Multiple-taper spectral analysis of terrestrial free oscillations: part II

In Part I of this paper, we derived a set of data tapers designed to minimize the spectral leakage of decaying sinusoids immersed in white noise. Multiplying a long-period seismic record by K of these tapers creates K time series. A decaying sinusoid is fit to these K time series in the frequency domain at a number of chosen frequencies by a least-squares procedure. The fit is tested at each frequency using a statistical F -test. In Part I, we demonstrated that the multiple-taper method is a more sensitive detector of decaying sinusoids than the conventional direct spectral-estimate.
In this paper, we present a number of extensions to the multiple-taper method. We explain how the technique can be modified to estimate the harmonic components of records containing gaps. We discuss how sinusoids at frequencies between FFT bin frequencies can be detected, and how this method can be combined with conventional multi-station stacking procedures.     

Earth-strain observations made with the Cambridge laser strainmeter

Summary. A span of 74 days of data from the 55-m iodine stabilized laser strainmeter in Queensbury tunnel, Yorkshire, England has been analysed in detail. The strain noise level observed by the instrument is similar to that observed by American laser strainmeters at low (tidal) frequencies, but is much greater at higher (seismic) frequencies. This is explained in terms of ocean loading and microseismic noise. A residual time series was obtained by subtracting a best-fit tide from the data, and the larger residuals correlate well with storm surges in the North Sea; this is a further manifestation of ocean loading. The high noise level at seismic frequencies renders the Queensbury site rather unsuitable for normal mode studies, but free oscillations have been observed following an M_s 7.6 earthquake.     

Estimation of uncertainties in eigenspectral estimates from decaying geophysical time series

Summary. The response of many dynamical systems to an impulse is a linear combination of decaying cosines. The frequencies of the cosines have generally been estimated in geophysics by periodogram analysis and little formal indication of uncertainty has been provided. This work presents an estimation procedure by the methods of complex demodulation and nonlinear regression that specifically incorporates in the basic model the decaying aspect of the cosines (periodogram analysis does not). The use of plots of the instantaneous phase as a function of time is shown to greatly enhance resolution. Expressions for the variances of eigenfrequencies, amplitudes, phases and damping constants Q are derived by non-linear least-squares. The results are illustrated, for the problem of the free oscillations of the Earth, by computations with the record made at Trieste of the Chilean earthquake of 1960 May 22. Sample values are periods and standard errors of 737.79 ± 0.13 s, 506.25 ± 0.13 s and 429.60 ± 0.14 s for ₀ T ₈, ₀ T ₁₃ and ₀ T ₁₆ with Q values and standard errors of 200 ± 14, 230 ± 28 and 215 ± 30, respectively.     

黄河GPS站噪声模型初探及稳定性分析

北极黄河科学考察站的GPS站位于挪威斯瓦尔巴群岛,该站对于我国在北极测绘领域的研究具有重要作用。由于极区条件的限制,该站建立在冻土之上,因此需要对其稳定性进行深入研究。本文在利用GAMIT/GLOBK软件处理黄河站及周边IGS站观测数据的基础上,估计了不同噪声模型下的噪声量级、站坐标序列参数和不确定度,分析了黄河GPS观测站与IGS站运动趋势之间的关联性。结果表明,黄河站及周边GPS时间序列不仅存在白噪声,还存在较大量级的闪烁噪声,个别站的一些分量还存在随机游走噪声,仅考虑白噪声会低估总噪声和参数不确定度;黄河GPS站与邻近的NYAL站相比,两者的水平和垂直运动趋势完全一致,仅在垂直方向上有2.15 mm·a~(–1)的差异。     

