Hydro-gravimetry in West-Africa: First results from the Djougou (Benin) superconducting gravimeter

The increasing number of hydro-gravimetry studies proves the rising interest of the hydrology community toward this monitoring method. The accuracy of superconducting gravimeters (SG) potentially allows the retrieval of small water storage changes (WSC) down to a few millimeters of equivalent water thickness. However, the importance of corrections applied to SG data to achieve such a precision in gravity residuals should be recalled. The Djougou permanent gravity station presented in this paper and located in northern Benin, West-Africa, provides a good opportunity to review these considerations. This station is equipped since July 2010 with the superconducting gravimeter SG-060 aimed at deriving WSC at different time-scales, daily to inter-annual. In this area, WSC are (1) part of the control system for evapotranspiration (ET) process, a key variable of the West-African monsoon cycle and (2) the state variable for resource management, a critical issue in storage-poor hard rock basement contexts such as in northern Benin. The potential for deriving WSC from time-lapse gravity data partly depends on environmental features such as topography and the instrument shelter. Therefore, this issue is addressed first, with the background idea that such sensitivity analysis should be undertaken before setting up any new instrument. In Djougou, local topography is quite flat leading to a theoretical straightforward relationship between gravity changes and WSC, close to the standard Bouguer value. However, the shelter plays a significant masking role, which is the principal limitation to the retrieval of fast hydrological processes such as ET following a rain event. Several issues concerning classical gravity corrections are also addressed in the paper. These include gap-filling procedures during rain-events and drift estimates for short time series. Special attention is provided to atmospheric corrections, and different approaches are tested: a simple scalar admittance, a filtered scalar admittance, a frequency-dependent admittance and direct atmospheric loading calculations. It is shown that the physically based approach of direct loading calculations performs better in both residual minimization and ET retrieval. Moreover, non-local hydrological effects are investigated and account for about 20% of the gravity residuals. Finally, gravity residuals are briefly analyzed at two distinct time scales: rapid (up to a few days) and seasonal. At the rapid time-scale, it is shown that ET retrieval is hardly achievable given shelter size and state-of-the-art atmospheric corrections. Still, mean values retrieved from this study are in accordance with known values of potential ET and lateral flow. Direct comparison of gravity changes with hydrological data (neutron probe monitoring and water table levels) show some discrepancies, particularly for the hydrological year of 2011, for which all hydrological data show a deficit, but SG and FG5 data do not. This preliminary analysis both provides a basis and call for further hydro-gravity modeling, to comprehensively investigate the water-cycle at the Djougou station.     

大气重力格林函数的理论计算

重力测量中需要扣除大气的影响.大气负荷对重力测量的影响可以分为大气质量变化引起的直接效应和大气负荷引起的地球变形带来的间接效应,大气负荷对重力观测值的直接影响,相对于间接效应量级较大.本文从理论上研究了大气负荷对重力观测的直接影响,仿照Farrell定义的负荷格林函数,引入大气重力格林函数,用来表示大气压变化对于重力观测的直接引力影响.在前人的基础上,本文采用了更为精细的大气模型,考虑大气温度随高程的变化,用离散褶积的方法求得了大气重力格林函数的理论值.实际计算时还要考虑地表温度、台站高程、周围地形等因素的影响,本文讨论了这些因素对大气重力格林函数的影响.考虑地表温度、台站高程、地形改正等各种影响因素以及地球变形引起的间接效应后,对台站周围区域积分即可求得大气变化引起的理论重力信号.     

