Impact of ambient temperature on spring-based relative gravimeter measurements

In this paper, we investigate the impact of ambient temperature changes on the gravity reading of spring-based relative gravimeters. Controlled heating experiments using two Scintrex CG5 gravimeters allowed us to determine a linear correlation (R \(^{2}>\) 0.9) between ambient temperature and gravity variations. The relation is stable and constant for the two CG5 we used: ?5 nm/s\(^{2}/^\circ \)C. A linear relation is also seen between gravity and residual sensor temperature variations (R \(^{2}>\) 0.75), but contrary to ambient temperature, this relation is neither constant over time nor similar between the two instruments. The linear correction of ambient temperature on the controlled heating time series reduced the standard deviation at least by a factor of 2, to less than 10 nm/s\(^{2}\). The laboratory results allowed for reprocessing the data gathered on a field survey that originally aimed to characterize local hydrological heterogeneities on a karstic area. The correction of two years of monthly CG5 measurements from ambient temperature variations halved the standard deviation (from 62 to 32 nm/s\(^{2}\)) and led us to a better hydrological interpretation. Although the origin of this effect is uncertain, we suggest that an imperfect control of the sensor temperature may be involved, as well as a change of the properties of an electronic component.     

Determination of the main Lunar waves generated by the third degree tidal potential and validity of the corresponding body tides models

Seventeen long series of tidal gravity observations with superconducting gravimeters (SGs) belonging to the GGP network allowed to determine the main tidal waves generated by the tidal potential of third degree in the Diurnal (M1), Semi-Diurnal (3MK2, 3MO2) and Ter-Diurnal (M3) bands with a precision of 0.1%, although the amplitudes of these waves are below 10 nm s⁻² (1 μgal). Special analysis techniques have been used to separate M1, 3MK2 and 3MO2 from the neighbouring waves generated by the second degree potential. The 11 European stations form a geographically homogeneous subgroup and it is thus possible to derive some conclusions concerning the ocean tides loading and the body tides models. The results for M1, 3MK2 and 3MO2 are not in contradiction with the recent models and the results for M3 are even in agreement with them.     

Sensitivity of superconducting gravimeters in central Europe on variations in regional river and drainage basins

As underpinned by various studies in the last years, temporal changes of the Earth’s gravity field contain a wealth of information on mass redistribution processes in the Earth’s system particularly associated with variations in continental water storage. By combining satellite and terrestrial observations with superconducting gravimeters (SG) a maximum of information can be gained due to the different temporal and spatial sampling. Esp. the cluster of superconducting gravimeters in central Europe is well suited for studies related to spatial and temporal changes in continental water storage. Due to the distribution of SG sites different sensitivities of the instruments are to be expected on changes in the various river and drainage basins which could, if sufficiently pronounced, be deployed to pinpoint areas in which main discrepancies between modelled and actual water storage changes occur and would thus allow us to fine-tune hydrological models. Based on the WaterGap Global Hydrological Model (WGHM), this sensitivity of the SG observations is investigated. One compartment of the WGHM is surface water, thus comprising rivers, flooding areas, and major reservoirs. This contribution is given for the total cell of 0.5° × 0.5° and not localized, e.g. in a riverbed, therefore the question arises to which extent localization or non-localization of this compartment affects the estimate if the respective surface waters are in the vicinity of 50 km around the SG stations. It can be shown, however, that the lateral distribution of the surface water masses plays only a negligible role for the central European stations meaning distributed surface water masses are an acceptable simplification when estimating hydrological effects. It emerges that variations in water storage in regions outside central Europe produce comparable effects on gravity at all sites and the impact of basins within central Europe is clearly distinguishable among the SG stations.     

