Gravity Gradient Measurements Research Articles

Edge detection of potential field data with improved structure tensor methods

Abstract Edge detection is a requisite task in the interpretation of potential field data. There are many methods based on horizontal and vertical derivative of potential field data for edge detection and enhancement. The large eigenvalue of structure tensor can well delineate the edges of geological bodies, but it cannot outline the edges of small amplitude geological bodies clearly. In order to overcome this problem, this paper proposes three different normalization methods to improve the edge detection ability of the large eigenvalue of structure tensor, so that they can display the large and small amplitude edges simultaneously. Also, they do not produce additional false edges when real geological bodies contain positive and negative anomalies simultaneously. These methods were tested on synthetic and measured gravity gradient data and magnetic data. All of the results have shown that the new improved methods are effective for edge detection.

A Wavelet-Based Assessment of Topographic-Isostatic Reductions for GOCE Gravity Gradients

Gravity gradient measurements from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE) contain significant high- and mid-frequency signal components, which are primarily caused by the attraction of the Earth’s topographic and isostatic masses. In order to mitigate the resulting numerical instability of a harmonic downward continuation, the observed gradients can be smoothed with respect to topographic-isostatic effects using a remove–compute–restore technique. For this reason, topographic-isostatic reductions are calculated by forward modeling that employs the advanced Rock–Water–Ice methodology. The basis of this approach is a three-layer decomposition of the topography with variable density values and a modified Airy–Heiskanen isostatic concept incorporating a depth model of the Mohorovicic discontinuity. Moreover, tesseroid bodies are utilized for mass discretization and arranged on an ellipsoidal reference surface. To evaluate the degree of smoothing via topographic-isostatic reduction of GOCE gravity gradients, a wavelet-based assessment is presented in this paper and compared with statistical inferences in the space domain. Using the Morlet wavelet, continuous wavelet transforms are applied to measured GOCE gravity gradients before and after reducing topographic-isostatic signals. By analyzing a representative data set in the Himalayan region, an employment of the reductions leads to significantly smoothed gradients. In addition, smoothing effects that are invisible in the space domain can be detected in wavelet scalograms, making a wavelet-based spectral analysis a powerful tool.

Sensitivity limits of a Raman atom interferometer as a gravity gradiometer

We evaluate the sensitivity of a dual cloud atom interferometer to the measurement of vertical gravity gradient. We study the influence of most relevant experimental parameters on noise and long-term drifts. Results are also applied to the case of doubly differential measurements of the gravitational signal from local source masses. We achieve a short term sensitivity of 3*10^(-9) g/Hz^(-1/2) to differential gravity acceleration, limited by the quantum projection noise of the instrument. Active control of the most critical parameters allows to reach a resolution of 5*10^(-11) g after 8000 s on the measurement of differential gravity acceleration. The long term stability is compatible with a measurement of the gravitational constant G at the level of 10^(-4) after an integration time of about 100 hours.

Observing coseismic gravity change from the Japan Tohoku‐Oki 2011 earthquake with GOCE gravity gradiometry

AbstractThe Japan Tohoku‐Oki earthquake (9.0 Mw) of 11 March 2011 has left signatures in the Earth's gravity field that are detectable by data of the Gravity field Recovery and Climate Experiment (GRACE) mission. Because the European Space Agency's (ESA) satellite gravity mission Gravity field and steady‐state Ocean Circulation Explorer (GOCE)—launched in 2009—aims at high spatial resolution, its measurements could complement the GRACE information on coseismic gravity changes, although time‐variable gravity was not foreseen as goal of the GOCE mission. We modeled the coseismic earthquake geoid signal and converted this signal to vertical gravity gradients at GOCE satellite altitude. We combined the single gradient observations in a novel way reducing the noise level, required to detect the coseismic gravity change, subtracted a global gravity model, and applied tailored outlier detection to the resulting gradient residuals. Furthermore, the measured gradients were along‐track filtered using different gradient bandwidths where in the space domain Gaussian smoothing has been applied. One‐year periods before and after earthquake occurrence have been compared with the modeled gradients. The comparison reveals that the earthquake signal is well above the accuracy of the vertical gravity gradients at orbital height. Moreover, the obtained signal from GOCE shows a 1.3 times higher amplitude compared with the modeled signal. Besides the statistical significance of the obtained signal, it has a high spatial correlation of ~0.7 with the forward modeled signal. We conclude therefore that the coseismic gravity change of the Japan Tohoku‐Oki earthquake left a statistically significant signal in the GOCE measured gravity gradients.

