Scattering and attenuation of elastic waves in random media

In seismic exploration, elastic waves are sent to investigate subsurface geology. However, the transmission and interpretation of the elastic wave propagation is complicated by various factors. One major reason is that the earth can be a very complex medium. Nevertheless, in this paper, we model some terrestrial material as an elastic medium consisting of randomly distributed inclusions with a considerable concentration. The waves incident on such an inhomogeneous medium undergo multiple scattering due to the presence of inclusions. Consequently, the wave energy is redistributed thereby reducing the amplitude of the coherent wave.The coherent or average wave is assumed to be propagating in a homogeneous continuum characterized by a bulk complex wavenumber. This wavenumber depends on the frequency of the probing waves; and on the physical properties and the concentration of discrete scatterers, causing the effective medium to be dispersive. With the help of multiple scattering theory, we are able to analytically predict the attenuation of the transmitted wave intensity as well as the dispersion of the phase velocity. These two sets of data are valuable to the study of the inverse scattering problems in seismology. Some numerical results are presented and also compared, if possible, with experimental measurements.     

Frequency-dependent attenuation of P and S waves in Yunnan region

Introduction Attenuation parameter Q~(-1) is an important factor for understanding the physical mechanism of seismic wave attenuation in relation to the composition and physical condition of the Earth′s interior (Sato, 1992) and it is also an indispensable parameter for the quantitative prediction of strong ground motion from the viewpoint of engineering seismology. Hence numerous studies of Q~(-1) have been carried out worldwide by using different methods and concentrate on seismically acti…     

Near-surface attenuation modelling based on rock shear-wave velocity profile

In a previous study published in this journal, the authors developed a comprehensive methodology for modelling the shear wave velocity profile in crustal rock, for purposes of seismic hazard assessment. The derived shear wave velocity profile was used to estimate the amplification and attenuation mechanisms in the transmission of seismic waves. The ability to conduct seismic hazard assessments in regions of low and moderate seismicity is greatly enhanced by this new modelling approach, given that developing a local attenuation model based on curve-fitting strong motion data is generally not feasible under such conditions. This paper reports a follow-up study conducted to evaluate the significance of near-surface attenuation in bedrock (as distinct from attenuation in unconsolidated soft soil sediments). The κ parameter is used to characterize the extent of this attenuation mechanism. Empirical correlations of κ with two forms of near-surface shear wave velocity parameter in crustal rock have been developed, employing information obtained from global sources in conjunction with that from local studies. The resulting development of two simple equations to predict median values of κ as functions of readily available shear wave velocity parameters represents the key outcome of this study. Applications of the proposed empirical approaches to determine κ have been provided, taking Hong Kong and Melbourne as case studies to illustrate different aspects of the proposed methodology. Consistency between the results obtained by the two recommended approaches has thereby been demonstrated.     

海洋含水合物沉积层的速度频散与衰减特征分析

随着水合物含量的增加,往往会引起纵、横波速度的增加,同时也会引起衰减的变化.针对含水合物沉积层的速度频散与衰减特征分析,有助于水合物含量的估计.本文以有效介质理论模型（EMT）为基础,研究了海洋未固结含水合物沉积层的纵、横波速度的非线性变化趋势.同时采用BISQ模型替代有效介质模型中的Gassmann方程,具体分析了全频带范围内海洋含水合物沉积层的速度频散与衰减特征.采用该模型,速度与衰减均随着水合物含量的增加而增加,且岩石孔隙度与泥质含量对衰减系数的影响较小.针对大洋钻探计划（ODP）164航次的实际数据,运用该模型方程计算采用声波测井数据（20 kHz）与VSP数据（100 Hz）,分别获取了水合物稳定带的饱和度数据,平均在5%～7%之间,由于速度频散的影响,VSP估算结果要弱低于声波测井估算数据,均与实测保压取芯的甲烷含量数据、他人研究成果以及神经网络趋势预测结果均有着较好的一致性.对南海神狐海域三口钻位开展了水合物含量预测,与保压取芯结果有着较好的吻合关系.同时基于层剥离法提取该区域某地震测线BSR层的等效Q值,采用本文方法估算了该区域的等效天然气水合物含量15%～30%.数值模拟与实际应用结果表明：含水合物沉积层的速度频散与衰减特征均随着水合物含量的变化而变化,联合利用这一些变化特征,有助于天然气水合物含量的估计.     

