THE AVERAGE HORIZONTAL GRAVITY GRADIENT

Geophysics ◽  
1962 ◽  
Vol 27 (5) ◽  
pp. 714-715
Author(s):  
Stephen Thyssen‐Bornemisza ◽  
W. F. Stackler
Keyword(s):  
Gravity Gradient ◽  
Horizontal Gradient ◽  
Theoretical Discussion ◽  
Gravity Gradients ◽  
Geophysical Exploration

The authors reported experiments of making measurements with the gravity meter at close spacings (Geophysics, 1956, 1958; Journal ASPG, 1960, 1962) for the purpose of obtaining gravity gradients and micro‐gravimetric maps. Since the average horizontal gradient seems to be of some interest for geophysical exploration, a brief theoretical discussion is presented.

Reduction to the pole of the North American magnetic anomalies

Geophysics ◽  
1990 ◽  
Vol 55 (2) ◽  
pp. 218-225 ◽  
Author(s):  
J. Arkani‐Hamed ◽  
W. E. S. Urquhart
Keyword(s):  
North America ◽  
Gravity Anomalies ◽  
Magnetic Anomalies ◽  
Gravity Gradient ◽  
Plate Boundaries ◽  
Gravity Gradients ◽  
The North ◽  
Vertical Gravity Gradient ◽  
Regional Tectonic ◽  
Vertical Gravity

Magnetic anomalies of North America are reduced to the pole using a generalized technique which takes into account the variations in the directions of the core field and the magnetization of the crust over North America. The reduced‐to‐the‐pole magnetic anomalies show good correlations with a number of regional tectonic features, such as the Mid‐Continental rift and the collision zones along plate boundaries, which are also apparent in the vertical gravity gradient map of North America. The magnetic anomalies do not, however, show consistent correlation with the vertical gravity gradients, suggesting that magnetic and gravity anomalies do not necessarily arise from common sources.

Microgravimetric and gravity gradient techniques for detection of subsurface cavities

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1084-1096 ◽  
Author(s):  
Dwain K. Butler
Keyword(s):  
Case History ◽  
Vertical Gradient ◽  
Gravity Gradient ◽  
Horizontal Gradient ◽  
Shallow Subsurface ◽  
Gradient Profile ◽  
First Case ◽  
Profile Line ◽  
Cavity System ◽  
Subsurface Cavities

Microgravimetric and gravity gradient surveying techniques are applicable to the detection and delineation of shallow subsurface cavities and tunnels. Two case histories of the use of these techniques to site investigations in karst regions are presented. In the first case history, the delineation of a shallow (∼10 m deep), air‐filled cavity system by a microgravimetric survey is demonstrated. Also, application of familiar ring and center point techniques produces derivative maps which demonstrate (1) the use of second derivative techniques to produce a “residual” gravity map, and (2) the ability of first derivative techniques to resolve closely spaced or complex subsurface features. In the second case history, a deeper (∼ 30 m deep), water‐filled cavity system is adequately detected by a microgravity survey. Results of an interval (tower) vertical gradient survey along a profile line are presented in the second case history; this vertical gradient survey successfully detected shallow (<6 m) anomalous features such as limestone pinnacles and clay pockets, but the data are too “noisy” to permit detection of the vertical gradient anomaly caused by the cavity system. Interval horizontal gradients were determined along the same profile line at the second site, and a vertical gradient profile is determined from the horizontal gradient profile by a Hilbert transform technique. The measured horizontal gradient profile and the computed vertical gradient profile compare quite well with corresponding profiles calculated for a two‐dimensional model of the cavity system.

scholarly journals Generalized gravity gradient analysis for 2-D inversion

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1018-1028 ◽  
Author(s):  
Dwain K. Butler
Keyword(s):  
Gravity Data ◽  
Vertical Gradient ◽  
Diagnostic Information ◽  
Effective Density ◽  
Gravity Gradient ◽  
Horizontal Gradient ◽  
Plate Model ◽  
Structural Interpretation ◽  
Gradient Profile ◽  
Inversion Procedure