Continuous GPS measurements across the Western Alps, 1996–1998

Global Positioning System (GPS) data are analysed from three permanent sites, two in the Western Alps (Grasse, France, and Zimmerwald, Switzerland) and the third in the Po Basin (Torino, Italy), for the 2.5-year period from 1 January 1996 to 1 July 1998. An analysis of the stochastic properties of the position time series reveals a significant amount of spatially and temporally correlated noise, which best fits a model combining white noise and flicker noise. The coloured noise is drastically reduced by spatially filtering the time series, suggesting that it is not due to site-specific effects such as monument motion, but rather to noise sources common to the three sites, such as reference frame, satellite orbit or Earth orientation errors. We find velocity uncertainties (95 per cent confidence interval) of 2.7  mm  yr⁻¹ at GRAS, 2.3  mm  yr⁻¹ at ZIMM, and 2.9  mm  yr⁻¹ at TORI. The residual velocity in the Eurasian reference frame is statistically greater than zero at ZIMM only, with 2.4 ± 2.3  mm  yr⁻¹ of motion in a NW direction. These uncertainties place an upper bound on the expected deformation in the Western Alps. Velocities relative to stable Eurasia do not exceed 3  mm  yr⁻¹, corresponding to a maximum strain rate of 0.03  μstrain  yr⁻¹ over the GRAS–TORI–ZIMM triangle.     

Polarization analysis and polarization filtering of three-component signals with the time–frequency S transform

From basic Fourier theory, a one-component signal can be expressed as a superposition of sinusoidal oscillations in time, with the Fourier amplitude and phase spectra describing the contribution of each sinusoid to the total signal. By extension, three-component signals can be thought of as superpositions of sinusoids oscillating in the x -, y -, and z -directions, which, when considered one frequency at a time, trace out elliptical motion in three-space. Thus the total three-component signal can be thought of as a superposition of ellipses. The information contained in the Fourier spectra of the x -, y -, and z -components of the signal can then be re-expressed as Fourier spectra of the elements of these ellipses, namely: the lengths of their semi-major and semi-minor axes, the strike and dip of each ellipse plane, the pitch of the major axis, and the phase of the particle motion at each frequency. The same type of reasoning can be used with windowed Fourier transforms (such as the S transform), to give time-varying spectra of the elliptical elements. These can be used to design signal-adaptive polarization filters that reject signal components with specific polarization properties. Filters of this type are not restricted to reducing the whole amplitude of any particular ellipse; for example, the 'linear' part of the ellipse can be retained while the 'circular' part is rejected. This paper describes the mathematics behind this technique, and presents three examples: an earthquake seismogram that is first separated into linear and circular parts, and is later filtered specifically to remove the Rayleigh wave; and two shot gathers, to which similar Rayleigh-wave filters have been applied on a trace-by-trace basis.     

Error propagation in non-linear delay-time tomography

Delay-time tomography can be either linearized or non-linear. In the case of linearized tomography, an error due to the linearization is introduced. If the tomography is performed in a non-linear fashion, the theory used is more accurate from the physical point of view, but if the data have a statistical error, a noise bias in the model is introduced due to the non-linear propagation of errors. We investigate the error propagation of a weakly non-linear delay-time tomography example using second-order perturbation theory. This enables us to compare the linearization error with the noise bias. We show explicitly that the question of whether a non-linear inversion methods leads to a better estimation of the model parameters than a linearized method is dependent on the signal-to-noisc ratio. We also show that, in cases of poor data quality, a linearized inversion method leads to a better estimation of the model parameters than a non-linear method.     

花园口站年最大洪峰流量时间序列的HHT分析

Hilbert-Huang变换能够定量描述非线性、非平稳复杂时间序列的时频特性,较传统分析方法更具优势。通过对时间序列进行EMD分解,得到变化过程的内在模态函数和趋势项函数,而后对各内在模态函数进行Hilbert-Huang变换,从而揭示出时间序列的多时间尺度特征。以黄河花园口站1952-2009年的年最大洪峰流量时间序列为例,对其进行多时间尺度分析,得到不同波动周期的振荡分量及趋势分量,具体分析了各分量的变化特征。结果表明,花园口年最大洪峰流量变化过程中存在准3.2a、准6.4a、准11.8a和准31.0a周期的波动,其中准3.2a和准6.4a的周期波动是引起原序列波动的主要原因,近60年来花园口年最大洪峰流量变化呈递减趋势,由此揭示了年最大洪峰流量变化过程的多时间尺度特征。在此基础上,探讨了各波动分量变化的影响因素,其变化与大气低频振荡、ENSO、太阳活动及气候变迁等因素有关。     

Implications of diurnal variations in land surface temperature to data assimilation using MODIS LST data

