子波变换在层析成象中的应用及前景

子波变换是对付里叶变换研究的巨大进展,它不仅能在传统使用付氏变换的场合,作为代替付氏变换,予以使用,而且因为它同时具有时间域和频率域的良好局部化性质,可对地震信号的高频成份逐步进行更为精细的时间域和空间域的采样,以便在地震层析成像中对更细微的细节予以聚焦。本文介绍了子波变换及其推广子啾变换及有关公式,并指出它们在图象编码、图象压缩、心电图、核磁共振成像和硬件芯片中的应用。     

Synthetic Seismograms for a Layered Earth Geological Model Using the Absorption and Dispersion Phenomena

—An algorithm has been developed to compute the dispersive and dissipative seismic response using FUTTERMAN’S (1962) third attenuation-dispersion relationship. In the computation, frequency-dependent velocity and quality factor Q have been used but in the case of the nondispersive synthetic seismogram, frequency-independent velocity has been used. The model’s parameters are density, phase velocity, quality factors and thicknesses of the layers. Dispersive and nondispersive synthetic seismograms have been computed with and without absorption for a layered earth geological model. Fast Fourier transform (FFT) technique has been adopted for converting the frequency domain response into the time domain. The frequency spacing, Δf = 0.976?Hz, has been considered to avoid the aliasing effect. The results have revealed changes in the reflected waveforms in the frequency domain as well as in the time domain for absorption and dispersion cases. It is also concluded that dispersion reduces the arrival time and this effect is increasing with the travel time. The effect of constant Q on the seismic response has also been studied.     

Rayleigh wave separation using high-resolution time-frequency polarization filter

Obtaining geological information from seismic data motivates researchers to innovate and improve seismic wave processing tools. Polarization-based methods have received much attention regarding their ability to discriminate between different phases of the seismic wave based on polarity. Combining the intuitive definition of polarity in the frequency domain (monochromatic waves) with the non-stationary properties provided by time-domain methods, time-frequency approaches are attracting widespread interest because they localize the information extracted from the seismic waves in the joint time and frequency domains. Due to the lack of high-resolution time-frequency maps, the time-frequency polarization approach was not able to resolve specific temporal polarity changes in the seismic signal. The main objective of this study was to devise a robust time-frequency-based polarization filtering method using high-resolution polarization attributes obtained directly from the sparse time-frequency map without using Eigen analysis or analytic signals. The method proposed here utilizes a computationally effective sparsity-based adaptive S-transform to obtain a high-resolution polarization map of an inherently non-stationary seismogram for the entire frequency content of the signal at different times. The superiority of the proposed method over the S-transform method was verified using synthetic and real data sets to calculate the polarization attributes in the time-frequency domain and separate the Rayleigh waves from the seismogram.     

Precise arrival time detection of polarized seismic waves using the spectral matrix

I present a statistical method for detecting the arrival times of polarized seismic waves on three-component seismic observations in the time and frequency domains. In this method, the polarization, which is a representation of the 3D particle motion of seismic waves, is evaluated on the basis of a spectral matrix in the time and frequency domains and the statistical parameters are defined by using the eigenvalues of the spectral matrix for detecting the arrival times of linearly and elliptically polarized waves, where the idea of a statistical test of hypothesis is introduced. An evaluation of a synthetic signal revealed that the method can detect the arrival times of linearly and elliptically polarized waves within 10 sampling points at signal-to-noise ratios of −7 dB. Application of the method to an earthquake suggested that it can be used to detect the arrival times of both linearly and elliptically polarized waves, which are difficult to identify manually.     

Influences of type of wave and angle of incidence on seismic bending moments in pile foundations

When analysing the seismic response of pile groups, a vertically‐incident wavefield is usually employed even though it does not necessarily correspond to the worst case scenario. This work aims to study the influences of both the type of seismic body wave and its angle of incidence on the dynamic response of pile foundations. To this end, the formulation of SV, SH and P obliquely‐incident waves is presented and implemented in a frequency‐domain boundary element‐finite element code for the dynamic analysis of pile foundations and piled structures. Results are presented in terms of bending moments at cap level of single piles and 3 × 3 pile groups, both in frequency and in time domains. It is found that, in general, the vertical incidence is not the most unfavourable situation. In particular, obliquely‐incident SV waves with angles of incidence smaller than the critical one, a situation in which the mechanism of propagation of the waves in the soil changes and surface waves appear, yield bending moments much larger than those obtained for vertically‐incident wavefields. It is also shown that the influence of pile‐to‐pile interaction on the kinematic bending moments becomes significant for non‐vertical incidence, especially for P and SV waves. Copyright © 2013 John Wiley & Sons, Ltd.     