大气重力信号的理论计算及其检测

基于标准大气定律和大气圆柱体分布模型,本文引进了大气重力格林函数,用离散格积方法求得了大气对重力场观测的影响,对台站高程、周围地形和地表温度变化等因素的影响问题进行了讨论．结果说明台站近区气压变化是大气重力信号的主要贡献者,考虑大气质量负荷引起的弹性地球形变效应后,对距台站0．5°的区域积分获得的大气重力导纳值为-0．3603μGal／hPa,占全球大气变化引起的总信号的90％以上,这一理论模型结果与超导重力仪实测结果相吻合,并能较有效地用于消除重力观测中的气压干扰成分．     

Loading effects in Metsähovi from the atmosphere and the Baltic Sea

Loading by atmosphere and by the Baltic Sea cause gravity change at Metsähovi, located 15 km from the open sea. Gravity is changed by both the Newtonian attraction of the loading mass and by the crustal deformation. We have performed loading calculations using appropriate Green's function for both gravity and deformation, for both atmospheric and Baltic loading. The loading by atmosphere has been computed using a detailed surface pressure field from high resolution limited area model (HIRLAM) for north Europe up to 10° distances. Baltic Sea level is modelled using tide gauge records. Calculations show that 1 m of uniform layer of water corresponds to 31 nm s⁻² in gravity and −11 mm in height. Modelled loading is compared with observations of the superconducting gravimeter T020 for years 1994–2002. The combination of HIRLAM and a tide gauge record decreases RMS of gravity residuals by 14% compared to single admittance in air pressure corrections without sea level data. Regression of gravity residuals on the tide gauge record at Helsinki (at 30 km distance) gives a gravity effect of 26 nm s⁻² m⁻¹ for Baltic loading.The gravity station is co-located with a permanent GPS station. We have also associated the loading effects of the atmosphere and of the Baltic Sea with temporal height variations. The range of modelled vertical motion due to air pressure was 46 mm and that due to sea level 18 mm. The total range was 38 mm. The effects of the Baltic Sea and of the atmosphere partly cancel each other, since at longer periods the inverse barometer assumption is valid. Regression of the modelled height on local air pressure gives −0.37 mm hPa⁻¹, corresponding approximately to width 6° for pressure system.We have tested the models using one year of daily GPS data. Multilinear regression on local air pressure and sea level in Helsinki gives the coefficient −0.34 mm hPa⁻¹ for pressure, and −11 mm m⁻¹ for sea level. These match model values. Loading by air pressure and Baltic Sea explains nearly 40% of the variance of daily GPS height solutions.     

Clear evidence for the sign-reversal of the pressure admittance to gravity near 3 mHz

The influence of the atmosphere on gravity measurements by Newtonian attraction and vertical displacements due to surface loading is well known and studied especially at frequencies below 1 mHz. Less work has been done at the higher seismic frequencies where inertial effects come into play. The sensor mass of a vertical accelerometer responds to several forces caused by the atmosphere, on global, regional and local scales. For the seismic frequencies the atmosphere above the observation site has the largest influence. A simple “Gedankenexperiment” demonstrates that the gravitational effect on one hand and the free air and inertial effects due to deformation on the other have opposite sign. Since the inertial effect is strongly frequency-dependent there should be a crossover-frequency where the pressure admittance to gravity changes sign. Simple analytical models clearly show this property near frequencies of a few mHz and are used here to amplify the variance reduction of the gravity residuals. The crossover-frequency depends on the properties of the models of the atmospheric phenomena and the elasticity of the Earth’s crust. Therefore in reality it must be expected to vary in time and space.We show one extremely clear example of this sign-reversal detected in the gravity data from the superconducting gravimeter GWR-C025 in Vienna among other examples which demonstrate the reality of this effect.     

Wavelet filter analysis of atmospheric pressure effects in the long-period seismic mode band

The importance of the reduction of atmospheric pressure effects becomes very clear when investigating seismic normal-mode spectra below 1.5 mHz. The usual simple correction method consists in subtracting a term converted from local atmospheric pressure (pressure multiplied by a frequency-independent admittance) from the gravity record in time domain. Thus, estimating an efficient admittance is the key for an improved correction. Band-pass filters derived from dyadic orthogonal wavelet transform, having narrow pass-bands with good frequency response but without Gibbs phenomenon and causing no phase lag, are very helpful to estimate an efficient admittance, which is both time and frequency-dependent. Processing of high quality superconducting gravimeter (SG) records for the great Sumatra earthquake (Mw = 9.3, Dec 26, 2004) with wavelet filters reveal the three very well resolved splitting singlets of overtone ₂S₁ with a single gravity record after correction with time-dependent and frequency-dependent admittances. We also observe all coupled toroidal modes below 1.5 mHz, except ₀T₅, ₀T₇ and ₁T₁, with good signal-to-noise ratio (SNR); moreover, toroidal modes ₁T₂ and ₁T₃ are for the first time unambiguously revealed in vertical components.     

