Analysis of coordinate time series of DORIS stations on Eurasian plate and the plate motion based on SSA and FFT

This study focuses on analyzing the time series of DORIS beacon stations and plate motion of the Eurasian plate by applying Singular Spectrum Analysis(SSA)and Fast Fourier Transform(FFT).First,the rend terms and periodic signals are accurately separated by SSA,then,the periodic seasonal signals are detected using SSA,and finally,the main components of the time series are reconstructed successfully.The test results show that the nonlinear trends and seasonal signals of DORIS stations are detected successfully.The periods of the seasonal signals detected are year,half-year,and 59 days,etc.The contribution rates and slopes in E,N,and U directions of the trend items of each beacon station after reconstruction are obtained by least-square fitting.The velocities of these stations are compared with those provided by the GEODVEL2010 model,and it is found that they are in good agreement except the DIOB,MANB,and PDMB stations.Based on the DORIS coordinate time series,the velocity field on the Eurasian plate is constructed,and the test shows that the Eurasian plate moves eastward as a whole with an average velocity of 24.19±0.11 mm/y in the horizontal direction,and the average velocity of it is1.74±0.07 mm/y in the vertical direction.

A new method for coseismic offset detection from GPS coordinate time series

Currently,the extraction of coseismic offset signals primarily relies on earthquake catalog data to determine the occurrence time of earthquakes.This is followed by the process of differencing the average GPS coordinate time series data,with a time interval of 3 to 5 days before and after the earthquake.In the face of the huge amount of GPS coordinate time series data today,the conventional approach of relying on earthquake catalog data to assist in obtaining coseismic offset signals has become increasingly burdensome.To address this problem,we propose a new method for automatically detecting coseismic offset signals in GPS coordinate time series without an extra earthquake catalog for reference.Firstly,we pre-process the GPS coordinate time series data for filtering out stations with significant observations missing and detecting and removing outliers.Secondly,we eliminate other signals and errors in the GPS coordinate time series,such as trend and seasonal signals,leaving the coseismic offset signals as the primary signal.The resulting coordinate time series is then modeled using the first-order difference and data stacking method.The modeling method enables automatic detection of the coseismic offset signals in the GPS coordinate time series.The aforementioned method is applied to automatically detect coseismic offset signals using simulated data and the Searles Valley GPS data in California,USA.The results demonstrate the efficacy of our proposed method,successfully detecting coseismic offsets from vast amounts of GPS coordinate time series data.

Study of the effects on GPS coordinate time series caused by higher-order ionospheric corrections calculated using the DIPOLE model

As one of the main error sources in high-precision Global Positioning System （GPS） data processing, higher-order ionospheric （HOI） delays cause significant effects on coordinate time series that cannot be ignored in analyses of long time series. Typically two geomagnetic models, DIPOLE model and Inter- national Geomagnetic Reference Field （IGRF） model, are used for calculating HOI corrections. This paper investigates the effects of HOI correction caused by the DIPOLE model on coordinate time series. GPS data from 104 globally distributed International GNSS Service （IGS） stations spanning from January, 1999 to December, 2003 were reprocessed following up-to-date processing strategies utilizing GAMIT and GLOBK software. Two coordinate time series solutions before and after applying HOI corrections using the DIPOLE model were derived for studying the effects in terms of seasonal variations and noise amplitudes. The results show that after applying the HOI corrections calculated with DIPOLE, the noise amplitudes of the coordinate time series increased, especially in the north and east directions, and the increased amplitudes of the flicker noise were larger than those of the white noise. Furthermore, spurious periodic signals that were probably introduced by the HOI corrections from the DIPOLE model were also found. Moreover, an apparent increase was confirmed for the power spectra of most of the stations, especially in the north direction, and the amplitudes of both the annual and semi-annual signals also increased in the north and east directions. It can be inferred that the quality of the external data sources such as the geomagnetic model might be the key factors that lead to the above results. The results also suggest that we should be very careful when the DIPOLE model is used for HOI corrections.

THE SYNTHESIS AND CHARACTERISTICS OF THE COORDINATION COMPOUNDS OF 2-MERCAPTOPYRIDINE-1-OXIDE WITH THE FIPST TRANSITION SERIES METALS

The stability of the coordination compounds of the first transition series metal ions(Mn(Ⅱ),Co(Ⅱ),Ni(Ⅱ),Cu(Ⅱ)and Zn(Ⅱ))with 2-mercaptopyridine-1- oxide is reported.A coordination compound CoL_2 is synthesized and characterized for the first time.

SOME PROPERTIES OF MULTIPLE TAYLOR SERIES AND RANDOM TAYLOR SERIES

Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there

SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND TAYLOR SERIES IN C^n

Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.

