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.     

The first absolute gravity measurements in Indonesia

For the purposes of the calibration of the superconducting gravimeter (SG) in Bandung and the establishment of the absolute gravity (AG) points, we carried out AG measurements for the first time in Indonesia in November 2002. The measurements in Bandung were conducted between November 15th and 20th by means of a FG5 (#210), and 14,520 effective drops were obtained. The gravity value newly determined at the AG point in Bandung is 977976701.2 μgal (1 μgal = 10⁻⁸ ms⁻²) and the scale factor for the SG is −52.22 μgal/V. We also established another AG point in Yogyakarta near Merapi volcano and carried out AG measurements in Yogyakarta between November 22nd and 26th. The gravity value determined for this station is 978203093.5 μgal.     

A search for atmospheric effects on gravity at different time and space scales

We investigate in this paper various approaches to correct gravity changes for the effect of atmospheric pressure changes. Two specific locations are considered: Strasbourg (France) as mid-latitude station, where regular pressure fronts occur and Djougou (Benin) as equatorial station with large thermally driven S₁ and S₂ waves of planetary extent. We first review the classical approaches based on a constant or frequency-dependent admittance using only local pressure and gravity data. We consider then a model of atmospheric loading and show the barometric admittance in terms of elastic, Newtonian and total load, as a function of the distance from the station. We consider both a 2D pressure model (surface loading) and a 2.5D model, where the density decreases with height (standard atmosphere). Assuming horizontal advection in the atmospheric dynamics, we convert this spatially dependent admittance into a frequency-dependent admittance. Using global pressure data from European Centre for Medium-Range Weather Forecasts (ECMWF) at about 12 km spatial resolution and 3 h sampling, we compute the model-predicted pressure admittance for Djougou and Strasbourg and we simulate the frequency dependence inferred from gravity and pressure observations below 4 cycle per day. A long gravity and pressure data set (1996–2013) from Strasbourg is used to investigate the low frequency part of the pressure admittance while a common 2.5 year data set (August 2010–February 2013) for Strasbourg and Djougou is then analyzed to investigate the high frequency part of the admittance. In both cases, our results are in close agreement with the predictions inferred from an atmospheric 2.5D loading model with a distance–time relationship due to horizontal advection. The frequency dependence of the barometric admittance is explained by the competing contributions of Newtonian attraction and elastic surface deformation according to the distance from the gravimeter. In the far field (low frequencies), the magnitude of the admittance decreases with frequency because of the combined elasticity effect and Newtonian attraction (when the atmosphere is below the horizon) while, on the contrary, in the near field (high frequencies), elasticity becomes negligible and the pressure admittance mainly decreases with increasing frequency because of the decreasing attraction effect of the atmospheric masses inside the cylindrical pressure cell centered on the sensor location of decreasing radius. In the last part, we show that there is variability in time in the pressure admittance for both stations.     

Gravity Changes and Internal Processes: Some Results Obtained from Observations at Three Volcanoes

Temporal gravity changes provide information about mass and/or density variations within and below the volcano edifice. Three active volcanoes have been under investigation; each of them related to a plate boundary: Mayon/Luzon/Philippines, Merapi/Java/Indonesia, and Galeras/Colombia. The observed gravity changes are smaller than previously expected but significant. For the three volcanoes under investigation, and within the observation period, mainly the increase of gravity is observed, ranging from 1,000 nm^–2 to 1,600 nms^–2. Unexpectedly, the gravity increase is confined to a rather small area with radii of 5 to 8 km around the summit. At Mayon and Merapi the parallel GPS measurements yield no significant elevation changes. This is crucial for the interpretation, as the internal pressure variations do not lead to significant deformation at the surface. Thus the classical Mogi-model for a shallow extending magma reservoir cannot apply. To confine the possible models, the attraction due to changes of groundwater level or soil moisture is estimated along the slope of Merapi exemplarily by 2-D modelling. Mass redistribution or density changes were evaluated within the vent as well as deeper fluid processes to explain the gravity variations; the results are compared to the model incorporating the additional effect of elastic deformation.     