Effective barometric admittance and gravity residuals

In the analysis of surface gravity signals that may originate from the Earth's core, the step of correcting for the atmospheric pressure fluctuations is one that must be done carefully. We apply two techniques for determining the local, or effective, barometric admittance function between simultaneous observations of surface gravity and pressure. The first is a frequency domain fit that computes the admittance on a band-by-band basis. Using data from both the Canadian and French superconducting gravimeters we determined that the magnitude of the local, or background, admittance increases smoothly and monotonically from about 0.2 μgal mbar⁻¹ at long periods (> 10 days) to about 0.35 μgal mbar⁻¹ at frequencies greater than 3 cycles per day (c.p.d.); the phase lag is within a few degrees of 180°. By comparison, the effective admittances of the large-scale harmonics of the solar heating tide (S₁---S₇) are much smaller, between 0.1 and 0.3 μgal mbar⁻¹, for most of the harmonics of a day. In the second approach we fit a symmetrical time domain admittance function having lengths between 1 and 19 h using both a standard least-squares fit to a white noise residual and a new, and clearly superior, fit assuming a brown noise residual. Both time and frequency domain approaches give comparable results and contribute to a significant lowering of the residual level in non-tidal bands.     

大气变化对位移、重力和倾斜观测影响的理论计算

利用弹性地球负荷理论和流体静力学平衡假设条件下的干空气及其垂直温度梯度分布,理论计算了大气压力作用下地表位移、重力和倾斜格林函数．详细讨论了不同地球模型、台站高程、周边地形、地表大气温度和水汽含量等因素对计算结果的影响．数值结果说明大气效应弹性项影响主要来自于远离台站的区域;引力项对重力的影响主要贡献来自于台站近区,对倾斜的影响来自于远离台站的区域．各种因素对大气重力和倾斜格林函数的影响分别在01°和1°角距范围内,但其综合影响较为复杂．     

The product spectra of gravity and barometric pressure in Europe

A total of 111 000 hourly values of gravity and barometric pressure from stations in Europe is analysed. The data consist of two sets of records from Brussels, an early set of 36 000 h length and a more recent set of 21 000 h length, a set of records from Bad Homburg of 24 000 h length, and a set of records from Strasbourg of 30 000 h length. All of the gravity measurements were made with similar superconducting instruments and the pressure data were recorded simultaneously at each superconducting gravimeter site. The four sets of records have different time bases, and to bring out common features and suppress individual station systematic errors, the product spectrum is introduced. Spectral density estimates are first computed for a common spectral window for each record, and the product spectrum is formed by multiplying individual spectral estimates across records. The cumulative distribution function is found for the product spectrum and confidence intervals are calculated from it by iteration. The product spectrum in gravity reveals a triplet of resonances in the subtidal band which are shown by an automated computer search to be uniquely associated with the translational modes of the solid inner core. The product spectrum in barometric pressure clearly reveals the first 10 solar heating tides in the atmosphere, but otherwise does not show common features with the gravity product spectrum. In particular, the triplet of resonances in the subtidal band of the gravity product spectrum do not show up in the product spectrum of barometric pressure, climinating the atmosphere as their source.     

