Seismologic applications of GRACE time-variable gravity measurements

The Gravity Recovery and Climate Experiment (GRACE) has been measuring temporal and spatial variations of mass redistribution within the Earth system since 2002. As large earthquakes cause significant mass changes on and under the Earth’s surface, GRACE provides a new means from space to observe mass redistribution due to earthquake deformations. GRACE serves as a good complement to other earthquake measurements because of its extensive spatial coverage and being free from terrestrial restriction. During its over 10 years mission, GRACE has successfully detected seismic gravitational changes of several giant earthquakes, which include the 2004 Sumatra–Andaman earthquake, 2010 Maule (Chile) earthquake, and 2011 Tohoku-Oki (Japan) earthquake. In this review, we describe by examples how to process GRACE time-variable gravity data to retrieve seismic signals, and summarize the results of recent studies that apply GRACE observations to detect co- and post-seismic signals and constrain fault slip models and viscous lithospheric structures. We also discuss major problems and give an outlook in this field of GRACE application.     

Volume and mass changes of the Greenland ice sheet inferred from ICESat and GRACE

This study examines the recent evolution of the Greenland ice sheet and its six major drainage basins. Based on laser altimetry data acquired by the Ice, Cloud and Land Elevation Satellite (ICESat), covering the period September–November 2003 to February–March 2008, ice surface height changes and their temporal variations were inferred. Our refined repeat track analysis is solely based on ICESat data and is independent of external elevation models, since it accounts for both ice height changes and the local topography. From the high resolution ice height change pattern we infer an overall mean surface height trend of −0.12 ± 0.006 m yr⁻¹. Furthermore, the largest changes could be identified at coastal margins of the ice sheet, exhibiting rates of more than −2 m yr⁻¹. The total ice volume change of the entire ice sheet amounts to −205.4 ± 10.6 km³ yr⁻¹. In addition, we assessed mass changes from 78 monthly Gravity Recovery and Climate Experiment (GRACE) solutions. The Release-04 gravity field solutions of GeoForschungsZentrum Potsdam cover the period between August 2002 and June 2009. We applied an adjusted regional integration approach in order to minimize the leakage effects. Attention was paid to an optimized filtering which reduces error effects from different sources. The overall error assessment accounts for GRACE errors as well as for errors due to imperfect model reductions. In particular, errors caused by uncertainties in the glacial isostatic adjustment models could be identified as the largest source of errors. Finally, we determined both seasonal and long-term mass change rates. The latter amounts to an overall ice mass change of −191.2 ± 20.9 Gt yr⁻¹ corresponding to 0.53 ± 0.06 mm yr⁻¹ equivalent eustatic sea level rise. From the combination of the volume and mass change estimates we determined a mean density of the lost mass to be 930 ± 11 kg m⁻³. This value supports our applied density assumption 900 ± 30 kg m⁻³ which was used to perform the volume–mass-conversion of our ICESat results. Hence, mass change estimates from two independent observation techniques were inferred and are generally in good agreement.     

利用GRACE时变重力场反演青藏高原的隆升速率

青藏高原隆升对中国、亚洲乃至世界的气候都有着重要影响,研究青藏高原地壳隆升速率具有重大意义.本文利用2004—2015年期间高覆盖度的卫星重力数据,通过去除陆地储水的重力效应获得地壳隆升引起的重力变化速率,基于直立长方体垂直运动与重力变化的关系模型反演了该区域的地壳隆升速率分布.研究结果表明在300 km的空间尺度下青藏高原隆升速率分布具有不均匀的特点,表现为以冈底斯山—唐古拉山—鲜水河断裂带为界线,其两侧的速率差异较大.位于界线以南,沿喜马拉雅推覆构造带的区域平均隆升速率为2.01±0.87 mm·a^-1,其中西侧的印度板块与东侧的缅甸板块隆升速率分别为~2.43 mm·a^-1、~2.89 mm·a^-1,位于两板块之间的区域隆升速率为~0.69 mm·a^-1;位于界线以北,除了天山区域和华北板块的隆升速率为~1 mm·a^-1,其他区域隆升现象不明显,其速率为~0 mm·a^-1.我们发现存在两条均穿过正断裂带区域的隆升速率梯度带,其中一条为从加德满都到塔里木盆地,其恰好穿过青藏高原内部的正断裂带,另一条为从那加山到四川盆地,其恰好穿过大理正断裂带.本文反演的青藏高原隆升速率与以往观测到的GPS结果有很好的一致性,为青藏高原隆升、地壳增厚等科学问题提供理论支持.