Temporal gravity and elevation changes at Pacaya volcano, Guatemala

Repetitive gravity surveys at Pacaya Volcano from 1975 to 1979 revealed time-dependent changes in the gravity field, which although related to volcanic activity, could not be uniquely attributed to elevation changes or mass redistributions because elevation control was lacking. Elevation control was established in July 1979 using precision leveling. Relative elevation and gravity measurements in June and July of 1979, January 1980 and June 1980 indicate concurrent gravity and elevation changes contemporaneous with variations in eruptive activity. From June 1979 to January 1980, while fumarolic activity was dominant, relative to the most remote station, the volcano deflated by at least 195 mm and the gravity field increased by up to 221 μgal. From January 1980 to June 1980, preceding a Strombolian eruption beginning about June 1980, the volcano inflated by at least 19 mm and the gravity field decreased by up to 231 μgal. Gravity change maps for the intervals of January 1978 to June 1979, June 1979 to January 1980, and January 1980 to June 1980 show areas subject to repeated positive and negative gravity change. Some of those areas coincide with areas of maximum elevation change observed in the June 1979–January 1980 and January 1980–June 1980 intervals; however, gravity changes were observed in areas lacking elevation changes. Adjusting observed gravity changes for elevation changes using a free-air value of −3.086 μgal/cm does not substantially alter the pattern, position, or amplitude of the gravity changes. The relationship between gravity changes, elevation changes, and volcanic activity requires a mechanism producing gravity decreases with little inflation during times of increased eruptive activity, and producing gravity increases with subsidence during times of declining eruptive activity. Such a pattern of changes could be produced by a near-surface magma body in which high-density degassed magma is displaced volume for volume by low-density vesiculated magma during time of increased eruptive activity, and in which loss of gasses by fumarolic activity produces a density increase and a reduction in volume of the magma body during periods of declining eruptive activity. Such a pattern of changes could also be induced by a low-density, vesiculated magma body moving upward in the volcanic pile by piecemeal stoping where the high-density rocks of the volcano are replaced on a volume for volume basis by low-density magma during periods of increasing eruptive activity; and by later density increases and magma body volume reductions accompanying devolatilization and devesiculation during periods of declining eruptive activity. Simple density change and density contrast models involving shallow magma bodies at depths of 100 to 200 m indicate density changes or contrasts of about 0.4 g/cm³ could produce the gravity changes.     

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.     

Determination of gravimetric parameters of the gravity pole tide using observations recorded with superconducting gravimeters

In this study, the loading gravity effect of air mass changes calculated with the three-dimension (3D) meteorological data from the European Centre for Medium-range Weather Forecasts (ECMWF) are removed from superconducting gravimeter (SG) observations. The global hydrological gravity effect is computed and removed with hydrological data from the Global Land Data Assimilation System (GLDAS). Otherwise, the gravity influences induced by a theoretical self-consistent ocean pole tide and variations in length of day (LOD) are considered in the calculation. After removing the influences mentioned previously and also considering the long term trend in the data, a very nice linear relationship between the theoretical gravity pole tide and observed gravity residual (containing the observed gravity pole tide) for each of the selected 9 GGP stations we considered can be obtained. Therefore, the gravimetric factor of the gravity pole tide can be estimated with a simple linear regression. The results show that no clear phase lag is found between the theoretical gravity pole tide and observed gravity residuals from the nine SG stations.     

Determination of the long period tidal waves in the GGP superconducting gravity data

Several results about the long period (LP) tidal waves are obtained by the analysis of series of superconducting gravity data, provided by the Global Geodynamics Project (GGP). The most important result is the determination of a single group called LPMF, composed by all LP tides but representing accurately the parameters of the M_f wave. As the LP tidal generating potential is vanishing at latitudes ±35°15′52″ we cannot determine accurate tidal amplitude factors for the stations located between ±40° and ±30°. However, it is still possible to obtain tidal residual vectors and compare them with oceanic tidal loading computations. For 15 stations the NAO99 oceanic model is giving a coherent picture. For nine stations with M_f amplitude larger than 3 μgal (1 μgal = 10 nm s⁻²) a global analysis is obtained by introducing the loading effect of the ocean directly in the observation equations. The mean amplitude factor obtained for LPMF is larger than expected from the models and there is a significant phase lag, showing the imperfection of the tidal oceanic models for M_f. Other new result is the first separate estimation of the parameters of the LP tides, generated by the tidal potential of third degree, dominated by a Lunar declinational monthly wave, called here 3M_md. Due to their small amplitudes (under 1 μgal) these waves are practically hidden by the noise. Nevertheless, the quality of the data and the flexibility of the VAV analysis method [Venedikov, A.P., Arnoso, J., Vieira, R., 2001. Program VAV/2000 for tidal analysis of unequally spaced data with irregular drift and colored noise. J. Geodetic Soc. Jpn. 47 (1), 281–286; Venedikov, A.P., Arnoso, J., Vieira, R., 2003. VAV: a program for tidal data processing. Comput. Geosci. 29, 487–502.] allow getting significant results, in agreement with the theory of the Earth deformation by the tidal potential of third degree.     

Thermal nature of the source of the Indian gravity anomaly

The non-hydrostatic part of the second zonal harmonic term has been included in the Indian gravity anomaly. The interpretation of the potential, gravity and deflection of the vertical has been produced by a new method. The depth of the source is 580 km and the solution satisfies the temperature gradient of 1°K/km. The ratio Δ V_p/Δp > 0 shows the thermal nature of the density distribution near 670 km.     