反应谱控制选波的地震动时频非平稳特性差异性分析

时程分析法中地震波的选取关乎结构抗震分析结果是否准确,基于规范反应谱进行选波分析,研究不同选波控制指标下所选出的地震波在时域、频域等方面的特性及误差大小,并进行工程验证。结果表明:采用拟合反应谱选波方法所选的地震动在时、频域上特性差异较大,是导致时程分析法中结构响应差异性较大的主要原因,且选用更为严格的控制指标并不能有效降低所选出地震动时频非平稳之间的差异性。     

Wave Propagation, Scattering and Imaging Using Dual-domain One-way and One-return Propagators

— Dual-domain one-way propagators implement wave propagation in heterogeneous media in mixed domains (space-wavenumber domains). One-way propagators neglect wave reverberations between heterogeneities but correctly handle the forward multiple-scattering including focusing/defocusing, diffraction, refraction and interference of waves. The algorithm shuttles between space-domain and wavenumber-domain using FFT, and the operations in the two domains are self-adaptive to the complexity of the media. The method makes the best use of the operations in each domain, resulting in efficient and accurate propagators. Due to recent progress, new versions of dual-domain methods overcame some limitations of the classical dual-domain methods (phase-screen or split-step Fourier methods) and can propagate large-angle waves quite accurately in media with strong velocity contrasts. These methods can deliver superior image quality (high resolution/high fidelity) for complex subsurface structures. One-way and one-return (De Wolf approximation) propagators can be also applied to wave-field modeling and simulations for some geophysical problems. In the article, a historical review and theoretical analysis of the Born, Rytov, and De Wolf approximations are given. A review on classical phase-screen or split-step Fourier methods is also given, followed by a summary and analysis of the new dual-domain propagators. The applications of the new propagators to seismic imaging and modeling are reviewed with several examples. For seismic imaging, the advantages and limitations of the traditional Kirchhoff migration and time-space domain finite-difference migration, when applied to 3-D complicated structures, are first analyzed. Then the special features, and applications of the new dual-domain methods are presented. Three versions of GSP (generalized screen propagators), the hybrid pseudo-screen, the wide-angle Padé-screen, and the higher-order generalized screen propagators are discussed. Recent progress also makes it possible to use the dual-domain propagators for modeling elastic reflections for complex structures and long-range propagations of crustal guided waves. Examples of 2-D and 3-D imaging and modeling using GSP methods are given.     

Comparison of source parameters estimated in the frequency and time domains for seismic events at the Rudna copper mine,Poland

Source parameters estimated in the frequency domain for 100 selected seismic events from the Rudna copper mine, with moment magnitude ranging from 1.4 to 3.6, were collected to study their scaling relations and to compare them with the parameters estimated in the time domain. The apparent stress and static stress drop, corrected for the limited bandwidth recording, increase slightly in a similar manner with increasing seismic moment. The ratio of apparent stress to static stress drop, a measure of radiation efficiency, is practically constant and its mean value is close to 0.1. For 37 seismic events, with moment magnitude between 1.9 and 3.4, source parameters were estimated in the time domain from relative source time functions, that displayed unilateral rupture propagation, and their rupture velocity could be estimated. It ranges from 0.23 to 0.80 of shear wave velocity and is almost independent of seismic moment. The fault length, estimated from the average source pulse width and rupture velocity, is clearly dependent on seismic moment and is smaller than the source radius estimated from the corner frequency on the average by about 25 percent. There is no correlation between the values of static stress drop estimated in the frequency and time domains, but the time domain stress drop is in general similar to that estimated in the frequency domain. The apparent stress increases with increasing rupture velocity, and the ratio of apparent stress to static stress drop seems also to depend on rupture velocity.     

