Gradiometer Data Research Articles

Spherical Tikhonov regularization wavelets in satellite gravity gradiometry with random noise

A special class of regularization methods for satellite gravity gradiometry based on Tikhonov spherical regularization wavelets is considered, with particular emphasis on the case of data blurred by random noise. A convergence rate is proved for the regularized solution, and a method is discussed for choosing the regularization level a posteriori from the gradiometer data.

Multiplexed resistivity survey at the roman town of Wroxeter

A detailed resistivity survey was made at the Roman Town of Wroxeter to investigate the performance of a recently introduced mobile resistivity multiplexing system. Measurements were made with six twin-array separations (0.25 m to 1.5 m), and with Wenner and double -dipole arrays. The resulting area plots are discussed and compared with existing fluxgate gradiometer data. The data sets were also: (i) used to create stacked pseudo-sections in X and Y directions; and (ii) combined using various weightings to create composite images. The overall results show that making simultaneous measurements with a range of different configurations enables a broader understanding to be made of the measurement processes, than if just a single configuration had been used. In the site surveyed, the narrower spacings emphasize the near-surface features, whereas the wide spacings reveal more substantial, underlying structures. Copyright © 2000 John Wiley & Sons, Ltd.

3-D inversions of magnetic gradiometer data in archeological prospecting: Possibilities and limitations

A vertical‐gradient magnetic system based on optically pumped Cesium sensors has been used to map subtle magnetic anomalies across infilled pit houses and ditches at a medieval archeological site in northern Switzerland. For estimating the locations and dimensions of these features from the recorded data, we have designed and implemented an appropriate inversion scheme. Tests of this scheme on realistic synthetic data sets suggested that suitable minimum magnetic susceptibility contrasts and smoothing parameters for the inversion may be directly extracted from the data. Inversions with minimum magnetic susceptibility contrasts generated causative bodies with maximum plausible sizes. By using higher magnetic susceptibility contrasts, a complete suite of models that matched the data equally well was produced. To constrain better the magnetic susceptibility constrast within a selected area of the archeological site, shallow samples of topsoil and sediment were analyzed in the laboratory. An inversion based on the measured magnetic susceptibility contrast yielded reliable estimates of the locations, 3-D geometries, and sizes of two small pit houses. The depth extent of one pit house was subsequently verified by shallow drilling. We concluded that inversions of vertical‐gradient magnetic data constrained by magnetic susceptibility or shallow borehole information are rapid and inexpensive means of providing key knowledge on the depth distribution of inductively magnetized bodies.

The Osservatorio Geofisico Sperimentale marine magnetic surveys in the Antarctic Seas

About 40 000 km of marine magnetic and gradiometric data have been collected during eight geophysical surveys conducted since the Austral summer 1987/1988 in the circum-antarctic seas, by the research vessel OGS-Explora. For the most surveyed areas (Ross Sea, Southwestern Pacific Ocean, and Southern Scotia Sea), the analysis of the acquired data have contributed to clarify important aspects of their geological structure and tectonic evolution. The main scientific results, obtained combining other available geophysical data (multichannel seismic profiles and satellite-derived data), will be briefly illustrated.

Gravity field recovery from airborne gradiometer data using collaction and taking into account correlated errors

Least squares collocation is a very comprehensive method for gravity field modelling, since it may use known noise characteristics of the data. In many earlier applications the errors affecting the data were considered uncorrelated, mainly due to the difficulty in estimating the systematic character of such kind of errors. In this study, error covariance functions of airborne gravity gradiometer data are estimated by comparing model covariance functions with empirical covariance functions of the gravity gradiometer data. The model covariance functions were estimated from accurate surface gravity data and continuated upward to the height of the airborne measurements using the covariance propagation law. The estimated error covariance functions were modeled as finite ones and used as an additional information for the prediction of gravity anomalies from gravity gradiometer data. The assessment of the prediction results was made by comparing the gravity values predicted from the airborne gradient data and showed up to 25% improvement compared to not using correlated errors.