Based on the Beijing Climate Center's land surface model BCC_AVIM(Beijing Climate Center Atmosphere-Vegetation Interaction Model), the ensemble Kalman filter(En KF) algorithm has been used to perform an assimilation experiment on the Moderate Resolution Imaging Spectroradiometer(MODIS) land surface temperature(LST) product to study the influence of satellite LST data frequencies on surface temperature data assimilations. The assimilation results have been independently tested and evaluated by Global Land Data Assimilation System(GLDAS) LST products. The results show that the assimilation scheme can effectively reduce the BCC_AVIM model simulation bias and the assimilation results reflect more reasonable spatial and temporal distributions. Diurnal variation information in the observation data has a significant effect on the assimilation results. Assimilating LST data that contain diurnal variation information can further improve the accuracy of the assimilation analysis. Overall, when assimilation is performed using observation data at 6-hour intervals, a relatively good assimilation result can be obtained, indicated by smaller bias(2.2 K) and root-mean-square-error(RMSE)(3.7 K) and correlation coefficients larger than 0.60. Conversely, the assimilation using 24-hour data generally showed larger bias(2.2 K) and RMSE(4 K). Further analysis showed that the sensitivity of assimilation effect to diurnal variations in LST varies with time and space. The assimilation using observations with a time interval of 3 hours has the smallest bias in Oceania and Africa(both1 K); the use of 24-hour interval observation data for assimilation produces the smallest bias(2.2 K) in March, April and July.     

Observed geomagnetic field intensity in London since 1820

Our main purpose is to collect all magnetic intensity data observed in the vicinity of London and to adjust these to a common site (Greenwich) to complement the 400-year series of declination ( D ) and inclination ( I ) data of Malin & Bullard (1981 ). The present series is necessarily shorter, since a method for the measurement of intensity in absolute units was not devised until 1832. We have also supplemented the D and I series of Malin & Bullard with recently acquired data.
We have also made observations of D , I and total intensity ( F ) at a number of the sites, partly to bring the series up to date and partly to check on the site differences. With the increasing urbanization of London it is necessary to seek data from remoter sites. It is shown that the site differences change significantly with time, but that allowance can be made for this.
We present curves of our best estimates of the variation of D , I , F and the horizontal intensity ( H ) that define the complete geomagnetic vector at Greenwich for the interval 1820–1998. Frequency analysis shows little support for a 60-year line in the power spectrum. Within the uncertainty of their determinations, there is good continuity between archaeomagnetic intensity measures and the present results. The moving eddy hypothesis of Malin & Bullard is found to be untenable.     

基于特征的时间序列聚类方法研究进展

时间序列聚类可以根据相似性将对象集分为不同的组, 从而反映出同组对象的相似性特征和不同组对象之间的差异特征。当序列维度较高时, 传统的时间序列聚类方法容易受噪声影响, 难以定义合适的相似性度量, 聚类结果往往意义不明确。当数据有缺失或不等长时, 聚类方法也难以实施。基于上述问题, 一些学者提出了基于特征的时间序列聚类方法, 不仅可以解决上述问题, 还可以发现序列本质特征的相似性。本文根据时间序列的不同特征, 综述了基于特征的时间序列聚类方法的研究进展, 并进行了分析和评述;最后对未来研究进行了展望。     

Maximum entropy regularization of time-dependent geomagnetic field models

We incorporate a maximum entropy image reconstruction technique into the process of modelling the time-dependent geomagnetic field at the core–mantle boundary (CMB). In order to deal with unconstrained small lengthscales in the process of inverting the data, some core field models are regularized using a priori quadratic norms in both space and time. This artificial damping leads to the underestimation of power at large wavenumbers, and to a loss of contrast in the reconstructed picture of the field at the CMB. The entropy norm, recently introduced to regularize magnetic field maps, provides models with better contrast, and involves a minimum of a priori information about the field structure. However, this technique was developed to build only snapshots of the magnetic field. Previously described in the spatial domain, we show here how to implement this technique in the spherical harmonic domain, and we extend it to the time-dependent problem where both spatial and temporal regularizations are required. We apply our method to model the field over the interval 1840–1990 from a compilation of historical observations. Applying the maximum entropy method in space—for a fit to the data similar to that obtained with a quadratic regularization—effectively reorganizes the magnetic field lines in order to have a map with better contrast. This is associated with a less rapidly decaying spectrum at large wavenumbers. Applying the maximum entropy method in time permits us to model sharper temporal changes, associated with larger spatial gradients in the secular variation, without producing spurious fluctuations on short timescales. This method avoids the smearing back in time of field features that are not constrained by the data. Perspectives concerning future applications of the method are also discussed.     