海南地区5口井水位对汶川地震的同震响应及其频谱分析

对比海南地震台网记录的汶川MS8.0地震的地震波形,分析了海南5口井的高采样率数字化水震波波形特征。采用傅立叶变换和小波分解方法,对海南前兆台网5个台水位仪在汶川MS8.0地震中记录到的高采样率数字化水震波进行了频谱分析,结果显示地震波的不同波组激发的水震波波组差别较大,5口井的水震波周期跨度很大,从10多秒到1000多秒,不同井孔的水震波幅度差别较大。同时还初步分析了水震波的形态和水震波各个频率组的形成机理。     

地震台阵上信号方位角和慢度的时、频域估计方法比较

地震台阵常用频率-波数分析法来估计地震信号的后方位角和慢度。尽管有关的算法是众所周知的,但不同的实现在某些情况下可能导致不同的结果。如应用在宽频带的澳大利亚WRA台阵的记录时,标准的f-k分析方法往往给出不正确的结果。本文发现错误是由FFT的频谱泄漏效应引起的,如在进行FFT之前对原始数据进行高通滤波则可以有效地避免这样的错误。进一步对在时域中直接估算信号方位角和慢度的一种算法进行了分析,比较发现时域方法的计算速度和精度都不低于频域方法,且在某些低信噪比的情况下,前者可以给出更可靠的结果。     

Increasing illumination and sensitivity of reverse‐time migration with internal multiples

Reverse‐time migration is a two‐way time‐domain finite‐frequency technique that accurately handles the propagation of complex scattered waves and produces a band‐limited representation of the subsurface structure that is conventionally assumed to be linear in the contrasts in model parameters. Because of this underlying linear single‐scattering assumption, most implementations of this method do not satisfy the energy conservation principle and do not optimally use illumination and model sensitivity of multiply scattered waves. Migrating multiply scattered waves requires preserving the non‐linear relation between the image and perturbation of model parameters. I modify the extrapolation of source and receiver wavefields to more accurately handle multiply scattered waves. I extend the concept of the imaging condition in order to map into the subsurface structurally coherent seismic events that correspond to the interaction of both singly and multiply scattered waves. This results in an imaging process referred to here as non‐linear reverse‐time migration. It includes a strategy that analyses separated contributions of singly and multiply scattered waves to a final non‐linear image. The goal is to provide a tool suitable for seismic interpretation and potentially migration velocity analysis that benefits from increased illumination and sensitivity from multiply scattered seismic waves. It is noteworthy that this method can migrate internal multiples, a clear advantage for imaging challenging complex subsurface features, e.g., in salt and basalt environments. The results of synthetic seismic imaging experiments, including a subsalt imaging example, illustrate the technique.     

三维沉积盆地对地震动的放大效应间接边界元法模拟

基于一种高精度间接边界元法(IBEM), 实现了沉积盆地三维地震响应的频域、 时域精细求解, 并以半空间中椭球形沉积盆地对平面P波和SV波的散射为例, 着重探讨了入射角度、 入射波型、 入射频率、 盆地长宽比和深宽比对沉积盆地地震动放大效应的影响规律． 结果表明: 盆地形状对地震波的放大效应和空间分布状态具有显著影响, 且具体规律受控于入射波频段． ① 随着盆地深度增大, 盆地边缘面波发育更为充分, 在较宽频段内均会出现显著的地震动放大效应, 且深盆地的放大区域集中于盆地中部． ② 圆形盆地对地震波的汇聚效应最为显著, 而狭长盆地对地震波的汇聚作用相对较弱, 高频情况下可在盆地内部形成多个聚焦区域． ③ 不同波型入射下, 盆地对地震动放大效应的机制有所差异: P波入射下, 竖向位移放大主要是由于盆地边缘面波由四周向中部汇聚所致; SV波入射下, 边缘面波汇聚效应相对较弱, 而当盆地较深时, 底部透射体波和边缘面波易形成同相干涉从而显著放大地震动． 按盆地内外介质波速比为1/2, P波和SV波垂直入射下频域最大放大倍数分别为25和15, 时域放大倍数约为4.0和3.7(雷克子波)． ④ 低频波入射下, 位移从盆地中部向边缘逐渐减小, 且浅层沉积盆地对地表位移幅值的放大作用不明显． ⑤ P波和SV波的入射角度对盆地地震动放大幅值及空间分布特征也具有显著影响．      