Effect of solid-earth-tide on GPS time series

The solid-earth-tide models IERS1992 and IERS2003 are used to analyze some GPS-baseline,vertical-component and zenith-tropospheric-delay data from the Crustal Movement GPS Continuous Observation Net-work of Shandong and IGS stations. The results show that the differences between the baselines computed with the different models are at sub-millimeter level, and the differences in vertical component is direct proportional to station latitude. Also the amplitude of ZTD differences is about 0. 6-1.0 mm, which is 6% -8% of the amplitude of solid-earth-tide differences. Although these effects are quite small, to analyze non-tidal deformation correctly, we should still use a single standard for processing GPS data.

Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain

A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn（f; t） with the new kernel function converges uniformly to any continuous function f（t） ∈ Cn（Ω） （the space of all continuous functions with period Ω） on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.

SCATTERING OF CIRCULAR CAVITY IN RIGHT-ANGLE PLANAR SPACE TO STEADY SH-WAVE

Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angle planar space which has no circular cavity is constructed; then the scattering solution which satisfies the free stress conditions of the two right-angle boundaries with the circular cavity existing in the space is formulated. Therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity. It can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential stress at the boundary of the circular cavity due to different dimensionless wave numbers, the location of the circular cavity, the loading center and the distributing range of the out-of-plane loading. The results show the efficiency and effectiveness of the mothod introduced here.

FURTHER APPLICATIONS OF POLAR COORDINATES IN C^n

Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, …, zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic functions in Cn.

On the Telegrapher’s Equation with Three Space Variables in Non-Rectangular Coordinates

This article provides a closed form solution to the telegrapher’s equation with three space variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar angle. The Dirichlet problem for general boundary conditions is solved in detail, on the basis of which Neumann and Robin conditions are easily handled. The solution to the simpler problem in cylindrical coordinates is also provided. Ways to efficiently implement the formulae are explained. Minor adjustments result in solutions to the wave equation and to the heat equation on the same domain as well, since the latter are particular cases of the more general telegrapher’s equation.

AN ANALYTIC AND APPLICATION TO STATE SPACE RECONSTRUCTION ABOUT CHAOTIC TIME SERIES

The state space, reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: AT. H. Packard, F. Takens, M. Casdagli, J. F. Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time tau were identified. The influence for state space reconstruction of lag time tau was discussed. The result tells us that is a good practical method for state space reconstruction.

Multi-scale interactions in interpersonal coordination

Background:Interpersonal coordination is an essential aspect of daily life,and crucial to performance in cooperative and competitive team sports.While empirical research has investigated interpersonal coordination using a wide variety of analytical tools and frameworks,to date very few studies have employed multifractal techniques to study the nature of interpersonal coordination across multiple spatiotemporal scales.In the present study we address this gap.Methods:We investigated the dynamics of a simple dyadic interpersonal coordination task where each participant manually controlled a virtual object in relation to that of his or her partner.We tested whether the resulting hand-movement time series exhibits multi-scale properties and whether those properties are associated with successful performance.Results:Using the formalism of multifractals,we show that the performance on the coordination task is strongly multi-scale,and that the multi-scale properties appear to arise from interaction-dominant dynamics.Further,we find that the measure of across-scale interactions,multifractal spectrum width,predicts successful performance at the level of the dyad.Conclusion:The results are discussed with respect to the implications of multifractals and interaction-dominance for understanding control in an interpersonal context.

一种大尺度区域GNSS坐标时间序列自适应时空滤波方法

提出一种GNSS坐标时间序列自适应时空滤波方法,在规定阈值下将滤波区域自适应分为若干个子区域,进行共模误差的提取和去除。对陆态网184个GNSS站点垂向坐标序列进行时空滤波,3组随机实验中,自适应PCA时空滤波后的站点序列平均RMS值减少约39.7%、38.4%和39.7%,且优于整体PCA滤波。进一步分析滤波前后站点噪声特性变化,结果显示,相比于整体PCA滤波,自适应滤波方法中站点残差序列幂律噪声减少约17.8%。

vbICA方法用于GNSS坐标序列共模误差提取研究

全球导航卫星系统(global navigation satellite system,GNSS)坐标序列精度主要受共模误差(common mode error,CME)影响。为提高GNSS坐标序列精度,采用变分贝叶斯独立分量分析方法(variational Bayesian independent component analysis,vbICA)提取实验区20个GNSS测站坐标序列的CME,并对比分析vbICA与主成分分析(principal component analysis,PCA)和独立分量分析(independent component analysis,ICA)的滤波性能。结果表明,vbICA滤波效果优于PCA和ICA;经vbICA滤波后,E、N、U方向坐标残差序列均方根(RMS)平均降低36.57%、31.63%、10.97%,距离相关系数平均降低60.53%、56.84%、25.80%;扣除CME后,GNSS速度场估计更加可靠和精确,可有效提高GNSS坐标序列精度,为地球动力学研究提供可靠的数据支撑。

