Gravimeter Research Articles

An airborne gravity study of eastern North Carolina

The Naval Research Laboratory (NRL) has developed a prototype airborne gravity measurement system. The core of the system is a LaCoste and Romberg air‐sea gravity meter mounted on a three‐axis stable platform. Corrections to the gravimeter data for altitude and variations in altitude are determined from a combination of highly precise radar and pressure altimeters. The original prototype system was designed for use over oceanic areas. We recently incorporated the pressure measurement to extend use of the airborne system to terrestrial regions where occasional radar altitudes over points of known topographic height can be obtained. The radar heights are used to relate the pressure altitudes to absolute altitudes and to determine the slopes of the isobaric surfaces. Vertical accelerations due to horizontal velocity over a curved, rotating earth (the Eötvös correction) and precise two‐dimensional positions are determined from a Texas Instrument P-code global positioning system. The updated system was tested over eastern North Carolina and the Outer Banks, an area that is difficult to survey by conventional means. Over one‐third of the region consists of low lying swampy terrain and another one‐third is the shallow water of the Pamlico and Albemarle Sounds. Neither the land method nor the shipboard gravity surveying method is well suited for these types of areas. Flying at an altitude of 600 m at 375 km/hr, we were able to cover an area over [Formula: see text] with a nominal track spacing of 9 km by 9 km in less than 18 hours of flying time. A comparison by the Defense Mapping Agency showed a 2.8 mGal rms and a −0.2 mGal mean difference between ground truth data and the airborne data at grid points when both data sets were interpolated to a common 9 km grid.

Bouguer anomalies and the geoid: a reassessment of Stokes' method

SUMMARY The classical gravimetric approach to determining the form of the geoid conventionally involves a global surface integral of free-air anomalies weighted by Stokes’ Function. While this approach is conceptually satisfactory at sea, where gravity observations are actually made on (or at least very close to) the geoid and there is consequently no topographic effect, it is only an approximation on land, where the precise definition of the geoid itself is somewhat vague. This paper discusses what is meant by the geoid on land and introduces a more precise definition which is practically realizable. Although this paper describes two small modifications of Helmert's condensation reduction (actually the procedure described by Stokes) so that it provides an acceptably rigorous determination of the geoid on land, such a method makes very inefficient use of the available information. The Stokes-Helmert method condenses the topographic masses to a surface density and then adds their resulting gravitational attraction to the Bouguer anomaly. The result, similar to a terrain-corrected free air anomaly, is then integrated to transform the gravity anomaly into its equivalent equipotential undulation. Here, a more efficient method is proposed whereby the two independent contributions to the geoid from subsurface anomalous density and from the topographic masses are computed in separate surface integrals and then added, thus finding the geoid as a correcting undulation on the Bouguer co-geoid. Gravity observations, reduced to Bouguer anomalies, are only required for the component of the geoid due to anomalous density, whereas most local detail and usually the larger contribution is due to the topographic masses and can be computed directly from topographic maps. The classical approach using free-air anomalies is conceptually equivalent to using a gravity meter as an altimeter to find the geometrical form of topography. A consequence of the ‘new’ approach (actually suggested by Stokes) is its ability to generate a satisfactory geoid from a much poorer coverage of gravity observations or, alternatively, it can give greatly increased detail with the same gravity data. Ibis is illustrated by a local geoid map computed for the highland region of northern Britain. Even greater local resolution can be achieved using new contour integrals to evaluate the potential due to local topography, but at the expense of much greater computation time. The contour integral approach is also probably the most efficient way to determine the small indirect effect of the Stokes-Helmert condensation reduction, that is, the difference in potential between the condensed topographic masses and those in situ. Unlike the classical approach it is shown that the indirect effect must be evaluated at the observation point rather than on the geoid.

Cooperative inversion of geophysical data

Geophysical inversion by iterative modeling involves fitting observations by adjusting model parameters. Both seismic and potential‐field model responses can be influenced by the adjustment of the parameters of the rock properties. The objective of this “cooperative inversion” is to obtain a model which is consistent with all available surface and borehole geophysical data. Although inversion of geophysical data is generally non‐unique and ambiguous, we can lessen the ambiguities by inverting all available surface and borehole data. This paper illustrates this concept with a case history in which surface seismic data, sonic logs, surface gravity data, and borehole gravity meter (BHGM) data are adequately modeled by using least‐squares inversion and a series of forward modeling steps.