Gravity reduction with three-dimensional atmospheric pressure data for precise ground gravity measurements

The redistribution of air masses induces gravity variations (atmospheric pressure effect) up to about 20 μgal. These variations are disturbing signals in gravity records and they must be removed very carefully for detecting weak gravity signals. In the past, different methods have been developed for modelling of the atmospheric pressure effect. These methods use local or two-dimensional (2D) surface atmospheric pressure data and a standard height-dependent air density distribution. The atmospheric pressure effect is consisting of the elastic deformation and attraction term. The deformation term can be well modelled with 2D surface atmospheric pressure data, for instance with the Green's function method. For modelling of the attraction term, three-dimensional (3D) data are required. Results with 2D data are insufficient.From European Centre for Medium-Range Weather Forecasts (ECMWF) 3D atmospheric pressure data are now available. The ECMWF data used here are characterised by a spacing of Δ and Δλ = 0.5°, 60 pressure levels up to a height of 60 km and an interval of 6 h. These data are used for modelling of the atmospheric attraction term. Two attraction models have been developed based on the point mass attraction of air segments and the gravity potential of the air masses. The modelling shows a surface pressure-independent part of gravity variations induced by mass redistribution of the atmosphere in the order of some μgal. This part can only be determined by using 3D atmospheric pressure data. It has been calculated for the Vienna Superconducting Gravimeter site.From this follows that the gravity reduction can be improved by applying the 3D atmospheric attraction model for analysing long-periodic tidal waves including the polar tide. The same improvement is expected for reduction of long-term absolute gravity measurements or comparison of gravity measurements at different seasonal times. By using 3D atmospheric pressure data, the gravity correction can be improved up to some μgal.     

琼中台重力非潮汐变化气压与海潮负荷改正

本文对琼中台连续重力观测数据进行收集整理并处理,基于处理后的数据,进行了潮汐分析和非潮汐分析。潮汐分析采用VAV调和分析方法;非潮汐分析则分别进行了零漂改正、固体潮改正、气压改正和海潮改正。其中,零漂改正采用一般多项式拟合零漂的方法;气压改正采用VAV软件;海潮改正运用SPOTL程序,以NAO.99b潮汐模型计算了琼中台海潮负荷值。最终获得了改正后的琼中台重力非潮汐变化,结果表明琼中台的重力气压导纳值为-0.34×10^-8m/s²/mbar,气压改正幅度约为10×10^-8m/s²,海潮改正幅度约为5×10^-8m/s²。改正后,琼中台重力非潮汐变化数据,比仅进行零漂固体潮改正后的重力非潮汐变化数据中的潮汐信号更加微弱,说明进行海潮改正后的效果是明显的,该方法可进一步去除其中的潮汐信号。     

中高频带地下水位对气压和固体潮的响应特征分析

我国前兆观测网络数字化改造的完成, 使得对地震地下水位观测的孕震信息提取和干扰因素排除的研究拓宽至更广的频率范围, 而对原有一些认识的重新考察也成为可能。 本文从中国地震前兆台网挑选出数据质量较好的10个台站, 分析各个台站2008年1月1日至5月11日的地下水位和气压资料及理论重力固体潮的频谱及其频域相关性特征, 并分析了地下水位对气压响应的时移。 结果表明, 中高频带地下水位对气压的响应没有低频带好, 两者相关性随周期的减小而减弱; 含水层岩性对中高频带地下水位的气压和固体潮响应特征有较大影响, 部分灰岩井在高频频段存在地下水位对气压响应异常的现象; 时移效应对水位的气压响应整体特征影响不大, 体现出两种信号自身的复杂性。     

Temporal variations in free core nutation period

Based on the nearly diurnal resonance in the tidal gravity observations,the temporal variations in period of the Earth's free core nutation (FCN) are investigated by using the tidal gravity observations of 18-year duration recorded continu-ously with a superconducting gravimeter (SG) at Brussels. The effects of the global oceanic tide loading and local barometric pressure on the SG observations have been removed by using eleven high-precision global digital models of oceanic tides and barometric pressure me...     

