地震学百科知识(十二)——地震波散射

正广义地说,由地球介质的任何三维非均匀性引起的地震波场畸变均可称为地震波散射。不过,通常地震波散射是指由地球小尺度(与波长相比)非均匀性引起的、不适合用射线理论(几何射线)研究的地震波场畸变现象。例如,波场传播方向的偏折和分裂,P波和S波的相互转换,地震尾波的产生,地震波的走时和振幅横跨观测台阵的随机起伏变化等。1地球介质的不均匀性及地震波散射随着对地球结构认识的深入,经典的球     

非均匀各向异性介质中弹性波的传播

平面波分解法是研究地震波场简捷有效的方法,各种复杂的波场可用平面波合成的方法得到．文中采用平面波方法研究非均匀各向异性介质中的弹性波．对时空域非均匀各向异性介质波动方程,运用f-k变换,可得到频率空间域波动方程(Christoffel方程)．利用非均匀各向异性介质中,弹性参数及其空间变化率与Christoffel矩阵元素关系,提出非均匀各向异性介质Christoffel矩阵方程的求解方法,并运用于非均匀TIV介质和非均匀EDA介质．在连续介质条件下,当波沿速度增加方向传播时,振幅的方向导数小于零,即振幅衰减;当波沿速度减小方向传播时,振幅的方向导数大于零,即振幅增强．波的振幅强度是传播方向的函数(各向同性条件下也是如此),但并不总是衰减．若只研究波沿速度增加方向传播的情况即得出波在连续介质中传播振幅衰减的结论是不全面的．      

各向同性介质中射线理论与有限差分地震波场模拟方法比较研究

地震波场数值模拟不仅是研究复杂地区地震资料采集、处理和解释的有效辅助手段,而且是研究地球深部精细构造和地球深部探测的有效工具.射线理论和波动方程理论是地震波场数值模拟的理论基础.射线理论主要刻画地震波在介质中传播的走时场、地震射线等运动学属性;波动方程理论通过求解波动方程来描述地震波在介质中传播的弹性动力学响应(能量衰减、相位特征、偏振属性、以及全波形等).基于波动方程理论的波场数值模拟由于能够引入丰富的波场信息,使得人们对不同介质中地震波的传播过程有了较全面的了解.本文以二维层状均匀介质模型为例,通过射线追踪法和交错网格有限差分法模拟得到的波场快照图、单炮地震记录剖面、合成理论地震图的分析比较,不但对地震波在各向同性层状均匀介质中的传播规律和特点有了深刻的理解和认识,同时又可以相互验证两种不同方法的正确性和有效性.     

电场平行于入射面的低频电磁波在导电界面的类全反射相角

根据非均匀电磁波在导电媒质中传播时其相移常数和振幅衰减常数方向的不一致性，利用低频非均匀电磁波在导电地层界面反射时的反射系数导出了电场偏振化方向在入射面内的低频电磁波类全反射相角.     

利用时频偏振分析技术研究面波传播的复杂性

介绍了一种新的时频偏振分析技术．该技术是传统的面波分析技术（移动窗方法及多重滤波方法）和奇异值分解法的结合,可用于测定不同周期的面波入射方位角;并将其用于分析穿过中国大陆不同块体的面波传播路径,并对穿过青藏高原不同区域的面波传播路径进行了分析．结果表明,　该方法能充分利用面波不同振型在频率成分及到时上的差异给出较准确的偏振分析结果,同时也便于考察面波偏振（入射方位）随周期而变化的情况．实际资料分析表明,岩石圈结构的横向不均匀性对面波的传播路径有很大影响．尤其是穿过青藏高原的面波路径对大圆路径的偏离角较大,并且穿过青藏高原的不同区域的面波其传播路径对大圆的偏离角也有很大区别．      

