Horizontal Gravity Gradient Research Articles

Hilbert transform of gravity gradient profiles: Special cases of the general gravity‐gradient tensor in the Fourier transform domain

The Hilbert transform has been extensively used in gravity gradient interpretation since the mid-1970s, when Stanley (1976) and Stanley and Green (1976) followed the work on the relationships between magnetic field components (Nabighian, 1972; Shuey, 1972) by showing that the vertical ( g z , z ) and horizontal ( g z , x ) gravity gradients of a 2-D truncated plate are related by the Hilbert transform. Butler (1983, 1995) has extended the use of the Hilbert transform in interpreting g z , z and g z , x resulting from additional geometries.

Regional gravity analysis of the crustal structure of Tunisia

Gravity data were integrated with seismic refraction/reflection data, well data and geological investigations to determine a general crustal structure of Tunisia. The gravity data analysis included the construction of a complete Bouguer gravity anomaly map, residual gravity anomaly maps, horizontal gravity gradient maps and a 2.5-D gravity model. Residual gravity anomaly maps illustrate crustal anomalies associated with various structural domains within Tunisia including the Sahel Block, Saharian Flexure, Erg Oriental Basin, Algerian Anticlinorium, Gafsa Trough, Tunisian Trough, Kasserine Platform and the Tell Mountains. Gravity anomalies associated with these features are interpreted to be caused either by thickening or thinning of Palæozoic and younger sediments or by crustal thinning. Analysis of the residual gravity anomaly and horizontal gravity gradient maps also determined a number of anomalies that may be associated with previously unknown structures. A north-south trending gravity model in general indicated similar subsurface bodies as a coincident seismic model. However, thinner Mesozoic sediments within the Tunisian Trough, thinner Palæozoic sediments in the Gafsa Trough, and a greater offset on the Saharian Flexure were required by the gravity data. Additionally, basement uplifts under the Kasserine Platform and Gafsa Trough, not imaged by seismic data, were required by the gravity data. The gravity model revealed two previously unknown basins north and south of the Algerian Anticlinorium (5 km), while the Erg Oriental Basin is composed of at least two sub-basins, each with a depth of 5 km.

Yucatán karst features and the size of Chicxulub crater

SUMMARY The buried Chicxulub impact structure is marked by a dramatic ring of sinkholes (called cenotes if containing water), and adjacent less prominent partial rings, which have been shown to coincide with maxima in horizontal gravity gradients and a topographic depression. These observations, along with the discreteness and spacing of the features, suggest a formation mechanism involving faulting in the outer slump zone of the crater, which would thus have a diameter of approximately 180 km. An opposing view, based primarily on the interpretation of gravity data, is that the crater is much larger than the cenote ring implies. Given the association of the known cenote ring with faults, we here examine northern Yucatan for similar rings in gravity, surface features and elevation, which we might expect to be associated with outer concentric faults in the case of a larger, possibly multiring, structure. No such outer rings have been found, although definite patterns are seen in the distribution of karst features outside the crater rim. We explain these patterns as resulting mainly from deformation related to the block fault zone that parallels the shelf edge of eastern Yucatan.

A least-squares minimization approach to depth determination from numerical horizontal gravity gradients : E.-S. M. Abdelrahman & S. M. Sharafeldin, Geophysics, 60(4), 1995, pp 1259–1260

A least-squares minimization approach to depth determination from numerical horizontal gravity gradients : E.-S. M. Abdelrahman & S. M. Sharafeldin, Geophysics, 60(4), 1995, pp 1259–1260

重力異常から見た甲府盆地の境界断層

The Kofu Basin is a tectonic basin in the South Fossa Magna. On the southeast and west margins of the Basin, there develop two tectonically peculiar terrains the Sane Hills and the Ichinose Upland bordered with active faults. These boundary faults are considered to play an important role in the tectonics of the Basin, but those subsurface structures are not yet known well. We carried out a dense gravity survey in and around the Basin and contoured a detailed Bouguer anomaly map in the area concerned. On the west and southeast of the Basin, steep horizontal gravity gradient zones distribute in parallel along the active faults and they develop on the mountain side of the faults. This gravity feature suggests that the mountains are thrust over the Basin. We made two-dimensional subsurface structure analysis along two sections to cross the Sone Hills and the Ichinose Upland. It is concluded that the density boundaries are on the northern edge of the Sone Hills and on the western edge of the Ichinose Upland, respectively.