Euler deconvolution methods used to determine the depth to archaeological features

Abstract Field techniques, instrumentation and data processing for geophysical location of archaeological remains are now at such a standard that clear maps of the subsurface detail are readily obtainable. Magnetic gradiometry and resistivity plots are widely used to locate diverse features such as walls, ditches and burial areas. However, information concerning the depth to these features is not often extracted from such plots and would be useful in planning any following excavation. Here we use Euler deconvolution methods, on a reasonably high-resolution magnetic gradiometer data set, to determine the depth to a buried Romano-British villa at the Wroxeter archaeological site. The interpretation of these depth estimates is compared to GPR sections taken over the same site.

Calibration of satellite gradiometer data aided by ground gravity data

Parametric least squares collocation was used in order to study the detection of systematic errors of satellite gradiometer data. For this purpose, simulated data sets with a priori known systematic errors were produced using ground gravity data in the very smooth gravity field of the Canadian plains. Experiments carried out at different satellite altitudes showed that the recovery of bias parameters from the gradiometer “measurements” is possible with high accuracy, especially in the case of crossing tracks. The mean value of the differences (original minus estimated bias parameters) was relatively large compared to the standard deviation of the corresponding second-order derivative component at the corresponding height. This mean value almost vanished when gravity data at ground level were combined with the second-order derivative data set at satellite altitude. In the case of simultaneous estimation of bias and tilt parameters from ∂2 T/∂z 2“measurements”, the recovery of both parameters agreed very well with the collocation error estimation.

Terrain Corrections are Critical for Airborne Gravity Gradiometer Data

Several developments aim to produce airborne gravity gradiometers with sufficient sensitivity to detect mineral deposits of several millions of tonnes at shallow depths. In a conventional ground gravity survey, a Bouguer slab correction is always necessary, with the terrain component of the full Bouguer correction often not needed unless the topography is severe. For airborne gravity gradiometers, however, the slab correction is exactly zero but the terrain corrections prove to be critical even with subdued or moderate topography.This paper reports on research into airborne gravity gradiometer corrections, especially aspects that assessed the importance of regolith and its constraints of surface and bedrock topography, together with predicted target anomalies. Using an example of topography typical of the Western Australian shield, calculations show that densities of both regolith and bedrock need to be determined to better than 0.1 t/m3 for adequate correction to be made to raw gravity gradiometer data. Topography also needs to be defined to about ±3 m on 10 m pixels for adequate gravity corrections.

ProcessingZ gradiometer magnetic data using linear transforms and analytical signal

For 25 years the fluxgate gradiometer has been in common use in magnetic archaeological prospecting. It constitutes a cheap and light solution well adapted for the detection of earth-filled and burned features and of elements built with brick or magnetic stones. Among the different processing techniques that can be applied to the magnetic data, we chose to use linear transforms, which aim at locating and delineating precisely the buried features and at correcting for field inclination using no a priori information about causative bodies. We applied these transforms to fluxgate ΔZ gradiometer data, by calculation in the spectral domain for both synthetic and measured data. The advantages of this application depend on the characteristics of the features searched for and of their environment, and several transformed maps can be calculated by the interpreter in order to choose the most convenient for a given survey. © 1997 John Wiley & Sons, Ltd.

Regional recovery of the gravity field from satellite gravity gradiometer and gravity vector data using collocation

The method of least squares collocation has been used to investigate the regional recovery of the gravity field from satellite gravity gradiometer (SGG) data and gravity vector data derived from, e.g., satellite‐to‐satellite tracking (SST). We chose a region centered over the European Alps where the gravity anomalies showed a (large) standard deviation of 60 mGal. Mean gravity anomalies were used to generate SGG data at a satellite altitude of 200 km. As SGG data we used the second‐order derivatives in radial direction, across‐track, and the mixed radial/cross‐track derivative, all assumed to have an associated noise equal to 0.01 EU (Eötvös unit =EU, 1 EU=10−9 s−2). As gravity data we used the three components of the gravity vector, assuming that the associated errors were uncorrelated noise with standard deviation equal to 1 mGal. The satellite data in the test area were used in combination to predict 0.5° mean gravity anomalies and geoid heights. Ground truth data were used to investigate the quality of the recovery. The difference between observed and computed values have a standard deviation equal to 22 mGal in the best case. The use of the gravity vector data gave no improvement when added to the SGG data. The use of topographic information with 5 arc min resolution (ETOPO5U) gave, after removal of severe errors, a 17‐mGal standard deviation of observed minus computed values. This is a much smaller improvement than expected but is due to errors in the topographic values.