Gravity changes before large earthquakes in China: 1998–2005

Although it is well known that coseismic gravity changes take place during an earthquake, previous research has not yielded convincing evidence demonstrating that significant gravity changes occur before large earthquakes. Furthermore, even if we suspect that gravity changes occur before large earthquakes, we have yet to demonstrate how to consistently observe these changes for useful earthquake forecast that would bring benefits to society. We analyzed ground gravity survey data obtained in 1998, 2000, 2002, and 2005 at stations of the Crustal Movement Observation Network of China (CMONOC) and examined gravity changes be-fore the occurrence of nine large (Ms≥6.8) earthquakes that ruptured within or near mainland China and Taiwan from November 2001 to August 2008. Results from this analysis show that significant gravity changes occurred across a large region before each of these nine large earthquakes, and these changes were detected by repeated ground gravity surveys through CMONOC. Although these gravity changes were significant, more research is needed to investigate whether these gravity changes could be viewed as precursors of large earthquakes. Limitations and uncertainties in the data include sparseness of the gravity monitoring network, long time intervals between consecutive gravity surveys, inevitable measurement errors, hydrological effects on gravity, and effects of vertical crustal movements on gravity. Based on these observations, we make several recommendations about possible future direc-tions in earthquake-related research using gravity monitoring data.     

Combination of temporal gravity variations resulting from superconducting gravimeter (SG) recordings, GRACE satellite observations and global hydrology models

Gravity recovery and climate experiment (GRACE)-derived temporal gravity variations can be resolved within the μgal (10^?8 m/s ²) range, if we restrict the spatial resolution to a half-wavelength of about 1,500 km and the temporal resolution to 1 month. For independent validations, a comparison with ground gravity measurements is of fundamental interest. For this purpose, data from selected superconducting gravimeter (SG) stations forming the Global Geodynamics Project (GGP) network are used. For comparison, GRACE and SG data sets are reduced for the same known gravity effects due to Earth and ocean tides, pole tide and atmosphere. In contrast to GRACE, the SG also measures gravity changes due to load-induced height variations, whereas the satellite-derived models do not contain this effect. For a solid spherical harmonic decomposition of the gravity field, this load effect can be modelled using degree-dependent load Love numbers, and this effect is added to the satellite-derived models. After reduction of the known gravity effects from both data sets, the remaining part can mainly be assumed to represent mass changes in terrestrial water storage. Therefore, gravity variations derived from global hydrological models are applied to verify the SG and GRACE results. Conversely, the hydrology models can be checked by gravity variations determined from GRACE and SG observations. Such a comparison shows quite a good agreement between gravity variation derived from SG, GRACE and hydrology models, which lie within their estimated error limits for most of the studied SG locations. It is shown that the SG gravity variations (point measurements) are representative for a large area within the accuracy, if local gravity effects are removed. The individual discrepancies between SG, GRACE and hydrology models may give hints for further investigations of each data series.     

Somigliana–Pizzetti gravity: the international gravity formula accurate to the sub-nanoGal level

 The Somigliana–Pizzetti gravity field (the International gravity formula), namely the gravity field of the level ellipsoid (the International Reference Ellipsoid), is derived to the sub-nanoGal accuracy level in order to fulfil the demands of modern gravimetry (absolute gravimeters, super conducting gravimeters, atomic gravimeters). Equations (53), (54) and (59) summarise Somigliana–Pizzetti gravity Γ(φ,u) as a function of Jacobi spheroidal latitude φ and height u to the order ?(10⁻¹⁰ Gal), and Γ(B,H) as a function of Gauss (surface normal) ellipsoidal latitude B and height H to the order ?(10⁻¹⁰ Gal) as determined by GPS (`global problem solver'). Within the test area of the state of Baden-Württemberg, Somigliana–Pizzetti gravity disturbances of an average of 25.452 mGal were produced. Computer programs for an operational application of the new international gravity formula with (L,B,H) or (λ,φ,u) coordinate inputs to a sub-nanoGal level of accuracy are available on the Internet. Received: 23 June 2000 / Accepted: 2 January 2001     