Lunar gravity gradiometry and requirement analysis

The current lunar gravity field models are mostly concluded from lunar exploration programs either by observations of satellite orbit perturbations or by intersatellite ranging and ranging rate measurements between two low-orbiting spacecrafts. Especially, the measurements from the Gravity Recovery and Interior Laboratory (GRAIL) have been used to produce the Moon’s gravity field models with spatial resolutions up to spherical harmonic degree 420 and 660 for the primary mission and extended mission, respectively. This paper presents a method using satellite gravity gradiometry, which not only can determine a moon’s gravity field model with a higher resolution, but also can obtain the medium and short wavelength components information with a higher accuracy. This advantage is still obvious in comparison with the results from GRAIL’s extended mission even though the maximum degree of the model derived from the mission is close to that achieved by the satellite gradiometry discussed in this study. Based on the simulations and analysis, a mission with the hypothesis of an orbit height of about 20km, a mission duration of about 14 days, and a gradiometer accuracy level of about 30mE/Hz is proposed, and it permits determination of a lunar gravity field model with a high accuracy of 14mGal and a geoid with an accuracy of 20.5cm, both at a spatial resolution of 7km, corresponding to spherical harmonic degree and order 789. The effects of gravity gradient measurement errors, orbit height, tracking accuracy, mission duration and sampling rate are analytically investigated by the direct relationship between the satellite gravimetry measurements and coefficients of the Moon’s gravitational potential, which is verified by the least-squares method.

Understanding gravity gradiometry processing and interpretation through the Kauring test site data

The Kauring Gravity Gradiometry Test site offers a unique opportunity to understand the information content of various types of gravity gradient measurements and the required processing and interpretation techniques. In this paper, we utilize the measured ground vertical gravity data to simulate realistic airborne gravity gradiometry data from several current and future systems using an equivalent-source technique. We then invert these simulated data for the underlying density contrast and evaluate the performance of these inversions. The study demonstrates the effectiveness of equivalent-source based method for data conversion in the presence of scattered observations. The major density features recovered from the optimally converted gradient data are highly consistent with those from the original ground gravity.

Simultaneous measurement of gravity acceleration and gravity gradient with an atom interferometer

We demonstrate a method to measure the gravitational acceleration with a dual cloud atom interferometer; the use of simultaneous atom interferometers reduces the effect of seismic noise on the gravity measurement. At the same time, the apparatus is capable of accurate measurements of the vertical gravity gradient. The ability to determine the gravity acceleration and gravity gradient simultaneously and with the same instrument opens interesting perspectives in geophysical applications.

Single-hole imaging using borehole gravity gradiometry

We study the feasibility of imaging density variations away from boreholes using gravity gradient measurements in a single borehole. The objective is to develop numerical interpretation tools and to understand the utility and limitations of borehole gravity gradiometry in anticipation of the development of such instruments for the exploration and production of minerals, oil, and gas. We develop an analytic solution for directly locating discrete off-hole mass anomalies and apply a generalized inverse approach to image anomalous density distribution. In the analytic approach, we solve for the distance and direction angles to a point source using the multiple components of the gravity gradient tensor from a set of observations in a single borehole; and then apply this approach to the scenarios of prismatic sources. In the generalized inverse approach, we invert multiple gradient tensor components to construct 3D density contrast distributions around the borehole. As few as two independent gravity gradient components in a single borehole can be used to locate and image isolated anomalous density bodies.