各向异性介质qP波传播描述I：伪纯模式波动方程

地球介质相对于地震波波长尺度的定向非均匀性会导致波速的各向异性,进而影响地震波场的运动学与动力学特征．各向异性弹性波动方程是描述该类介质波场传播的基本工具,在正演模拟、偏移成像与参数反演中起着关键作用．为了面向实际应用构建灵活、简便的各向异性波场传播算子,人们一直在寻求简化的各向异性波动方程．本文借鉴各向异性弹性波波型分离思想,通过对平面波形式的弹性波方程(即Christoffel方程)实施一种代表向波矢量方向投影的相似变换,推导出了一种适应任意各向异性介质、运动学上与原始弹性波方程完全等价,在动力学上突出qP波的新方程,即qP波伪纯模式波动方程．文中以横向各向同性(TI)介质为例,给出了相应的qP波伪纯模式波动方程及其声学与各向同性近似,并在此基础上开展了正演模拟和逆时偏移试验,展示了这种描述各向异性波场传播的新方程的特点与优势．     

高阶交错网格有限差分法纵横波波场分离数值模拟

本文给出了一种等价的弹性波动方程,以解决完全弹性波场中不能完全分离耦合的纵横波波场问题.对该弹性波动方程进行公式换算,推导出新型等价一阶双曲型方程,应用高阶交错网格有限差分法求解该方程,并给出了相应的最佳匹配层(PML)吸收边界条件,对均匀介质模型、复杂Marmousi模型和实际地质模型进行波场分离数值试验,准确得到了混合波场、完全分离的纯纵横波波场.数值结果表明,本文方法具有比传统方法更好的数值模拟精度和边界吸收效果,同时分析分离后的纵横波纯波场,可观察到较为丰富的能量转换信息,并发现纯纵波场中的非均匀平面波现象,该波为S波以临界角入射情况下的反射SP波,这对认识复杂弹性波的传播规律及弹性波理论具有重要意义.     

剪切波在双层方位各向异性介质传播中分裂参数的变化特性

以质元运动方程和应力应变关系为基础建立了各向异性介质的波动方程．从数学上对体波在各向异性介质中的传播进行了严格的数学推导,给出了各向异性介质中三种体波波速与介质弹性常数及波传播方向的数学关系．由此对剪切波在单层和双层弱方位各向异性介质中的分裂行为进行了系统讨论,给出了合成分裂参数、每一层分裂参数与入射剪切波偏振方向的数学表达式．假定每一层分裂参数之后,得到了合成分裂参数随入射方位角变化的合成地震图．研究表明,剪切波在双层各向异性介质中传播时产生的两对分裂剪切波可用一合成分裂因子来描述．由合成分裂因子确定的分裂参数随入射剪切波偏振方向的变化呈现出π／2的变化周期．其结果可用于双层各向异性介质反演研究,对进一步解释板块运移、地幔对流规模、深源地震成因、浅部地震构造及深部力源问题等有参考意义．     

正交各向异性介质中qP波入射的二阶近似反射系数与透射系数

地震波在各向异性介质中以一个准P波(qP)和两个准S波(qS1和qS2)的形式传播.研究三种波的相速度、群速度以及偏振方向等传播性质能够为各向异性介质中的正反演问题提供有效支撑.具有比横向各向同性(TI)介质更一般对称性的正交各向异性介质通常需要9个独立参数对其进行描述,这使得对传播特征的计算更为复杂.当两个准S波速度相近时具有耦合性,从而令慢度的计算产生奇异性.因此,奇异点(慢度面的鞍点和交叉点)附近的反射与透射(R/T)系数的求解不稳定,会导致波场振幅不准确.本文首次通过结合耦合S波射线理论和基于迭代的各向异性相速度与偏振矢量的高阶近似解,得到了适用于正交各向异性介质以qP波入射所产生的二阶R/T系数的计算方法.与基于一阶近似的结果相比,基于二阶近似的方法提高了qP波R/T系数的精度,能得到一阶耦合近似无法表达的准确的qP-qS转换波的R/T系数解,且方法适用于较强的各向异性介质.     

