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）Hust-IGG04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.

     

利用动力学方法解算GRACE时变重力场研究

本文利用动力学方法建立GRACE (Gravity Recovery And Climate Experiment) K波段距离变率 (KBRR)观测、轨道观测与重力场系数的观测方程, 通过GRACE Level 1B观测数据,成功解算出全球月时变重力场模型——IGG时变重力场模型,并将2008—2009年的解算结果与GRACE三大数据处理机构美国德克萨斯大学空间中心CSR (Center for Space Research)、美国宇航局喷气推进实验室JPL(Jet Propulsion Laboratory)和德国地学研究中心GFZ (GeoForschungs Zentrum) 发布的最新全球时变重力场模型进行详细对比分析.结果表明:IGG结果在全球质量异常、中国及周边地区质量异常的趋势变化、全球质量异常均方差、2~60每阶位系数差值以及亚马逊流域和撒哈拉沙漠等典型区域平均质量异常等方面与CSR、JPL和GFZ解算的RL05结果较为一致.其中,IGG解算结果在2~20阶与CSR、GFZ和JPL最新解算结果基本一致,20~40阶IGG解算结果与GFZ、JPL单位最新解算结果较为接近,大于40阶IGG结果介于CSR与GFZ、JPL之间;亚马逊流域平均质量异常周年振幅IGG、CSR、GFZ和JPL获取到的结果分别为17.6±1.1 cm、18.9±1.2 cm、17.8±0.9 cm和18.9±1.0 cm等效水柱高.利用撒哈拉沙漠地区的平均质量异常做反演精度评定,IGG、CSR、GFZ和JPL的时变重力场获取到的平均质量异常均方差分别为1.1 cm、0.9 cm、0.8 cm和1.2 cm,表明IGG解算结果与CSR、GFZ和JPL最新发布的RL05结果在同一精度水平.     

新一代GRACE重力卫星反演地球重力场的预期精度

基于低低卫卫跟踪模式,本文主要探讨利用动力学法融合精密轨道数据和星间测距或距离变率数据求解地球重力场的基本原理与方法,该方法既可对两颗低低跟踪卫星的初始状态误差进行有效校正,也可充分利用低轨卫星轨道所包含的低频重力场信息.为探讨适合我国国情的低低跟踪模式下的重力卫星指标,本文以不同星载设备精度指标的组合进行模拟计算,模拟结果显示:(1)把GRACE卫星的星间距离变率指标提高一个量级,其余指标保持与GRACE卫星设计指标一致时,可使地球重力场的精度获得同量级的提高;(2)若星间距离变率为1.0×10-8 m·s-1,轨道高度为300 km,加速度计精度为3.0×10-10 m·s-2,轨道精度为0.03 m, 星间距离100 km,与利用GRACE的设计指标反演出的重力场精度相比,可提高约121倍,并建议我国未来低低跟踪重力卫星计划参考此指标.     

重复绝对重力测量观测的滇西地区和拉萨点的重力变化及其意义

根据近年来在滇西地区和西藏拉萨绝对重力点上的一些新的绝对重力重复观测结果 ,对1990年以来在这些点上绝对重力重复观测结果进行了分析. 滇西地区的5个绝对重力观测 点的近10年的重复观测结果表明,大部分观测时段没有出现与地球动力学事件有关的重力变 化,只有丽江和洱源2个绝对重力观测点的观测结果显示丽江地震前后有变化. 为了研究该 重力变化的原因,本文正演模拟了出现重力变化期间丽江地震同震位错引起的重力变化,模 拟结果与实际观测结果有较好的一致性. 西藏拉萨近10年以来的重复观测结果给出了拉萨点 的绝对重力值以-1.82±0.9×10-8m·s-2·a-1速率下降,这从重力学 的角度反映出青藏高原的隆升. 对拉萨点的重力变化机制进行了探讨,根据印度板块与欧亚 大陆俯冲模型计算的拉萨点重力变化速率与观测到的重力变化速率较一致,表明现今拉萨地 区重力变化是由于印度板块与欧亚大陆俯冲所引起. 根据印度板块向欧亚大陆俯冲的位错模 型计算的拉萨点的重力变化与地表垂直位移的关系,将重力变化转换为拉萨点的隆升速率为 8.7mm/a.      