Gravity gradient profiles across subsurface structures that are approximately 2-D contain diagnostic information regarding depth, size, and structure (geometry). Gradient space plots, i.e., plots of horizontal gradient versus vertical gradient, present the complete magnitude and phase information in the gradient profiles simultaneously. Considerable previous work demonstrates the possibility for complete structural interpretation of a truncated plate model from the gradient space plot. The qualitative and quantitative diagnostic information contained in gradient space plots is general, however. Examination of the characteristics of gradient space plots reveals that 2-D structures are readily classified as extended or localized. For example, the truncated plate model is an extended model, while the faulted plate model is a localized model. Comparison of measured or calculated gradient space plots to a model gradient space plot catalog allows a rapid, qualitative determination of structure or geometry. “Corners” of a polygonal cross‐section model are then determined as profile points corresponding to maxima on the vertical gradient profile. A generalized approach to structural interpretation from gravity data consists of (1) determining vertical and horizontal gradient profiles perpendicular to the strike of a 2-D gravity anomaly, (2) determining the structural geometry from the gradient space plot, and (3) locating profile positions of structural corners from the vertical gradient profile. This generalized inversion procedure requires no quantitative information or assumption regarding density contrasts. Iterative forward modeling then predicts the density contrasts. Application of this generalized gravity gradient inversion procedure to high quality gravity data results in an effective density prediction consistent with measured near‐surface densities and the known increase in density with depth in deep sedimentary basins.

scholarly journals Exploiting Aeromagnetic and Gravity Data Interpretation to Delineate Massif Deposits of Rehamna Area (Western Meseta-Morocco)

2021 ◽  
Vol 54 (2C) ◽  
pp. 13-28
Author(s):  
Kawtar Benyas
Keyword(s):  
Gravity Data ◽  
Precious Metals ◽  
Data Interpretation ◽  
Structural Features ◽  
Magnetic Data ◽  
Gravity Gradient ◽  
Horizontal Gradient ◽  
Geological Structures ◽  
Magnetic Signatures ◽  
First Vertical Derivative

The analysis of the magnetic signatures and gravity gradient values of the Rehamna Massif south of the Moroccan Western Meseta by using Geosoft Oasis Montaj 7.0.1 software, allowed us to detect several useful anomalies to be exploited and which are related to magmatic bodies and structural features within the study area. These data were analyzed by applying several techniques, including the horizontal gradient filters combined with the first vertical derivative. Subsurface structures; such as geological boundaries, faults, dykes and folds, were visualized as lineaments on geophysical maps, then results were compared with structural features provided by previous studies in the region. Thus, the Rehamna Massif structural map shows sets of linear features which may represent faults or boundaries of geological structures, which can be either faults or boundaries of geological structures, and they are mostly oriented in the directions: N-S, NNE-SSW, NE-SW, E-W with the predominance of the NNE-SSW to NE-SW directions. In addition, the super position of the minerals bearing beds or formations were distinguished from gravity and magnetic data processing results. Some of the recognized anomalies are related to the existence of precious metals which belong to the granitic bodies within the study area.

The space-wise approach for cold-atom interferometry geodetic data analysis: the MOCASS study

2020 ◽  
Author(s):  
Federica Migliaccio ◽  
Mirko Reguzzoni ◽  
Khulan Batsukh
Keyword(s):  
Data Analysis ◽  
Hydrological Cycle ◽  
Cold Atom ◽  
Atom Interferometer ◽  
Geodetic Data ◽  
Gravity Models ◽  
Relative Mass ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
The Earth