Aeromagnetic Gradiometers-a Perspective

Measurements of horizontal or vertical gradients of the magnetic field intensity can add a new dimension to high resolution aeromagnetic surveys of shallow basement areas. Although a number of vertical, horizontal and triaxial aeromagnetic gradiometers are in operation throughout the world, very little has been documented on the relative merits of horizontal and vertical gradiometer measurements or of measured versus calculated gradients. Our results demonstrate that there are differences in spatial resolution and bandwidth between measured and calculated gradients and that horizontal and vertical gradients provide complementary information. Finally our results indicate that better geo-referencing of horizontal gradiometer data is needed before we can derive reliable vertical gradient data from the measured longitudinal and transverse gradients Development of short-baseline aeromagnetic gradiometers began in 1975 with construction of the Geological Survey of Canada vertical gradiometer. The success of current short-baseline gradiometers depends on the use of high sensitivity optical pumping magnetometers, usually caesium vapour sensors and effective compensation for aircraft manoeuvre noise. Practical advantages of measured gradients include elimination of the diurnal problem and improved spatial resolution of small shallow sources. Transient signals have the same effect on all the magnetometer sensors so the effects are cancelled out in the gradients and diurnal-free total magnetic intensity can then be reconstructed by integrating the gradient data. The gradient data effectively remove the main field of the earth and enhance smaller scale, shallow anomalies while attenuating longer wavelength, deeper seated anomalies. In addition, measurement of the transverse horizontal gradient provides extra information between flight lines, leading to a reduction in flight line dependency of magnetic anomalies and a reduction in aliasing effects. The vertical gradient can also be derived from the longitudinal and transverse horizontal gradients with less line dependence and probably lower noise levels than the measured vertical gradient. Data from a conventional Canadian vertical gradiometer system, an Australian horizontal gradiometer system and a Southern African triaxial gradiometer system are evaluated. The measured vertical gradient data appear to provide better resolution of shallow sources than the vertical gradient calculated from the total field. The horizontal gradient data allow us to derive the vertical gradient from the horizontal gradients and provide much improved enhanced total magnetic intensity grids. The choice of a vertical or horizontal gradiometer system depends on survey objectives and both systems have their advantages. The vertical gradient appears to be marginally easier to measure and simpler to interpret. A triaxial gradiometer system provides the advantages of both at the cost of an additional sensor and retractable boom installation, compared to a horizontal gradiometer. Unfortunately, in Australia, CAA certification of a retractable tail boom may prove difficult. The viability of deriving the vertical gradient profiles from measured horizontal gradients needs more research, but if this can be done routinely, we think this would tilt the balance towards the horizontal gradiometer system. The improvement in total magnetic intensity grids using the transverse gradient information can be quite dramatic in many cases and there is always some improvement in the data. The combination of transverse gradient enhanced total magnetic intensity data and high spatial resolution 'texture' filters provides excellent definition of lower amplitude anomalies. In contrast, the calculated vertical magnetic gradient is often very similar to the measured data and the benefits of the measured vertical gradient may be small in many cases. Gradiometer performance deteriorates rapidly as the source becomes deeper and existing gradiometers are probably close to the noise level at 500m depth. Rugged topography also causes fixed wing gradiometer performance to deteriorate.

Advantages of using the vertical gradient of gravity for 3-D interpretation

Gravity gradiometric data or gravity data transformed into vertical gradient can be efficiently processed in three dimensions for delineating density discontinuities. Model studies, performed with the combined use of maxima of analytic signal and of horizontal gradient and the Euler deconvolution techniques on the gravity field and its vertical gradient, demonstrate the superiority of the latter in locating density contrasts. Particularly in the case of interfering anomalies, where the use of gravity alone fails, the gravity gradient is able to provide useful information with satisfactory accuracy.

An inverse problem related to a finite part of a compact surface: Potential deduced from gravity gradients in space

Mean values for gravity and potential at the surface of the Earth are derived for limited areas in terms of mean anomalies using the cross‐track and radial components of the Eötvös tensor derived from space‐borne gradiometer data at satellite altitude. Stability, resolution, and precision are investigated, and reliability criteria are established. The inverse boundary value problem is discussed for specific solutions for smaller and larger areas at the Earth's surface; discrete area means and point values are considered.