Size and structure of the Chicxulub crater revealed by horizontal gravity gradients and cenotes

IT is now widely believed that a large impact occurred on the Earth at the end of the Cretaceous period, and that the buried Chicxulub structure in Yucatan, Mexico, is the resulting crater24. Knowledge of the size and internal structure of the Chicxulub crater is necessary for quantifying the effects of the impact on the Cretaceous environment. Although much information bearing on the crater's structure is available, diameter estimates range from 170 to 300 km (refs 1a¤-7), corresponding to an order of magnitude variation in impact energy. Here we show the diameter of the crater to be ˜180 km by examining the horizontal gradient of the Bouguer gravity anomaly over the structure. This size is confirmed by the distribution of karst features in the Yucatan region (mainly water-filled sinkholes, known as cenotes). The coincidence of cenotes and peripheral gravity-gradient maxima suggests that cenote formation is closely related to the presence of slump faults near the crater rim.

A least‐squares minimization approach to depth determination from numerical horizontal gravity gradients

The sphere and the horizontal cylinder models can be very useful in quantitative interpretation of gravity data measured in a small area over buried structures. Several graphical and numerical methods have been developed by many workers for interpreting the residual gravity anomalies caused by these models to find the depth of most geologic structures. Excellent reviews are given in Saxov and Nygaard (1953) and Bowin et al. (1986). The numerical approaches (Odegard and Berg, 1965; Gupta, 1983; Sharma and Geldart, 1968; Lines and Treitel, 1984; and Shaw and Agarwal, 1990) may have advantages in theory and practice over graphical depth estimation techniques (Pick et al., 1973: Nettleton, 1976; Telford et al., 1976). However, effective quantitative interpretation procedures using the least‐squares method based on the analytical expression of simple numerical horizontal gravity gradient anomalies are yet to be developed.

A new method for combining gravimetric and geological data

Application of the gravity method to structural geology makes it possible to highlight local variations of the gravitational field that are caused by density heterogeneities related to the composition and structure of the crust. These density heterogeneities and their boundaries, which correspond to gravity discontinuities, can be identified using the properties of the vertical and horizontal derivatives of the field. Gravity data on the Huelgoat granite in the Armorican Massif (France) were subjected to a new two-step geological analysis. First, the gravity discontinuities derived from Bouguer anomaly data were automatically identified; and second these discontinuities were combined with existing geological data. The first step was made possible by a software program that defines and visualizes the gravity discontinuities through an automatic analysis of the horizontal and vertical gravity gradient functions. The result is a map on which gravity discontinuities separate areas of different densities. The vertical and horizontal derivatives of the field were computed from the gravity data using frequency domain transformations. The second step corresponds to the geological interpretation of the gravity discontinuity map. A petrostructural map is used, which mainly shows the structure and the syntectonic internal fabric of the area, along with fracture data obtained on the granite and its host rocks. The latter illustrates late brittle deformation. The petrostructural map is used to adjust and rearrange the gravity discontinuities in order to obtain a gravity image deduced from the fabric of the rocks, a “fabric/gravity image”. After this, a “fracture/gravity image” is derived by using the fracture data as a filter to obtain priority directions in the gravity discontinuities. Superimposing the two images provides a structural sketch map that gives a more integrated insight into the ductile and brittle deformation of the area than can be obtained from field observations alone.