&lt;p&gt;In recent years, an innovative mission concept has been proposed for gravity measurements with the aim of continuously monitoring the Earth gravity and its changes. The concept is based on a satellite-borne interferometer exploiting ultra-cold atom technology. Among other studies, a team of researchers from Italian universities and research institutions proposed and carried out the MOCASS project, to investigate the performance of a cold atom interferometer flying on a low Earth orbiter and its impact on the modeling of different geophysical phenomena.&lt;/p&gt;&lt;p&gt;In this study, the basic idea was that of a GOCE follow-on mission, with a unique spacecraft carrying an instrument capable of measuring functionals of the Earth gravitational potential. The geodetic data analysis of the gravity gradient data attainable by such a mission was carried out following the space-wise approach developed at Politecnico di Milano. The mathematical model for the processing of the MOCASS data was formulated, including the filtering strategy applied to take into account the cold atom interferometer transfer function. Numerical simulations were performed, with different configurations of the satellite orbit and pointing mode of the interferometer; data were simulated for two cases: (i) a single-arm gradiometer observing T&lt;sub&gt;xx&lt;/sub&gt; or T&lt;sub&gt;yy&lt;/sub&gt; or T&lt;sub&gt;zz &lt;/sub&gt;gradients; (ii) a double-arm gradiometer observing T&lt;sub&gt;xx &lt;/sub&gt;and T&lt;sub&gt;zz &lt;/sub&gt;gradients or T&lt;sub&gt;yy &lt;/sub&gt;and T&lt;sub&gt;zz&lt;/sub&gt; gradients. The results of the simulations will be illustrated, showing the applicability of the proposed concept and the neat improvement in modeling the static gravity field with respect to GOCE.&lt;/p&gt;&lt;p&gt;Moreover, a new study called MOCAST+ has been lately started proposing an enhanced cold atom interferometer which can deliver not only gravity gradients but also time measurements. The study will investigate whether this could give the possibility of improving the estimation of gravity models even at low harmonic degrees, with inherent advantages in the modeling of mass transport and its global variations: this will represent fundamental information, e.g. in the study of variations in the hydrological cycle and relative mass exchange between atmosphere, oceans, cryosphere and solid Earth.&lt;/p&gt;

GRAVITY GRADIENTS AND THE INTERPRETATION OF THE TRUNCATED PLATE

Geophysics ◽  
1976 ◽  
Vol 41 (6) ◽  
pp. 1370-1376 ◽  
Author(s):  
John M. Stanley ◽  
Ronald Green
Keyword(s):  
Hilbert Transform ◽  
Theoretical Data ◽  
Vertical Gradient ◽  
Density Contrast ◽  
Horizontal Gradient ◽  
Gravity Gradients ◽  
Gravity Method ◽  
Commercially Important ◽  
Dip Angle ◽  
Vertical Gradients

The truncated plate and geologic contact are commercially important structures which can be located by the gravity method. The interpretation can be improved if both the horizontal and vertical gradients are known. Vertical gradients are difficult to measure precisely, but with modern gravimeters the horizontal gradient can be measured conveniently and accurately. This paper shows how the vertical gradient can be obtained from the horizontal gradient by the use of a Hilbert transform. A procedure is then presented which easily enables the position, dip angle, depth, thickness, and density contrast of a postulated plate to be precisely and unambiguously derived from a plot of the horizontal gradient against the vertical gradient at each point measured. The procedure is demonstrated using theoretical data.

The role of a laterally varying density contrast for gravity inversion of the Moho depth

2020 ◽  
Author(s):  
Peter Haas ◽  
Joerg Ebbing ◽  
Wolfgang Szwillus ◽  
Philipp Tabelow
Keyword(s):  
Global Scale ◽  
Density Contrast ◽  
Gradient Field ◽  
Moho Depth ◽  
Gravity Gradient ◽  
Gravity Inversion ◽  
Gravity Gradients ◽  
Regional Study ◽  
Satellite Gravity ◽  
Amazonian Craton

