黏弹性介质中瑞利波频散曲线和衰减系数曲线的反演

瑞利波具有能量大、信噪比高等特点,可以用来反演介质内部的力学信息,近年来在浅层地球物理勘探、深层地震学研究以及超声波无损检测等多个领域都有较广泛的应用。目前大多数瑞利波的应用中都假设介质是弹性的,然而实际中岩石、土壤和金属等介质都在一定程度上体现出了黏弹性。当介质的黏弹性较强时仍然采用弹性假设研究其中瑞利波的反演将增大误差,因此有必要考虑黏弹性介质中的瑞利波反演,但是目前这方面的研究仍不够深入。本文研究黏弹性介质中瑞利波频散曲线和衰减系数曲线的反演问题,给出其在半空间中联合反演的方法,并对该方法的误差进行分析。     

Effects of site stiffness and source to receiver distance on surface wave tests׳ results

By using six 4.5 Hz geophones, surface wave tests were performed on four different sites by dropping freely a 65 kg mass from a height of 5 m. The receivers were kept far away from the source to eliminate the arrival of body waves. Three different sources to nearest receiver distances (S), namely, 46 m, 56 m and 66 m, were chosen. Dispersion curves were drawn for all the sites. The maximum wavelength (λ_max), the maximum depth (d_max) up to which exploration can be made and the frequency content of the signals depends on the site stiffness and the value of S. A stiffer site yields greater values of λ_max and d_max. For stiffer sites, an increase in S leads to an increase in λ_max. The predominant time durations of the signals increase from stiffer to softer sites. An inverse analysis was also performed based on the stiffness matrix approach in conjunction with the maximum vertical flexibility coefficient of ground surface to establish the governing mode of excitation. For the Site 2, the results from the surface wave tests were found to compare reasonably well with that determined on the basis of cross boreholes seismic tests.     

地震波散射研究的新进展——第25届IASPEI大会S13专题报告会“地震波散射与衰减”简介

本文以IASPEI的“地震波的散射与衰减”专题报告会为主,评述了近几年在地震波散射方面的研究进展.述评所涉及的方面有:1.关于地震尾波的起源;2.大震前尾波包络的前兆性变化;3.地震尾波包络衰降的机理;4.区分散射和吸收的新方法;5.新领域的开拓和研究.     

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。     

小应变硬化模型(HSS)在Rayleigh波作用下场地响应分析中的应用

为研究冲击荷载或地震作用下产生的,以Rayleigh波为主的面波对浅层地表土体动力响应特征以及数值模拟中土层阻尼的设置方法,以厦门地区浅层的素填土及粉质黏土为研究对象,采用有限元动力分析,土体本构采用小应变硬化模型(HSS),利用模型本身的滞回环特性,输入变化的小应变参数,考察HSS模型的小应变参数对场地动力响应的影响,并与土体采用摩尔-库伦模型结合Rayleigh阻尼(\"MC+Rayleigh阻尼\")的计算结果进行对比。研究表明:当采用带有滞回环的HSS模型时,波速随初始剪切模量Gref0的增大而增大,但振幅减小,残余变形量也有所减小;小应变参数γ0.7对波的影响较小;HSS模型能够给出残余变形量,而\"MC+Rayleigh阻尼\"由于本构模型为理想弹塑性模型,在卸载重加载条件下表现为纯弹性行为,无法反映出卸载重加载过程中塑性应变的积累及其累积阻尼效应;但HSS模型还不能够全面反映循环加载作用下塑性体积应变的累积,因此在考虑滞回阻尼的基础上,仍然建议借助Rayleigh阻尼来更加全面地模拟土体的实际阻尼特性。     

Constituents of Vertical-component Coda Waves at Long Periods

Aki (1969) first modeled coda waves of a local earthquake as a superposition of scattered surface waves. This paper attempts to clarify the constituents of surface-wave coda at long periods at very long lapse times. For a large earthquake of magnitude 7 or larger, vertical component oscillation in periods from 90 to 180 s persists for more than 20 hours from the earthquake origin time. Although the early portion of the coda envelope is successfully modeled by assuming incoherent scattered Rayleigh waves by heterogeneities distributed all over the Earth, the later potion of the observed coda envelope (roughly later than 35,000 s) has systematically larger amplitude than theoretical prediction. To clarify the cause of this discrepancy, we studied the constituents of vertical-component seismograms of three large earthquakes recorded by the F-net in Japan using the f-k power spectral analysis. We found that the direct and scattered fundamental-mode Rayleigh waves of velocity about 3.7 km/s are dominant in the earlier part of each envelope. It justifies the use of a scattering model of the fundamental Rayleigh waves for synthesizing the envelope. At lapse times later than 20,000 s–35,000 s, higher modes with phase velocities around 20 km/s become dominant. The transition time to the dominance of higher modes is found to become earlier for a deeper focus earthquake. The small coda attenuation factor from (1.90±0.23) × 10⁻³ to (2.38±0.32) × 10⁻³ estimated from later coda envelopes recorded at IRIS stations distributed worldwide also agrees with the attenuation factor of spheroidal modes according to PREM. We may interpret that higher mode waves are uniformly distributed at large lapse time due to large velocity dispersion and/or scattering and they dominate over the fundamental mode waves because of smaller attenuation in the lower mantle. The coda attenuation measurement proposed by Aki is found to be useful even for long periods and at very large lapse times.     

