigation show that there is a strong correlation between the velocity dispersion and attenuation of Stoneley wave and the anisotropic parameters of the medium especially in a sandstone (fast) medium.     

大别-苏鲁及其邻近地区基于背景噪声的瑞雷波和勒夫波相速度层析成像

采用与作者2014年发表的“大别-苏鲁及其邻近地区基于背景噪声的勒夫波群速度成像”文章相同的资料,用频时分析提取5 000余条瑞雷波和4 000余条勒夫波相速度频散曲线,反演得到了8—32 s的瑞雷波和勒夫波相速度分布图像．结果显示,瑞雷波与勒夫波相速度分布具有很好的一致性．8 s的相速度分布与地表构造特征相吻合,造山带与隆起区均表现为高速,盆地因其规模不同而显示不同程度的低速．随着周期的增大,大别 苏鲁的高速带由强变弱,但始终存在．16—24 s的高速可能主要受到中地壳高速的控制,而32 s的高速则可能与上地幔顶部的高速有关．比较大别造山带与苏鲁造山带的平均频散曲线,发现大别造山带和苏鲁造山带的勒夫波频散曲线均高于AK135模型计算的理论频散曲线,而瑞雷波则没有这一现象. 这可能意味着两个地区有比较强烈的径向各向异性．      

A note on the approximate determination of the dispersion of Love waves in a laterally nonhomogeneous layer lying over a homogeneous half-space

Rayleigh's principle and the concept of the local wave number have been utilised for the approximate determination of the dispersion of Love waves propagating in a laterally heterogeneous layer lying over a homogeneous half-space. The shear wave velocity and the rigidity in the surface layer have been assumed to decrease with the increase of the lateral distance from the origin. The range of validity of the dispersion equation obtained by this method has been examined critically. It was found that: (a) for existence of Love waves the minimum value of shear wave velocity in the layer must be less than that in the matter below, and (b) the phase velocity of Love waves decreases with the increase of the lateral distance from the origin.     

Crustal structure beneath Liaoning province and the Bohai Sea and its adjacent region in China based on ambient noise tomography

The velocity structure of the crust beneath Liaoning province and the Bohai sea in China was imaged using ambient seismic noise recorded by 73 regional broadband stations. All available three-component time series from the 12-month span between January and December 2013 were cross-correlated to yield empirical Green's functions for Rayleigh and Love waves. Phasevelocity dispersion curves for the Rayleigh waves and the Love waves were measured by applying the frequencytime analysis method. Dispersion measurements of the Rayleigh wave and the Love wave were then utilized to construct 2D phase-velocity maps for the Rayleigh wave at8–35 s periods and the Love wave at 9–32 s periods,respectively. Both Rayleigh and Love phase-velocity maps show significant lateral variations that are correlated well with known geological features and tectonics units in the study region. Next, phase dispersion curves of the Rayleigh wave and the Love wave extracted from each cell of the 2D Rayleigh wave and Love wave phase-velocity maps,respectively, were inverted simultaneously to determine the3 D shear wave velocity structures. The horizontal shear wave velocity images clearly and intuitively exhibit that the earthquake swarms in the Haicheng region and theTangshan region are mainly clustered in the transition zone between the low-and high-velocity zones in the upper crust, coinciding with fault zones, and their distribution is very closely associated with these faults. The vertical shear wave velocity image reveals that the lower crust downward to the uppermost mantle is featured by distinctly high velocities, with even a high-velocity thinner layer existing at the bottom of the lower crust near Moho in central and northern the Bohai sea along the Tanlu fault, and these phenomena could be caused by the intrusion of mantle material, indicating the Tanlu fault could be just as the uprising channel of deep materials.     

CALCULATION OF DISPERSION CURVES AND AMPLITUDE-DEPTH DISTRIBUTIONS OF LOVE CHANNEL WAVES IN HORIZONTALLY-LAYERED MEDIA*

We present dispersion curves, and amplitude-depth distributions of the fundamental and first higher mode of Love seam waves for two characteristic seam models. The first model consists of four layers, representing a coal seam underlain by a root clay of variable thickness. The second model consists of five layers, representing coal seams containing a dirt band with variable position and thickness. The simple three-layer model is used for reference. It is shown that at higher frequencies, depending on the thickness of the root clay and the dirt band, the coal layers alone act as a wave guide, whereas at low frequencies all layers act together as a channel. Depending on the thickness, and position of the dirt band and the root clay, in the dispersion curves of the group velocity, secondary minima grow in addition to the absolute minima. Furthermore, the dispersion curves of the group velocity of the two modes can overlap. In all these cases, wave groups in addition to the Airy phase of the fundamental mode (propagating with minimum group velocity) occur on the seismograms recorded in in-seam seismic surveys, thus impeding their interpretation. Hence, we suggest the estimation of the dispersion characteristics of Love seam waves in coal seams under investigation preceding actual field surveys. All numerical calculations were performed using a fast and stable phase recursion algorithm.     

