GRACE时变重力场各向异性高斯组合滤波方法

受测量误差等因素影响，直接使用GRACE时变重力场模型的地表质量变化反演结果呈现严重条带噪声，必须采用滤波消除。本文对不同滤波方法进行了试验分析，以信噪比最大为准则，确定了不同滤波方法的最优滤波参数，并在此基础上提出了一种各向异性组合滤波方法。该方法根据时变重力场模型球谐系数误差特性，结合各向异性高斯滤波和均方根滤波特点，对精度较高的低次项系数采用较大权重以保留更多有效信号，而对精度较差的高次项系数采用较小权重以压制噪声。不同于传统的两步法组合滤波，该方法仅需进行一步滤波处理。试验结果表明，本文提出的各向异性组合滤波方法计算步骤简单，能够有效消除条带噪声；与单一滤波和传统两步法组合滤波方法相比，提高了反演结果信噪比，保留了更多真实信号。     

多通道奇异谱组合滤波反演水储量变化

针对GRACE时变重力场球谐系数的高阶次项中含有的较高噪声会造成反潢结果产生误差的问题,该文采用多通道奇异谱分析和高斯滤波相结合的方案来滤除GRACE数据中的噪声,并与普遍使用的去相关滤波和高斯滤波相结合的方案进行了对比验证。首先利用这两种方法分别计算了2007年4、10月份的全球水储量变化,结果显示,这两种方法反演的结果基本相同,而多通道奇异谱分析与高斯滤波相组合的方法提高了信噪比,减弱了信号泄露误差,验证了该组合方案的可行性。然后又分别计算了亚马逊流域2004—2010年的水储量时间变化序列,并与GLDAS水文模型进行了对比验证,结果显示,这两种方法得到的水储量时间序列变化趋势基本相同,各自之间具有强相关性,进一步说明了该文方案在GRACE数据滤波中的可行性。     

利用GRACE RL05模型监测长江流域水储量变化

本文基于GRACE最新重力场模型RL05序列研究了高斯滤波、Wiener滤波、各向异性滤波三种方法在长江流域水储量变化监测中的适用性,计算了应用三种方法得到的水储量变化速率。通过与长江流域水文模型的比较,高斯滤波平滑半径为430km时所得的结果与Wiener滤波基本一致,但各向异性滤波反演的结果与水文模型更为接近,并且优于前面两种方法。研究结果表明GRACE RL05时变重力场球谐系数误差存在各向异性的分布特征,因此各向异性滤波更适用于GRACE区域水储量变化的研究。     

GRACE时变重力位系数扇形滤波算法分析

卫星重力探测技术为监测全球陆地水储量变化提供了新的技术手段。采用Level-2 Release-05版本GRACE时变重力场模型数据计算了2010年全球陆地水储量的月变化;着重研究了扇形滤波对反演结果的影响;并结合GLDAS水文模型数据对反演结果进行了验证分析。实验结果表明:GRACE反演结果 GLDAS水文模型结果在时空分布上符合较好;扇形滤波能够削弱GRACE时变重力场模型的高阶项误差影响,有效去除反演结果中的条带状噪声。     

GRACE时变重力位系数误差的改进去相关算法

GRACE卫星时变重力场模型的高阶位系数存在较大误差,用它反演的重力场结果中表现为严重的条带噪声。Swenson提出的滑动窗多项式拟合去相关误差方法在赤道两侧区域取得了显著效果,但其在文献中并没有说明实现的具体步骤,因而许多学者在利用其思想进行滤波时并没有达到其文献中的滤波效果。针对滑动窗的特点,使用反向边界延拓技术,对滑动窗去相关误差数据处理方法作了改进。改进的滑动窗去相关误差方法应用于GRACE时变重力场模型时,在赤道两侧区域取得了显著的去条带误差效果,并利用全球地面资料同化系统GLDAS土壤湿度资料验证该方法的正确性。     

GRACE时变重力场的滤波理论及质量变化分析

正由于GRACE(gravity recovery and climate experiment)时变重力场模型直接解算质量变化时存在较大的误差,需要对其进行相应的滤波处理,提高质量变化的反演精度。本文总结了GRACE监测全球与区域质量变化的研究进展,分析了最新时变重力场模型的精度及其滤波方法;提出了基于重力位系数协方差阵的时变重力场滤波方法;分析了南极冰盖的质量变化、亚马孙流域陆地水质量和海平面变化。本文的研究成果及创新点主要包括以下几个方面:     

采用点质量模型方法反演中国大陆及周边地区陆地水储量变化

研究了反演区域陆地水储量变化的点质量模型方法,采用Tikhonov正则化方法解决了反演过程中参数估计病态问题。利用GRACE（gravity recovery and climate experiment）时变重力场模型数据,用点质量模型方法反演了中国大陆及其周边地区陆地水储量变化,将点质量模型反演结果与球谐系数法反演结果、GLDAS（global land data assimilation）水文模型数据进行了验证分析,并选取了4个特征点计算了陆地水储量变化时间序列。实验结果表明,由于点质量模型方法将研究区域内不同网格质量变化对地球重力场的影响分离开来,所得区域陆地水储量变化局部信号更明显,并且点质量模型方法反演结果与GLDAS水文模型数据相关性更强。     