Variability of the Gravity-to-Height Ratio Due to Surface Loads

We study the ratio between the gravity variation and vertical displacement on the surface of a self-gravitating earth model when a surface load is applied. We adopt a theoretical and numerical point of view, excluding any observations. First, we investigate the spectral behavior of the ratio of the harmonic components of the gravity variation and vertical displacement. Then, we model the gravity-to-height ratio for different surface loads (continental hydrology, atmospheric pressure, ocean tides) using outputs of global numerical models in order to relate the predicted spatial values to theoretical mean values deduced from the spectral domain. For locations inside loaded areas, the ratio is highly variable because of the Newtonian attraction of the local masses and depends on the size of the load. For the hydrological loading (soil moisture and snow), the mean ratio over the continents is  ?0.87 μGal mm^?1, but increases with decreasing size of the river basins. For the atmospheric loading, assuming an inverted-barometer response of the ocean, the ratio is positive, with larger values for high latitudes (0.49 μGal mm^?1)—particularly on the coasts—than for lower latitudes (0.30 μGal mm^?1). The ratio, however, is much less variable outside the loaded areas: in desert areas such as the Sahara and Arabia, its mean value is  ?0.28 μGal mm^?1. For the ocean tidal loading, we find a mean ratio of  ?0.26 μGal mm^?1 over the continents for the diurnal tidal waves. Both results are close to the theoretical mean value of  ?0.26 μGal mm^?1 combining elastic and remote attraction contributions.     

武汉九峰地震台超导重力仪观测分析研究

连续重力观测和GPS的技术结合能够监测到物质迁移和地壳垂直形变之间的量化关系.和相对重力测量以及绝对重力测量技术相比,其避免了时间分辨率和观测精度低,无法精细描述观测周期内的物质迁移过程问题.本文利用武汉九峰地震台超导重力仪SGC053超过13000 h连续重力观测数据;同址观测的绝对重力仪观测结果;气压数据;周边GPS观测结果;GRACE卫星的时变重力场;全球水储量模型等资料,采用同址观测技术、调和分析法、相关分析方法在扣除九峰地震台潮汐、气压、极移和仪器漂移的基础上,利用重力残差时间序列和GPS垂直位移研究物质迁移和地壳垂直形变之间的量化关系.结果表明:在改正连续重力观测数据的潮汐、气压、极移的影响后,不仅准确观测到2009年的夏秋两季由于水负荷引起的约(6~8)×10^-8m·s^-2短期的重力变化.而且在扣除2.18×10^-8(m·s^-2)/a仪器漂移和水负荷的影响后,验证了本地区长短趋势垂直形变和重力变化之间具有一致的负相关性规律.同时长趋势表明该地区地壳处于下沉,重力处于增大过程,增加速率约为1.79×10^-8(m·s^-2)/a.武汉地区重力梯度关系约为-354×10^-8(m·s^-2)/m.     

地球物理场观测中的大气效应问题研究

作用在地表的大气质量不仅产生引力位的扰动，而且会引起各种地球物理场的附加效应，本文综述了近年来国内外同行在研究地表位移、重力、倾斜和应变固体潮观测中实施的大气效应改正问题，包括利用台站气压资料建立的实测模型，建立大气重力格林函数，利用全球和区域气象数据计算大气效应，建立大气改正的误差模型等，最后文章讨论了今后研究展望。     

基于EEMD分解的气压改正方法研究

利用超导重力仪观测数据精确测定低于1 mHz的地球自由振荡简正模式的分裂频率,是在不与任何弹性系数发生联系的情况下改善一维密度模型的有效方法.但在该频段台站局部气压变化对重力观测数据的影响成为主要干扰来源,且具有频率依赖特性,因此精细地开展气压改正成为利用超导重力数据检测低频自由振荡信号的必要手段.本文基于EEMD方法,提出了一种具有频率依赖特性的气压改正方法.该方法将重力观测和气压变化分解成处于不同频段的本征模态函数,并在相应频段上分别进行重力-气压变化的回归分析,计算得到具有频率依赖特性的气压导纳值,精细地消除气压变化对重力观测的影响,并以此对微弱低频地球自由振荡信号开展高分辨率分析.基于本文提出的气压改正方法,利用大地震后的超导重力数据检测了频率小于1.5 mHz的低频地球自由振荡及其频谱分裂现象.研究结果表明：利用该方法进行气压改正后检测得到的各简正模具有更高的信噪比,估计的本征频率误差水平明显降低,获得的基频球型振荡₀S₂和₀S₃以及一阶球型振荡₁S₂的分裂谱峰的估计精度更高,同时还检测到了部分环型振荡在重力观测中的耦合现象.对低频地球振荡的高分辨率检测结果验证了基于EEMD分解提出的气压改正方法的有效性,同时再次证明了超导重力仪观测数据在低频地球自由振荡检测中的优势.     

