应用平滑先验信息方法移除GRACE数据中相关误差

由于GRACE卫星数据解算的时变重力场模型中高阶位系数存在误差,这些误差在重力异常图中表现为南北向的条带噪声,在应用GRACE时变重力场数据时必须进行滤波.本文在空间域引入了一种有效消除GRACE时变重力场条带噪声的平滑先验信息方法,并将其与目前常用的高斯滤波和去相关误差等滤波方法分别应用于合成的质量变化趋势数字模型,检测不同滤波方法消除条带噪声的能力及其对真实信号的影响.滤波结果显示,与目前常用的高斯滤波和去相关误差滤波器相比,本文滤波方法在有效移除条带噪声的同时,具有有效信号幅度衰减小、有效信号形变小以及保存了更多的短波长细节信息等优势;此外,统计结果显示,本文滤波结果在信号最大值、最小值以及残差均方根等方面均与模拟真实信号最为接近.相比300km高斯平滑和组合滤波结果,有效信号振幅的极小值和极大值分别提高了约18%和6%,残差均方根分别降低了25%和33%.说明本文滤波方法移除GRACE相关误差的同时,在保留有效信号方面具有明显的优势.     

GOCE卫星重力测量中有色噪声滤波器设计

本文根据卫星重力梯度测量的有色噪声特性,设计了Wiener、AR、FIR三种滤波器,并利用模拟的有色噪声数据对其滤波效果进行了测试,结果表明:对于文中采用的有色噪声数据,AR的滤波效果最好,其次为Wiener滤波器,FIR的滤波效果最差;三种滤波器均可用于GOCE卫星重力测量中有色噪声数据滤波,但其实用性尚需利用实测数据进行检验;可以利用不同的滤波器对含有色噪声的卫星重力梯度数据进行多次滤波,以进一步减弱有色噪声对卫星重力梯度测量精度的影响.     

利用径向基函数RBF解算GRACE全球时变重力场

本文利用GRACE(Gravity Recovery And Climate Experiment)level 1b数据和径向基函数RBF(radial basis function)方法解算了全球时变地球重力场.RBF基函数相比传统球谐(spherical harmonic)基函数,其高度的空域局部特性使得正则化过程易于添加先验协方差信息,从而可能揭示更加准确的重力场信号.本文研究表明,RBF基函数算法在精化现有的GRACE全球时变重力场模型,如提升部分区域信号幅度等方面具有一定优势.本文通过将RBF的尺度因子作为待解参数,基于GRACE卫星的Level 1b数据和变分方程法,成功获取了2009-2010年90阶无约束全球时变重力场RBF模型Hust-IGG03,以及正则化全球时变重力场RBF模型Hust-IGG04.通过与GRACE官方数据处理中心GFZ发布的最新90阶球谐基时变模型RL05a进行对比,结果表明:(1)无约束RBF模型Hust-IGG03和GFZ RL05a在空域和频域表现基本一致;(2)正则化RBF模型Hust-IGG04无需进行后处理滤波已经显示较高信噪比,噪音水平接近于球谐基模型GFZ RL05a经400 km高斯滤波后的效果;(3)HustIGG04相比400 km高斯滤波GFZ RL05a在周年振幅图和趋势图上显示出更多的细节信息,并且呈现出更强的信号幅度,如在格陵兰冰川融化趋势估计上Hust-IGG04比GFZ RL05a提高了24.2%.以上结果均显示RBF方法有助于进一步挖掘GRACE观测值所包含的时变重力场信息.     

Applications of Savitzky-Golay Filter for Seismic Random Noise Reduction

This article utilizes Savitzky–Golay (SG) filter to eliminate seismic random noise. This is a novel method for seismic random noise reduction in which SG filter adopts piecewise weighted polynomial via leastsquares estimation. Therefore, effective smoothing is achieved in extracting the original signal from noise environment while retaining the shape of the signal as close as possible to the original one. Although there are lots of classical methods such as Wiener filtering and wavelet denoising applied to eliminate seismic random noise, the SG filter outperforms them in approximating the true signal. SG filter will obtain a good tradeoff in waveform smoothing and valid signal preservation under suitable conditions. These are the appropriate window size and the polynomial degree. Through examples from synthetic seismic signals and field seismic data, we demonstrate the good performance of SG filter by comparing it with the Wiener filtering and wavelet denoising methods.     