     

利用GRACE时变重力场反演青藏高原的隆升速率

青藏高原隆升对中国、亚洲乃至世界的气候都有着重要影响,研究青藏高原地壳隆升速率具有重大意义.本文利用2004—2015年期间高覆盖度的卫星重力数据,通过去除陆地储水的重力效应获得地壳隆升引起的重力变化速率,基于直立长方体垂直运动与重力变化的关系模型反演了该区域的地壳隆升速率分布.研究结果表明在300 km的空间尺度下青藏高原隆升速率分布具有不均匀的特点,表现为以冈底斯山—唐古拉山—鲜水河断裂带为界线,其两侧的速率差异较大.位于界线以南,沿喜马拉雅推覆构造带的区域平均隆升速率为2.01±0.87 mm·a^-1,其中西侧的印度板块与东侧的缅甸板块隆升速率分别为~2.43 mm·a^-1、~2.89 mm·a^-1,位于两板块之间的区域隆升速率为~0.69 mm·a^-1;位于界线以北,除了天山区域和华北板块的隆升速率为~1 mm·a^-1,其他区域隆升现象不明显,其速率为~0 mm·a^-1.我们发现存在两条均穿过正断裂带区域的隆升速率梯度带,其中一条为从加德满都到塔里木盆地,其恰好穿过青藏高原内部的正断裂带,另一条为从那加山到四川盆地,其恰好穿过大理正断裂带.本文反演的青藏高原隆升速率与以往观测到的GPS结果有很好的一致性,为青藏高原隆升、地壳增厚等科学问题提供理论支持.     

GRACE和地面重力测量监测到的中国大陆长期重力变化

自2002年以来,GRACE卫星探测计划可提供高精度的时变地球重力场,用以探测地球系统的物质分布.自1998年中国大陆重力监测网建立以来,利用FG5绝对重力仪和LCR-G型相对重力仪每2年对该网进行重复测量获取重力场时变信息.基于此,本文利用GRACE和地面重力测量获得了中国大陆重力场的长期年变率,利用位错理论根据USGS发布的断层模型计算了2008年汶川Ms8.0级地震的同震重力变化并进行了300 km高斯滤波.GRACE卫星重力和地面重力结果均表明华北地区地下水流失严重,在绝对重力基准站上,GRACE卫星重力与绝对重力变化率较为一致,汶川区域的地面重力变化结果可视为大地震前兆信息.     

基于GRACE资料研究南极冰盖消减对海平面的影响

利用5年的GRACE重力数据,计算了南极1°×1°等效水量时间序列,得到每个格网的趋势项,结果表明在西南极Amundsen区域有明显的负增长,超过-80 mm/a,南极半岛存在着负增长,东南极Enderby Land地区质量增长;计算得到2002年7月到2007年9月南极、东南极和西南极冰盖的等效体积变化分别为-78±37 km3/a,-3±46 km3/a和-75±50 km3/a,对应海平面变化的贡献为0.21±0.1 mm/a,0.008±0.127 mm/a和0.2±0.14 mm/a.该结果与国际最新研究结果一致.同时发现冰后回弹是影响利用GRACE研究南极冰盖质量变化的关键因素.     

顾及非线性改正的动力学方法反演GRACE时变重力场模型

本文利用解的叠加原理求解了轨道扰动微分方程组,构建了扰动位系数与轨道和星间距变率的观测方程,并分别引入非线性改正项.通过惯性坐标系与运动坐标系的转换求解状态转移方程组,分析了观测方程的低频误差特征,导出了目前常用的消除剩余星间距变率低频误差的五参数或七参数经验公式.此外,根据非惯性力模型误差是分段标定的特点,提出利用三次样条函数来处理低频误差,通过模拟计算表明三次样条函数处理低频误差略优于七参数.最后,处理实际的GRAEC Level-1b数据,解算了2006年1月至2009年12月期间的月时变重力场模型UCAS_Grace01,通过在不同区域进行比较可以得出本文计算的时变重力场模型与国际官方机构精度基本是一致的结论.