GPS时间序列共模误差提取方法及对比分析

区域GPS网中,各个测站坐标时间序列会存在共模误差(CME),该误差会对GPS测站坐标精度产生一定影响,因此去除共模误差对提高站点观测精度具有重要意义。本文在叠加滤波方法的基础上,以各个GPS站点相关性大小为权重进行加权,利用相关加权滤波方法对辽宁及周边省份GPS观测数据进行处理分析,提取共模误差向量,并与叠加滤波的结果进行对比和分析。结果表明,两者均能在一定程度上提取共模误差向量,相关加权叠加滤波法比叠加滤波法具有更好的适用性,均方根提升更为明显,能够更好地提取共模误差。

中国内地GPS坐标时间序列噪声模型特征及其对站点速率影响

为了进一步评估全球定位系统(GPS)时间序列噪声模型水平和垂直速率的大小,及其对误差的影响,选取中国内地227个GPS连续基准站2010—2020年南北、东西和垂直3个方向的坐标时间序列,采用6种噪声模型或噪声组合模型对其进行噪声分析。结果表明,中国内地GPS坐标时间序列噪声模型存在多样性,且部分站点在不同方向的噪声模型也存在差异,主要以一阶高斯马尔可夫+随机漫步噪声(GGMWN)和闪烁噪声+白噪声(FNWN)为主;在100°E附近的GPS站点噪声特性差异最为显著;噪声模型与速率之间的关系分析表明噪声模型对水平向速率的大小和误差影响较小,在现实计算中可不考虑噪声对水平速度的影响,但对垂向速率的大小和误差影响显著;考虑噪声模型可有效提高垂向速率的精度,同时也可能会改变部分站点的垂向运动方向,所以在现实计算中须考虑噪声对垂向速率的影响。

基于坐标时间序列的地心运动分析与预测

地心运动会影响地球参考框架原点的准确性,是地球参考框架进行非线性维持必须考虑的因素之一,因此提出对地心运动进行多尺度的建模和预测,以实现毫米级地球参考框架的建立和维持。采用网平移法计算的地心运动、全球地球物理流体中心(global geophysical fluids center,GGFC)和国际GNSS服务(international gnss service,IGS)第三次重处理(IGSR03)提供的3组地心运动数据,首先对其一致性和差异进行了分析,然后分别利用谐波模型和Diff-LSTM模型对地心运动进行了长期和短期的建模与预测,结果显示,GGFC地心运动的预测精度优于1.5 mm,而Diff-LSTM模型的地心运动预测结果在短期内优于谐波模型,当预测步长为17时,GGFC和IGSR03的地心运动预测精度均能达到甚至优于1 mm。表明地心运动的预测精度能够满足基于地球质量中心(center of mass of the total earth system,CM)的瞬时地球参考框架的建立与维持。

改进BIC的GNSS站坐标时序有色噪声特性分析

为了有效解决传统的极大似然估计方法存在的未知数多导致结果不准确的问题,提出一种改进BIC的GNSS站坐标时序有色噪声特性分析方法:选取全球范围内100个基准站2008—2022年坐标时序及仿真的100组坐标时序,采用赤池信息准则(AIC)、贝叶斯信息准则(BIC)、改进的贝叶斯信息准则(BIC_tp)对不同有色噪声模型进行噪声特性分析,获取基准站坐标序列的最优噪声模型及速度参数;探讨BIC_tp对噪声模型及速度估计的影响。结果表明,基准站坐标序列噪声模型呈现出多样性特征,在北(N)和东(E)方向主要表现为闪烁噪声+白噪声(FNWN)模型,天顶(U)方向主要表现为幂律噪声+白噪声(PLWN)模型;相比于AIC和BIC噪声模型估计准则,BIC_tp方法对有色噪声模型估计具有较高的准确性,尤其是闪烁噪声+随机游走噪声(RW)+白噪声(FNRWWN)模型对全球卫星导航系统(GNSS)站速度不确定度的影响在N与E方向远大于U方向;正确获取模型参数估计的实际不确定度及改正噪声分量对于合理应用GNSS坐标时间序列数据具有重要意义。

SSA-VMD与小波分解结合的GNSS坐标时序降噪方法

利用麻雀搜索算法(sparrow search algorithm, SSA)优化变分模态分解(VMD),然后结合小波分解(WD),提出一种GNSS坐标时间序列降噪方法IVMD-WD。利用仿真信号和10个基准站的实测数据进行GNSS坐标时间序列降噪实验。结果表明,IVMD-WD方法的降噪效果优于经验模态分解(EMD)、集合经验模态分解(EEMD)和WD,能够更加有效地剔除GNSS坐标时间序列中的噪声。