Reference gravity stations on the IGSN71 standard in Britain and Greece

SUMMARY The International Gravity Standardisation Net 1971 (Morelli et al. 1974) includes no reference sites in Greece. We describe composite observations with LaCoste and Romberg (LCR) gravity meters which tie a newly established site at Athens Airport to IGSN71 sites in Rome and Edinburgh, as well as determining the absolute scale of the Greek National Calibration Line on Mount Parnis. As a by-product, the manufacturers' scale of the LCR meter G-275 is found to require correction by the factor 1.000 622 f 0.000 027 against IGSN71. Using this factor, we confirm the IGSN71 scale in Britain by deducing a gravity difference of 387.185 f 0.018 mGal between Edinburgh A and Teddington A, compared with the IGSN71 value of 387.19 f 0.030 mGal. The same interval for the National Gravity Reference Net 1973 (Masson Smith et al. 1974) is 397.128 f 0.023 mGal, so that our observations confirm Turnbull's (1986) conclusion that the NGRN73 connection to Edinburgh Turnhouse Airport was faulty. There are now no significant differences in either overall scale or individual station values between our observations on a selection of NGRN73 sites and those obtained under a program of re-observation by the British Geological Survey. However, we found an error exceeding 0.2 mGal in one of the original NGRN73 values.

First results with the transportable absolute gravity meter JILAG-3

A transportable absolute gravity meter has been built at the Joint Institute for Laboratory Astrophysics (JILA) of the University of Colorado and delivered in January 1986 to the Institut fur Erdmessung (IFE), Universitat Hannover. Instrumental investigations, software improvements and absolute gravity determinations on 15 stations performed byIFE in 1986 are reported here. The main conclusion from one year experience with the instrument is that absolute gravity can be observed on a station within one day with a precision of a few μgal and an accuracy of about 10 μgal.

On: “Evaluation of the BGM-3 sea gravity meter system onboard R/V Conrad by Robin E. Bell and A. B. Watts (GEOPHYSICS, 51, 1480–1493, July 1986.)

I would like to comment on Bell and Watt’s interesting article. First, the following statement is incorrect, “Of the new generation of axially symmetric sea gravity systems, only the Bodenseewerk KSS-30 and the Bell Aerospace BGM-3 systems are presently available.” Actually, LaCoste and Romberg Gravity Meters, Inc., owns U.S. Patent No. 3,717,036 which describes the axially symmetric sea gravity meter being built and sold by LaCoste and Romberg. The actual gravity meter is described in my article “LaCoste and Romberg straight‐line gravity meter” (LaCoste, 1983) Also, field tests of the first of these straight‐line gravity meters are described in Valliant (1983). In addition, a comparative sea test between the straight‐line sea gravity meter and the Bodensee KSS-30 has been made (Macnab et al., 1985). Since late 1985, we have had our straight‐line meters available for immediate sale, and they were available on order as early as 1983. Our straight‐line (axially symmetric) gravity meters are definitely available and proven.

Reply by the authors to L. LaCoste

We thank Lucien LaCoste for his interest and discussion of our recent article on the BGM‐3 gravity meter system.

Modeling gravity and trilateration data in Long Valley, California, 1983–1984

During the period July 1982 through July 1984 a series of repeated, high‐precision gravity measurements have been undertaken in and around Long Valley, California. Data were collected at about 40 sites using three Lacoste‐Romberg model G gravity meters. At the same time the U.S. Geological Survey was conducting a program of high‐precision line length measurements throughout the same area. Significant changes were observed with both types of data during the intervals 1982–1983 and 1983–1984. Previous work by us has shown that deformation data during the interval 1975–1983 are consistent with a model for the inflation of Long Valley caldera which includes magma injection beneath the south central caldera at a depth of only 5 km. Simultaneous inversion of the trilateration and gravity data for the period 1983–1984 shows that most of the previous model is still reasonably consistent with the data and implies injected volumes of between 0.01 and 0.02 km3. Additionally, uplift during this period occurred along the Inyo Domes chain of vents and flows, indicating perhaps a new source of inflation in the northwest part of the caldera. This uplift amounts to a few centimeters and implies a volume increase of perhaps 0.004 km3 at reasonably shallow depth (3 km?). The total amount of uplift in the northwest is small in comparison to the total uplift centered on the central resurgent dome (total vertical displacement well in excess of half a meter). For purposes of comparison we examine several models, one of which involves injection at the base of the crust. This model implies much higher injected volumes, as much as 0.15–0.2 km3.