新一代GRACE重力卫星反演地球重力场的预期精度

基于低低卫卫跟踪模式,本文主要探讨利用动力学法融合精密轨道数据和星间测距或距离变率数据求解地球重力场的基本原理与方法,该方法既可对两颗低低跟踪卫星的初始状态误差进行有效校正,也可充分利用低轨卫星轨道所包含的低频重力场信息.为探讨适合我国国情的低低跟踪模式下的重力卫星指标,本文以不同星载设备精度指标的组合进行模拟计算,模拟结果显示:(1)把GRACE卫星的星间距离变率指标提高一个量级,其余指标保持与GRACE卫星设计指标一致时,可使地球重力场的精度获得同量级的提高;(2)若星间距离变率为1.0×10^-8 m·s^-1,轨道高度为300 km,加速度计精度为3.0×10^-10 m·s^-2,轨道精度为0.03 m, 星间距离100 km,与利用GRACE的设计指标反演出的重力场精度相比,可提高约121倍,并建议我国未来低低跟踪重力卫星计划参考此指标.     

An efficient and adaptive approach for modeling gravity effects in spherical coordinates

The need to obtain more reliable Earth structures has been the impetus for conducting joint inversions of disparate geophysical datasets. For seismic arrival time tomography, joint inversion of arrival time and gravity data has become an important way to investigate velocity structure of the crust and upper mantle. However, the absence of an efficient approach for modeling gravity effects in spherical coordinates limits the joint tomographic analysis to only local scales. In order to extend the joint tomographic inversion into spherical coordinates, and enable it to be feasible for regional studies, we develop an efficient and adaptive approach for modeling gravity effects in spherical coordinates based on the longitudinal/latitudinal grid spacing. The complete gravity effects of spherical prisms, including gravitational potential, gravity vector and tensor gradients, are calculated by numerical integration of the Gauss–Legendre quadrature (GLQ). To ensure the efficiency of the gravity modeling, spherical prisms are recursively subdivided into smaller units according to their distances to the observation point. This approach is compatible with the parameterization of regional arrival time tomography for large areas, in which both the near- and far-field effects of the Earth's curvature cannot be ignored. Therefore, this approach can be implemented into the joint tomographic inversion of arrival time and gravity data conveniently. As practical applications, the complete gravity effects of a single anomalous density body have been calculated, and the gravity anomalies of two tomographic models in the Taiwan region have also been obtained using empirical relationships between P-wave velocity and density.     

基于重力卫星数据监测地表质量变化的三维点质量模型法

利用卫星重力测量手段监测全球质量变化取得了巨大成功,本文基于牛顿万有引力定律在三维空间直角坐标系中导出利用重力卫星观测数据监测全球质量变化的三维点质量模型法,该方法可直接利用重力卫星的轨道和星间观测数据或时变重力场模型计算全球质量变化,由于利用卫星观测数据计算地表质量变化的向下延拓过程以及观测数据噪声的影响,需要采用合适的空间约束方程或正则化技术对解算结果进行约束或平滑处理.利用合成全球质量变化模型模拟一个月的GRACE双星轨道和星间距离变率数据计算全球质量变化,对三维点质量模型法进行分析验证,采用零阶Tikhonov正则化技术处理病态问题.结果表明,三维点质量模型法可有效用于重力卫星观测数据监测全球质量变化,为利用重力卫星观测数据监测全球质量变化提供一种可选的途径.

     

On the effect of a low viscosity asthenosphere on the temporal change of the geoid—A challenge for future gravity missions

New satellite technology to measure changes in the Earth’s gravity field gives new possibilities to detect layers of low viscosity inside the Earth. We used density models for the Earth mantle based on slab history as well as on tomography and fitted the viscosity by comparison of predicted gravity to the new CHAMP gravity model. We first confirm that the fit to the observed geoid is insensitive to the presence of a low viscosity anomaly in the upper mantle as long as the layer is thin ( 200 km) and the viscosity reduction is less than two orders of magnitude. Then we investigated the temporal change in geoid by comparing two stages of slablet sinking based on subduction history or by advection of tomography derived densities and compared the spectra of the geoid change for cases with and without a low viscosity layer, but about equal fit to the observed geoid. The presence of a low viscosity layer causes relaxation at smaller wavelength and thus leads to a spectrum with relatively stronger power in higher modes and a peak around degrees 5 and 6. Comparing the spectra to the expected degree resolution for GRACE data for a 5 years mission duration shows a weak possibility to detect changes in the Earth’s gravity field due to large scale mantle circulation, provided that other causes of geoid changes can be taken into account with sufficient accuracy. A discrimination between the two viscosity cases, however, demands a new generation of gravity field observing satellites.     