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.     

Long period edge waves off Southern Africa

Long gravity wave height oscillations of up to 60 cm with periods between 12 min and 1 h have been observed on tide gauge recordings from the southern coast of South Africa. Short period (30 min to 1 h), small height (3 mb) air pressure pulses were recorded at stations along the same coastline. Two separate events of contrasting nature are described in detail. The simple model of Snodgrass et al. (1962, Journal of Marine Research, 20, 3–30) is used to explain the sea waves as resonant, coastally trapped, edge waves on the Agulhas Bank forced by the atmospheric pulses.     

Prospects for a truly portable absolute gravimeter

We are in the process of developing a small portable absolute gravimeter that employs a cam-based dropping mechanism. The resulting high data rate (100 drops in 30 s) serves to compensate for the short (2 cm) dropping distance. We hope to achieve a measurement accuracy with this instrument of ±5 μgal.     

RECENT DEVELOPMENTS IN UNDERGROUND GRAVITY SURVEYS1

Underground gravity observations in deep coal mines using the conventional gravity meters Worden (type Master) and LaCoste-Romberg (model D), both of which have been adapted to the fire damp regulations, can be accurate to ± 10 and ± 3 μgal, respectively. For underground determination of the vertical gradient of gravity the LaCoste-Romberg meter is used together with a specially designed measuring tower. Using this euipment an accuracy in tower gradient observations of ± 30 E was obtained. To apply the equipment to precision gravity observations in underground situations an additional correction, i.e. a gallery correction, is needed. High accuracy in correction is achieved by a new method of three-dimensional modelling. The gravity effect is computed for bodies with a surface approximated by triangular elements, which are generated from corner points of the body. The combination of gallery correction with tower gradient data leads to a new method for in situ density determination. It offers the possibility of horizontal instead of vertical density profiling. To demonstrate the effectiveness of the developments in underground observations the localization of a pump room is presented. Microgravity and tower gradient observations were carried out to detect the cavity. The horizontal gradient was also calculated to give a more reliable location.     

Performance of superconducting gravimeters from long-period seismology to tides

The first phase (1997–2003) of the Global Geodynamics Project (GGP) has now been completed. Data from superconducting gravimeters (SGs) within GGP have shown great capabilities in a wide spectrum of geophysical applications from the tidal studies to the long-period seismology. Here, we compare the noise levels of the different contributing stations over the whole spectrum. We use three different processing procedures to evaluate the combined instrument-plus-site noise in the long-period seismic band (200–600 s), in the sub-seismic band (1–6 h) and in the tidal bands (12–24 h). The analysis in the seismic band has demonstrated that SGs are particularly well suited for the studies of the long-period normal modes and thus are complementary to long-period seismometers. In the sub-seismic band, the power spectral densities, computed over a period of 15 continuous days for every GGP station, cross the New Low Noise Model of Peterson from T = 16 min to T = 4.6 h. SG data are therefore appropriate for studying long-period seismic and sub-seismic modes. In the tidal bands, the noise comparison is realised by a least-squares fit to tides, local air pressure and instrumental drift, leading to gravity residuals where we estimate a standard deviation and average noise levels in different tidal frequency bands. Tidal gravity observations using SGs have also shown to be an independent validation tool of ocean tidal models, and they are therefore complementary to tide gauge and altimetric data sets. Knowledge of the noise levels at each station is important in a number of studies that combine the data to determine global Earth parameters. We illustrate it with the stacking of the data in the search for the gravity variations associated with the sub-seismic translational motions of the inner core, the so-called Slichter triplet.     

青藏高原春季积雪在南海夏季风爆发过程中的作用

本文应用欧洲中期预报中心（ECMWF,European Centre for Medium\|Range Weather Forecasts—ERA\|40）资料和美国国家环境预测中心和国家大气研究中心(NCEP/NCAR, National Centers for Environmental Prediction/National Center for Atmospheric Research)资料,研究了青藏高原雪深变化对南海夏季风爆发的影响和ENSO对青藏高原降雪的影响.结果表明：（1）ECMWF的雪深资料是可信的,可以用来研究青藏高原雪深变化对南海夏季风爆发的影响;（2）青藏高原的积雪异常影响到500 hPa以上的温度异常和印度洋与大陆间的气温对比,一方面使上层的南亚高压移动速度发生变化,另一方面也影响到低层大气的运动和东西向风异常,在青藏高原少雪年,东印度洋产生西风异常和一个气旋对,而在青藏高原多雪年,东印度洋产生东风异常和一个反气旋对;（3）ENSO与青藏高原春季积雪关系密切.东太平洋SST正异常时,东印度洋和南海气压偏高,从而导致该区海陆经向压强梯度增强和西风异常.另外,此时青藏高原北部气压偏高,北风偏强,副热带锋面增强,同时,印度洋的SST偏高,为青藏高原降雪提供了水汽保障,这些都有利于青藏高原的降雪.     