含流体复杂孔隙介质地震波衰减与频散

含流体孔隙介质中地震波的速度频散和衰减在指导复杂储层含油气性识别领域具有重要意义.本文构建了包含微观挤喷流与介观层间流影响的跨尺度模型, 并使用求解介质等效模量的方式得到了模型中地震波的频散速度与衰减因子, 克服了前人在高频段计算结果出现异常值以及不同尺度衰减峰无法分离的缺陷.在该双尺度模型的基础上, 本文又综合考虑宏观尺度Biot流, 将三种地震波衰减理论耦合, 建立了相对统一的三尺度地震波衰减岩石物理模型.在Biot理论框架下, 分析了非均匀性流体、孔裂隙结构、微观挤喷流以及介观层间流对流体压力与弹性模量的影响, 得到了该三尺度模型中地震波的波动方程, 并求解得到了相应的地震波衰减与频散曲线, 分析了不同介质参数对衰减与频散曲线的影响.我们推导了在该模型上覆均匀各向同性介质情况下, 分界面处各类极性波的反射、透射系数特征方程, 并得到了随频率以及入射角变化的反射、透射系数三维曲面.

     

TTI介质弹性波相速度与偏振特征分析

相速度和偏振方向是研究地震波传播规律和描述介质特性的重要参数,在理论研究和实际应用中有重要作用.本文假定倾斜横向各向同性(TTI)介质对称轴位于观测坐标系XOZ面内,在此观测坐标系下直接推导了TTI介质弹性波相速度和偏振方向的解析表达式,再进一步利用Thomsen弱各向异性理论,推导了弱各向异性近似条件下弹性波相速度以及qP波和qSV波偏振方向表达式.理论分析和数值试例表明,在相速度方面,随着各向异性介质参数改变,qP波和qSH波速度变化较为平缓,qSV波速度变化较为剧烈.弹性波相速度近似式误差均较小,能较好地近似精确相速度.在偏振方向方面,SH波偏振方向只是传播方向和对称轴倾角的函数,而与各向异性参数无关,SH波偏振方向既垂直于传播方向,又垂直于TTI介质对称轴方向.除特定方向外,qP波和qSV波的偏振方向与传播方向均成一定角度,并且随TTI介质对称轴倾角的改变而改变;在精确和近似情况下,qP波和qSV波的偏振方向始终垂直;在精度允许范围内,偏振方向的弱各向异性近似式与理论解析式吻合较好.     

Research on propagation properties of elastic waves in two-phase anisotropic media

IntroductionItiswellknownthatanisotropylieswidelyintheundergroundmedia.Anisotropicmediawhicharemetintheseismicengineeringandseismicexplorationofenergyaremainlycausedbytheperiodicthinlayers(PTL)andextensivedilatancyanisotropy(EDA).Insuchmedia,anisotropyleadstomorecomplicatepropagationofseismicwave,thesignificantfeatureinanisotropicmediaisvelocityanisotropy.Infact,undergroundstrataareverycomplicated,whichareusuallycomposedofsolidframeandfluid(suchasoil,gasesorwater)inpores.Inordertostudyseism…     

The attenuation of stress waves in fluid saturated porous rock

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非饱和岩石中的纵波频散与衰减: 双重孔隙介质波传播方程

本文采用Rayleigh理论描述纵波激励下非饱和岩石中气泡的局域流体流动,从经典力学的哈密顿原理导出了双重孔隙介质中的波传播方程,即Biot-Rayleigh方程.方程的格式简洁,参数少,所有相关参数物理可测,因此,方程具有较好的物理可实现性.基于相同的岩石与前人理论对比,初步验证了本理论的有效性.对三个地区的砂岩储层进行了分析,结果显示:地震频段内纵波对储层是否含气非常敏感,但对含气饱和度指示性不佳,且随着孔隙度降低,纵波频散与衰减在中低频段更为显著;含甲烷与含二氧化碳的砂岩储层均呈第三类AVO响应特征,很难从叠前分析技术中鉴别;理论预测的纵波频散随饱和度与频率变化的趋势与特征,与多频段实验观测结果一致.     

