Absolute Gravimetry Research Articles

Land subsidence using absolute and relative gravimetry: a case study in central Taiwan

We experiment with absolute and relative gravimetry to determine land subsidence. A gravity network in the Yunlin County of central Taiwan is established to determine gravity variations that are largely due to land subsidence. Every 6 months, gravity values at two absolute gravity stations were measured by a FG5 gravimeter and those at 7 relative stations by a Graviton-EG and a Scintrex CG-5 relative gravimeter. A weighted constraint network adjustment was carried out by holding fixed gravity values at the absolute stations. Correction models for temporal gravity changes are developed and applied to raw gravity measurements. The adjusted gravity values oscillate, but in general increase with time, showing signature of land subsidence. An empirical gravity-to-height admittance factor is determined using gravity change (from FG5) and height change (from levelling) at the two absolute gravity stations. At most gravity stations, there is good agreement between subsidence rates from gravimetry and levelling. Some large discrepancies (> 1 cm/year) also exist and are caused by uncertainties in relative gravity accuracy, hydrological effects and the admittance factor. This study suggests that gravimetry has the potential to determine land subsidence to cm accuracy and is more efficient and economic than tools such as levelling and GPS.

THE CAPACITY OF THE SCINTREX AUTOGRAV CG-3M NO. 4492 GRAVIMETER FOR "ABSOLUTE-SCALE" SURVEYS

In autumn 2001, the Institut für Erdmessung (IfE), received the new Scintrex Autograv CG-3M spring gravimeter no. 4492 (SC-4492). Compared with LaCoste-Romberg gravimeters, the Scintrex instrument offers the advantage of a more simple calibration function. Due to the straightforward sensor design (no micrometer screws and gearboxes, no astatisation), a modelling of periodical calibration terms and of a higher order polynomial calibration function is not required. The costly calibration measurements can be reduced to some relative observations between two reliable absolute gravity stations. No complex calibration system should be necessary. A reliable evaluation of the SC-4492 was done with respect to the stability of the calibration, measurement accuracy and precision, drift behaviour, and gravity range dependency of the calibration factor. Measurements were performed on the Hannover vertical calibration line (200 μm/s2 (20 mGal) range, 20-storied building, 10 μm/s2 interval), on the Cuxhaven-Harz north-south line (3000 μm/s2 range, 34 stations, 90 μm/s2 interval) of the gravimeter calibration system Hannover, and in the absolute gravimetry net of the Fennoscandian land uplift area (6200 μm/s2 range). A total gravity range of almost 0.015 m/s2 has been covered. In addition, the gravimeter was employed in the determination of vertical gravity gradients and centring to safety points for absolute gravimetry, and the observation of the horizontal gradient field at the IfE absolute gravity reference station in Clausthal. This paper presents the results as obtained in regional, local and microgravimetric surveys. The achieved accuracies are in the order of ±10 to 100 nm/s2 (±1 to 10 μGal). No instability of the calibration and no gravity range dependency could be proven within the order of 1·10-4. Overall, the gravity meter SC-4492 meets fully the expectations of IfE.

Expected temporal absolute gravity change across the Taiwanese Orogen, a modeling approach

The island of Taiwan is located on the convergent boundary between the Philippine Sea plate and the Chinese continental margin. It offers very active mountain building and collapsing processes well illustrated by the rugged topography, rapid uplift and denudation, young tectonic landforms, active faulting and numerous earthquakes. In this paper, using simple models, we have estimated vertical movements and associated absolute gravity variations which can be expected along a profile crossing the southern part of the island and probably suffering the highest rates of rising. The two different tectonic styles proposed for the island, thin-skinned and thick-skinned, were taken into account. Horizontal and vertical movements were modeled by an elastic deformation code. Gravity variations due to these deformations are then modeled at a second step. They are dominated by plate and free-air effects, i.e. elevation of the topography, with several Gal yr −1 . By comparison, gravity changes generated by mass transfers are weak: maximum 0.1Gal yr−1 with the thin-skinned tectonic and 0.3Gal yr−1 with the thick-skinned tectonic. Though elastic rheology has limitations, this modeling offers interesting results on what gravity signal can be expected from the AGTO project (Absolute Gravity in the Taiwanese Orogen), which proposes to study the dynamic of these mountain ranges using absolute gravimetry (AG) and also including relative gravimetry (RG) and GPS measurements.