     

基于GRACE时变重力场的三峡水库补给水系水储量变化

利用22个月的GRACE时变重力场,反演了三峡水库补给水系的水储量变化,并按月给出了数值结果.与水文学同化模型（CPC）的两组比较说明基于GRACE重力的反演结果是合理的.当高斯平均半径为1000 km时,该区总水储量变化的峰谷差为14 cm,其年变化振幅为5.8 cm,相位为-40.8天,与CPC模型合成重力数据的反演结果进行比较,其总水储量变化均方差为1.3 cm,年变化振幅相差0.1 cm,相位相差1.0天.为进一步检验GRACE能否监测该区真实水储量变化,还将其反演结果与CPC模型的真实平均结果进行比较,结果发现总体均方差为2.1 cm,年变化振幅相差1.7 cm,相位相差9.3天.因此,第一种比较过高地估计了GRACE监测该区水储量变化的能力,第二种比较则较真实地反映了实际情况,尽管反演结果与水文学的结果差别较大,但仍然显示GRACE能监测该区每月的水储量变化.     

联合星载GPS和KBRR星间测速数据反演GRACE时变重力场模型

高精度GRACE卫星时变重力场反演一直是卫星重力测量中的难题.为了恢复高精度的时变地球重力场模型,本文联合GRACE卫星的星载GPS和KBR星间测速观测数据,在对GRACE卫星进行精密定轨的同时,解算出60阶月平均地球重力场模型.通过对GRACE卫星的定轨精度、星载GPS相位和KBR星间测速数据的拟合残差以及时变地球重力场模型解算精度等分析,表明:(1)与美国宇航局喷气推进实验室(JPL)发布的约化动力学精密轨道相比,本文确定GRACE卫星轨道三维位置误差小于5 cm.(2)星载GPS相位数据拟合残差为5~8 mm,KBR星间测速数据拟合残差为0.18~0.30μm·s~(-1).(3)解算的月平均重力场模型与美国德克萨斯大学空间研究中心(CSR)、德国地学研究中心(GFZ)和JPL发布的RL05模型精度接近,时变信号在全球范围内具有很好的空间分布一致性.通过计算亚马逊流域和长江流域的水储量变化,本文与上述三个机构的计算结果无明显差异,且相关系数均达0.9以上.可见,本文建立的卫星轨道与重力场同解算法具有反演高精度GRACE时变重力场能力,为我国卫星重力场反演提供了重要的技术支持.     

Using ground gravity to improve ice mass change estimation from GOCE gravity gradients in mid-west Greenland

Vertical gravity gradient anomalies from the Gravity and steady-state Ocean Circulation Explorer (GOCE) DIR-3 model have been used to determine gravity anomalies in mid-west Greenland by using Least-Squares Collocation (LSC) and the Reduced Point Mass (RPM) method. The two methods give nearly identical results. However, compared to LSC, the RPM method needs less computational time as the number of equations to be solved in LSC equals the number of observations. The advantage of the LSC, however, is the acquired error estimates. The observation periods are winter 2009 and summer 2012. In order to enhance the accuracy of the calculated gravity anomalies, ground gravity data from West Greenland is used over locations where the gravity change resulting from ice mass changes is negligible, i.e. over solid rock. In the period considered, the gravity anomaly change due to changes in ice mass varies from ?5 mGal to 4 mGal. It is negative over the outlet glacier Jacobshavn Isbræ, where the mass loss corresponds to a gravity change of approximately ?4 mGal. When using only GOCE vertical gravity gradients, the error estimates range from 5 mGal at the coast to 17 mGal over the ice sheet. Introducing the ground gravity data from West Greenland in the prediction reduces the errors to range from 2 to 10 mGal.     