地震波散射理论及应用研究综述

回顾了地震波散射的概念、研究历史及分类.对散射理论及应用研究成果进行了系统评述,特别对前人关于散射波数值模拟和应用研究的不足进行了总结：(1)观测系统设计不合理;(2)对散射波的特征研究缺乏系统性;(3)对复杂散射波场的识别方法没有进行系统研究;(4)适合散射成像的处理软件还有待开发.并介绍了作者关于地震散射波场特征数值模拟研究的初步成果.     

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.     

离散网格中瑞利阻尼对波动的影响分析

在波动数值模拟中,瑞利阻尼可近似描述介质耗散特性,且可用于抑制人工边界引发的高频和零频失稳,但瑞利阻尼对波动的影响尚未清晰认识。针对集中质量有限元模拟的一维波动,利用傅里叶模态分析了有阻尼离散网格中波动的性质。理论分析表明alpha阻尼必然使得波数为零及邻近的波动对应为非行进波,其使行波衰减一致,而beta阻尼不会导致波数为零及邻近的非行进波,其使行波衰减随着波数增大而增大。数值实验验证了上述结论。本文研究结果为进一步推进瑞利阻尼在波动数值模拟中的应用提供一定的理论依据。     

平面P、SV和Rayleigh波入射下沉积河谷地震响应IBEM宽频模拟

沉积河谷对地震波的高频散射规律尚不明确。采用一种高精度间接边界元法(IBEM)用于沉积河谷对平面P、SV和Rayleigh波的二维散射宽频求解分析。数值结果表明:IBEM可高效精确地模拟地震波的宽频散射;中低频段(无量纲频率η5.0),河谷地形对地震波的放大效应显著;高频波段(η10.0),河谷放大效应减弱甚至出现缩幅效应。随河谷深度增加,位移放大频段的带宽逐渐减小,第一峰值频率降低,且在低频段频谱曲线振荡剧烈。阻尼比对沉积河谷地表位移幅值具有显著影响,尤其是在高频段衰减作用明显。实际沉积河谷场地地震反应分析,需充分考虑波型、入射波频率和角度、河谷深宽比等因素,以更科学地进行震害解释和地震安全性评价。     

云南地区尾波衰减特征研究

利用22个云南区域数字地震台网近震资料,研究了云南地区地震尾波在1~20 Hz内6个频段的衰减特征. 首先使用单次散射模型计算各台站的尾波衰减系数; 然后利用随机各向同性散射介质均匀分布的多次散射模型, 使用多流逝时间窗分析方法,计算各台站的平均自由程Le和地震反照率B0得到总衰减系数,并从中分离散射衰减系数 、吸收衰减系数 . 云南地区基本衰减特征是Le主要集中在10~30 km内, 在2~6 Hz之间有最大值;B0在1~2 Hz大致为0.5左右,在其它频段则小于0.5. 也即在1~2 Hz, 与 数值相当, 其它频段 逐渐大于,成为尾波总衰减的主要原因. 除1~2 Hz外,其它频段 值接近. 云南地区的Q-1尤其是, 在空间上有较大的差异,滇东略微高于滇西北, 滇西北高于滇西南地区. 与全球其它区域的研究结果比较发现,云南地区 略低于平均水平, 略高于平均水平, 而则处于其它区域结果的中间.      

Characteristics of coda wave attenuation in Yunnan area

The characteristic of seismic coda wave attenuation in Yunnan area in 7 frequency-bands range from 1 Hz to 20 Hz was estimated by using the local earthquake's waveform data recorded from 22 Yunnan digital seismic stations.Coda attenuation Q-c1 of each station was firstly calculated by single scattering method. Then, mean free path Le and seismic albedo Bo of each station were calculated, and scattering attenuation Q-1s and intrinsic attenuation Q-1i were separated from total attenuation Q-1t by multiple lapse time window analysis based on the multiple scattering model in uniform random isotropic scattering medium. The attenuating characteristics in Yunnan show that most value of Le are in 10～30 km, with maximal within 2～6 Hz;Bo are about 0.5 at 1～2 Hz, but less than 0.5at other frequency-bands, which means Q-1i is comparable with Q-1s at 1～2 Hz, and after 1～2 Hz, Q-1i is greater than Q-1s and dominates the attenuation process. Q-1c is close to Q-1i at other frequency bands except 1～2 Hz.Results show that Q-1 especially Qs-1 varies spatially, Q-1 in eastern Yunnan zone is a bit higher than in northwestern Yunnan zone;northwestern Yunnan zone higher than southwestern Yunnan zone. Comparing with other results in global, Qs-1 in Yunnan is lower than the global average value among these results, Q-1i is higher than the global average value, and Q-1t lies the middle among these results.     

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.