横向非均匀介质多道瑞雷波频散曲线正演

作为近地表横波速度结构成像的主要手段之一,面波多道分析法的正问题研究对现场观测系统设计及后续反演计算具有重要意义.目前面波频散曲线的正演主要分为两类:一是对水平层状介质中面波的本征值问题进行求解,该类方法计算效率高但较难考虑地下介质在横向上的不均匀性;二是基于波动方程的全波场模拟,该类方法在理论上可考虑任意复杂的地质模型但计算成本相对较高.本文基于振幅归一化加权的聚束分析,提出了一种适用于横向非均匀介质模型的多道瑞雷波频散曲线正演方法.首先,基于聚束分析的计算公式推导得到了经振幅归一化加权后输出功率谱中相速度与局部相速度之间的关系,然后通过黄金分割极值搜索算法计算得到了多道瑞雷波数据的理论频散曲线.数值分析结果表明,该算法能够快速地实现横向非均匀介质中多道瑞雷波频散曲线的正演计算,所求取的频散曲线与采用二维弹性波时间域有限差分模拟分析得到的结果误差较小,这在一定程度上说明了该计算方法的可靠性,从而可为面波多道分析法中的观测系统快速优化设计以及横向非均匀介质中频散曲线的反演解释提供理论支撑.     

Time-domain Pure-state Polarization Analysis of Surface Waves Traversing California

-- A time-domain pure-state polarization analysis method is used to characterize surface waves traversing California parallel to the plate boundary. The method is applied to data recorded at four broadband stations in California from twenty-six large, shallow earthquakes which occurred since 1988, yielding polarization parameters such as the ellipticity, Euler angles, instantaneous periods, and wave incident azimuths. The earthquakes are located along the circum-Pacific margin and the ray paths cluster into two groups, with great-circle paths connecting stations MHC and PAS or CMB and GSC. The first path (MHC-PAS) is in the vicinity of the San Andreas Fault System (SAFS), and the second (CMB-GSC) traverses the Sierra Nevada Batholith parallel to and east of the SAFS. Both Rayleigh and Love wave data show refractions due to lateral velocity heterogeneities under the path, indicating that accurate phase velocity and attenuation analysis requires array measurements. T he Rayleigh waves are strongly affected by low velocity anomalies beneath Central California, with ray paths bending eastward as waves travel toward the south, while Love waves are less affected, providing observables to constrain the depth extent of anomalies. Strong lateral gradients in the lithospheric structure between the continent and the ocean are the likely cause of the path deflections.     

Application of the time-frequency polarization analysis to study the complexity of surface wave propagation

A new technique called the time-frequency polarization analysis was introduced in this paper. The technique combined the traditional surface wave analysis techniques (moving window and multi-filter) with the singular value decomposition method to measure the incidence azimuth of surface waves with different wavelengths. It was applied to study the progagation paths of surface waves across the different blocks of Chinese continent and different zones of Qinghai-Xizang (Tibet) plateau. The results show that the method can make full use of the differences in frequency compositions and arrival times of different surface wave modes, and give better polarization analysis results. The analysis by actual data shows that the lateral heterogeneity of the lithospheric structure influences the propagation paths of surface waves severely. Deviations of the paths across the Qinghai-Xizang plateau from great circle paths are great. Deviations of the surface waves across the different zones in Qinghai-Xizang plateau are different. This project was sponsored by the Joint Earthquake Science Foundation.     