含黏滞流体各向异性孔隙介质中弹性波的频散和衰减

基于Biot理论,考虑液相的黏弹性变形和固液相接触面上的相对扭转,提出了含黏滞流体VTI孔隙介质模型.从理论上推导出,在该模型中除存在快P波、慢P波、SV波、SH波以外,还将存在两种新横波－慢SV波和慢SH波.数值模拟分析了6种弹性波的相速度、衰减、液固相振幅比随孔隙度、频率的变化规律以及快P波、快SV波的衰减随流体性质、渗透率、入射角的变化规律.结果表明慢SV波和慢SH波主要在液相中传播,高频高孔隙度时,速度较高;大角度入射时,快P波衰减表现出明显的各向异性,而快SV波的衰减则基本不变;储层纵向和横向渗透率存在差异时,快SV波衰减大的方向渗透率高.     

含流体致密砂岩的纵波频散及衰减:基于双重双重孔隙结构模型描述的特征分析

致密砂岩普遍具有低孔、低渗及微裂缝发育的地质特征,并且呈现出很强的非均匀性.致密砂岩储层与常规砂岩储层比较,具有明显的岩石物理性质、渗流力学性质方面的差异.致密砂岩内部的非均匀性对弹性波频散、衰减有显著影响,其中包括孔隙结构的非均匀性,即岩石内部孔隙参数的不均一性,以及孔隙内部不相混溶流体的非均匀分布;此外,非均匀性的尺度也决定了波出现显著频散与衰减的频段.综合考虑致密砂岩孔隙结构非均匀性及流体斑块状饱和的非均匀性,本文采用双双重孔隙介质结构模拟了致密砂岩的弹性波响应,分析了同时具备两类非均质性岩石中的波传播特征.调查分析了两组分别来自中国鄂尔多斯盆地苏里格气田及四川盆地广安气田的不同类型致密砂岩储层的岩芯超声波实验数据,给出了岩石样本的弹性波速度频散与衰减曲线.结果显示理论模型预测结果与完全饱和、部分饱和岩石的实验数据吻合良好.对两个地区致密砂岩岩芯数据进行对比分析,苏里格致密砂岩样本总体上比广安致密砂岩渗透率高,在各孔隙度范围内,特征模拟显示苏里格样本的裂隙尺寸明显大于广安样本.广安致密砂岩在低孔隙度范围内发育了更多、更小的颗粒裂隙/接触.致密砂岩的速度频散与衰减结果受流体黏度、晶体破裂及流体斑块状饱和的共同影响.此外,孔隙度越大,部分饱和岩石中斑块状饱和机制对总衰减的贡献越低,与之相对,结构非均质性所占的比重则有所增强.     

基于微观孔隙结构特征的速度频散和衰减模拟

孔隙尺度的喷射流流动是引起地震波速度频散和衰减的重要机制之一. 目前,大多数喷射流模型仅考虑硬孔隙与微裂隙之间的局部流动,而忽略了具有不同孔隙纵横比微裂隙间的喷射流作用. 为了研究各种类型孔隙间的流体流动效应,本文对经典喷射流模型进行了扩展,通过结合等效介质理论和孔隙结构模型,根据从干燥岩石超声速度-压力曲线中提取的微裂隙孔隙纵横比分布,求取出岩石中各种微裂隙的体积压缩系数,并在此基础上,利用孔隙空间的压力松弛效应对微裂隙间的喷射流效应进行了模拟,并运用Biot理论描述了硬孔隙间的宏观流动效应. 扩展后的理论模型不仅考虑了微裂隙与硬孔隙间的局部流动、硬孔隙与硬孔隙间的Biot宏观流,还加入了微裂隙与微裂隙间的喷射流作用,且模型的高、低频极限始终与Mavko-Jizba理论和Gassmann方程保持一致. 模型应用分析发现,对于砂岩和大部分致密灰岩样品,扩展模型均能给出与超声实验测量数据吻合良好的估计结果. 此外,扩展模型预测的速度频散及衰减表明,喷射流机制在地震和测井频段发挥着重要作用,其速度频散曲线由低频至高频呈逐渐增大趋势,不具有明显的快速变化特征,与经典频散曲线形态存在显著差异;在低有效压力下,频散和衰减程度较大,喷射流机制发挥主要作用,而随着有效压力的增加,Biot宏观流机制开始占主导,频散和衰减程度逐渐减小.