Gravity field approximation using airborne gravity gradiometer data

A set of airborne Gravity Gradiometer Survey System (GGSS) data was used in combination with the OSU89B geopotential model to predict gravity anomalies and deflections of the vertical. The gradiometer data were collected during an airborne survey of the GGSS in the Texas/Oklahoma area. Nineteen flight tracks were in our disposal for further analysis. These tracks resulted from 54 initial distinct tracks from which a processing was performed by the Analytic Sciences Corporation. In order to assess the quality of the GGSS measurements, a first crossover analysis was carried out. The results showed large discrepancies at the crossing points between East‐West (EW) and North‐South (NS) tracks. The least squares collocation method and the fast fourier transform technique were used to produce gravity anomalies and deflections of the vertical referred to geoid surface from second‐order derivatives measured at the flight level. The predicted gravity values were then compared to “truth‐based” point free air gravity anomalies with a standard deviation (s.d.) of the differences at the level of 3 mGal in the best cases. Presumably, improved GGSS data would have given improved predictions of surface gravity values. The predicted deflections of the vertical were compared to “truth‐based” values at a small number of ground stations. The very low accuracy of this prediction (s.d.=5.62 arc sec for ξ and 6.78 for η) should be studied in combination with the inherent characteristics of the gravity field and the validation of GGSS data in the test area.

New developments in resolving detail in aeromagnetic data

Stacked profiles of aeromagnetic data often fail to resolve and display detail as this can be obliterated by larger amplitude features on adjacent flight lines. Contours and images of interpolated data can also obscure detail because they are sensitive to survey levelling errors and can show erroneous distortions caused by the interpolation method. Mclntyre (1981) showed that shaded stacked profiles of the second horizontal differences of flight-line data are effective in detecting and displaying detail in aeromagnetic data. Mclntyre used a square-root function to control the dynamic range of the computed difference so that both small and large amplitude features could be displayed without being obliterated by larger amplitude features on adjacent flight-lines. The shaded profile preferentially enhances positive values. Improvements on Mclntyre's shaded stacked profiles of horizontal differences form the basis of a new method of presenting horizontal differences of aeromagnetic data: the bipole map. This is a series of stacked flight-line profiles of bar-graphs of the horizontal difference values. The heights of the bar-graphs are controlled by the amplitude of the difference values whilst polarity is depicted with colour: red for positive values and blue for negative values. The bar-graphs are centred and located precisely on the curved flight-line; the flight-line forming the centre-line of the profile. Wavelength dependent automatic gain control (AGC) filters are used to modify the dynamic range of the horizontal differences so that both small and large amplitude anomalies can be displayed. The bipole map visually enhances both negative and positive values, more precisely positions the data and does not depend upon dubious magnetic values interpolated between the flight-lines. Bipole maps of the first, third and fourth horizontal differences are effective in resolving detail in other parts of the frequency spectrum. They supplement contours and images of longer wavelength features. Magnetic models show the responses of the horizontal differences for various inclinations of the Earth's magnetic field and different widths of the magnetic source. In areas of steep inclination, the horizontal differences delineate the strike axis of thin bodies and the edges of thick bodies. Bipole maps of horizontal differences may find useful application in displaying other types of geophysical data such as VLF-EM and aeromagnetic gradiometer data. Bipole maps of higher order differences are an effective means of resolving high frequency (instrument) noise in geophysical data. For aeromagnetic data from the Mt Magnet goldfield, located in the Archean greenstone belt of Western Australia, bipole maps of the second horizontal differences revealed that an anomaly from a banded iron formation might be caused by several close-spaced banded iron bodies rather than a single body, as might first be interpreted from the contours and images of the gridded data. Bipole maps of the fourth horizontal differences revealed a series of NNE striking magnetic lineaments which are not apparent in the contours and images of the gridded data.