Validation of GOCE time-wise gravity field models using GPS-levelling, gravity, vertical deflections and gravity gradient measurements in Hungary

With the advantage of satellite gravity gradiometry (SGG) high standard global gravity determination could attain in the static part of the gravitational field. This paper presents the validation of the first and second generation GOCE-only models using terrestrial data sets in Hungary. GOCE global geopotential models (GGM) are consistent models with global coverage in sense that GGMs have been compiled utilizing measurements refer to short time period. Besides GOCE-based GGMs satellite only GRACE models were evaluated to assess the improvements by GOCE observations with respect to GRACE in gravity field determination. EGM2008 as the state-of-the-art model and SRTM3 elevation model were applied to provide that measurements involving Hungarian data sets and model derived gravity field functionals have almost the same spectral content. Results with GPS-levelling and gravity data support that there is an improvement in the determination of medium-wavelength parts of the gravitational field with GOCE models. Alth ough vertical deflections characterize the short-wave part of the gravity field, they are also capable to sense the advancement of SGG observations. Our experiences show that torsion balance measurements depict the fine structure of the gravity field, and hence they are not adequate in low-degree GGM validation.

Simultaneous gravity and gradient measurements from a recoil-compensated absolute gravimeter

This paper discusses simultaneous gravity and vertical gravity gradient measurements obtained with a newly designed recoil-compensated dropping chamber adapted to an FG5 absolute gravimeter. The new dropping chamber incorporates counterweights to compensate recoil effects. It has the same physical length as the standard FG5 dropping chamber but the free-fall distance was increased from 20 cm to 25 cm. The new drive train pulls on the centre of the system to reduce unwanted horizontal velocity and rotation of the free-falling test mass. The test-mass material was chosen to reduce possible magnetic eddy-current damping caused by external magnetic field gradients. External lead masses were used to change the gravity and vertical gravity gradient. The measurements agree well with the theoretical gravity field changes derived from the position of the external weights. The experiment clearly demonstrates the efficacy of using an absolute gravity meter to measure both the gravity and the gravity gradient signals caused by variations in the external gravity field. This technique shows promise for passive gravity-monitoring applications.

Conforming Falcon‡ gravity and the global gravity anomaly

ABSTRACTGravity derived only from airborne gravity gradient measurements with a normal error distribution will have an error that increases with wavelength. It is straightforward in principle to use sparsely sampled regional gravimeter data to provide the long wavelength information, thereby conforming the derived gravity to the regional gravity. Regional surface or airborne gravimeter data are not always available and can be difficult and expensive to collect in many of the areas where an airborne gravity gradiometer survey is flown. However the recent release by the Danish National Space Centre of the DNSC08 global gravity anomaly data has provided regional gravity data for the entire earth of adequate quality for this purpose. Studies over three areas, including comparisons with ground, marine and airborne gravimetry, demonstrate the validity of this approach. Future improvements in global gravity anomaly data are expected, particularly as the product from the recently launched Gravity field and steady‐state Ocean Circulation Explorer (GOCE) satellite becomes available and these will lead directly to an improvement in the very wide bandwidth gravity available after conforming gravity derived from gravity gradiometry with the global gravity.

The use of microgravity technique in archaeology: A case study from the St. Nicolas Church in Pukanec, Slovakia

The use of microgravity technique in archaeology: A case study from the St. Nicolas Church in Pukanec, SlovakiaThe detection of subsurface cavities, such as crypts, cellars and tunnels, in churches and castles belongs to successful applications of the employment of surface gravity measurement techniques in archaeo-prospecting. The old historic building exploration requires using of non-invasive methods, and hence the microgravity technique is a proper candidate for this task. On a case study from the Roman-Catholic Church of St. Nicolas in the town Pukanec the results of using microgravity for detection and delineation of local density variations caused by a near-surface void are shown. The acquired negative anomaly in the residual Bouguer anomalies field suggested the presence of a possible void feature. Euler deconvolution and 3D modelling were used to estimate the depth and shape of the anomalous source. Additionally, measurements of the vertical gravity gradient on several stations were performed. We tested how the use of a downward continuation of gravity, utilizing the real vertical gravity gradient, influences the shape and amplitude of the final Bouguer anomaly map.

