Polarization analysis in the stationary wavelet packet domain: Application to HVSR method

Microzonation studies using ambient noise measurements have become very popular in the last years for local soil characteristics determination. For defining the capabilities of the ambient noise based methods, a physical understanding of the nature of noise is essential. In this way, many studies have shown that the noise wavefield composition is heterogeneous, comprising both body and surface waves with fundamental and upper modes.In this work, a recently developed method of time-frequency polarization analysis, based on the stationary wavelet packet transform, is used to study how the waves’ polarization influences in the application of the HVSR method. For this purpose, each recorded signal is first decomposed into a set of sub-signals, according to their reciprocal ellipticity. After that, the H/V analysis is carried out on the raw recorded signal, as well as on the obtained sub-signals, evaluating the contribution of each sub-signal (i.e., each reciprocal ellipticity range) to the expected H/V result.For the study, single station seismic noise was recorded at 11 sites around the province of Alicante (southeastern Spain). The obtained results illustrate that high frequency peaks, above 1–2 Hz, are clearly represented by just using the sub-signals associated to the ellipticity range of [0–0.1], whereas low frequency peaks, down 0.5 Hz, need a wider ellipticity interval for being properly retrieved, i.e., [0–0.4] or even [0–0.6]. Therefore, linearly polarized waves’ contribution, range [0–0.1], is enough for retrieving the high frequency H/V peaks, but not for obtaining the complete H/V curve, especially the low frequency peaks. In these cases, the elliptical polarized Rayleigh waves’ contribution cannot be misestimated in HVSR computation.     

Seismic signal analysis based on the dual-tree complex wavelet packet transform

We tried to apply the dual-tree complex wavelet packet transform in seismic signal analysis. The complex wavelet packet transform (CWPT) combine the merits of real wavelet packet transform with that of complex continuous wavelet transform (CCWT). It can not only pick up the phase information of signal, but also produce better “focalizing” function if it matches the phase spectrum of signals analyzed. We here described the dual-tree CWPT algorithm, and gave the examples of simulation and actual seismic signals analysis. As shown by our results, the dual-tree CWPT is a very effective method in analyzing seismic signals with non-linear phase. Foundation item: Cultural Heritage Protection Program of State Administration of Cultural Heritage (200001).     

像域分解特征高斯波包地震数据模拟

分波型或时空局部特征波场的层析成像与叠前深度偏移成像组合是全波形反演成像方法(FWI)实用化的途径之一.其中如何高效稳健地获得具有时空局部特征的地震数据目前仍然是一个挑战.在前人提出的基于高斯束和高斯波包的Gabor框架散射波模拟的基础上, 本文提出了一种基于像域分解的特征高斯波包地震数据模拟方法.新方法利用具有空间局部特征的Gabor函数在成像剖面上实现数据的分解, 不仅可以利用成像剖面地质意义更加直观的特点来拾取特征反射界面, 还能有效地克服传统方法在数据域分解效率和精度不高等问题, 保证了分解后的反射数据具有更加明确的地质意义.此外, 不同于波动方程有限差分模拟, 基于时空局部特征的高斯波包模拟的一次反射波数据包含更多的数据属性, 比如反射波的到达时、空间位置和波场的传播方向, 这在层析反演中用于数据测量和偏移成像等处理时更具优势.数值实验测试表明了本文提出的分解方法的有效性.

     

基于高斯束与高斯波包的Gabor框架散射波模拟方法

在给出真实模型和相应光滑背景模型的情况下,如何计算扰动模型(散射体)产生的散射波场是一个有实际意义的正演问题.在Gabor变换域描述散射体,且入射波场为短时宽带信号时,散射波场可以在频率域用高斯束或时间域用高斯波包描述.相对于波动方程方法,高斯束和高斯波包的计算效率更高;背景模型光滑时,高斯束和高斯波包方法的精度也接近波动方程方法.文中导出了声波假设下应用高斯束和高斯波包计算散射波的方法.测试分析了高斯波包的计算精度.给出了一般散射体的散射波模拟策略.同时针对一个理论模型完成了本文方法计算散射波的实验,实验结果表明高斯波包散射波计算方法是有效可行的.     

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage. This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform (WPT). The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum (WPES) has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.     

一种时间域全波形反演中的地震子波估计方法

全波形反演具有高精度成像能力,然而由理论走向实际应用还存在很多问题.全波形反演通过匹配波形来更新模型,数据的波形与地震子波有直接的关系.本文介绍了一种针对时间域波形反演的子波估计方法,并将其应用到全波形反演中.由于在频率域子波反演可表示为一个线性优化问题,因此本文先给定一个试探子波,在时间域通过有限差分法正演得到地震波场,并在频率域与观测数据比较分析,反演得到预测子波.此外,本文还简要地介绍了如何使用伴随状态法计算全波形反演的梯度.数值实验证明,本文方法反演得到地震子波与真实子波具有很好的吻合度,并在全波形反演中取得了不错的效果.相比不依赖于子波的方法,提前进行子波估计可提高反演效率.此外,本文方法适用于全波形反演中常使用的多尺度反演策略.     