2010玉树M_S7.1地震前后青藏高原东缘绝对重力变化

2010年4月14日青海省玉树发生MS7.1地震后,中国地震局及时组织实施了地震科学考察,其中对玉树、西宁、姑咱和西昌等4个绝对重力点进行复测,通过比对前期成果,分别给出了2007年以来(地震前后)3～4期各测点H=1.0m(距墩面高)和H=0.0m(墩面)处的绝对重力变化(观测精度均优于3.0×10-8 m.s-2).结合已有区域地质构造运动、地震活动机制、形变测量成果等,主要结论或认识有:1)地震前后(含同震)玉树、姑咱、西昌绝对重力变化明显呈上升变化,玉树点和姑咱点尤为突出;2)同震模拟结果表明,地震前后玉树点绝对重力变化(H=1.0m)与同震破裂效应基本相当;3)从重力变化角度检核了玉树地震左旋破裂运动对羌塘块体东流运动和川滇菱形块体的南东-南南东运动具有明显激励作用,川滇菱形块体北段尤为强烈,南段可能因南南东向运动遇到中部贡嘎山隆起的阻挡吸收而有所减弱.     

Temporal variations of rotational origin in the absolute value of gravity

Summary When correcting precise gravity measurements for polar motion, the Earth's rotational deformation must be considered, as this will increase the correction based on a rigid Earth by about 15%. Conversely the gravity observations can be used to estimate the Love numbers h₂ and k₂ at the Chandler frequency.     

Error propagation in absolute geodetic networks a continuous approach

Summary Studies of error propagation in geodetic networks of an absolute type have already been carried through by several authors using various mathematical techniques. The geodetic elasticity theory relies on a continuation of the actual, discrete network. The traditional observation and normal equation matrices are substituted by partial differential equations with corresponding boundary conditions. The continuous approach only reflects the global error behaviour opposed to the discrete case, and produces only asymptotic results. An advantage of the method is that we may directly profit from existing mathematical knowledge. The fundamental solution of the partial differential equations acts as a formal covariance function and yields the best linear unbiased estimates for estimable functions of the adjustment parameters. Levelling networks and networks with distance and azimuth measurements are studied in this framework.Invited paper presented at the International Symposium on Optimisation of Design and Computation of Control Networks, Sopron, July 4–8, 1977.     

利用运动学轨道提高GRACE时变重力场解算

基于变分方程法,本文利用GARCE高精度K波段星间测速数据KBRR,结合德国格拉茨大学发布的运动学轨道和GFZ发布的简动力学轨道作为两种伪观测值,分别解算了2005-2010年60阶全球时变重力场模型Hust-IGG01与Hust-IGG02.通过与GRACE官方机构发布的模型和其他国际主流权威模型进行对比,发现基于运动学轨道结合KBRR解算的模型Hust-IGG01优于基于简动力学轨道结合KBRR解算的模型Hust-IGG02：在重力场系数C₂₀时间序列的统计数据上,Hust-IGG01比Hust-IGG02更接近SLR结果,在如C₆₀、C₇₀、C₈₀以及C₉₀等重力场低阶项上的数学统计均更接近CSR RL05;Hust-IGG01的重力场系数误差分布和GFZ RL05在同一水平,而Hust-IGG02的误差估计过于乐观;Hust-IGG02在主要质量变化区域上存在5%~10%信号低估,而Hust-IGG01能完全达到国际主流机构利用GPS观测数据的解算水平,Hust-IGG01与官方机构CSR、JPL和GFZ最新模型在格陵兰岛的冰川消融年际趋势分别是-125.4、-125.4、-127.3、-124.3 Gt·a^-1,在亚马逊流域的平均等效水高周年振幅分别是17.56、17.40、17.46、17.22 cm,在撒哈拉沙漠的平均等效水高均方差分别是0.87、0.77、1.10、0.87 cm;另外在Hust-IGG01的实际应用上,本文分析了全球32个主要流域质量变化的年际趋势、周年振幅和半周年振幅三种信号模式,统计结果显示Hust-IGG01与CSR RL05结果基本吻合.

     

Some results on the approach of a slowly-varyng gravity wave to a beach

Abstract

Results from the theory of slowly-varying solutions of the non-linear shallow water equations (Varley et al. (1971)) are used to estimate maximum wave height amplifications on a beach of arbitrary shape. Carrier's solution (1966) for a large disturbance out at sea is used as input. Generalizations of the slowly-varying results to non-plane situations are also presented.     