利用ICESat数据解算南极冰盖冰雪质量变化

南极冰盖冰雪质量变化反映了全球气候变化,并且直接影响着全球海平面变化.ICESat测高卫星的主要任务之一就是要确定南北两极冰盖的质量变化情况并评估其对全球海平面变化的影响.本文利用2003年10月至2008年12月的ICESat测高数据,针对南极DEM分辨率有限的特殊性,通过求解坡度改正值,解决重复轨道地面脚点不重合的问题,计算了南极大陆(86°S以北区域,后文所述南极冰盖均不包括86°S以南区域)在这5年里的冰雪质量变化情况,得到东南极冰盖的质量变化为-18±20 Gt/a,西南极-26±6 Gt/a,南极冰盖的冰雪质量变化为-44±21 Gt/a,对全球海平面上升的影响约为0.12 mm·a-1.解算结果表明,南极冰盖质量亏损主要集中在西南极阿蒙森海岸附近冰川以及东南极波因塞特角区域.     

基于GRACE KBRR数据的动力积分法反演时变重力场模型

基于动力积分法恢复了一组60阶的时变重力场模型WHU-Grace01s,且在位系数解算过程中仅使用KBRR数据.通过与CSR、GFZ和JPL发布的Release 05模型的阶方差和位系数误差谱对比可知,WHU-Grace01s模型在高阶次部分的阶方差较小,且对轨道共振现象不敏感.将WHU-Grace01s时变重力场模型与CSR、GFZ、JPL、DEOS、Tongji、ITG、AIUB和GRGS等8家机构发布模型通过相同的滤波处理,获得了全球地表质量变化的时空分布,从结果可以看出:各个模型计算的时变信号在空域上分布十分接近,且WHU-Grace01s模型计算的太平洋中心和撒哈拉沙漠区域的质量变化较小;对比几个典型质量变化区域,WHU-Grace01s模型和JPL模型计算的长江流域和珠江流域时变信号呈强相关,其相关系数分别为0.948和0.976,且与上述8个模型计算的两个流域时变信号的相关系数均达到0.9以上;在南极区域和格陵兰岛,WHU-Grace01s模型和其他各个模型均能反映区域冰川质量的积累或消融,且各模型计算获得的长期趋势变化结果相当.研究结果表明,WHU-Grace01s模型和国内外已发布机构模型具有很好的一致性,且受到轨道共振影响较小.     

Late Weichselian relative sea-level changes and ice sheet history in southeast Greenland

Relative sea-level (RSL) observations from the margins of the Greenland Ice Sheet (GIS) provide information regarding the timing and rate of deglaciation and constraints on geophysical models of ice sheet evolution. In this paper we present the first RSL record for the southeast sector of the GIS based on field observations completed close to Ammassalik. The local marine limit is c. 69 m above sea-level (asl) and is dated to c. 11 k cal. yrs BP (thousand calibrated years before present) and is a minimum date for ice free conditions at the study site. RSL fell to c. 24 m asl by 9.5 k cal. yrs BP and continued to fall at a decreasing rate to reach close to present by 6.5 k cal. yrs BP. Our chronology agrees with radiocarbon dates from offshore cores that indicate ice free conditions on the adjacent mid-shelf by 15 k cal. yrs BP. We compare the new RSL data with predictions generated using two recently published glaciological models of the GIS that differ in the amount and timing of ice loading and unloading over our study area. These two GIS models are coupled to the same Earth viscosity model and background (global) ice model to aid in the data-model comparison. Neither model provides a close fit to the RSL observations. Based on a preliminary sensitivity study using a suite of Earth viscosity models, we conclude that the poor data-model fit is most likely due to an underestimate of the local ice unloading. An improved fit could be achieved by delaying the retreat of a thicker ice sheet across the continental shelf. A thick ice sheet extending well onto the continental shelf is in agreement with other recent observations elsewhere in east and south Greenland.     