GRACERL05反演南极冰盖质量变化方法比较

利用UTCSR发布的2003-01~2013-07GRACE RL05月平均重力场模型,分析比较了高斯滤波、各向异性滤波、扇形滤波和维纳滤波,并结合去相关滤波在反演南极地区冰盖质量变化方面的差异。通过计算得到以下结论:1基于121组重力场模型阶方差分布得到维纳滤波与半径为300km的高斯滤波效果最为接近,说明300km滤波半径完全可以满足质量变化信号的提取;2在一定范围内,提高滤波半径能提高反演结果信噪比,建议南极区域的滤波半径为500km;采用相同滤波半径,不同空间滤波算法计算的质量变化率基本一致,在南极区域可以选取任一滤波方法;3与其他算法相比,去相关滤波算法能在一定程度消除球谐系数中存在的系统误差,改善反演结果。     

GRACE离散时变重力场的大尺度动态变化模型构建分析

针对GRACE月时变重力场的离散球谐系数,提出联合经验正交函数分解和多通道奇异谱分析的方法,在有效实现空间维数压缩和条带噪声去除的同时,提取、分析其动态变化特征并构建相应的变化模型。结果表明,GRACE离散球谐系数存在显著的周年项和长期趋势项变化成分,其中,周年项模态的方差贡献达到50.6%,扣除周年项成分后长期趋势项的累积方差贡献达到77.4%。以长期趋势项和周年项成分构建的非线性模型能较好地反映离散球谐系数及其反演结果的动态变化特征,其对全球陆表等效水柱高的拟合标准差介于0.3~14.0 cm,平均标准差为1.8 cm。研究结果可为分析地球重力场各参量变化特征及地球动力学变化提供重要参考。     

利用GOCE卫星轨道反演地球重力场模型

根据积分方程法反演地球重力场的数学模型,利用GOCE卫星2009-11-02～2010-01-02共61d的精密轨道数据反演了几组地球重力场模型。结果表明,GOCE卫星轨道能有效提取地球重力场的长波信息,弥补了GOCE卫星重力梯度带宽的限制,在106阶次的大地水准面误差为±9.6cm,该阶次精度优于EIGEN-CHAMP03S及GRACE卫星两个月轨道反演地球重力场的精度,但由于两极空白,反演的带谐位系数精度偏低。联合GOCE及GRACE卫星轨道反演的模型在106阶次的大地水准面误差为±6.9cm,弥补了GOCE卫星轨道的缺陷。     

Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models

We discuss a new method for approximately decorrelating and non-isotropically filtering the monthly gravity fields provided by the gravity recovery and climate experiment (GRACE) twin-satellite mission. The procedure is more efficient than conventional Gaussian-type isotropic filters in reducing stripes and spurious patterns, while retaining the signal magnitudes. One of the problems that users of GRACE level 2 monthly gravity field solutions fight is the effect of increasing noise in higher frequencies. Simply truncating the spherical harmonic solution at low degrees causes the loss of a significant portion of signal, which is not an option if one is interested in geophysical phenomena on a scale of few hundred to few thousand km. The common approach is to filter the published solutions, that is to convolve them with an isotropic kernel that allows an interpretation as smoothed averaging. The downside of this approach is an amplitude bias and the fact that it neither accounts for the variable data density that increases towards the poles where the orbits converge nor for the anisotropic error correlation structure that the solutions exhibit. Here a relatively simple regularization procedure will be outlined, which allows one to take the latter two effects into account, on the basis of published level 2 products. This leads to a series of approximate decorrelation transformations applied to the monthly solutions, which enable a successive smoothing to reduce the noise in the higher frequencies. This smoothing effect may be used to generate solutions that behave, on average over all possible directions, very close to Gaussian-type filtered ones. The localizing and smoothing properties of our non-isotropic kernels are compared with Gaussian kernels in terms of the kernel variance and the resulting amplitude bias for a standard signal. Examples involving real GRACE level 2 fields as well as geophysical models are used to demonstrate the techniques. With the new method, we find that the characteristic striping pattern in the GRACE solutions are much more reduced than Gaussian-filtered solutions of comparable signal amplitude and root mean square.     

GRACE时变重力场滤波方法

针对GRACE时变重力场模型高阶项误差较大导致的"南-北"条带噪声,该文利用模拟的GRACE数据分析了去相关滤波、Gaussian滤波、组合滤波和平滑先验信息滤波方法对噪声的滤除效果和对真实信号的衰减程度。实验表明:4种滤波算法均能有效降低条带噪声,但单独使用去相关滤波时效果较差,需与其他算法结合使用;Guass滤波和组合滤波在减小噪声条带的同时,也在一定程度上牺牲了空间分辨率;平滑先验信息滤波在移除噪声、保留有效信号方面比其他3种算法有较为明显的优势。     

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model’s spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components \(V_{xy}\) and \(V_{yz}\) of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE’s inclination of \(96.7^{\circ }\). With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of \(V_{xy}\) and \(V_{yz}\) are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT_R1’s accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/leveling data.     