0.9 m薄煤层SH型槽波频散特征及波形模式

在0.9 m薄煤层中使用放炮方法做微震震源的条件,通过对所采集到的薄煤层槽波信号进行分析,发现薄煤层槽波在频域中存在高频和低频两个独立并且不连续的波段.其中高频区大约以2000 Hz为中心,低频域的中心频率约为490 Hz,并且高频域和低频域的能量差异不显著.通过时频分析,可以清晰地看到高、低两个频域几乎在同一时刻触发,并且其小波相关系数在这两个域中的分布规律表现出一定的相似性.通过对0.9 m薄煤层槽波频散曲线的理论分析可知,现场观测到的Airy震相的频率及速度和其理论值较为接近.震源置于煤层中心,且炸药能量对顶底板的扰动,对第二阶对称波形模式下槽波高频部分的形成起着关键作用.在这一对称高阶波形模式下槽波的波速基本上和煤层顶底板中S波的波速一致.由于这两个触发的波形模式在时间域中具有相似的特征,建议在高频域和低频域同时发育较好的薄煤层槽波勘探中,可以采用在同一时间域中高低频相结合的方法提高利用槽波勘探分析的效果.     

基于地震波叠加模式的空间域划分及质点运动空间差异——以SV波入射为例

针对地震动空间差异问题,以半无限空间内平面SV波入射为例,采用波动理论和叠加原理相结合的方法研究地震动的空间特征。首先,分析入射波和反射波在空间内形成质点运动的叠加模式差异,并依此对空间域进行划分;其次,针对不同泊松比和SV波入射角情形研究叠加区与分离区的分界线控制情况;最后,对比分析不同空间域内的质点运动在峰值、持时等方面的特征。研究结果显示:当SV波入射时,叠加区与分离区的分界线通常由z₃ （反射P波与反射SV波的分离线）控制;同时存在两种特殊情况,当SV波垂直入射时,分界线由z₁ （入射SV波与反射SV波的分离线）控制,当反射SV波幅值为零时,分界线由z₂ （入射SV波与反射P波的分离线）控制。在入射波和反射波的影响下,质点运动时程的形状具有水平不变性。三波贡献时段只出现在深度小于z₁的质点的运动时程中,且持时随着深度的增加线性减少;双波贡献时段出现在位于叠加区内的质点的运动时程中,持时沿深度先增加后减少;单波贡献时段随着深度的增加而逐渐加长,在分离区达到最大值。质点运动总持时随深度逐渐增加,在分离线z₂和z₃深度处存在两个拐点。在质点运动峰值方面,靠近自由面的叠加区质点运动峰值变化较大,深度较大的叠加区和分离区的质点运动峰值一般不变。      

Simulations of non‐stationary frequency content and its importance to seismic assessment of structures

To verify the importance of the non‐stationary frequency characteristic of seismic ground motion, a joint time–frequency analysis technique of time signals, called chirplet‐based signal approximation, is developed to extract the non‐stationary frequency information from the recorded data. The chirplet‐based signal approximation is clear in concept, similar to Fourier Transform in mathematical expressions but with different base functions. Case studies show that the chirplet‐based signal approximation can represent the joint time–frequency variation of seismic ground motion quite well. Both the random models of uniform modulating process and evolutionary process are employed to generate artificial seismic waves. The joint time–frequency modulating function in the random model of evolutionary process is determined by chirplet‐based signal approximation. Finally, non‐linear response analysis of a SODF system and a frame structure is performed based on the generated artificial seismic waves. The results show that the non‐stationary frequency characteristic of seismic ground motion can significantly change the non‐linear response characteristics of structures, particularly when a structure goes into collapse phase under seismic action. It is concluded that non‐stationary frequency characteristic of seismic ground motion should be considered for the assessment of seismic capacity of structures. Copyright © 2002 John Wiley & Sons, Ltd.     