Tectonic fabric map of the ocean basins from satellite altimetry data

Satellite altimetry data provide a new source of information on the bathymetry of the ocean floor. The tectonic fabric of the oceans (i.e., the arrangement of fracture zones, ridges, volcanic plateaus and trenches) is revealed by changes in the horizontal gravity gradient as recorded by satellite altimetry measurements. SEASAT and GEOSAT altimetry data have been analyzed and a global map of the horizontal gravity gradient has been produced that can be used to identify a variety of marine tectonic features. The uniformity of the satellite coverage provides greater resolution and continuity than maps based solely on ship-track data. This map is also the first global map to incorporate the results of the GEOSAT mission, and as a result, new tectonic features are revealed at high southerly latitudes. This map permits the extension of many tectonic features well beyond what was previously known. For instance, various fracture zones, such as the Ascension, Tasman, and Udintsev fracture zones, can be extended much closer to adjacent coninental margins. The tectonic fabric map also reveals many features that have not been previously mapped. These features include extinct ridges, minor fracture zone lineations and seamounts. In several areas, especially across aseismic plateaus or along the margins of the continents, the map displays broad gravity anomalies whose origin may be related to basement structures.

Gravity domains and assembly of the North American continent by collisional tectonics

Trends of geophysical anomalies have made important contributions to local and regional structural studies within the North American continent1,2, particularly in examining the Precambrian basement underlying the relatively undeformed Phanerozoic sediments that cover ∼45% of North America3–5. Here we present a gravity trend map of North America, based on a horizontal Bouguer gravity gradient map6 produced from gravity data for Canada and the conterminous United States, and use it to define a continental mosaic of gravity trend domains akin to structural domains. Contrasting trend characteristics at gravity domain boundaries support the concept of the outward growth of the continent primarily by accretionary (collisional) tectonics. Gravity patterns, however, indicate a different style of tectonics dominated in the development of now-buried Proterozoic orogenic belts in the south`central United States, supporting a view that these belts formed along the leading edge of a southward-migrating Proterozoic continental margin7.

Horizontal gravity gradient: An aid to the definition of crustal structure in North America

A map of the magnitude of the horizontal Bouguer gravity gradient over the North American continent is used to delineate lateral discontinuities in upper crustal density and/or thickness associated with such processes as suturing and rifting. The usefulness of gradient trends in mapping major structural boundaries, which are sometimes poorly exposed or completely buried, is demonstrated by examples such as the buried southward extension of the Grenville Front and buried boundaries of the Superior Province. Gradient trends also draw attention to poorly known structures, which may have major tectonic significance, and to a continent‐wide structural fabric, which may provide a record of the tectonic growth of the North American continent.

Relative precision of vertical and horizontal gravity gradients measured by gravimeter

Several recent publications advocate the use of the vertical gradient of gravity from gravimeter measurements at two elevations in a portable tower (Thyssen‐Bornemisza, 1976; Fajklewicz, 1976; Mortimer, 1977). Contrary opinions have also been expressed (Hammer and Anzoleaga, 1975; Stanley and Green, 1976; Thysen‐Bornemisza, 1977; Arzi, 1977). The disagreement revolves around the question of practically attainable precision of the vertical gradient tower method. Although it is possible to calculate both horizontal and vertical gradients from conventional gravity survey data by use of the Hilbert transform (Stanley and Green, 1976), it should be noted that highly precise gravity data are required. Also the need for connected elevation and location surveys, the major cost in gravity surveying, is not avoided. This is a significant advantage of the gradient methods. The purpose here is to present a brief consideration of the relative precision of the horizontal and vertical gradients, as measured in the field by special gravimeter observations.