Gravity tide measurements with a feedback gravity meter

We have analyzed gravity tide data obtained using a calibrated gravity meter with electrostatic feedback. We find good agreement between the measured amplitude and phase of the major semidiurnal components and the corresponding values to be expected using current earth models and ocean load calculations. Both local and global barometric pressure changes make significant contributions to the power in the tidal bands and are included in the fitting function. The admittance estimates at diurnal frequencies can be used to determine the frequency and to set a lower bound on the dissipation of the nearly diurnal resonance in the tidal response. These estimates are in reasonable agreement with results obtained by other methods but are somewhat different than the values to be expected on the basis of theoretical considerations.

Gravimetry for monitoring vertical crustal movements: Potential and problems

Through recent developments in absolute and relative techniques, gravimetry has reached an accuracy of a few hundredths to a few tenths of μm s −2 ∗ ∗ 1 μm s −2 = 0.1 mGal. in small or large-scale networks, respectively. Consequently, gravimetric techniques can now be employed as one efficient tool for detecting vertical crustal movements. Gravity data are necessary for converting the results of geometric levelling to heights defined in the gravity field, and—by repeated surveys—to control time variations of the height-reference surface. More important is the use of repeated gravity surveys for strengthening and partly replacing levelling, being a time-consuming procedure with unfavourable error propagation over larger distances. The successful application of observed gravity variations with time in the detection of vertical crustal movements depends on the reliability of the conversion factor between gravity and height changes, and on the accuracy of the gravity measurements. The conversion factor should be determined through simultaneous levelling and gravimetry, in representative parts of the survey region. Strategies for establishing gravimetric control are changing now with the availability of transportable absolute gravity meters, and the possibility of accurately calibrating relative instruments and observing small gravity differences with feed-back-systems. Consequently, more attention has to be given now to disturbing effects of environmental character, such as microseismics, atmospheric pressure and groundwater table variations, and to periodic effects such as gravimetric earth tides and polar motion.

An inherently linear electrostatic feedback method for gravity meters

A pulse‐width‐modulated signal provides inherently linear electrostatic force feedback for application in gravity meters. Previous methods were linearized through the use of dual‐force rebalance plates and careful adjustment. The suggested system works equally well with single‐ and dual‐plate systems and requires no adjustment. Although dial‐setting errors and noise limit individual observations to a few microGals, a calibration accuracy of 0.25% was achieved. A careful analysis of residuals after regression analysis revealed no evidence of nonlinearity.

Behaviour of quartz gravity meters under high frequency vertical motion

Tests on the vertical vibrating table in the frequency range of70–110 Hz indicate that quartz gravity meters are10–100 times more sensitive at some frequencies than under low-frequency excitation. At high frequencies, the reading beam is at rest and deflected from the correct position. Slow fluctuations of amplitude and frequency near resonance could cause slow irregular motion of the beam with absence of low-frequency ground motion of sufficient intensity.

Absolute gravity measurements in California

We have constructed an absolute gravity meter that determines the local gravitational acceleration by timing a freely falling mass with a laser interferometer. The instrument has made measurements at 11 sites in California, four in Nevada, and one in France. The uncertainty in the results is typically 10μGal (1 Gal ≡ 1 cm/s2; 1 μGal = 10−6 Gal = 10−8 m/s2). Repeated measurements have been made at several of the sites; only one shows a substantial change in gravity.

Limitations to the application of electrostatic feedback in gravity meters

Application of an electrostatic restoring force to the mass of a gravity meter is equivalent to introducing a springlike force working in opposition to the mainspring. This destabilizing effect increases with feedback force and for astatic instruments becomes an important factor in design for operating ranges as small as 5 mGal. With short‐period instruments the operating range can be extended by 2 or 3 orders of magnitude before the destabilizing effect becomes important. Theoretical results are verified by experiments conducted on a LaCoste and Romberg model G gravity meter.