A bias-free geodetic boundary value problem approach to height datum unification

A geodetic boundary value problem (GBVP) approach has been formulated which can be used for solving the problem of height datum unification. The developed technique is applied to a test area in Southwest Finland with approximate size of 1.5° × 3° and the bias of the corresponding local height datum (local geoid) with respect to the geoid is computed. For this purpose the bias-free potential difference and gravity difference observations of the test area are used and the offset (bias) of the height datum, i.e., Finnish Height Datum 2000 (N2000) fixed to Normaal Amsterdams Peil (NAP) as origin point, with respect to the geoid is computed. The results of this computation show that potential of the origin point of N2000, i.e., NAP, is (62636857.68 ± 0.5) (m²/s²) and as such is (0.191 ± 0.003) (m) under the geoid defined by W ₀ = 62636855.8 (m²/s²). As the validity test of our methodology, the test area is divided into two parts and the corresponding potential difference and gravity difference observations are introduced into our GBVP separately and the bias of height datums of the two parts are computed with respect to the geoid. Obtaining approximately the same bias values for the height datums of the two parts being part of one height datum with one origin point proves the validity of our approach. Besides, the latter test shows the capability of our methodology for patch-wise application.     

Determination of Geopotential of Local Vertical Datum Surface

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Absolute gravity measurements in Switzerland: Definition of a base network for geodynamic investigations and for the Swiss fundamental gravity net

Summary Results of two absolute gravity surveys performed in Switzerland between 1978 and 1979 are presented and discussed in the framework of the uplift history of the Swiss Alps. Five absolute stations have been established as a contribution to the Swiss fundamental gravity net as well as to geodynamic investigations on the Alpine uplift. Two sites (Interlaken—Jungfraujoch) form the end points of a calibration line for field gravimeters. The gravity range of this line amounts to 605×10⁻⁵ ms⁻² (=605 mgal). It can be traversed in a relatively short time interval of less than 3 hours. Two other sites (Brig and Chur) are located in the area of the most negative gravity anomalies and highest uplift rates encountered in Switzerland. They serve as reference stations for a more extended gravity net for studying non—periodic secular gravity variations associated with the Alpine uplift. Institut für Geod?sie und Photogrammetrie, ETH-Zürich, Separata No. 13. Institut für Geophysik, ETH-Zürich, Contribution No. 333.     

Results of the first North American comparison of absolute gravimeters, NACAG-2010

The first North American Comparison of absolute gravimeters (NACAG-2010) was hosted by the National Oceanic and Atmospheric Administration at its newly renovated Table Mountain Geophysical Observatory (TMGO) north of Boulder, Colorado, in October 2010. NACAG-2010 and the renovation of TMGO are part of NGS’s GRAV-D project (Gravity for the Redefinition of the American Vertical Datum). Nine absolute gravimeters from three countries participated in the comparison. Before the comparison, the gravimeter operators agreed to a protocol describing the strategy to measure, calculate, and present the results. Nine sites were used to measure the free-fall acceleration of g. Each gravimeter measured the value of g at a subset of three of the sites, for a total set of 27 g-values for the comparison. The absolute gravimeters agree with one another with a standard deviation of 1.6?μGal (1 Gal ≡ 1?cm s ^?2). The minimum and maximum offsets are ?2.8 and 2.7?μGal. This is an excellent agreement and can be attributed to multiple factors, including gravimeters that were in good working order, good operators, a quiet observatory, and a short duration time for the experiment. These results can be used to standardize gravity surveys internationally.     

National height datum,the Gauss–Listing geoid level value w0 and its time variation 0 (Baltic Sea Level Project: epochs 1990.8, 1993.8, 1997.4)