Description of and Results from a Novel Borehole Gravity Gradiometer

SummaryGravitec Downhole Instruments Ltd. is in the final stages of adapting its gravity gradiometer technology for deployment in the borehole environment for use in exploration as well as for time-lapse reservoir monitoring. The project, named Scorpius, is in cooperation with partners Kenda Capital and QinetiQ Ltd.Laboratory testing of the sensor has produced gravity gradient measurements. Work has also been done to forward model the effects of gravity gradient measurements in the borehole environment.

Gravity Gradiometer Systems – Advances and Challenges

Gravity gradiometry has been heralded as one of the top five developments in advancing airborne geophysics in the past decade. There are presently nine deployed gradiometer systems operating in various configurations (partial tensor and full tensor) on numerous platforms in support of global exploration activities. There are also numerous development programs underway with an aim of producing lower noise gradient measurements. We will review the broad scope of developments in gravity gradient instrumentation, with a view toward how the projected improved performance will require greater attention to other error sources. It is easy to see how improved gradient data will benefit the explorationist, yet lower noise sensors alone do not provide the answer. Improved operational capability will need to come from lower sensor and system noise, as well as addressing the external error sources associated with terrain and geology. This paper discusses a wide range of technologies and operational scenarios under development to achieve a robust gravity gradient measurement. The significant challenges associated with improved gravity gradiometer operational capability including vehicle dynamic noise, terrain noise, geologic noise and other noise sources will be a key focus of this paper.

Case histories of high-accuracy land gravity gradient measurements

The concept of using gravity gradient measurements for gaining knowledge of the subterranean zone is not new. Instruments have been built and field measurements have been conducted over the past 100 years. Improvements in both sensor performance and survey procedures have resulted in the present capability of making high accuracy (sub-Eotvos) measurements in real-world areas of interest. A summary of recent field activity using Lockheed Martin gradiometer systems will be presented in this paper. Recent improvements have resulted in a land-based gravity gradiometer system capable for use in a broad range of land applications, including void and tunnel detection, void characterization, and time-lapse reservoir monitoring.

Efficient automatic denoising of gravity gradiometry data

Gravity gradiometry data are prized for the high frequency information they provide. However, as any other geophysical data, gravity gradient measurements are contaminated by high‐frequency noise. Separation of the high‐frequency signal from noise is a crucial component of data processing. The separation can be performed in the frequency domain, which usually requires tuning filter parameters at each survey line to obtain optimal results. Because a modern gradiometry survey generates more data than a traditional gravity survey, such time‐consuming manual operations are not very practical. In addition, they may also introduce subjectivity into the process.To address this difficulty, we propose an automatic, data‐adaptive 1D wavelet filtering technique specially designed to process gravity gradiometry data. The method is based on the thresholding of the wavelet coefficients to filter out high‐frequency noise while preserving localized sharp signal features. We use an energy analysis across scales (specific for gravity gradiometry data) to select denoising thresholds and to identify sharp features of interest. We compare the proposed method with traditional Fourier‐domain filters by applying them to synthetic data sets contaminated with either correlated or uncorrelated noise. The results demonstrate that the proposed filter is efficient and, when applied in the fully automated mode, produces results that are comparable to the best results achievable through frequency‐domain filters. We further illustrate the method by applying it to a set of gravity gradiometry data acquired in the Gulf of Mexico and by characterizing the removed noise. Both synthetic and field examples show that the proposed method is an efficient and better alternative to other traditional frequency domain methods.

Error assessment of GOCE SGG data using along track interpolation

Abstract. GOCE will be the first satellite gravity mission measuring gravity gradients in space using a dedicated instrument called a gradiometer. High resolution gravity field recovery will be possible from these gradients. Such a recovery requires a proper description of the gravity gradient errors, where the a priori error model is for example based on end-to-end instrument simulations. One way to test the error model against real data, i.e. to see if the a priori model really describes the actual error, is to compare along track interpolated gradients with the measured gradients. The difference between the interpolated and measured gravity gradients is caused by, among others, the interpolation error and the measurement errors. The idea is that if the interpolation error is small enough, then the differences should be predicted reasonably well by the error model. This paper discusses a simulation study where the gravity gradient errors are generated with an end-to-end instrument simulator. The measurement error will be compared with the interpolation error and we will assess the latter as a function of the sampling interval.