基于GRACE RL06数据监测和分析南极冰盖27个流域质量变化

本文基于CSR最新公布的GRACE RL06版本数据,采用Slepian空域反演法估算了南极冰盖27个流域的质量变化.Slepian空域反演法结合了Slepian空间谱集中法和空域反演法的技术优势,能够有效降低GRACE在小区域反演时信号出现的严重泄漏和衰减,进而精确获得南极冰盖在每个流域的质量变化.相对于GRACE RL05版本数据,RL06在条带误差的控制上要更加优化,获得的南极冰盖质量变化时间序列也更加平滑,但在趋势估算上差别并不明显（小于10 Gt/a）.本文的估算结果显示：在2002年4月至2016年8月期间,整个南极冰盖质量变化速率为-118.6±16.3 Gt/a,其中西南极为-142.4±10.5 Gt/a,南极半岛为-29.2±2.1 Gt/a,东南极则为52.9±8.6 Gt/a.南极冰盖损失最大的区域集中在西南极Amundsen Sea Embayment（流域20-23）,该地区质量变化速率为-203.5±4.1 Gt/a,其次为南极半岛（流域24-27）以及东南极Victoria-Wilkes Land（流域13-15）,质量变化速率分别为-29.2±2.1 Gt/a和-19.0±4.7 Gt/a,其中Amundsen Sea Embayment和南极半岛南部两个地区的冰排放呈现加速状态.南极冰盖质量显著增加的区域主要有西南极的Ellsworth Land（流域1）和Siple Coast（流域18和19）以及东南极的Coats-Queen Maud-Enderby Land（流域3-8）,三个地区质量变化速率分别为17.2±2.4 Gt/a、43.9±1.9 Gt/a和62.7±3.8 Gt/a,质量增加大多来自降雪累积,比如：Coats-Queen Maud-Enderby Land在2009年和2011年发生的大规模降雪事件,但也有来自冰川的增厚,如：Siple Coast地区Kamb冰流的持续加厚.此外,对GRACE估算的南极冰盖质量变化年际信号进行初步分析发现,GRACE年际信号与气候模型估算的冰盖表面质量平衡年际信号存在显著的线性相关关系,但与主要影响南极气候年际变化的气候事件之间却不存在线性相关关系,这说明南极冰盖质量变化的年际信号主要受冰盖表面质量平衡的支配,而气候事件对冰盖表面质量平衡的影响可能是复杂的非线性耦合过程.

     

冰盖消融的海平面指纹变化及其对GRACE监测结果的影响

全球变暖背景下的冰盖消融以及由此带来海平面上升日益明显,直接影响地球表面的陆地水质量平衡,以及固体地球瞬间弹性响应,研究冰盖质量变化的海平面指纹能够帮助深入了解未来海平面区域变化的驱动因素.本文基于海平面变化方程并考虑负荷自吸效应（SAL）与地球极移反馈的影响,借助美国德克萨斯大学空间研究中心（Center for Space Research,CSR）发布的2003年到2012年十年期间的GRACE重力场月模型数据（RL05）,结合加权高斯平滑的区域核函数,反演得到格陵兰与南极地区冰盖质量变化的时空分布,并利用海平面变化方程计算得到了相对海平面的空间变化,结果表明：格陵兰与南极冰盖质量整体呈明显的消融趋势,变化速率分别为-273.31 Gt/a及-155.56 Gt/a,由此导致整个北极圈相对海平面降低,最高可达约-0.6 cm·a^-1;而南极地区冰盖质量变化趋势分布不一,导致西南极近海相对海平面下降,而东南极地区近海相对海平面上升,最高可达约0.2 cm·a^-1.远离质量负荷区域的全球海平面以上升趋势为主,平均全球相对海平面上升0.71 mm·a^-1,部分远海地区相对海平面上升更加突出（例如北美与澳大利亚）,高出全球平均海平面上升速率将近30%.此外,本文也重点探讨了GRACE监测冰盖消融结果中由于极地近海海平面变化导致的泄漏影响,经此项影响校正后的结果表明：海平面指纹效应对GRACE监测格陵兰与南极地区2003-2012期间整体冰盖消融速率的贡献分别为约3%与9%,建议在后期利用GRACE更精确地估算研究区冰盖质量变化时,应考虑海平面指纹效应的渗透影响.