利用FG5绝对重力仪观测数据确定重力垂直梯度

本文建立了利用FG5实测数据求解重力垂直梯度的数据处理模型与算法.通过对多次自由落体实验的下落距离拟合残差叠加求均值,发现下落距离观测量中存在明显的有色噪声.通过对有色噪声的建模,并以剩余残差为依据选取可靠的下落时段,解算测站点的重力垂直梯度.利用本文所提出的数据处理方法分别对FG5-214绝对重力仪在两个测站上的观测数据进行处理,以相对重力仪测量的重力垂直梯度结果为参考值,本文处理得到的重力垂直梯度结果相比于未考虑有色噪声并依据经验选取下落时段的解算方法得到了显著改善.

     

利用小波分析重力的长期变化

运用小波滤波方法估算Chandler和周年项的潮汐因子.本文分析了四个台站(Brussels, Boulder, Membach以及Strasbourg)的观测记录,运用合成潮方法得到重力残差后,用Daubechies小波带通滤波器滤波残差,得到256～512 d时间尺度上的序列,根据标准差最小原则确定观测极潮周年和Chandler项的周期,然后利用最小二乘法估算它们的潮汐因子,同时给出未经模型改正的周年重力.由于高阶Daubechies小波构造的滤波器具有良好的频率响应,且能压制信号中的高阶异常成分,使滤波的信号更加光滑,因此计算结果具有更小的均方差,更加可靠.     

Spatial and temporal variation of gravity field in the capital region

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A coupled hierarchical modeling approach to simulating the geomorphic response of river systems to anthropogenic climate change

Anthropogenic climate change is expected to change the discharge and sediment transport regime of river systems. Because rivers adjust their channels to accommodate their typical inputs of water and sediment, changes in these variables can potentially alter river morphology. In this study, a hierarchical modeling approach was developed and applied to examine potential changes in reach‐averaged bedload transport and spatial patterns of erosion and deposition for three snowmelt‐dominated gravel‐bed rivers in the interior Pacific Northwest. The modeling hierarchy was based on discharge and suspended‐sediment load from a basin‐scale hydrologic model driven by a range of downscaled climate‐change scenarios. In the field, channel morphology and sediment grain‐size data for all three rivers were collected. Changes in reach‐averaged bedload transport were estimated using the Bedload Assessment of Gravel‐bedded Streams (BAGS) software, and the Cellular Automaton Evolutionary Slope and River (CAESAR) model was used to simulate the spatial pattern of erosion and deposition within each reach to infer potential changes in channel geometry and planform. The duration of critical discharge was found to control bedload transport. Changes in channel geometry were simulated for the two higher‐energy river reaches, but no significant morphological changes were found for a lower‐energy reach with steep, cohesive banks. Changes in sediment transport and river morphology resulting from climate change could affect the management of river systems for human and ecological uses. Copyright © 2015 John Wiley & Sons, Ltd.     

On selecting the excess density in gravity modeling of inhomogeneous media

In this paper, a relatively simple and physically solid algorithm is developed for solving the problem of reference density selection for the models of heterogeneous media. The way is suggested for determining the excess density of the individual elements of the structured model against the background varying density of the hosting rocks: in the calculations, the latter should be replaced by the hydrostatic density of the normal model, which only depends on depths. It is shown that the excess density of the elements within the inhomogeneous layer, referred to the depth-varying hydrostatic density of the normal model, has a significantly lower value throughout the entire depth of the studied domain and minimizes the gravitational effect of density contact along a curvilinear boundary. The efficiency of the algorithm is demonstrated by the model example and case study. Within the density model for the lithosphere of the Timan–Pechora plate, the structural layers corresponding to the sedimentary cover, crystalline crust, and upper mantle are isolated. For each of them, the fields are calculated within the gravitational model of a heterogeneous layer with curvilinear boundaries.     

华北时变重力场离散小波多尺度分解

利用华北地区地震重力监测网的绝对重力与相对重力多期重复观测资料,处理获取不同时空尺度的华北区域重力场动态变化图像.利用二维小波分解技术,将不同场源深度异常进行了分离,并对不同时空尺度的重力变化给出了解释,提高了对华北地区重力场变化趋势的认识水平.在此基础上,通过对小波细节的功率谱分析,可以获得各阶小波变换逼近及小波细节分析图所对应的场源深度.研究结果表明,不同时空尺度的重力场变化对于深入认识华北地区潜在地震危险性具有一定的科学意义.