Measurement and use of the vertical gravity gradient in correcting repeat microgravity measurements for the effects of ground subsidence in geothermal systems

Changes in mass resulting from production and reinjection in geothermal fields can be monitored using repeat microgravity measurements. The measured changes in gravity, however, need to be corrected for the effects of any exploitation-induced ground subsidence. The correction required at each measurement point is the product of the amount of ground subsidence and the vertical gravity gradient at that point. Measurements of the gravity gradient, made using a portable tower, show that it varies from place to place depending mainly on the local topography. Measured gradients, in areas of high subsidence rate, range between −276 and −339 μgal/m at 30 sites in the Wairakei–Tauhara field and between −296 and −321 μgal/m at nine sites in the Ohaaki field (New Zealand). These values are similar to those used previously. At 37 sites measured in the Yanaizu–Nishiyama field (Japan) the gradient varied between −244 and −352 μgal/m. Measurements at six sites showed no significant change in gravity gradient with height above the ground surface; a single value for the gradient can therefore be used at each site to correct for the gravitational effect of any ground movement. Calculations show the effects on the vertical gravity gradient of groundwater level variations, mass changes associated with the ground subsidence, and reservoir mass changes are negligible at Wairakei.

Metalliferous mining geophysics—State of the art in the last decade of the 20th century and the beginning of the new millennium

The downturn in mining activity experienced during the 1990s did not preclude significant new developments in various areas of mining geophysics. The methodology for acquiring and compiling data has kept pace with the latest technological developments, from Global Positioning System navigation to raster displays and parallel computing. Wavelet transforms, principal component analysis, and fractals have begun to find successful applications in both processing and interpretation of geophysical data. Methods of quantitatively interpreting/inverting anomalies in terms of 2‐D and 3‐D models of causative bodies are becoming common.For the first time it is possible to make airborne gravity gradient measurements suitable for use in mineral exploration. Lower transmitter frequencies for airborne time‐domain electromagnetic (EM) systems have enabled surveys in areas where conductive cover previously screened basement conductors. The use of approximation algorithms has allowed the transformation of either time‐domain or frequency‐domain data into conductivity‐depth images (CDIs) which expedite interpretation. Full‐waveform recording and the use of multiple receivers are becoming common for ground EM techniques.In radiometrics it is now common practice to record 256 channels of spectral data which, by using statistical methods, has led to a dramatic reduction of noise in aerial gamma‐ray surveys. Finally, advances in 3‐D oil‐field seismic reflection methods have been introduced into the search for mineral deposits, thereby providing new tools for studying the environment of orebody emplacement as well as detailed geometrical information of value for both exploration and mine‐planning applications.Thus, at the beginning of the 21st century, we find the geophysical techniques used by the mining industry to be at the forefront of the latest technological developments.

The complete gravity gradient tensor derived from the vertical component of gravity: a Fourier transform technique

A technique has been to developed to determine the complete gravity gradient tensor from pre-existing vertical gravity data using the fast Fourier Transform (FFT). Since direct measurement of the entire gravity gradient tensor is generally unavailable, our technique provides an alternative determination of the gravity gradient tensor components. Traditionally, derivatives of vertical gravity ( g z,x , g z,y , and g z,z ) have been the only gravity gradient tensor components that have been computed directly. Gravity gradient tensor components are computed for four different, three-dimensional (3-D), idealized horst-and-graben models, with varying depths to the horst. Comparing the FFT results with calculated gradient components from the 3-D models shows that the RMS error for each component, between the two results, is at most ∼3.3 Eötvos Units. In addition, measured gravity gradient components from an airborne survey over the Wichita Uplift and Anadarko Basin region of southwest Oklahoma compare favorably with the FFT-derived results using available vertical gravity data. No error analysis was attempted between the two results due to a low signal-to-noise ratio in the measured data. Our technique offers a novel way to transform and visualize the available data, and it also offers an inexpensive and previously unavailable subsurface mapping capability.