Present rate of uplift in Fennoscandia from GRACE and absolute gravimetry

Fennoscandia is a key region for studying effects of glacial isostatic adjustment. The associated mass variations can be detected by the Gravity Recovery and Climate Experiment (GRACE) satellite mission, which observes the Earth's gravity field since April 2002, as well as by absolute gravimetry field campaigns. Since 2003, annual absolute gravity (AG) measurements have been performed in Fennoscandia by the Institut für Erdmessung (IfE, Institute of Geodesy) of the Leibniz Universität Hannover, Germany, within a multi-national cooperation. This offers a unique opportunity for validation and evaluation of the GRACE results. In this preliminary study, the GRACE results are compared to secular gravity changes based on the surveys from 2004 to 2007 with the FG5-220 gravimeter of the IfE. The results from GRACE monthly solutions provided by different analysis centres show temporal gravity variations in Fennoscandia. The included secular variations are in good agreement with former studies. The uplift centre is located west of the Bothnian Bay, the whole uplift area comprises Northern Europe. Nevertheless, the differences between the GRACE solutions are larger than expected and the different centre-specific processing techniques have a very strong effect on possible interpretations of GRACE results. The comparison of GRACE to the AG measurements reveals that the determined trends fit well with results from GRACE at selected stations, especially for the solution provided by the GFZ. Variations of land hydrology clearly influence results from GRACE and the AG measurements.

Geothermal reservoir monitoring with a combination of absolute and relative gravimetry

Microgravity monitoring is a valuable tool for mapping the redistribution of subsurface mass and for assessing changes in fluid recharge from reservoir boundaries associated with geothermal exploitation. To further the development of a high-precision absolute/relative hybrid gravity-measurement technique, we conducted measurements using an absolute gravimeter in two geothermal fields in Japan. The absolute gravity measurements were performed in the central production areas to directly measure gravity changes caused by fluid withdrawal. We succeeded in measuring long-term trends within an accuracy of a few microgals in the Okuaizu and Ogiri fields, which have been producing electricity for several years. Absolute measurements in the center of the field provide reliable and local reference datum anchor points for more widely distributed relative gravity measurements. In the Ogiri field, we carried out time-lapse hybrid measurements with this combination of absolute and relative gravimetry and delineated the spatial distributions of long- and short-term changes. The long-term changes are relatively small, considering the four-year observation interval. This suggests a near balance between the mass withdrawal rate from wells and mass recharge from peripheral regions. The apparent balance is reproduced fairly well by a preliminary numerical reservoir simulation study. The observed long- and short-term changes are thought to be useful constraints for planned history-matching studies based on refined reservoir models with greater spatial resolution that incorporate detailed well-by-well production histories.

Absolute gravity monitoring of water storage variation in a karst aquifer on the larzac plateau (Southern France)

In this study we attempt to understand the water storage variations in a karst aquifer on the Larzac Plateau (South of France) using absolute gravimetry. On this karst system, water input is exclusively rainfall and draining occurs at the Durzon perennial spring in a karstic valley. Our basis assumption is that water storage in the vadose zone (epikarst and infiltration zone) has a significant effect on surface gravity through Newtonian attraction. The karst aquifer is hence being monitored since January 2006 with monthly absolute gravity measurements at three sites. The gravity measurements are corrected for regional scale gravity using water storage models in order to obtain gravity variations related exclusively to the local water storage variations. The gravity variations exhibit an important seasonal component (10–15 μgal corresponding to a variation of equivalent water slab thickness of ∼24–36 cm). Water storage variation seen by gravimetry is not spatially uniform on the studied karst system, corroborating current geomorphologic observations and interpretations. Finally, we use a global mass balance consideration linking rainfall, evapotranspiration and spring discharge to provide a conceptual framework for the understanding of observed gravity variations.

Multi-technique monitoring of ocean tide loading in northern France

We have organised afield study of ocean tide loading in the northwestern part of France, where tidal amplitudes are known to be among the highest in the world. GPS and gravimetric techniques have already proved their capability to measure such weak and high-frequency signals. In this study, these classical observations are complemented with less usual techniques, such as tiltmeter and Satellite Laser Ranging (SLR) measurements. We present here the preliminary results for a common period of observations spanning from 12–19 May 2004. Additional measurements from the French Transportable Laser Ranging Station (FTLRS) were available during September and October 2004. Observation residuals are computed as the difference between the observed and the predicted time signals. We obtain small RMS residuals for GPS measurements (2.5/3.1/4.5 mm for the eastward, northward and upward components), for absolute and relative gravimetry (9 nm/s 2 and 13 nm/s 2) and for tiltmeters (0.05 μrad for EW component). We also fit the amplitude of the main M2 tidal constituent to FTLRS observations and we find a value of 3.731 cm, which is comparable to the theoretical value.