利用数字化速度记录仿真加速度时程与合成场地设计地震波

研究利用测震台网数字化宽频带速度型记录仿真加速度时程,并通过提取其相位信息和拟合场地设计反应谱(目标谱)的方法来获得场地设计地震波的有关技术途径与应用实例,所提供的具体算式采用便于编程和利用快速傅氏变换(FFT)技术进行计算的离散化傅氏正逆变换的复数表达式。有关研究结果可拓宽现有地震观测资料的使用价值,减少地面运动模拟中人造地震波与原始地震记录存在的差异,并可使所合成的设计地震波满足给定的目标谱,且能较好地反映其非平稳性特征,因此在地震工程中具有实际的应用价值。     

对人造地震动反应谱求解及拟合的几个相关问题探讨

为更高效合理地生成与设计反应谱相符的人造地震动信号,本文基于自主开发的地震动信号处理软件EQSignal对人造地震动生成过程中涉及的几个问题进行了探讨,并通过对单自由度简谐共振体系的响应分析,提出了具体的解决建议:① 反应谱求解时应该对高频段和低频段分别采用频域传递函数法和逐步积分法求解;② 反应谱周期控制点的分布模式也应分段处理,短周期段宜采用对数平均分布,长周期段宜采用线性平均分布,反应谱总周期控制点不宜少于120个;③ 人造地震动反应谱与设计反应谱拟合的过程中,使用频域方法与时域方法相结合可兼顾效率与收敛性。      

Time domain procedure of FE-BE-IBE coupling for seismic interaction of arch dams and canyons

A procedure for three-dimensional (3-D) coupling of finite elements (FEs), boundary elements (BEs) and infinite boundary elements (IBEs) is presented for the numerical modelling of seismic interaction between arch dams and rock canyons. First, a system of coupling 3-D boundary and infinite boundary elements is developed for simulation of infinite and irregular canyons and for determination, in the frequency domain, of impedance functions on the dam-canyon interface. Secondly, the impedance functions for all degrees-of-freedom are transformed approximately into frequency independent discrete parameters by a curve fitting technique. Finally, these discrete parameters are combined with the dam structure which is discretized by finite elements, thus allowing the response of the arch dam-canyon system to be evaluated. The proposed procedure is efficient because it permits the seismic analysis of arch dam-canyon interaction by the substructure technique in the time domain. To demonstrate both the validity and efficiency of the present procedure, the response of an arch dam-canyon system is obtained under unit impulse acting on the dam-canyon interface as the free field input. Very good agreement is noted when comparing the frequency response determined from the time domain with that from the frequency domain under harmonic excitation applied on the interface of the dam-canyon.     

含峭壁V形峡谷对地震SH波散射的解析解

地表地形常引起地震动的局部放大,这是由于地震波传播至局部地形时产生了散射现象.本文利用波函数展开方法和区域匹配技术,提出了含峭壁V形峡谷对平面SH波散射问题的解析解,并进行了退化验证.通过频域内的参数分析,揭示了峭壁深度、入射波频率和角度等因素对峡谷场地地面运动的影响规律,发现上部峭壁会增强峡谷对地震动的地形放大效应.研究结果不仅为数值方法提供了验证基准,还可为含峭壁峡谷周边建筑物的抗震设计提供顺河向地震动输入.     

孔隙介质地震电磁信号的数值模拟研究

本文利用最近开发的孔隙介质震电波场算法开展了数值模拟研究,重点探讨不同结构模型中双力偶点源以及有限断层面源作用下产生的地震波及其伴随的电磁信号的时域和频域特征,考察了不同震源时间函数类型对震电波场数值模拟结果的影响,并以Ricker子波为例讨论了震电波场的频率响应特征.结果表明:地震电磁信号的波形、振幅和持续时间等都不同程度受到模型结构的影响,结构越复杂,波形也越复杂;不同震源(双力偶点源与有限断层面源、震源时间函数类型、Ricker子波峰值频率)产生的位移场和电磁场在波形和频谱响应方面整体上呈现相似的特征,但在波形和频谱的幅度和复杂程度方面存在一定差异.