Seismic data interpolation using frequency‐domain complex nonstationary autoregression

We have developed a novel method for missing seismic data interpolation using f‐x‐domain regularised nonstationary autoregression. f‐x regularised nonstationary autoregression interpolation can deal with the events that have space‐varying dips. We assume that the coefficients of f‐x regularised nonstationary autoregression are smoothly varying along the space axis. This method includes two steps: the estimation of the coefficients and the interpolation of missing traces using estimated coefficients. We estimate the f‐x regularised nonstationary autoregression coefficients for the completed data using weighted nonstationary autoregression equations with smoothing constraints. For regularly missing data, similar to Spitz f‐x interpolation, we use autoregression coefficients estimated from low‐frequency components without aliasing to obtain autoregression coefficients of high‐frequency components with aliasing. For irregularly missing or gapped data, we use known traces to establish nonstationary autoregression equations with regularisation to estimate the f‐x autoregression coefficients of the complete data. We implement the algorithm by iterated scheme using a frequency‐domain conjugate gradient method with shaping regularisation. The proposed method improves the calculation efficiency by applying shaping regularisation and implementation in the frequency domain. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.     

基于小波变换的地震反应分析

从小波变换的基本原理出发，提出了地震地面运动的小波模型，以具有时频特性的小波基来表示，并用于多自由度的地震反应分析，导出了相应的公式，实例表明，这种方法是可行的。     

Seismic velocity analysis in the scattering-angle/azimuth domain

Migration velocity analysis is carried out by analysing the residual moveout and amplitude variations in common image point gathers (CIGs) parametrized by scattering angle and azimuth. The misfit criterion in the analysis is of the differential-semblance type. By using angles to parametrize the imaging we are able to handle and exploit data with multiple arrivals, although artefacts may occur in the CIGs and need to be suppressed. The CIGs are generated by angle migration, an approach based on the generalized Radon transform (GRT) inversion, and they provide multiple images of reflectors in the subsurface for a range of scattering angles and azimuths. Within the differential semblance applied to these CIGs, we compensate for amplitude versus angle (AVA) effects. Thus, using a correct background velocity model, the CIGs should have no residual moveout nor amplitude variation with angles, and the differential semblance should vanish. If the velocity model is incorrect, however, the events in the CIGs will appear at different depths for different angles and the amplitude along the events will be non-uniform. A standard, gradient-based optimization scheme is employed to develop a velocity updating procedure. The model update is formed by backprojecting the differential semblance misfits through ray perturbation kernels, within a GRT inverse. The GRT inverse acts on the data, subject to a shift in accordance with ray perturbation theory. The performance of our algorithm is demonstrated with two synthetic data examples using isotropic elastic models. The first one allows velocity variation with depth only. In the second one, we reconstruct a low-velocity lens in the model that gives rise to multipathing. The velocity model parametrization is based upon the eigentensor decomposition of the stiffness tensor and makes use of B-splines.     

基于统计的小波包分析的输电塔结构损伤预警

本文针对输电塔结构的损伤特点,提出了基于统计过程控制理论和小波包分析实现输电塔结构损伤预警的方法。首先将振动测试信号进行小波包分解,然后以小波包系数节点能量作为识别损伤的特征向量建立相应的损伤因子,通过统计过程控制理论计算其单侧置信上限,实现输电塔结构的损伤预警。为了证明该方法,对一个三层输电塔结构模型进行了试验研究,结果表明该方法能够有效地识别损伤的发生。     

地震与爆破的小波包识别判据研究

利用sym5小波包基函数对小震级天然地震和人工爆破波形进行4层小波包分解并绘制了时频谱图.通过时频谱图可直观得出, 爆破频率成分简单, 时频谱聚集性较好. 为寻求定量的识别指标, 综合P波和S波小波包变换结果, 提出并定义了P/S能量比. 分析识别效果较好的 P/S能量比判据得出爆破的P波主频集中在频段3.125—9.375 Hz处, \t地震频率成分较复杂, S波在高频12.5—23.4375 Hz处也较发育, 在这些频段上, 爆破的P波与S波差异要大于地震的P波与S波差异. 作为小波包判据研究的补充, 文中也提取分析了P波的能量比与S波的能量比. 能量比判据识别结果表明, 人工爆破与天然地震的频率成分存在差异, 通过小波包变换能够提取有效的识别判据.     