青藏高原东部Love波偏振研究

利用布设在云南西部的50个流动观测台站记录的三分量数字面波资料，采用频率域奇异值分解法，分析了中短周期Love波在青藏高原东部传播中的偏振状况. 结果显示Love波的传播呈现明显的有规律的偏离大圆路径的异常，地壳-上地幔速度结构显著的横向不均匀性可能是造成这些偏振异常的主要原因. 同时利用以前研究中得到的剪切波速度模型计算了Love波到达台站的理论偏离情况，大多数理论计算与实际观测结果的偏离方向基本一致，但理论偏离角通常小于观测值. 这样的结果在一定程度上验证了所采用的青藏高原速度结构模型是基本正确的，同时也说明了模型对研究区域复杂的速度结构的反映还不够精细.     

On the theory of the microseismic sounding method

Based on the theory of surface waves in a media with weak lateral heterogeneities, an explanation is given for the peculiarities that are considered as prospecting indicators in the microseismic sounding method (MSM). According to this theory, during the propagation of surface waves in such media, their local characteristics are the same as in the case of propagation in a horizontally homogeneous medium characterized by the same vertical velocity section as underlying a given point. Since the wave energy flux through a semiinfinite vertical strip is conserved, the amplitude of the wave is redistributed along the vertical. Based on this principle and simple physical considerations, it is shown that above a low-velocity domain, the amplitudes of microseisms should increase at wavelengths approximately exceeding the depth of the anomaly by a factor of three and decrease at small wavelengths. The model calculations show that variation of spectral amplitudes only allows a depth to the anomaly to be estimated rather than its average extent. Practically identical spectra characterize the anomalies in which the product of the vertical extent of the anomaly and the velocity contrast is approximately similar.     

角度域叠前时间偏移:非均匀介质中的单程波方法

从单程波方程出发,推导出角度域叠前时间偏移的走时、入射波与反射波夹角、成像幅值计算方法;构建了可直接生成角度域成像道集的叠前时间偏移方法与偏移流程.文中定量分析了速度梯度对走时、角度、幅值的影响,给出了可更好考虑介质非均匀性的角度、幅值计算方法.理论模型以及实际数据验证了本文方法的有效性.     

Numerical study on transient harbor oscillations induced by successive solitary waves

Tsunamis are traveling waves which are characterized by long wavelengths and large amplitudes close to the shore. Due to the transformation of tsunamis, undular bores have been frequently observed in the coastal zone and can be viewed as a sequence of solitary waves with different wave heights and different separation distances among them. In this article, transient harbor oscillations induced by incident successive solitary waves are first investigated. The transient oscillations are simulated by a fully nonlinear Boussinesq model, FUNWAVE-TVD. The incident successive solitary waves include double solitary waves and triple solitary waves. This paper mainly focuses on the effects of different waveform parameters of the incident successive solitary waves on the relative wave energy distribution inside the harbor. These wave parameters include the incident wave height, the relative separation distance between adjacent crests, and the number of elementary solitary waves in the incident wave train. The relative separation distance between adjacent crests is defined as the ratio of the distance between adjacent crests in the incident wave train to the effective wavelength of the single solitary wave. Maximum oscillations inside the harbor excited by various incident waves are also discussed. For comparison, the transient oscillation excited by the single solitary wave is also considered. The harbor used in this paper is assumed to be long and narrow and has constant depth; the free surface movement inside the harbor is essentially one-dimensional. This study reveals that, for the given harbor and for the variation ranges of all the waveform parameters of the incident successive solitary waves studied in this paper, the larger incident wave heights and the smaller number of elementary solitary waves in the incident tsunami lead to a more uniform relative wave energy distribution inside the harbor. For the successive solitary waves, the larger relative separation distance between adjacent crests can cause more obvious fluctuations of the relative wave energy distribution over different resonant modes. When the wave height of the elementary solitary wave in the successive solitary waves equals to that of the single solitary wave and the relative separation distance between adjacent crests is equal to or greater than 0.6, the maximum oscillation inside the harbor induced by the successive solitary waves is almost identical to that excited by the single solitary wave.     