 A methodology for precise determination of the fundamental geodetic parameter w ₀, the potential value of the Gauss–Listing geoid, as well as its time derivative ₀, is presented. The method is based on: (1) ellipsoidal harmonic expansion of the external gravitational field of the Earth to degree/order 360/360 (130 321 coefficients; http://www.uni-stuttgard.de/gi/research/ index.html projects) with respect to the International Reference Ellipsoid WGD2000, at the GPS positioned stations; and (2) ellipsoidal free-air gravity reduction of degree/order 360/360, based on orthometric heights of the GPS-positioned stations. The method has been numerically tested for the data of three GPS campaigns of the Baltic Sea Level project (epochs 1990.8,1993.4 and 1997.4). New w ₀ and ₀ values (w ₀=62 636 855.75 ± 0.21 m²/s², ₀=−0.0099±0.00079 m²/s² per year, w ₀/&γmacr;=6 379 781.502 m,₀/&γmacr;=1.0 mm/year, and &γmacr;= −9.81802523 m²/s²) for the test region (Baltic Sea) were obtained. As by-products of the main study, the following were also determined: (1) the high-resolution sea surface topography map for the Baltic Sea; (2) the most accurate regional geoid amongst four different regional Gauss–Listing geoids currently proposed for the Baltic Sea; and (3) the difference between the national height datums of countries around the Baltic Sea. Received: 14 August 2000 / Accepted: 19 June 2001     

Equatorial radius of the Earth: A dynamical determination

An intrresting variation on the familiar method of determining the earth's equatorial radius a_e, from a knowledge of the earth's equatorial gravity is suggested. The value of equatorial radius thus found is 6378,142±5 meters. The associated parameters are GM=3.986005±.000004 × 10²⁰ cm³ sec-⁻² which excludes the relative mass of atmosphere ≅10⁻⁶ ξ GM, the equatorial gravity γ_e 978,030.9 milligals (constrained in this solution by the Potsdam Correction of 13.67 milligals as the Potsdam Correction is more directly, orless indirectly, measurable than the equatorial gravity) and an ellipsoidal flattening of f=1/298.255.     

Gravity field approximation in the area of Greece with emphasis on local characteristics

The accuracy of the gravity field approximation depends on the amount of the available data and their distribution as well as on the variation of the gravity field. The variation of the gravity field in the Greek mainland, which is the test area in this study, is very high (the variance of point free air gravity anomalies is 3191.5mgal ²). Among well known reductions used to smooth the gravity field, the complete isostatic reduction causes the best possible smoothing, however remain strong local anomalies which disturb the homogeneity of the gravity field in this area. The prediction of free air gravity anomalies using least squares collocation and regional covariance function is obtained within a ±4 ... ±19mgal accuracy depending on the local peculiarities of the free air gravity field. By taking into account the topography and its isostatic compensation with the usual remove-restore technique, the accuracy of the prediction mentioned obove was increased by about a factor of 4 and the prediction results become quite insensitive to the covariance function used (local or regional). But when predicting geoidal heights, in spite of using the smoothed field, the prediction results remain still depend on the covariance function used in such a way that differences up to about 50cm/100km result between relative geoidal heights computed with regional or local covariance functions.     

Accuracy assessment of the National Geodetic Survey’s OPUS-RS utility

OPUS-RS is a rapid static form of the National Geodetic Survey’s On-line Positioning User Service (OPUS). Like OPUS, OPUS-RS accepts a user’s GPS tracking data and uses corresponding data from the U.S. Continuously Operating Reference Station (CORS) network to compute the 3-D positional coordinates of the user’s data-collection point called the rover. OPUS-RS uses a new processing engine, called RSGPS, which can generate coordinates with an accuracy of a few centimeters for data sets spanning as little as 15 min of time. OPUS-RS achieves such results by interpolating (or extrapolating) the atmospheric delays, measured at several CORS located within 250 km of the rover, to predict the atmospheric delays experienced at the rover. Consequently, standard errors of computed coordinates depend highly on the local geometry of the CORS network and on the distances between the rover and the local CORS. We introduce a unitless parameter called the interpolative dilution of precision (IDOP) to quantify the local geometry of the CORS network relative to the rover, and we quantify the standard errors of the coordinates, obtained via OPUS-RS, by using functions of the form