利用SAR影像时间序列的耕地提取研究

卫星遥感是耕地资源调查的一种重要技术手段,利用遥感时间序列数据进行耕地提取具有很强的实践意义。光学遥感成像过程易受光照和大气条件影响,在云雨多发地区所能获取的可用数据十分有限;合成孔径雷达(SAR)能够全天时、全天气进行对地观测,但受斑点噪声影响,少见利用其构建时间序列进行信息提取的研究。本文研究了SAR影像时间序列在耕地提取中的适用性,利用江苏省徐州市2009年12月-2010年12月共11景ENVISAT ASAR 影像构建时间序列,目视选取30个5像元×5像元大小的耕地样区,分别统计样区内(相邻位置)与样区间(不同位置)耕地时域后向散射特征的一致性(变异系数);然后利用欧氏距离法、相关系数法以及动态时间弯曲法(DTW)进行研究区的耕地提取。结果显示：相邻位置耕地像元后向散射特性较为一致,平均变异系数为9.96%;不同位置耕地像元后向散射特性一致性也较好,平均变异系数为15.27%。在所选的3种方法中,相关系数法耕地提取精度最高,正确率与完整率分别为86.25%与80.70%;欧氏距离法精度次之,正确率与完整率分别为76.40%与71.93%;DTW效果较差,正确率和完整率分别为62.15%和77.78%。SAR影像时间序列作为一种新的数据组织形式,可用于耕地的有效提取。     

经验模态分解下中国气温变化趋势的区域特征

用经验模态分解(EMD) 方法对中国700 多个站(1951-2001 年) 月平均气温进行了分析, 提取气温变化趋势项, 作空间分型, 并计算各站气温变化率, 以地理信息系统为数据处理平台, 以1km×1km 分辨率的DEM 数据作为地形的综合反映, 得到了中国平均气温空间分型和变化率精细化分布图。结果表明: 近50 年来中国北方大部分地区气温变化率多在0.4 ^oC/10a 以上, 西南和长江中下游部分地区气温变化率较小, 气温变化率为负值区零星状散落 在西南等地区。同时, 1881-2001 年中国9 个区域的气温资料分析表明, 近百年来中国气温变 化趋势以东北、华北、华东、华南、西北和新疆区是持续上升, 西南区呈下降型; 华中区呈倒"V" 型变化, 西藏区趋势不明显。     

黄河下游河相关系与平滩流量特征关系的随机演化模拟

Extreme weather is an important noise factor in affecting dynamic access to river morphology information.The response characteristics of river channel on climate disturbances draw us to develop a method to investigate the dynamic evolution of bankfull channel geometries(including the hydraulic geometry variables and bankfull discharges)with stochastic differential equations in this study.Three different forms of random inputs,including single Gaussian white noise and compound Gaussian/Fractional white noise plus Poisson noise,are explored respectively on the basis of the classical deterministic models.The model parameters are consistently estimated by applying a composite nonparametric maximum likelihood estimation(MLE)method.Results of the model application in the Lower Yellow River reveal the potential responses of bankfull channel geometries to climate disturbances in a probabilistic way,and,the calculated average trends mainly run to synchronize with the measured values.Comparisons among the three models confirm the advantage of Fractional jump-diffusion model,and through further discussion,stream power based on such a model is concluded as a better systematic measure of river dynamics.The proposed method helps to offer an effective tool for analyzing fluvial relationships and improves the ability of crisis management of river system under varying environment conditions.     

Instantaneous deformation from continuous GPS: contributions from quasi-periodic loads

Continuous GPS (CGPS) coordinate time-series are known to experience repeating deformation signals with seasonal and other periods. It is unlikely that these signals represent perfect sinusoids with temporally constant amplitude. We develop an analysis method that accommodates temporal variations in the amplitudes of sinusoidal signals. We apply the method to simulated coordinate time-series to numerically explore the potential consequences of neglecting decadal variation in amplitude of annual motions on the residual-error spectra of CGPS measurements, as well as potential bias in estimates for secular site velocity. We find that secular velocity bias can be appreciable for shorter time-series, and that residual-error time-series of longer duration may contain significant power in a broad band centred on semi-annual frequency if temporal variation in the amplitude of annual motions is not accounted for in the model used to reduce the observations to residuals. It may be difficult to differentiate the bandpass filtered signature of mismodelled loading signals from power-law noise, using residual-error spectra for shorter time-series. We provide an example application to a ∼9-yr coordinate time-series for a CGPS station located in southern California at Carbon Creek Control Structure (CCCS), which is known to experience large amplitude seasonal motions associated with the Santa Ana aquifer system.     