Evaluation of the BGM-3 sea gravity meter system onboard R/V Conrad

The first Bell Aerospace BGM-3 Marine Gravity Meter System available for academic use was installed on R/V Robert D. Conrad in February, 1984. The BGM-3 system consists of a forced feedback accelerometer mounted on a gyrostabilized platform. Its sensor (requiring no cross‐coupling correction) is a significant improvement over existing beam and spring‐type sea gravimeters such as the GSS-2. A gravity survey over the Wallops Island test range together with the results of subsequent cruises allow evaluation of the precision, accuracy, and capabilities of the new system. Over the test range, the BGM-3 data were compared directly to data obtained by a GSS-2 meter onboard R/V Conrad. The rms discrepancy between free‐air gravity anomaly values at intersecting ship tracks of R/V Conrad was ±0.38 mGal for BGM-3 compared to ±1.60 mGal for the GSS-2. Moreover, BGM-3’s platform recovered from abrupt changes in ship’s heading more rapidly than did the platform of GSS-2. The principal factor limiting the accuracy of sea gravity data is navigation. Over the test range, where navigation was by Loran C and transit satellite, a two‐step filtering of the ship’s velocity and position was required to obtain an optimal Eötvös correction. A spectral analysis of 1 minute values of the Eötvös correction and the reduced free‐air gravity anomaly determined the filter characteristics. To minimize the coherence between the Eötvös and free‐air anomaly, it was necessary to prefilter the ship’s position and velocity. Using this procedure, reduced free‐air gravity anomalies with wavelengths as small as a few kilometers can be resolved.

Vertical distortion in Long Valley, California, associated with the January 1983 earthquake swarm

Beginning in the summer of 1982, a series of repeated, high‐precision, gravity measurements have been undertaken in Long Valley, California. Benchmarks have been established from south of Crowley Lake outside the caldera, to Mono Craters in the north. Stations are reobserved at frequent intervals with three Model G, LaCoste‐Romberg gravity meters. We observed significant changes in surface gravity associated with the January 1983 earthquake swarm in the south moat of Long Valley caldera. These changes indicate that the ground around the Casa Diablo hot springs area was uplifted at the time of the swarm. The uplift pattern agrees with that predicted by the model of Rundle and Whitcomb, that is, injection of magma into two chambers at 5 to 8 km depth beneath Long Valley Caldera.

Rheological modelling of measuring systems of quartz gravity meters

Some phenomena, recorded during pressure tests of quartz gravity meters, are studied theoretically using a model of the visco-elastic continuum. Expressions, describing the response of the measuring system as a function of the time variation of pressure disturbances, are derived by solving the appropriate rheological equations.

A microprocessor‐based controller and data acquisition system for LaCoste and Romberg air‐sea gravity meters

A microprocessor‐based controller and data acquisition system for LaCoste and Romberg dynamic gravity meters has been designed, tested, and is now operationally functional. The system controls the motion about the three axes of the stable platform and the gravity meter, as well as acquiring gravity data and storing it on magnetic tape. Output format is compatible with LaCoste and Romberg format. Extensive testing has assured that the digital system functions correctly. Recent deep‐ocean surveys using the new straight‐line meter (SL-1) in conjunction with the new electronics, have resulted in unadjusted cross‐over differences of 1.35 mGal.

A more precise mechanical theory of askania gravity meters

The measuring systems of Askania gravity meters are assumed to have 3 degrees of freedom. The axis of rotation of the beam can also be displaced in the vertical and horizontal directions. The equations of equilibrium of this system (25)–(27) were used to derive the expressions for the effect of displacing the calibration ball, for the scale equation and for the sensitivity of the gravity meter. Equations (33), (34) and (39) refer to gravity meters with a photoelectric transducer, and Eqs (46), (47) and (49) to gravity meters with a capacitive transducer.

Negative gravity anomaly over spreading rift valleys: Mid-Atlantic Ridge at 26°N

A pronounced negative free-air gravity anomaly commonly occurs over the median valley of slow spreading ocean ridges. Previous results, using Wiener filtering and cross-spectral analysis techniques for the Mid-Atlantic Ridge, obtained estimates of the elastic plate thickness in the range of 7–13 km and the existence of a residual negative gravity anomaly over the median rift valley, suggesting that the rift valley has a response function different than the remainder of the spreading ridge. In this paper we have improved the derivation of the topography-gravity admittance function for spreading ocean crust by carefully avoiding several sources of spectral splattering when processing the data: (1) selecting data from a cruise that followed a flowline of central North Atlantic relative plate motion and hence is least corrupted by fracture zones; and (2) accounting for the difference in distance between the gravity meter and the regional variation in elevation as the ridge crest is traversed. Improvements of lesser importance include the use of cubic splines to interpolate to equally spaced data rather than linear interpolation, and correction of the free-air anomaly values for long-wavelength variations of the indirect effect. Comparison of the resulting admittance function to elastic flexure response functions suggests an elastic plate thickness of about 8 km. The improved admittance function, when convolved with the ridge topography, provides a predicted gravity profile that accounts very well for the negative anomaly over the rift valley. Therefore, the isostatic response function for the rift valley is similar to that for the topography away from the rift valley.