北京至东京、巴黎、香港首次国际重力联测评介

一九八四年四、五月间使用6台拉科斯特隆贝格(LCR-G)重力仪,在国家重力基本网1985系统(85网)与位于东京、巴黎、香港的分属于多个可靠已知重力基准系统之间,并在日本境内的若干城市间进行了高精度相对重力联测。这次联测的目的在于:1)建立外部条件以检核85网的实际精度;2)利用可靠的已知国际点对85网已知点不足的地区加强控制,并通过与85网的一并平差使85网与国际基准取得一致;3)精化LCR-G重力仪的格值函数。在23个点上所获得的约3000个观测数据参加了与85网的一并平差。计算分析表明:85网平差精度平均达土10微伽[10~(-8)ms~(-2)],外部检核精度达20微伽。网的尺度和基准可靠且与国际系统一致。北京点作为首先国际化的重力点,其重力值精确。LCR-G重力仪灵敏度与点位重力值有关;局部磁场给观测带来不可忽视的误差。本文还分析比较了有关国际重力系统的数据处理方法和计算结果,简评了1985年国家地震局与日本中川一郎教授合作进行的区域性重力测量结果。指出东京B点重力值不稳定。     

Mapping and classification of hydrological parameters from digital terrain data in the Musandam Peninsula,UAE and Oman

Groundwater exploration and modelling requires hydrological parameters and a large volume of hydrologic database. This study integrates remote sensing and geographic information system (GIS) to map and classify hydrological parameters indicates areas of groundwater recharge and discharge. Bivariate quadratic surfaces with moving window size of 5 × 5 were fitted to the digital elevation model and drainage basins, drainage network, topographic wetness index (TWI) and hydroforms were derived. The eight-direction algorithm (D8) that determines in which neighbouring pixel any water in a central pixel will flow naturally was used to delineate drainage basin and drainage network in the study area. The TWI was used to quantify the effect of local topography on hydrological processes and for modelling soil moisture. The results indicate the presence of intensive of stream network (1336 km²), wettest zones and accumulation zones (63.99 km²) within Wadi Bih, the UAE and Wadi Khasb, Oman, suggesting regional recharge.     

Absolute gravity measurements on the canadian gravity standardization network

Summary Absolute measurements of gravity have been made at 6 locations ranging from Ottawa, Ont., in southern Canada, to Alert, N.W.T., the world's most northerly permanent settlement, as part of a program to provide scale and level for the Canadian Gravity Standardization Network (CGSN). Except at Resolute, N.W.T., CGSN-74 gravity values, upon which our gravity reductions are currently based, agree with the absolute gravity meter results to within about .25µm/s². The scale of our CGSN-80 gravity network, upon which our spring-balance type gravity meter scale constants are derived, agrees with the scale defined by the absolute gravity measurements to within about one part in ten thousand.     

The CARIB97 high-resolution geoid height model for the Caribbean Sea

A 2×2 arc-minute resolution geoid model, CARIB97, has been computed covering the Caribbean Sea. The geoid undulations refer to the GRS-80 ellipsoid, centered at the ITRF94 (1996.0) origin. The geoid level is defined by adopting the gravity potential on the geoid as W ₀=62 636 856.88 m²/s² and a gravity-mass constant of GM=3.986 004 418×10¹⁴ m³/s². The geoid model was computed by applying high-frequency corrections to the Earth Gravity Model 1996 global geopotential model in a remove-compute-restore procedure. The permanent tide system of CARIB97 is non-tidal. Comparison of CARIB97 geoid heights to 31 GPS/tidal (ITRF94/local) benchmarks shows an average offset (h–H–N) of 51 cm, with an Root Mean Square (RMS) of 62 cm about the average. This represents an improvement over the use of a global geoid model for the region. However, because the measured orthometric heights (H) refer to many differing tidal datums, these comparisons are biased by localized permanent ocean dynamic topography (PODT). Therefore, we interpret the 51 cm as partially an estimate of the average PODT in the vicinity of the 31 island benchmarks. On an island-by-island basis, CARIB97 now offers the ability to analyze local datum problems which were previously unrecognized due to a lack of high-resolution geoid information in the area. Received: 2 January 1998 / Accepted: 18 August 1998