Very high-frequency and seasonal cave atmosphere PCO2 variability: Implications for stalagmite growth and oxygen isotope-based paleoclimate records

Cave air P_CO2 at two Irish sites varied dramatically on daily to seasonal timescales, potentially affecting the timing of calcite deposition and consequently climate proxy records derived from stalagmites collected at the same sites. Temperature-dependent biochemical processes in the soil control CO₂ production, resulting in high summer P_CO2 values and low winter values at both sites. Large Large-amplitude, high-frequency variations superimposed on this seasonal cycle reflect cave air circulation. Here we model stalagmite growth rates, which are controlled partly by CO₂ degassing rates from drip water, by considering both the seasonal and high-frequency cave air P_CO2 variations. Modeled hourly growth rates for stalagmite CC-Bil from Crag Cave in SW Ireland reach maxima in late December (0.063 μm h^− 1) and minima in late June/early July (0.033 μm h^− 1). For well-mixed ‘diffuse flow’ cave drips such as those that feed CC-Bil, high summer cave air P_CO2 depresses summer calcite deposition, while low winter P_CO2 promotes degassing and enhances deposition rates. In stalagmites fed by well-mixed drips lacking seasonal variations in δ¹⁸O, integrated annual stalagmite calcite δ¹⁸O is unaffected; however, seasonality in cave air P_CO2 may influence non-conservative geochemical climate proxies (e.g., δ¹³C, Sr/Ca). Stalagmites fed by ‘seasonal’ drips whose hydrochemical properties vary in response to seasonality may have higher growth rates in summer because soil air P_CO2 may increase relative to cave air P_CO2 due to higher soil temperatures. This in turn may bias stalagmite calcite δ¹⁸O records towards isotopically heavier summer drip water δ¹⁸O values, resulting in elevated calcite δ¹⁸O values compared to the ‘equilibrium’ values predicted by calcite–water isotope fractionation equations. Interpretations of stalagmite-based paleoclimate proxies should therefore consider the consequences of cave air P_CO2 variability and the resulting intra-annual variability in calcite deposition rates.     

The role of gravity in the WEGENER project

Variations in the gravity field are introduced by mass or density redistribution in the vicinity of the measuring point as well as far field or global effects but also any crustal process which involves a height variation has a direct implication on the temporal variation of the gravity field.The measuring techniques involved in the WEGENER project include absolute and high precision relative gravity measurements and stationary measurements with superconducting gravity meters. The state of the art for both techniques is discussed and shown that systematic errors or the measurement of their changes can be detected by inter-comparison with other absolute gravimeters and frequently repeated measurements at a reference station monitored by a superconducting gravimeter. In the combination of the available gravity techniques it is possible to achieve a precision at the micro-Gal level for secular trends and a higher accuracy for period events which enable improvements in the modelling of environmental effects induced by ocean, atmospheric and ground water loading effects from the long term processes.     

Using postglacial sea level, crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.     

The evolution of andesite volcano structures: new evidence from gravity studies in Costa Rica

Published gravity data on active volcanoes generally reflecteither the low density scoriaceous/pumiceous deposits that are localized within ring-fracture collapse depressions, such as the calderas of mature silicic volcanoes,or the high density frozen magma conduits that occur beneath basaltic shields and cones. The intensive gravity surveys reported here over three complex andesite volcanoes reveal features of both types. Their multi-component gravity fields have crater-centred positive anomalies (1–2 km diameter) surrounded by broader zones of negative gravity with similar amplitudes but greater width (5–10 km). The former are thought to reflect sub-crater magma pipes ofnormal density (ca. 2.5–2.6 Mg m⁻³) surrounded by pyroclastic scoria, ashes and occasional lava flows of muchlower net density (1.8–2.4 Mg m⁻³) which, in turn, account for the negative anomalous zones because the deeper, more consolidated and older parts of these andesite volcano edifices have more normal densities (2.3–2.6 Mg m⁻³).The low density materials are particularly interesting because they appear to have filled topographic depressions to depths of several hundred metres, especially where old caldera-like structures have been postulated from the steep gravity gradients over perimeter ring faults. A model is developed whereby short periods of caldera collapse, associated with intermittent, large high level magma bodies, are interspersed by normal crater-like activity with narrow sub-surface magma pipes. Dominantly pyroclastic activity from summit craters generates the materials that gradually fill earlier-formed topographic depressions. This study demonstrates the unique value of detailed gravity surveys, combined with surface geological information, for modelling and understanding the evolution of active volcano summit regions.