PRINCIPLES OF DIGITAL WIENER FILTERING*

The theory of statistical communication provides an invaluable framework within which it is possible to formulate design criteria and actually obtain solutions for digital filters. These are then applicable in a wide range of geophysical problems. The basic model for the filtering process considered here consists of an input signal, a desired output signal, and an actual output signal. If one minimizes the energy or power existing in the difference between desired and actual filter outputs, it becomes possible to solve for the so-called optimum, or least squares filter, commonly known as the “Wiener” filter. In this paper we derive from basic principles the theory leading to such filters. The analysis is carried out in the time domain in discrete form. We propose a model of a seismic trace in terms of a statistical communication system. This model trace is the sum of a signal time series plus a noise time series. If we assume that estimates of the signal shape and of the noise autocorrelation are available, we may calculate Wiener filters which will attenuate the noise and sharpen the signal. The net result of these operations can then in general be expected to increase seismic resolution. We show a few numerical examples to illustrate the model's applicability to situations one might find in practice.     

基于区域滤波的GOCE稳态海面动力地形和地转流

基于频域法,利用最新的GOCE卫星重力场模型和卫星测高数据计算了稳态海面动力地形.结合海洋表层漂流浮标的观测结果,对稳态海面动力地形进行了最优空间滤波尺度分析,给出了区域、纬度带和全球稳态海面动力地形的最优空间滤波尺度因子.在此基础上,给出了全球和区域地转流.结果表明:在中高纬度和全球区域,可以分别获得空间尺度优于102km和127km的稳态海面动力地形信息.与海洋表层漂流浮标对比可知,在强流区域,采用稳态海面动力地形得到的地转流速可以解释观测浮标流速的70%;在中高纬度区域,由GOCE重力场得到的地转流略优于对应的GRACE结果;在近赤道区域,由GOCE重力场得到的地转流精度略低于对应的GRACE结果;在北大西洋和阿古拉斯强流区域,由GOCE得到的地转流场明显优于对应的GRACE结果,其精度分别提高了16%和24%.     

Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America

Monthly geopotential spherical harmonic coefficients from the GRACE satellite mission are used to determine their usefulness and limitations for studying glacial isostatic adjustment (GIA) in North-America. Secular gravity rates are estimated by unweighted least-squares estimation using release 4 coefficients from August 2002 to August 2007 provided by the Center for Space Research (CSR), University of Texas. Smoothing is required to suppress short wavelength noise, in addition to filtering to diminish geographically correlated errors, as shown in previous studies. Optimal cut-off degrees and orders are determined for the destriping filter to maximize the signal to noise ratio. The halfwidth of the Gaussian filter is shown to significantly affect the sensitivity of the GRACE data (with respect to upper mantle viscosity and ice loading history). Therefore, the halfwidth should be selected based on the desired sensitivity.It is shown that increase in water storage in an area south west of Hudson Bay, from the summer of 2003 to the summer of 2006, contributes up to half of the maximum estimated gravity rate. Hydrology models differ in the predictions of the secular change in water storage, therefore even 4-year trend estimates are influenced by the uncertainty in water storage changes. Land ice melting in Greenland and Alaska has a non-negligible contribution, up to one-fourth of the maximum gravity rate.The estimated secular gravity rate shows two distinct peaks that can possibly be due to two domes in the former Pleistocene ice cover: west and south east of Hudson Bay. With a limited number of models, a better fit is obtained with models that use the ICE-3G model compared to the ICE-5G model. However, the uncertainty in interannual variations in hydrology models is too large to constrain the ice loading history with the current data span. For future work in which GRACE will be used to constrain ice loading history and the Earth's radial viscosity profile, it is important to include realistic uncertainty estimates for hydrology models and land ice melting in addition to the effects of lateral heterogeneity.     

重力卫星精密星间测距系统滤波器技术指标论证

本文基于重力卫星精密星间测距测量模式,从星间测距观测值与地球重力场频谱关系的角度,建立了距离观测值关于重力位系数的敏感矩阵,分析了各阶次重力场位系数对应的敏感矩阵的频谱特性,讨论了星间测距信息中能反应地球重力场信息的有效信号频带,给出了能最大限度保留地球重力场信息的低通滤波器的通带截止频率、通带增益波纹和频率采样率技术指标设计方案,可为我国首期卫星跟踪卫星重力测量计划的主要技术指标的初步设计提供参考.     

Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America

Monthly geopotential spherical harmonic coefficients from the GRACE satellite mission are used to determine their usefulness and limitations for studying glacial isostatic adjustment (GIA) in North-America. Secular gravity rates are estimated by unweighted least-squares estimation using release 4 coefficients from August 2002 to August 2007 provided by the Center for Space Research (CSR), University of Texas. Smoothing is required to suppress short wavelength noise, in addition to filtering to diminish geographically correlated errors, as shown in previous studies. Optimal cut-off degrees and orders are determined for the destriping filter to maximize the signal to noise ratio. The halfwidth of the Gaussian filter is shown to significantly affect the sensitivity of the GRACE data (with respect to upper mantle viscosity and ice loading history). Therefore, the halfwidth should be selected based on the desired sensitivity.It is shown that increase in water storage in an area south west of Hudson Bay, from the summer of 2003 to the summer of 2006, contributes up to half of the maximum estimated gravity rate. Hydrology models differ in the predictions of the secular change in water storage, therefore even 4-year trend estimates are influenced by the uncertainty in water storage changes. Land ice melting in Greenland and Alaska has a non-negligible contribution, up to one-fourth of the maximum gravity rate.The estimated secular gravity rate shows two distinct peaks that can possibly be due to two domes in the former Pleistocene ice cover: west and south east of Hudson Bay. With a limited number of models, a better fit is obtained with models that use the ICE-3G model compared to the ICE-5G model. However, the uncertainty in interannual variations in hydrology models is too large to constrain the ice loading history with the current data span. For future work in which GRACE will be used to constrain ice loading history and the Earth's radial viscosity profile, it is important to include realistic uncertainty estimates for hydrology models and land ice melting in addition to the effects of lateral heterogeneity.     

优化滤波方法及其在中国大陆布格重力异常数据处理中的应用

在优选延拓法的理论基础上,研究提出基于格林等效层概念和维纳滤波器的优化滤波法,用于对重力异常数据进行去噪和分离.与传统向上延拓法和优选延拓法相比,优化滤波法分离异常与延拓高度无关,不需要已知延拓高度,具有一定的优势.理论重力模型数据的去噪和异常分离试验表明优化滤波法有效,异常分离效果优于传统向上延拓法和带通滤波法.利用优化滤波法对中国大陆重力异常数据去噪和异常分离,得到有效的布格重力异常和区域重力异常.以中国大陆深地震探测推断的莫霍面深度信息为约束,对区域重力异常数据进行密度界面约束反演,得到中国大陆莫霍面深度分布.本文方法为中国大陆深部探测和区域构造研究提供一定的技术支撑.     

Tackling mass redistribution phenomena by time-dependent GRACE- and terrestrial gravity observations

Time variable gravity field models derived from the satellite mission GRACE have been demonstrated to be consistent with water mass variations in the global hydrological cycle. Independent observations are provided by terrestrial measurements. In order to achieve a maximum of reliability and information gain, ground-based gravity observations may be deployed for comparison with the gravity field variations derived from the GRACE satellite mission. In this context, the data of the network of superconducting gravimeters (SG) of the ‘Global Geodynamics Project’ (GGP) are of particular interest. This study is focused on the dense SG network in Central Europe with its long-term gravity observations. It is shown that after the separation and reduction of local hydrological effects in the SG observations especially for subsurface stations, the time-variable gravity signals from GRACE agree well with the terrestrial observations from the SG station cluster.Station stability of the SG sites with respect to vertical deformations was checked by GNSS based observations. Most of the variability can be explained by loading effects due to changes in continental water storage, and, in general, the stability of all stations has been confirmed.From comparisons based on correlation and coherence analyses in combination with the root mean square (RMS) variability of the time series emerges, that the maximum correspondence between the SG and GRACE time series is achieved when filtering the GRACE data with Gaussian filters of about 1000 km filter length, which is in accordance with previous publications.Empirical Orthogonal Functions (EOF) analysis was applied to the gravity time series in order to identify common characteristic spatial and temporal patterns. The high correspondence of the first modes for GRACE and SG data implies that the first EOF mode represents a large-scale (Central European) time-variable gravity signal seen by both the GRACE satellites and the SG cluster.     