Synthetic tidal parameters for gravity over China and its neighbor area

The synthetic tidal parameters with high spatial resolution for gravity over China and its neighbor area are constructed with Earth’s tidal model and ocean tide loading calculated using TPXO7 global ocean tide model as well as tidal data over China seas. The comparison between synthetic parameters and ones observed by spring gravimeters at some seismic network stations and Hong Kong station and one observed by super-conducting gravimeter at Wuhan station shows that the average differences in amplitude factors and phases are smaller than 0.005 and 0.5° respectively; and that the discrepancies between observational and synthetic parameters are dependent on gravimetric technique in that the synthetic parameters are in well agreement with the superconducting gravimetric observations. This also indicates that the synthetic result is a good estimation for tidal gravity, and the numerical results in the present paper not only can provide ground and space gravimetry such as absolute gravimetry with correction model of tidal gravity, but also provide effective tidal parameters over areas where no observation is carried out.

A method for adjusting the centre of mass of a freely falling body in absolute gravimetry

In absolute gravimeters, rotation of the falling body causes a systematic error. This error can be minimized by coinciding the centre of mass (COM) of the body with its optical centre (OC). A method to measure the distance between these centres in 3D space is described. The method is based on a mechanical balancing technique. Using this method, the COM of a hollow corner cube mirror assembly is adjusted to the OC to within (43 ± 16) µm. An uncertainty budget is given.

On the diffraction correction in absolute gravimetry

The field distribution of a Gaussian light beam introduces additional space-dependent phase shifts compared with that of a flat wave front. An expression for these phase corrections is derived for the case of a two-beam interferometer. The contribution from these diffraction-induced shifts to the g-value determined in absolute gravimetry is calculated. It is found that in the case of a beam waist of a few millimetres or smaller and, particularly, for unbalanced interferometers, a careful consideration of this effect is crucial if high accuracy is desired.

Long-term monitoring by absolute gravimetry: Tides to postglacial rebound

Absolute gravity measurements over nearly a decade at 10 field sites in North America have provided insights on a range of phenomena from tides to postglacial rebound. In this overview we demonstrate the potential of long-term, terrestrial gravity measurements at selected sites to assist in the interpretation of temporal variations in the global gravity field from the Gravity Recovery and Climate Experiment (GRACE) mission. Absolute gravity measurements can be used to calibrate annual soil moisture effects observed by GRACE and to complement GRACE results over periods longer than the expected mission lifetime. Although the preferred terrestrial gravity monitoring system is a global network of superconducting gravimeters (Global Geodynamics Project) in combination with regular absolute gravity measurements, major advances can be made using absolute gravimetry alone. Operating the FG5 gravimeter in continuous mode at a near-shore site shows that special attention must be paid to possible sea-level related biases on gravity values as a result of near-shore hydrological effects. Where soil becomes saturated annually, simple soil moisture models can be used to remove the annual soil moisture effect from gravity, or to invert gravity observations for the soil moisture effect on space missions. Our measurements show that the phenomenon of “episodic tremor and slip” (ETS) in the Cascadia Subduction Zone is accompanied by gravity change that is most likely caused by mass redistribution and not height change. An inter-annual variation of unknown origin with a “period” of around 7 years is present at 10 North American field sites, as well as in data from Table Mountain Gravity Observatory, Boulder, Colorado. Correcting the long-term gravity trends for the inter-annual variation brings the trends into line with GPS vertical rates from four, co-located, continuous, GPS sites in the mid-continent and allows conclusions to be drawn on the thickness of the Laurentide ice-sheet.

Absolute gravimetry in a shifted Legendre basis

A formalism, based on standard least squares techniques, is presented in which analytic expressions can be derived for the study of the influence of hypothetic perturbations in absolute gravimetry. The model function derived from the equation of motion of the test mass and possible perturbations is expanded in an orthogonal basis composed of the shifted Legendre polynomials, and projections onto the model space and the space orthogonal to this serve to isolate the contributions to the model parameters and to the residuals. The part of the perturbation remaining in the orthogonal space can be compared with those retrieved from the residuals of the fit of the model function to the experimental data. The analysis of the structure of these residuals is a major means of gaining information about the character of the perturbations. Finally, some explicit examples are given and a discussion concerning how such an analysis can be made is included.

A method to estimate the time–position coordinates of a free-falling test-mass in absolute gravimetry

As part of the research activity carried on at the Institute of Metrology ‘G Colonnetti’ IMGC-CNR in Turin on the development of the IMGC02 absolute gravimeter, a method to estimate the time occurrences of interference fringes was developed and tested. The capabilities of the IMGC02 have been enhanced by: increased flexibility in timing measurement, the possibility of real-time analysis and the removal of frequency-dependent time delays introduced by the timing electronics. A Monte Carlo simulation has shown, in the case of an ideal frequency and length reference, that the resolution of the waveform digitizer that samples the interference signal can limit the accuracy of the timing measurement. Nevertheless, the expected systematic bias in the absolute measurement of the acceleration due to gravity, g, introduced by this data processing technique is negligible when compared to the current instrument uncertainty.