小波分析在数字地震资料中的应用

安徽省霍山地区在 2002 年发生了两次震群,主震都为 ML4.0 地震,但表现为不同的衰减形式,7 月 14 日主震发生后只有 8 次小震（ML>1.0）,而 8 月 29 日主震后面有 60 多次小震（ML>1.0）。小波分析是 20 世纪 80 年代兴起的一门新学科,由于它在时频两域具有良好的局部特性,故在数学上被喻为“数字显微镜”。本文运用小波分析方法,对两个震群的主震作小波分析,希望能提取不同震群系列主震的一些频谱特性。     

Ground roll wave suppression based on wavelet frequency division and radial trace transform

Ground roll waves interfere with seismic data. The suppression of ground roll waves based on the division of wavelet frequencies considers the low-frequency characteristics of ground roll waves. However, this method will not be effective when the ground roll wave and the effective signal have the same frequency bands because of overlapping. The radial trace transform (RTT) considers the apparent velocity difference between the effective signal and the ground roll wave to suppress the latter, but affects the low-frequency components of the former. This study proposes a ground roll wave suppression method by combining the wavelet frequency division and the RTT based on the difference between the ground roll wave velocity and the effective signal and their energy difference in the wavelet domain, thus making full use of the advantages of both methods. First, we decompose the seismic data into different frequency bands through wavelet transform. Second, the RTT and low-cut filtering are applied to the low-frequency band, where the ground roll waves are appearing. Third, we reconstruct the seismic record without ground roll waves by using the inverse RTT and the remaining frequency bands. The proposed method not only improves the ground roll wave suppression, but also protects the signal integrity. The numerical simulation and real seismic data processing results suggest that the proposed method has a strong ability to denoise while preserving the amplitude.     

利用小波包方法分析新疆南部地震前长波辐射异常

以新疆南部为主要研究区域,选取2003-2010年MS＞5．0典型震例进行分析,将长波辐射日值数值与历年日值数据均值相减,排除年际数据波动干扰,采用小波包方法,对均一化处理后的差值进行分解重构,发现新疆南部地区地震前小波包重构信息均有不同程度的能量衰减现象,且能量衰减时间长短与地震震级之间存在一定对应关系。该现象可以作为地震前兆异常信息参考,为地震预报提供辅助监测手段。     

利用相关域小波变换进行SWD资料预处理

随钻地震(SWD)的波场十分复杂,对钻头有效信号和地表机械干扰成分的分析是SWD重要的资料预处理步骤.本文利用有效信号和噪声带有周期性或时延差异等时间结构特征,引入相关域小波变换进行SWD信号检测和分析.有效信号在钻柱内往复多次传播,因而带有严格的周期性,泥浆泵等机械发出的噪声也是周期性的,这些成分在自相关域内可以得到很好的凸显.SWD波场的各种成分,由于到达各个接收道的时延不同,在互相关域的特定时延处也能够得到凸显.利用小波变换对这些在相关域内得到凸显的成分进行多分辨分析,能够获得优势频率范围、周期、衰减等主要特征.根据这些信息,设计出合理的SWD处理方法,初步得到了有效信号的直达波.数据试处理结果表明,相关域小波变换是随钻地震的一个有效的预处理方法.     

二维多尺度离散小波/小波包分析进行重力区域场和局部异常分离的模型分析

建立了三个不同的重力异常模型,在MATLAB下,利用二维离散小波/小波包变换分别对这三个模型的区域场和局部异常进行分离.(1)通过用相同的模型,选择不同的小波进行重力场分离具有良好的效果,但不同小波分析之间存在着较小的差异;(2)小波包分解比小波分解更精确,但小波分解能够直接确定低频成分,而小波包分解需要建立与实际地质情况更相符的模型来确定低频系数;(3)针对本文所建立的模型,在小波分析中Coiflets小波系的精度更高,但在小波包分解中Daubechies小波系的精度更高.     

利用小波变换提取面波群速度

选取了几种常见的小波母函数,分别提取了同一理论下的面波数据的群速度,并与理论群速度进行对比,结果表明Morlet小波提取面波群速度的效果最好.此外,将Morlet小波与常用的多重滤波提取群速度的结果进行了比较,结果表明: ① 多重滤波法非常依赖高斯滤波系数α的取值,α的取值应随面波周期的增大而减小;② 在α取值得当的前提下,在20—35 s周期范围内多重滤波法提取面波群速度的相对误差比Morlet小波小,在周期大于35 s时,两者相对误差相近; ③ 合适的α值的选取需在不同周期段耗费大量时间进行大量试验,这说明多重滤波法不具备自适应性;而采用小波变换分析短周期信号时,时间窗变窄,频率窗变长,当分析长周期信号时,时间窗变长,频率窗变窄,具有对信号的自适应性,这是小波变换相比多重滤波法的最大优点.      

基于小波分析和神经网络的框架结构损伤诊断方法

本文提出了基于“能量—损伤”原理，综合利用小波包分析和神经网络的框架结构损伤诊断方法。在结构损伤诊断中，时域信号经小波分析后其缺损特征会更加明显，把分布在不同频带的结点能量作为神经网络的训练样本能够很好地反映结构缺损特征。以美国土木工程师学会提出的基准结构为例，阐述了结构损伤的发生、位置和程度诊断过程，取得了令人满意的结果。