Significance of secular trends of mass variations determined from GRACE solutions

Since 2002 the Earth’s gravity field is globally observed by the Gravity Recovery and Climate Experiment (GRACE) satellite mission. The GRACE monthly gravity field solutions, available from several analysis centres, reflect mass variations in the atmosphere, hydrosphere and geosphere. Due to correlated noise contained in these solutions, it is, however, first necessary to apply an appropriate filtering technique. The resulting, smoothed time series are applied not only to determine variations with different periodic signatures (e.g., seasonal, short and medium-term), but to derive long-periodic mass variations and secular trends as well. As the GRACE monthly solutions always show the integral effect of all mass variations, for separation of single processes, like the GIA (Glacial isostatic adjustment)-related mass increase in Fennoscandia, appropriate reduction models (e.g. from hydrology) are necessary.In this study we show for the example of the Fennoscandian uplift area that GRACE solutions from different analysis centres yield considerably different secular trends. Furthermore, it turns out that the inevitable filtering of the monthly gravity field models affects not only the amplitudes of the signals, but also their spatial resolution and distribution such as the spatial form of the detected signals. It also becomes evident that the determination of trends has to be performed together with the determination of periodic components. All periodic terms which are really contained in the data, and only such, have to be included. The restricted time span of the available GRACE measurements, however, limits the separation of long-periodic and secular signals. It is shown that varying the analysis time span affects the results considerably. Finally, a reduction of hydrological signals from the detected integral secular trends using global hydrological models (WGHM, LaDWorld, GLDAS) is attempted. The differences among the trends resulting from different models illustrate that the state-of-the-art hydrology models are not suitable for this purpose as yet. Consequently, taking the GRACE monthly gravity field solutions from one centre, choosing a single filter and applying an insufficiently reliable reduction model leads sometimes to a misinterpretation of considered geophysical processes. Therefore, one has to be cautious with the final interpretation of the results.     

分离重磁区域场与局部场的维纳滤波器

本文从最佳线性滤波理论出发,对目前重磁资料数据处理中分离区域场与局部场的两种滤波器--匹配滤波和维纳滤波的频率响应特性作了分析比较,指出了匹配滤波只是一般维纳滤波的一个特例。将该两种滤波器与一般情况的维纳滤波器的误差作了对比,并通过简单的理论试例,说明它们的局限性和应用范围。     

Improved daily GRACE gravity field solutions using a Kalman smoother

Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly solutions. These temporal mean fields cannot model the variations occurring during the respective time span. The aim of our approach is to extract as much temporal information as possible out of the given GRACE data. Therefore the temporal resolution shall be increased with the goal to derive daily snapshots. Yet, such an increase in temporal resolution is accompanied by a loss of redundancy and therefore in a reduced accuracy if the daily solutions are calculated individually. The approach presented here therefore introduces spatial and temporal correlations of the expected gravity field signal derived from geophysical models in addition to the daily observations, thus effectively constraining the spatial and temporal evolution of the GRACE solution. The GRACE data processing is then performed within the framework of a Kalman filter and smoother estimation procedure.The approach is at first investigated in a closed-loop simulation scenario and then applied to the original GRACE observations (level-1B data) to calculate daily solutions as part of the gravity field model ITG-Grace2010. Finally, the daily models are compared to vertical GPS station displacements and ocean bottom pressure observations.From these comparisons it can be concluded that particular in higher latitudes the daily solutions contain high-frequent temporal gravity field information and represent an improvement to existing geophysical models.     

Calibration/Data Assimilation Approach for Integrating GRACE Data into the WaterGAP Global Hydrology Model (WGHM) Using an Ensemble Kalman Filter: First Results

We introduce a new ensemble-based Kalman filter approach to assimilate GRACE satellite gravity data into the WaterGAP Global Hydrology Model. The approach (1) enables the use of the spatial resolution provided by GRACE by including the satellite observations as a gridded data product, (2) accounts for the complex spatial GRACE error correlation pattern by rigorous error propagation from the monthly GRACE solutions, and (3) allows us to integrate model parameter calibration and data assimilation within a unified framework. We investigate the formal contribution of GRACE observations to the Kalman filter update by analysis of the Kalman gain matrix. We then present first model runs, calibrated via data assimilation, for two different experiments: the first one assimilates GRACE basin averages of total water storage and the second one introduces gridded GRACE data at \(5^\circ\) resolution into the assimilation. We finally validate the assimilated model by running it in free mode (i.e., without adding any further GRACE information) for a period of 3 years following the assimilation phase and comparing the results to the GRACE observations available for this period.     