AUTOMATIC INTERPRETATION OF GRAVITY GRADIOMETRIC DATA IN TWO DIMENSIONS: VERTICAL GRADIENT1

AbstractThe magnetic and gravity field produced by a given homogeneous source are related through Poisson's equation. Starting from this consideration, it is shown that some 2D interpretation tools, widely applied in the analysis of aeromagnetic data, can also be used for the interpretation of gravity gradiometric data (vertical gradient). This paper deals specifically with the Werner deconvolution, analytic signal and Euler's equation methods. After a short outline of the mathematical development, synthesized examples have been used to discuss the efficiency and limits of these interpretation methods. These tools could be applied directly to airborne gravity gradiometric data as well as ground gravity surveys after transformation of the Bouguer anomalies into vertical gradient anomalies. An example is given of the application of the Werner deconvolution and Euler's equation methods to a microgravity survey.

Simulation of regional gravity field recovery from satellite gravity gradiometer data using collocation and FFT

When planning a satellite gravity gradiometer (SSG) mission, it is important to know the quality of quantities to be recovered at ground level as a function of e.g. satellite altitude, data type and sampling rate, and signal variance and noise. This kind of knowledge may be provided either using the formal error estimates of wanted quantities using least-squares collocation (LSC) or by comparing simulated data at ground level with results computed by methods like LSC or FFT.

Magnetometer and Gradiometer Surveys for Detection of Underground Storage Tanks

In recent years there has been a surge of interest in methods for rapid and reliable detection and location of underground storage tanks and other cultural features related to hazardous substances in the subsurface. In the United States much of the motivation comes from recent environmental protection legislation that regulates underground storage tanks, including both existing and new installations. U.S. regulatory matters aside, ground-water contamination is a problem that knows no national borders; remediation of sites where hazardous substances can invade or have invaded ground-water supplies is a global concern. Detection and location of underground steel storage tanks can be readily accomplished using magnetometer and magnetic gradiometer surveys, which are a passive variety of remote sensing. This paper presents investigations at two sites at Hill Air Force Base, northern Utah. In each case, magnetometer and gradiometer data have proven to be valuable for assessing the possibilities of existence and location of buried underground storage tanks. Relevant magnetic-field principles are reviewed and methods of data acquisition, reduction, analysis and interpretation are described.

Low altitude tethered mars probe

A long tether connects a Martian orbiter to a small probe orbiting in the dense atmosphere of the planet. The minimum altitude reachable by the probe is estimated based upon considerations of dynamic stability, tether temperature, resistance of the tether material, and propellant consumption required to maintain a constant orbital altitude. The results obtained by means of a static-force model are then verified by dynamics simulation carried out by using a lumped-mass computer code. The scientific applications of this tethered system include probing of the Martian upper atmosphere and gravity mapping of the planet carried out by collecting gradiometric data from the probe. Another application involves the release of Martian rovers and penetrators from the probe at low altitude.

Resolution and variance operators of gravity and gravity gradiometry

Gravity gradiometry represents a new potential field data set which may better constrain the density structure of the earth. Using singular value (spectral) decomposition of the gravity and gravity gradient kernels, the model parameter resolution and model parameter variance of the two data types are compared using data from the Defense Mapping Agency and a recently acquired collection of airborne gradient measurements from Bell Aerospace Textron’s Gravity Gradient Survey System (GGSS). The GGSS was flown over a portion of southwestern Oklahoma, where the gravitational anomaly from the buried Wichita basement rocks is over 60 mGal. The corresponding maximum vertical gravity gradient was found to be 46.2 Eötvös. The determination of the subsurface density structure is cast as a linear inverse problem and, for comparison, a nonlinear inverse problem. For both the linear and nonlinear inversions, the gravity gradients improve the resolution and result in smaller variances than the vertical component of gravity. The density resolution and variance were computed for a subset of tracks from an airborne gravity gradient survey made in the summer of 1987. For the linear inversion, the resolution of the density is not adequate below the second layer (20 km). Furthermore, the estimated error of the actual gradient observations for a resolution of 0.9 km is 10E, for which the maximum error of the density values is [Formula: see text]. The linearized resolution of the boundary perturbations is better, with most parameters being well resolved. The standard errors for the layer perturbations are less than 1 km for the shallower layer (5.0 km) when using the gradiometer data. For the deeper layer (25.0 km), the maximum error is larger, 4.3 km.