Accuracy assessment of data analysis in absolute gravimetry

This paper presents an accurate assessment of fringe processing in absolute gravimetry. The use of a computer-based digitizer and digital data processing proved effective in the validation of gravity measurements.

Propagation of error analysis in a total least-squaresestimator in absolute gravimetry

High-precision measurements often resort to least-squares estimation via observation models in whichthe quantity of interest is one of the unknowns. The case when both the dependent and independent variables of the model are stochastic is of particular interest. An example is absolute gravimetry, where the orbit of a test mass is tracked by a laser interferometer and is reconstructed by the least-squares method. In orbit reconstruction, space and time enter symmetrically and both time and position are stochastic. We present orbit reconstruction as a total least-squares problem to establish an error model for the propagation of tracking errors. We also give an asymptotic formula expressing the relevant contribution to the uncertainty of gravity determination.

Thirty years of progress in absolute gravimetry: a scientific capability implemented bytechnological advances

The application of technological advances has dramatically improved our ability to measure the absolutevalue of g, the free-fall acceleration due to gravity. Over the past thirty years this improvement has been nearly three orders of magnitude! Today, the value of gcan be determined with an accuracy approaching 1 µGal (10-8 m/s2) and measured with a precision that is at least ten times better. This paper reviews the history of and the reasons for this progress as well as taking a look to the future.

First detection of absolute gravity change caused by earthquake

Unequivocal coseismic gravity change was detected for the first time by absolute gravimetry. The measurements were done just one day before and only 7 days after a M6.1 earthquake (M6.1). The absolute gravity change was −6 microgal, significantly larger than the observational error of about 1 microgal. Of particular interest is that the observed spatial gravity variations agree remarkably well with those expected from an elastic dislocation model constructed on displacement data alone. The result strongly encourages us to perform a simultaneous inversion of both gravity and displacements to have better insight of earthquakes.

A new fiber optic gradiometer for 4‐D absolute differential gravity

We introduce the concept of absolute differential gravimetry using fiber optic‐based laser interferometry. Absolute differential gravimetry provides an instantaneous determination of the difference in gravity between two or more points on or beneath the surface of the earth. Applications include enhancing the resolution of the gravity field, as well as subsurface fluid and structure monitoring. With a network of sensors, observation of time dependent variations of the gravity field is also possible. Results from a proof‐of‐concept prototype instrument using fiber‐optic coupler technology represent the first time absolute laser interferometric differential gravity data have been collected. Implications of the new measurement method in terms of geophysical studies and future research plans are discussed.

Continuous gravity record at Mount Vesuvius: A tool to monitor its dynamics

The results of more than three years of continuous gravity record on Mt. Vesuvius (Southern Italy) are presented and discussed.The goal of this research is to determine whether continuous gravity records can improve the overall monitoring efforts at the volcano specifically by detecting a gravity signal of “non-tidal” origin.The ocean and atmospheric effects have been taken into account for the computation of the tidal parameters and gravity residuals. Tidal analyses have been carried out by means of classical and recent methodologies and the results compared.The time dependent behaviour of the main tidal parameters and of the gravity residuals have been compared with features of the vesuvian dynamics, namely with the seismic activity and the temporal gravity changes detected by absolute and relative gravimetry.

Methods and experiences of high precision gravimetry as a tool for crustal movement detection

Whenever vertical dislocation is of primary interest, purely geometric surveying techniques, such as GPS, VLBI etc, are deficient in detecting and interpreting geodynamic phenomena such as subsidence and uplift. Absolute gravimetry meanwhile became so accurate that it can successfully be applied under usual conditions. However, for dense field observations in regional and/or local studies relative gravimetry still cannot yet be fully replaced by absolute gravimetry. The basic advantage of gravimetry, in combination with satellite or traditional surveying techniques, lies in its “integrating effect”, which means that height and gravity changes together enable, at least in principle, the solution of a four-dimensional boundary value problem, so that a clearer interpretation of uplift and subsidence becomes available. Two examples are outlined where gravity networks are intended to resolve vertical displacement or changes in potential in relation to earthquake events. A local network in the Friuli seismic risk zone, where highest accuracy of about 5 microgal † † Throughout this paper the unit microgal, with 1 microgal = 10 nm/s 2, is used for convenience. is obtained, is compared to a large scale gravity net in South America, where 10–20 μgal accuracy is demonstrated for gravity variations between consecutive epochs. However, in both cases deficiencies still exist which make it necessary to carry out additional observations before unique results can be expected. In case of South America extreme environmental conditions prevented the accuracy usually achieved with 3 or 4 repeated campaigns to be obtained. In case of Friuli the second measurement clearly reveals still unexplained phenomena when compared with the first campaign. Thus possibilities as well as limitations are pointed out.