基于核函数主分量的维纳滤波方法研究

针对强随机噪声地震资料背景下经典维纳滤波方法在信号的保幅及高维数据空间求解过程中产生病态矩阵的问题,提出利用核函数主分量维纳滤波压制强地震勘探随机噪声.首先利用线性核函数将地震信号映射到特征空间,再通过主分量分析方法提取地震数据主分量进行数据降维,并得到核主分量维纳滤波因子,从而进行核主分量维纳滤波（K-WPC）.正演仿真及对实际地震资料处理表明,该方法对随机噪声有较好的压制作用,保幅效果也令人满意.     

Seasonal water storage change of the Yangtze River basin detected by GRACE

1 Introduction Large-scale mass redistribution, or temporal varia- tion of mass within the Earth system, the driving force of interactions between solid Earth and geophysical fluids envelope (i.e., atmosphere, ocean, and hydro- sphere), is an important geophysical process critical to human life. Most of the interactions between solid Earth and the atmosphere/oceans happen at seasonal and inter-annual time scales. One important contribu- tor of mass redistribution at seasonal and inter-annual …     

Assimilation of geodetic dynamic ocean topography using ensemble based Kalman filter

Estimation of ocean circulation is investigated via assimilation of satellite measurements of the dynamic ocean topography (DOT) into the global finite-element ocean model (FEOM). The DOT was obtained by means of a geodetic approach from carefully cross-calibrated multi-mission altimeter data and GRACE gravity fields. The spectral consistency was achieved by consistently filtering both, the sea surface and the geoid. The filter length is determined by the spatial resolution of the gravity field and corresponds to approximately 241 km half width for the GRACE-based gravity field model ITG-Grace03s.The assimilation of the geodetic DOT was performed by employing a local singular evolutive interpolated Kalman (SEIK) filter in combination with the method of weighting of observations. It is shown that this approach leads to a successful assimilation technique that reduced the RMS difference between the model and the data from 16 cm to 5 cm during one year of assimilation. The ocean model returns an optimized mean dynamic ocean topography. The effects of assimilation on transport estimates across several hydrographic World Ocean Circulation Experiment (WOCE) sections show improvements compared to the FEOM run without data assimilation. As a result of the assimilation, DOT estimates are available in the polar or coastal regions where the geodetic estimates from satellite data alone are not adequate. Furthermore, more realistic features of the ocean can be seen in these areas compared to those obtained using the filtered data fields.     

OPTIMUM DIGITAL FILTERING AND INVERSE FILTERING IN THE FREQUENCY DOMAIN*

Two distinct filters are developed in the frequency domain which represent an attempt to increase the resolution of fine structure contained in the signal whilst keeping the expected filtered noise energy within reasonable bounds. A parameter termed the White Noise Amplification is defined and used together with a measure of the deconvolved pulse width in order to provide a more complete characterisation of the filters. Each of the two main types of frequency domain filters discussed varies in properties with respect to a single adjustable parameter. This may be contrasted with a time domain Wiener filter which in general has three variables: length, delay and an adjustable noise parameter or weight. The direct frequency domain analogue of the Wiener filter is termed a gamma-Fourier filter, and is shown to have properties which span the range from those of a spiking filter with zero least square error at one extreme, to those of a matched filter at the other extreme of its variable parameter's range. The second type of filter considered—termed the modulated Gaussian filter—is similarly shown to be a perfect spiking filter at one extreme of its parameter range, but adopts the properties of an output energy filter at the other extreme.     

基于ARMA模型非因果空间预测滤波(英文)

常规频域预测滤波方法是建立在自回归(autoregressive,AR)模型基础上的,这导致滤波过程中前后假设的不一致,即首先利用源噪声的假设计算误差剖面,却又将其作为可加噪声而从原始剖面中减去来得到有效信号。本文通过建立自回归-滑动平均(autoregres sive/moving-average,ARMA)模型,首先求解非因果预测误差滤波算子,然后利用自反褶积形式投影滤波过程估计可加噪声,进而达到去除随机噪声目的。此过程有效避免了基于AR模型产生的不一致性。在此基础上,将一维ARMA模型扩展到二维空间域,实现了基于二维ARMA模型频域非因果空间预测滤波在三维地震资料随机噪声衰减中的应用。模型试验与实际资料处理表明该方法在很好保留反射信息同时,压制随机噪声更加彻底,明显优于常规频域预测去噪方法。