平面P波在饱和半空间中洞室周围的散射(II):数值结果

本文通过数值计算研究了入射平面P波在饱和半空间中洞室周围散射问题,分析了入射波频率和角度、边界渗透条件、孔隙率、泊松比等参数对散射的影响。研究表明,平面P波入射情况下,饱和半空间和单相(干土)半空间中洞室附近地表位移幅值的差别很大,干土情况的水平位移幅值相对较大,饱和情况的竖向地表位移幅值相对较大;由于波在洞室附近的干涉,饱和情况与干土情况的地表位移出现相位漂移。随着孔隙率的增大,洞室附近水平地表位移幅值逐渐减小,竖向地表位移幅值则逐渐增大;当孔隙率较低时,边界渗透条件对地表位移幅值的影响很小,而当孔隙率较大时,边界渗透条件的影响则不可忽视,不透水情况下,水平和竖向地表位移幅值的峰值均相对较大;随着入射频率的增加,孔隙率的影响逐渐增大,而且不透水情况下孔隙率的影响相对较大。随着泊松比的增大,洞室附近水平地表位移幅值逐渐降低,竖向地表位移幅值则逐渐增大;泊松比较小时,边界渗透条件对位移幅值的影响较大,泊松比较大时,边界渗透条件对位移幅值的影响则较小;随着入射频率的增加,泊松比的影响逐渐增大。当孔隙率较小时,半空间地表和洞室表面孔隙水压幅值较小,但空间变化比较剧烈,随着孔隙率的增大,孔隙水压逐渐增大但空间变化逐渐平缓;随着入射频率的增加,孔隙水压幅值逐渐增大,且孔隙水压的空间变化逐渐变得复杂。     

Scattering of plane sh waves by a semi-cylindrical canyon

The two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical canyon is analysed for a general angle of wave incidence. The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves only when the wavelengths of incident motion are short compared to the radius of a canyon. The surface amplification of displacement amplitudes around and in the canyon changes rapidly from one point to another, but the amplification is always less than 2. The over-all trends of amplification pattern are determined by two principal parameters: (1) γ, the angle of incidence of plane SH waves, and (2) η, the ratio of radius of the canyon to one-half wave length of incident waves. The higher η leads to greater complexity of the pattern of surface displacement amplitudes characterized by more abrupt changes of amplification from one point to another, while γ mainly determines the over-all trends of displacement amplitudes. For grazing and nearly grazing incidences, for example, a strong shadow zone is developed behind the canyon. The qualitative analysis of the topographic effects on the Pacoima Dam accelerogram,¹ based on the semi-cylindrical canyon, suggests that this strong-motion record was not seriously affected by surface topography of the recording site.     

复杂场地条件下地震动空间效应研究

产生地震动空间效应的主要原因是地质构造的变化会极大地改变复杂场地条件下到达不同观测点的地震波,因此地震波振幅和相位发生明显变化。本文利用有限元和边界元耦合的方法,通过建立雷克子波入射时的非线性响应模型求解复杂场地条件下的波动积分方程,进行复杂近地表构造中地震波场数值模拟,旨在分析复杂场地条件下入射方向不同的地震波的动力响应规律。研究结果显示近地表会极大地改变地震波传播特征,导致地震波传播趋向不一致性的因素是由于复杂场地条件重建了地震波的传播路径,尤其须指出的是非一致性地表位移响应源于软土层中低频子波的传播。在地震响应分析中导致系统不同动力响应的其他原因是主频和地震波速度结构的改变,同时地震波入射角度的改变会引起到达观测点的时间滞后,地表位移响应随着入射角度的增大而增加,地震动的空间效应随着入射角度的减小而愈趋明显。     

Kelvin wave generation by a semi-infinite barrier

A closed form solution is given for the problem of simple harmonic plane waves incident obliquely on a semi-infinite barrier. The amplitude of the Kelvin wave component is considered and it is found that increased amplitudes of the Kelvin waves can be expected for certain wave numbers, depending upon the angle of incidence.