Sudden Local Conductivity Changes in the Ionosphere

Summary. An attempt is made to describe the transient magnetic change caused by a sudden local change of conductivity in the ionosphere. In a rough illustrative model, electric current is taken to be flowing uniformly in a thin plane rigid sheet of uniform isotropic integrated conductivity, I/ϱO e.m.u. A particular type of perturbing current system is defined, and the type of conductivity anomaly which could produce it is derived. It is shown that the problem is equivalent to that of the free decay of the perturbing current system. For a very small change of conductivity, the current system is found to spread radially at a uniform rate, while decaying. The case of a large conductivity anomaly is analysed by a numerical method. It is concluded that effects at a distance would be similar to those produced by a very small change, and that near the anomaly there would be as well, a local decaying current vortex system. It is found in particular, that at a large distance L cm, the magnetic change would commence immediately and reach an extremum after time of order L × 10⁻⁶ s.     

西畴县近48年来降水及气温小波分析

利用连续小波分析1962～2009年西畴县年降水量和年平均气温序列的小波变化特征,揭示了西畴县降水量与平均气温存在多时间尺度的周期变化特征。其中降水有2个明显的特征时间尺度,分别是4年和8年,平均气温存在以准2～4年为周期的周期振荡。此外,也可以看出近48年来,平均气温存在明显升高的趋势,降水也有减少的趋势,为掌握西畴县的气候变化规律及今后的气象预报服务工作提供了一定的参考价值。     

Crosshole seismic waveform tomography – I. Strategy for real data application

The frequency-domain version of waveform tomography enables the use of distinct frequency components to adequately reconstruct the subsurface velocity field, and thereby dramatically reduces the input data quantity required for the inversion process. It makes waveform tomography a computationally tractable problem for production uses, but its applicability to real seismic data particularly in the petroleum exploration and development scale needs to be examined. As real data are often band limited with missing low frequencies, a good starting model is necessary for waveform tomography, to fill in the gap of low frequencies before the inversion of available frequencies. In the inversion stage, a group of frequencies should be used simultaneously at each iteration, to suppress the effect of data noise in the frequency domain. Meanwhile, a smoothness constraint on the model must be used in the inversion, to cope the effect of data noise, the effect of non-linearity of the problem, and the effect of strong sensitivities of short wavelength model variations. In this paper we use frequency-domain waveform tomography to provide quantitative velocity images of a crosshole target between boreholes 300 m apart. Due to the complexity of the local geology the velocity variations were extreme (between 3000 and 5500 m s⁻¹), making the inversion problem highly non-linear. Nevertheless, the waveform tomography results correlate well with borehole logs, and provide realistic geological information that can be tracked between the boreholes with confidence.     

Mapping Air Temperature in the Lancang River Basin Using the Reconstructed MODIS LST Data

Air temperature is an important climatological variable and is usually measured in meteorological stations. Accurate mapping of its spatial and temporal distribution is of great interest for various scientific disciplines, but low station density and complexity of the terrain usually lead to significant errors and unrepresentative spatial patterns over large areas. Fortunately the current studies have shown that the regression models can help overcome the problem with the help of time series remote sensing data. However, noise induced by cloud contamination and other atmospheric disturbances variability impedes the application of LST data. An improved Savizky-Golay (SG) algorithm based on the LST background library is used in this paper to reconstruct MODIS LST product. Data statistical analysis included 12 meteorological stations and 120 reconstructed MODIS LST images of the period from 2001 to 2010. The coeffificient of correlations (R²) for 80% of the stations was higher than 0.5 (below 0.5 for only 2 stations) which illustrated that there is a considerably close agreement between monthly mean TA (air temperature) and the reconstructed LST in the Lancang River basin. Comparing to the regression model for every month with only LST data, the regression model with LST and NDVI had higher R² and RMSE. Finally, the LST-NDVI regression method was applied as an estimate model to produce distributed maps of air temperature with month intervals and 1 km spatial in the Lancang River basin of 2010.