Local and global hydrological contributions to gravity variations observed in Strasbourg

We investigate the contribution of local and global hydrology to the superconducting gravimeter (SG) installed in the Strasbourg observatory. A deterministic approach is presented to account for the contribution of water storage variations in the soils in the vicinity of the gravimeter: both amount and distribution of water masses are determined before calculating Newtonian attraction. No adjustment is performed on gravity time series.Two multi-depth Frequency Domain Reflectometer (FDR) probes have been installed to monitor the amount of water stored in the soil layer above the gravimeter. Since August 2005, they have been monitoring the variation of the water content of the entire soil thickness. Several investigations have been undertaken in order to estimate the distribution of water masses: a precise local DEM (Digital Elevation Model) has been determined using differential GPS. The geometry and heterogeneity of the soil layer have been evaluated thanks to geophysical and geomechanical prospections. The comparison between observed and modelled gravity variations shows that daily up to seasonal variations are in good agreement. For long-term variations, deep water storage and other processes have to be modelled to explain recorded gravity variations.     

Local hydrology, the Global Geodynamics Project and CHAMP/GRACE perspective: some case studies

We first quantify the influence of aquifers on gravity variations by considering local, regional and continental scales. We show that locally only the direct attraction of the underlying aquifer has to be taken into account. At continental (or global scales), the underground water masses act by direct attraction (due to the earth curvature), loading flexure and potential redistribution. We show that at the intermediate regional scale (saying a few kilometres to a few hundreds of kilometres), groundwater contributions can be neglected in practice. Afterwards, we illustrate the difficulties in tackling the local hydrological context by studying comparatively the geological and hydrogeological surroundings of three European Global Geodynamics Project (GGP) superconducting gravimeter stations (Strasbourg, Moxa, and Vienna). Finally, it appears clearly that hydrological variability and cycle characterisations constitute the up-to-date challenge while studying gravity variations in a large spectral range. That is why, gravity is used to quantify hydrological transfers, and overall when seeking for small signals from the Earth's deep interior or other environmental signals (atmosphere, oceans) where groundwater influence can be seen as a disturbance.     

Amplitude Corrections for Regional Seismic Discriminants

—?A fundamental problem associated with event identification lies in deriving corrections that remove path and earthquake source effects on regional phase amplitudes used to construct discriminants. Our goal is to derive a set of physically based corrections that are independent of magnitude and distance, and amenable to multivariate discrimination by extending the technique described in Taylor and Hartse (1998). For a given station and source region, a number of well-recorded earthquakes is used to estimate source and path corrections. The source model assumes a simple Brune (1970) earthquake source that has been extended to handle non-constant stress drop. The discrimination power in using corrected amplitudes lies in the assumption that the earthquake model will provide a poor fit to the signals from an explosion. The propagation model consists of a frequency-independent geometrical spreading and frequency-dependent power law Q. A grid search is performed simultaneously at each station for all recorded regional phases over stress-drop, geometrical spreading, and frequency-dependent Q to find a suite of good-fitting models that remove the dependence on m _b and distance. Seismic moments can either be set to pre-determined values or estimated through inversion and are tied to m _b through two additional coefficients. We also solve for frequency-dependent site/phase excitation terms. Once a set of corrections is derived, effects of source scaling and distance as a function of frequency are applied to amplitudes from new events prior to forming discrimination ratios. Thus, all the corrections are tied to just m _b (or M ₀) and distance and can be applied very rapidly in an operational setting. Moreover, phase amplitude residuals as a function of frequency can be spatially interpolated (e.g., using kriging) and used to construct a correction surface for each phase and frequency. The spatial corrections from the correction surfaces can then be applied to the corrected amplitudes based only on the event location. The correction parameters and correction surfaces can be developed offline and entered into an online database for pipeline processing providing multivariate-normal corrected amplitudes for event identification. Examples are shown using events from western China recorded at the station MAKZ.