     

地震波在孔隙介质中低频衰减现象的粘弹性特征分析及近似（英文）

由于介观尺度的孔隙流体流动,弹性波传播过孔隙岩层时在地震频段表现出较强的频散和衰减。Johnson理论给出了在任意孔隙形状的条件下,部分气水饱和孔隙介质的理论相速度和品质因子的解析解。本文在Johnson模型的基础上,通过对Q值曲线的低频和高频近似,推导了Q值曲线的近似公式,以及基于孔隙介质基本地球物理参数和孔隙斑块几何形态参数T和比表面积S/V的最大衰减Qmin近似公式。通过与理论值的对比,对Qmin近似公式存在的线性误差进行改正,进一步提高了精度。复杂的斑块形态对最大衰减Qmin和过渡频率ftr的都产生一定影响,且对ftr影响更大。因为数值模拟直接求解介观尺度的Biot孔隙介质方程需要极大的计算量,我们使用Zener模型建立了等效粘弹模型,有效地模拟了地震频带内的衰减和频散现象。     

Laboratory measurements of spatial fluctuation and attenuation of elastic waves by scattering due to random heterogeneities

To study the effects of strong scattering on elastic waves, spatial fluctuation and scattering attenuation ofP waves were examined by laboratory experiments for 2-D models of random media approximately characterized by a triangular correlation function in the range of 2<ka<33, wherek is the wave number anda is the correlation distance of the heterogeneities, i.e., the heterogeneity size. The results obtained are as follows: (1) Forka>10, both the intensity and the correlation distance of the amplitude fluctuation are approximate for any phase of theP-wave train. The correlation distance nearly agrees with the heterogeneity size. These fluctuation properties are quite consistent with the theoretical prediction by the forward-scattering approximation. (2) For 3<ka<6, the fluctuation intensity becomes stronger in later phases of theP-wave train. This shows that scattering is approximately isotropic, and therefore, the scattered energy increases with time within theP-wave train. The correlation distance of the amplitude fluctuation disagrees with the heterogeneity size, and it shows a frequency-dependent property decreasing from 7a to 4a with the increase ofka from 3 to 6. These properties for 3<ka<6 have not yet been predicted theoretically. (3) Forka<3, though the fluctuation is considerably smaller compared with that ofka>10 and 3<ka<6, the fluctuation property is considered similar to that of 3<ka<6. (4) The observed scattering attenuation,Q ^–1, increases withka forka<3, has a peak aroundka=35, and then decreases withka. (5) When _min = 15° and = 0.075, the theoreticalQ ^–1 curve, predicted by the approximate theory of Wu, roughly matches the observedQ ^–1 values, where _min is the minimum scattering angle measured from the propagation direction of theP waves and is the rms of fractional velocity fluctuation. This suggests that the energy scattered in the range of >15° is lost from theP waves, while the energy scattered in the range of <15° is retained; and that the approximate theory overestimates by about three times the value of the model media used owing to the neglect of multiple scattering. (6) When the size of velocity heterogeneities responsible for forward scattering at 3<ka<6 is estimated from the _min value of 15° on the basis of Wu's theory, it nearly agrees with the correlation distance for the initial phase of theP-wave train.     

含泥质低孔渗各向异性黏弹性介质中的波频散和衰减研究

本文定义了各向异性黏弹性参数修正因子,并将其引入到黏弹性模型中以体现泥质含量对黏弹性机制的影响,同时将波传播过程中孔隙介质骨架黏弹性力学机制与两种孔隙流体流动力学机制（Biot流动和喷射流动机制）有机地统一起来处理,从而给出了描述含泥质低孔渗孔隙各向异性介质中波传播规律的黏弹性Biot/squirt (BISQ)模型.数值计算结果表明,入射波的方位角、各向异性渗透率以及泥质含量等对含流体复杂孔隙介质中波频散和衰减的影响具有显著的方位各向异性特征,在低频范围内（地震波勘探频率）黏弹性力学机制对波传播能量的衰减起主导作用.     