     

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust. These gravity data have many applications, such as surface deformation, groundwater storage changes, and mass migration before and after earthquakes. Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region (SYR) from 2015 to 2017, we determine a time series of degree 120 gravity fields using the localized spherical harmonic (Slepian) basis functions. Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR. The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features. The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.     

利用GRACE重力和重力梯度变化估计2012年苏门答腊地震断层参数

2012年4月11日苏门答腊北部附近海域发生M_W=8.6地震,国际上采用不同数据获得了该地震的断层滑动模型,但断层走滑性质存在较大差异.卫星重力GRACE（Gravity Recovery and Climate Experiment）观测覆盖震中区域,可以提供很好的断层参数估计约束.本文采用GRACE月重力场模型数据提取了此次地震同震重力和重力梯度变化,表明了北向分量的优越性.并与断层模型理论计算结果进行了比较,分析了T_xx（北-北向重力梯度）分量对断层参数的敏感性,以及基于粒子群算法以及Okubo位错模型反演了该地震断层参数.结果表明GRACE观测到的同震重力梯度变化在空间形态分布上与断层模型模拟结果符合较好,但振幅差异较大.重力和重力梯度的北向分量可以很好地压制条带误差,其中g_N（北向重力变化）和T_xx的误差最小,其次是T_xz（北-上向重力梯度）,误差最大和对条带误差抑制效果最差的是T_xy（北-东向重力梯度）.T_xx对断层的深度不敏感,对其余断层参数较敏感.基于GRACE反演得到的断层的走向角为113.63°,倾角为89.99°,滑移角为175.26°,平均滑移量为28.18 m,相应的矩震为8.71级,且此次地震的走滑性质为右旋走滑.

     

用GRACE卫星跟踪数据反演地球重力场

利用141天GRACE卫星观测资料,包括K波段、星载加速度和卫星轨道数据,反演了80阶地球重力场模型IGGGRACE01S,该模型在半波长为500km的空间分辨率上,确定大地水准面的精度约为0012m,中长波(<80阶)精度优于重力卫星发射以前研制的重力场模型. 与EIGEN_GRACE02S、EIGEN_CHAMP03S和EGM96模型的位系数相比,该模型系数最接近于EIGEN_GRACE02S,与另两个模型差异较大. 比较几种模型确定的全球重力异常和大地水准面起伏,结果发现IGGGRACE01S与EIGEN_GRACE02S模型的计算结果比较接近,与EGM96模型结果差异较大,差别较大地区主要在南极等地区. 对于中国大陆,比较IGGGRACE01S模型（前72阶）计算的重力异常和NIMA重力异常数据（25°×25°网格）,两者之间的标准偏差为48mGal.     

On the computation of mass-change trends from GRACE gravity field time-series

Time-variable GRACE (Gravity Recovery and Climate Experiment) gravity field solutions are routinely exploited to derive secular and seasonal mass changes on and near the Earth's surface. However, the quantification of mass redistribution from space gravimetry is not a straightforward process. For instance, published linear deglaciation rates of the Greenland ice sheets vary from ≈100 Gt/yr to ≈300 Gt/yr; the discrepancies are subject to applied methodologies, the considered gravity field time-series and the period of investigation. Furthermore, in the recent past discussion has come to the fore whether the temporal behavior of mass variation might be better represented by a second-order polynomial rather than a linear regression model. In summary, the degrees of freedom inherent to GRACE analysis make the detection of mass trends to become a delicate topic. This contribution sensitizes for a more careful review of trends derived from GRACE mass-variation time-series. We point to possible misinterpretation and propose “rules” that improve the consistency of results.     

联合GRACE、Swarm、GRACE-FO卫星观测确定格陵兰岛冰盖质量时空变化特征

GRACE(Gravity Recovery and Climate Experiment)重力卫星任务的成功实施,极大推进了极地冰盖质量平衡、全球水循环和海水质量变化等领域的研究,其后续任务GRACE-FO(Gravity Recovery and Climate Experiment Follow-On)于2018...