Dispersion Energy Analysis of Rayleigh and Love Waves in the Presence of Low-Velocity Layers in Near-Surface Seismic Surveys

High-frequency surface-wave analysis methods have been effectively and widely used to determine near-surface shear (S) wave velocity. To image the dispersion energy and identify different dispersive modes of surface waves accurately is one of key steps of using surface-wave methods. We analyzed the dispersion energy characteristics of Rayleigh and Love waves in near-surface layered models based on numerical simulations. It has been found that if there is a low-velocity layer (LVL) in the half-space, the dispersion energy of Rayleigh or Love waves is discontinuous and ‘‘jumping’’ appears from the fundamental mode to higher modes on dispersive images. We introduce the guided waves generated in an LVL (LVL-guided waves, a trapped wave mode) to clarify the complexity of the dispersion energy. We confirm the LVL-guided waves by analyzing the snapshots of SH and P–SV wavefield and comparing the dispersive energy with theoretical values of phase velocities. Results demonstrate that LVL-guided waves possess energy on dispersive images, which can interfere with the normal dispersion energy of Rayleigh or Love waves. Each mode of LVL-guided waves having lack of energy at the free surface in some high frequency range causes the discontinuity of dispersive energy on dispersive images, which is because shorter wavelengths (generally with lower phase velocities and higher frequencies) of LVL-guided waves cannot penetrate to the free surface. If the S wave velocity of the LVL is higher than that of the surface layer, the energy of LVL-guided waves only contaminates higher mode energy of surface waves and there is no interlacement with the fundamental mode of surface waves, while if the S wave velocity of the LVL is lower than that of the surface layer, the energy of LVL-guided waves may interlace with the fundamental mode of surface waves. Both of the interlacements with the fundamental mode or higher mode energy may cause misidentification for the dispersion curves of surface waves.     

非均匀黏弹性介质中声波模拟的非规则网格方法

本文研究了满足衡Q模型的黏弹性介质中声波模拟的时间域数值解法.通过采用有理式基函数描述频率相关的体积模量,使模型满足地震波黏性吸收的衡Q要求.结合弹性波模拟的非规则、非结构网格方法——格子法,本文提出了一种非均匀黏弹性介质中声波模拟的非规则网格方法.非规则、非结构网格的使用,可以精细地刻画地下介质中复杂速度、Q值的变化,及界面的形状.通过和解析解的比较及复杂模型算例分析,验证了该方法的精度及有效性.     

土中Love波弥散特性

利用有限单元法及解析法建立和求解了土中Love波特征方程以及位移计算公式．计算结果表明,这一计算方法比纯解析法优越,可以用来分析均质和非均质上中Love波弥散性．本文利用这一方法详细讨论了Love波在上软下硬地基及软夹层地基中的传播特性和弥散特性．上软下硬地基Love波具有弥散性,土层的剪切波及厚度对Love波弥散曲线影响较大,而质量密度的相对变化对Love彼弥散曲线影响较小．软夹层地基中低频时Love波以第一模态波为主,现场所测为第一模态波波速;高频时存在多个高模态波,土中传播的波为这几个高模态波的叠加波,现场所测波速随两传感器的位置不同而有波动．     

Advantages of Using Multichannel Analysis of Love Waves (MALW) to Estimate Near-Surface Shear-Wave Velocity

As theory dictates, for a series of horizontal layers, a pure, plane, horizontally polarized shear (SH) wave refracts and reflects only SH waves and does not undergo wave-type conversion as do incident P or Sv waves. This is one reason the shallow SH-wave refraction method is popular. SH-wave refraction method usually works well defining near-surface shear-wave velocities. Only first arrival information is used in the SH-wave refraction method. Most SH-wave data contain a strong component of Love-wave energy. Love waves are surface waves that are formed from the constructive interference of multiple reflections of SH waves in the shallow subsurface. Unlike Rayleigh waves, the dispersive nature of Love waves is independent of P-wave velocity. Love-wave phase velocities of a layered earth model are a function of frequency and three groups of earth properties: SH-wave velocity, density, and thickness of layers. In theory, a fewer parameters make the inversion of Love waves more stable and reduce the degree of nonuniqueness. Approximating SH-wave velocity using Love-wave inversion for near-surface applications may become more appealing than Rayleigh-wave inversion because it possesses the following three advantages. (1) Numerical modeling results suggest the independence of P-wave velocity makes Love-wave dispersion curves simpler than Rayleigh waves. A complication of “Mode kissing” is an undesired and frequently occurring phenomenon in Rayleigh-wave analysis that causes mode misidentification. This phenomenon is less common in dispersion images of Love-wave energy. (2) Real-world examples demonstrated that dispersion images of Love-wave energy have a higher signal-to-noise ratio and more focus than those generated from Rayleigh waves. This advantage is related to the long geophone spreads commonly used for SH-wave refraction surveys, images of Love-wave energy from longer offsets are much cleaner and sharper than for closer offsets, which makes picking phase velocities of Love waves easier and more accurate. (3) Real-world examples demonstrated that inversion of Love-wave dispersion curves is less dependent on initial models and more stable than Rayleigh waves. This is due to Love-wave’s independence of P-wave velocity, which results in fewer unknowns in the MALW method compared to inversion methods of Rayleigh waves. This characteristic not only makes Love-wave dispersion curves simpler but also reduces the degree of nonuniqueness leading to more stable inversion of Love-wave dispersion curves.     

A Fast Method of Computing Group-Velocity Partial Derivatives for Love Waves Propagating in a Layer on a Half-Space

The dispersion relation for Love waves in a layer on a half-space is modified by introducing the wave number and its square instead of the phase velocity. The implicit function theorem is then used to derive the analytical formulae for the group velocity and for the phase- and group-velocity partial derivatives with respect to the parameters of the medium. The formulae are compared with those obtained by Novotný (1971) where the traditional formulation of the dispersion relation was used.