Plumb line deflection near the North Pole

In April 1969 the deflection of the plumb line in the vicinity of the Lomonosov ridge near the north pole was determined from a drifting ice station by measuring the displacement between two drift paths, one determined astronomically and the other determined by means of a Transit Satellite receiver. In addition, the fine structure of the drift path relative to the ocean floor was obtained from acoustic measurements. The mean plumb line deflection at 89°40′N, 77°W was found to be 9 arc sec in the direction of 34°E, pointing away from the Lomonosov ridge. Computations were made concerning the perturbation of the gravity vector on the basis of a hypothetical model of the Lomonosov ridge. This model involves a density structure consistent with a continental origin of the ridge and shows that deflection gradients of up to 0.7 arc sec/km and horizontal gravity gradients of up to 3.4 mGal/km can occur. The measured plumb line deflection and gravity observations carried out in the vicinity of the ridge are consistent with the model, but because of the scarcity of observations and the very incomplete bathymetric data, no final conclusions on the origin of the Lomonosov ridge can be made. Continuous plumb line deflection measurements are ideally suited to be carried out from a drifting sea ice station where they will complement the gravity measurements in an area where regional gravity observations are scarce.

THE GRADATIONAL DENSITY CONTRAST AS A GRAVITY INTERPRETATION MODEL

The basic equations are presented for the gravity effect of a horizontal slab with density varying linearly between limits. A series of type curves and interpretation nomograms are presented showing the characteristics of the gradational model. A notable characteristic is the horizontal gravity gradient which is nearly constant over most of the width of the variable density zone. Maximum slope and curvature of the gravity effect vary directly with the density change, depth, and thickness of the slab and inversely with the width of the variable density zone. Practically identical gravity effects are sometimes produced by step models with different dimensions and density contrasts. However, if the variable density zone is sufficiently wide, the gravity effect cannot be approximated by a simple step model.

Interpolation of the vertical deflection from horizontal gravity gradients

A method is described for the interpolation of deflections of the vertical from horizontal gravity gradients that can be done with considerable accuracy. From the interpolated deflections and astronomic observations, the geodetic coordinated can then be determined. The accuracy of the interpolated deflections or of the geodetic coordinates have a maximum standard error of 0.5′′ for lines 30–40 km long. The method is very efficient for the densification of deflections of the vertical where otherwise a very detailed gravity survey is required, but for geodetic coordinate determination, the procedure generally cannot be considered superior to conventional methods of establishing horizontal control. A potential application may be found, however, in photogrammetry.

DOUBLE‐TRACK PROFILING WITH THE GRAVITY METER

This technique, providing, simultaneously, gravity values and horizontal gravity gradients, is briefly discussed because of its possible advantage in marine exploration using the underwater gravity meter. Operating these remote‐control meters at greater depth is rather cumbersome and costly if compared to surveys at the ground surface (Dobrin, 1960). However, a profile of average horizontal gradients, in addition to a regular gravity profile, would indicate positive or negative anomalies located away from the profile itself, and would help avoid gravity stations with insignificant interpretative value.

RECONNAISSANCE SURVEY USING AVERAGE HORIZONTAL GRADIENTS OF GRAVITY

Some time ago, Romberg (1956/57) pointed out the advantage of reading horizontal gravity gradients rather than vertical gradients with the gravity meter. Several years later, in March, 1960, an experimental profile of gravity‐meter‐determined horizontal gradients was run for the author in the South Houston field by courtesy of Texas Instruments Incorporated. Since then, this gradient technique was repeatedly discussed but only very few results could be published (Thyssen‐Bornemisza et al., 1960, 1962a, 1962b). Stackler (1963) more recently pointed out again the value of the average gravity gradient for reconnaissance surveys predominantly in inaccessible areas.

The Connexion between the Eotvos Magnitudes

IN the problem of locating subterranean anomalies of density, the Eotvos balance measures two quantities, the horizontal gravity gradient and the difference between the principal curvatures of the level surface at the point of observation. In the two-dimensional case these reduce to Uxz and − Uxx denoted by G(x) and K(x) respectively. In all treatments of the subject, which I have seen G(x) and K(x) appear to be considered independent of one another. It can be shown, however, that there is a one-to-one relation between the two functions, namely, that they are conjugate trigonometrical integrals of one another;1 in fact :where P denotes the principal part of the subsequent integral.