基于纵横波分离FCT弹性波正演频散压制

有限差分方法被广泛应用于地震波数值模拟和传播.传统有限差分法采用Taylor级数展开实现空间偏导数的差分, 但该方法会因为网格离散化而产生数值频散, 降低地震波模拟的精度.优化差分系数正演方法能在一定程度上压制部分频散, 然而纵、横波速度取值差异较大, 在弹性波有限差分正演模拟中, 在满足纵波最大速度确定的稳定性条件下, 浅层低速横波波场往往会产生明显的频散现象.为了削弱弹性波场正演数值频散, 提高数值模拟精度, 本文首先采用优化差分网格系数降低数值频散, 然后再采用通量校正传输(Flux-Correction Transport, FCT)法来进一步压制弹性波场有限差分数值频散.常规的FCT法是对弹性波场直接进行频散压制, 但由于弹性波场中纵、横波速度差异明显, 横波波场频散明显强于纵波, 为了压制横波波场的数值频散, 往往需要选取较大的频散压制参数, 但这会使频散较弱的纵波产生假象.因此本文提出基于纵横波分离FCT弹性波正演频散压制方法, 对分离之后的纵横波场分别选择合适的频散压制参数进行通量校正, 可以有效压制数值频散, 削弱纵波FCT产生的假象.通过理论分析和数值算例发现, 本文方法能有效削弱弹性波场有限差分数值频散, 相对于常规FCT方法没有假象产生.

     

具有低频超宽衰减域的部分埋入式表面波屏障

针对低频Rayleigh表面波,设计了部分埋入式工字形截面周期波屏障。利用有限元方法计算了结构的频散曲线,分析了带隙的形成机理,讨论了屏障埋入土体深度和截面参数对带隙的影响,在此基础上设计了具有低频超宽衰减域的梯度及分段梯度波屏障并计算了其传输谱。结果表明:周期波屏障存在较宽带隙,板埋入深度和端部尺寸是影响带隙的关键参数,通过参数调节可实现不同频段Rayleigh波的调控。工字形变截面波屏障比等截面具有更优越的隔震性能且节省材料。梯度及分段梯度波屏障显著拓宽了衰减域的频率范围,对1.5~20 Hz范围内的Rayleigh表面波实现了全覆盖,用小尺寸控制了大波长。     

Distribution characteristics of Rayleigh wave group velocity in China mainland and its adjacent sea areas

Making use of 75 earthquake data of China mainland and adjacent areas recorded by long period seismometers of 27 stations of China and 3 stations of WWSSN and processed by match-filtering frequency-time analysis technique and grid dispersion inversion, the authors obtain pure-path dispersion curves of Rayleigh surface wave in 147 grids in this paper. The distribution characteristics of group velocity are as follows:the China mainland and its adjacent sea areas are divided into two parts of east and west by South-North belt and are separated in blocks of south and north with boundaries of 44°–44°N,28°N (in the west part) and 28°–32°N (in the east part), the first and third boundaries may extend eastward into sea regions, in the west side of island arc and continental shelves, appears belt-form distribution of group velocity striping NE direction. These distribution characteristics correspond to zonation of tectonic structure. In addition, the results also indicate that the differences of group velocity dispersion curves exist between tectonic elements of next order. It is revealable for the differences of group velocity among different tectonic elements until periodT = 113s (corresponding depth is about 170km). The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 32–38, 1993.     

壳-幔过渡带首波传播特征

上地幔速度结构是影响Pn波几何衰减特征的主要因素,本文利用合成理论地震图方法,研究了壳-幔过渡带速度梯度对Pn波几何衰减特征的影响.结果表明,Pn波的衰减特征对上地幔的速度梯度十分敏感,如：1000 km处Pn波的振幅,在相当于将均匀上地幔经展平变换后的等效速度梯度(0.0013 s-1)模型下,约为在半无限空间上叠加一层的简单模型下的10倍;当震中距大于某一距离后,具有速度梯度模型下的Pn波振幅随震中距衰减的速度明显小于无速度梯度的半无限空间模型下Pn波振幅的衰减速度,速度梯度越大,衰减速度越慢,在某一距离范围内,振幅甚至有增大的趋势;当存在速度梯度时,Pn波的几何衰减随频率而变化.上述结果对深入理解Pn波在区域震中距范围内的衰减规律提供了理论依据.