A simulation study of the errors of omission and commission for GRACE RL01 gravity fields

This paper examines the influence that certain omission and commission errors can have on the gravity field models estimated from the initial release of data (RL01) from the Gravity Recovery And Recovery Experiment (GRACE) satellite mission. The effects of omission errors were analyzed by limiting the degree and order to which the GPS and K-band range-rate (KBR) measurement partials were extended in the solution process. The commission error studies focused on the impact of an imperfect mean reference gravity field model on the solution. Combinations of both of these error sources were also explored. The nature of these errors makes them difficult to distinguish from the true gravity signal, so the exploration of these error sources was performed using simulations; however, comparisons to real-data solutions are provided. The results show how each of the specific error sources investigated influences the gravity field solution. The simulations also show how all of the errors examined can be sufficiently mitigated through the appropriate choice of processing parameters.     

Comparison of present SST gravity field models

Taking the main land of Europe as the region to be studied, the potential of the new satellite gravity technique: satellite-to-satellite tracking (SST) and improving the accuracy of regional gravity field model with the SST models are investigated. The drawbacks of these models are discussed. With GPM98C as the reference, the gravity anomaly residuals of several other models, the latest SST global gravity field models (EIGEN series and GGM series), were computed and compared. The results of the comparison show that in the selected region, some systematic errors with periodical properties exist in the EIGEN and GGM's S series models in the high degree and order. Some information that was not shown in the classic gravity models is detected in the low and middle degree and order of EIGEN and GGM's S series models. At last, the effective maximum degrees and orders of SST models are suggested.     

Reducing errors in the GRACE gravity solutions using regularization

The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth’s monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003–Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE.     

Comparison of Present SST Gravity Field Models

IntroductionSince 2000 , with the launch of CHAMP satellite,several series of high-accuracy and high-resolutionstatic Earth’s gravityfield models have been createdbased on aboundent SST data. With these models ,the research in solid geophysics ,oceangraphy,andgeodesy can be promoted greatly[1].In this paper ,the SSTgravity models’accura-cyin various frequently domainis studied.First-ly,the difference among these models is compu-ted and compared,and then their accuracyis an-alyzed. Fina…     

天问一号拓展任务对火星低阶重力场解算的潜在贡献分析

天问一号是中国首次独立开展的行星际探测任务,实现了对火星的环绕、着陆、巡视探测。天问一号正常科学任务阶段环绕以极轨设计为主,与历史火星任务类似,对当前火星重力场模型精度改进有限,因此其拓展任务轨道选取至关重要。通过对极轨圆轨道和近赤道大偏心率轨道进行仿真模拟,分析两种典型轨道构型对现有火星重力场模型改进的可能性,基于不同误差考量仿真解算了对应6个重力场模型。借助重力场功率谱分析,发现在测量噪声为0.1 mm/s的情况下,不论采用极轨还是近赤道轨道,一个月的跟踪数据均可较好地反演出42阶次的火星重力场模型;考虑综合误差影响之后,发现两种轨道对于重力场解算精度类似,其中实施近赤道大偏心率轨道对35阶次以上约束略强。     

A numerical study of the divergence of spherical harmonic series of the gravity and height anomalies at the earth's surface

The problem of the divergence of the geopotential spherical harmonic series at the earth's surface is investigated from a numerical, rather than a theoretical, approach. A representative model of the earth's potential is devised on the basis of a density layer, which, in the spherical approximation, generates a gravity field whose harmonic constituents decay according to an accepted degree variance model. This field, expanded to degree 300, and a topographic surface specified to a corresponding resolution of 67 km are used to compute the differences between truncated inner and outer series of the gravity and height anomalies at the surface of the earth model. Up to degree 300, these differences attain RMS values from 0.33 μgal to 86 μgal for the gravity anomaly and from 0.32 μm to 410 μm for the height anomaly, in areas ranging respectively from near the equator to the vicinity of the pole. In addition to these values, there is an expected truncation effect, caused by the neglect of higher degree components of the inner series, of about 30 mgal and 36 cm, respectively. The field is then subjected to a Gaussian filter which effectively cuts off information at degree 300 (at the 5% level). The RMS error to degree 300 is thereby reduced by factors of 10 to 20, with a concomitant reduction in the truncation effect to about 0.3 mgal and 0.7 cm.     

基于信噪比的InSAR干涉图自适应滤波

提出了一种基于信噪比的InSAR干涉图相位噪声抑制算法。该算法对Goldstein滤波方法进行了改进，使Goldstein滤波参数 依赖于局部信噪比，从而实现对低信噪比区域进行强滤波、高信噪比区域弱滤波。采用模拟数据和真实数据进行验证，结果表明新算法能有效抑制InSAR干涉图的噪声。