&lt;p&gt;We present a new inverse approach to invert satellite gravity gradients for the Moho depth under consideration of a laterally varying density contrast between crust and mantle. The inverse problem is linearized and solved with the classical Gauss-Newton algorithm in a spherical geometry. To ensure stable solutions, the Jacobian is smoothed with second-order Tikhonov regularization. During the inversion, the Moho depth is discretized into tesseroids by reference Moho depth and density contrast, from which the gravitational effect can be calculated. As a computational benefit, the Jacobian is calculated only once and afterwards weighted with the laterally varying density contrast. We look for a Moho depth model that simultaneously explains the gravity gradient field and a least misfit to existing seismic Moho depth determinations. We perform the inversion both on regional and global scale.&lt;/p&gt;&lt;p&gt;The laterally varying density contrast is based on different tectonic units, which are defined by independent global geological and geophysical data, such as regionalization of dispersion curves. This is beneficial in remote areas, where seismic investigations are very sparse and the crustal structure is to a large extent unknown. Applying the inversion to the Amazonian Craton and its surroundings shows a lower density contrast at the Moho depth for the continental interior compared to oceanic domains. This is in accordance with the tectono-thermal architecture of the lithosphere. The inverted values of the density vary between 300-450 kg/m&lt;sup&gt;3&lt;/sup&gt;. The inverted Moho depth shows a clear separation between the Sao Francisco Craton and shallower Amazonian Craton.&lt;/p&gt;&lt;p&gt;Gravity inversion with a laterally varying density contrast requires a uniform reference Moho depth. On a global scale, we utilize our inversion to estimate a reference Moho depth that is in accordance with crustal buoyancy. The inverted density contrasts show a similar trend like the regional study area. The inverted Moho depth shows expected tectonic features. Our method of computing the Jacobian once and weighting with lateral variable density contrasts is a valuable optimization of standard gravity inversion.&lt;/p&gt;

EXPLORING FOR STRATIGRAPHIC TRAPS WITH GRAVITY GRADIENTS

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 256-268 ◽  
Author(s):  
Sigmund Hammer ◽  
Rodolfo Anzoleaga
Keyword(s):  
Gradient Method ◽  
Torsion Balance ◽  
Important Application ◽  
Theory And Practice ◽  
Horizontal Gradient ◽  
Gravity Gradients ◽  
Limited Extent ◽  
Field Surveys ◽  
New Instrumentation ◽  
Vertical Gradients

The vast and growing literature on the search for stratigraphic traps for petroleum ignores gravity gradients, for which the theory has been available since the heyday of the Eötvös torsion balance decades ago. These are discussed in this paper. The horizontal and vertical gradients can be measured with available gravimeters and (to a limited extent) with the Eötvös torsion balance. A major advantage of the gradient method is that surveying to determine position and elevation of the station is not required. Both theory and practice have been reported in the geophysical literature, but the important application to stratigraphic traps has not been mentioned. We evaluate here the method for locating “pinchouts”, a term which embraces “stratigraphic” and “unconformity” traps in Halbouty’s (1972) classification. Both position and depth of the assumed pinchout are determined by the gradient anomaly. The magnitudes of anomalies of horizontal and vertical gradients are about equal. However, pending new instrumentation, only the horizontal gradient is practically useful for field surveys. The gradient method is quantitatively promising and, used in conjunction with other methods, should significantly advance the search for stratigraphic traps for petroleum.

Using gravity gradients to estimate fault parameters in the Wichita Uplift region

2020 ◽  
Vol 222 (3) ◽  
pp. 1704-1716
Author(s):  
Sibel Uzun ◽  
Kamil Erkan ◽  
Christopher Jekeli
Keyword(s):  
Gravity Gradient ◽  
Gravity Gradients ◽  
Strong Constraint ◽  
North American Continent ◽  
The North ◽  
Field Curvature ◽  
Fault Parameters ◽  
Gravitational Gradients ◽  
Southern Oklahoma ◽  
Dip Angle

SUMMARY The geological setting of southwestern Oklahoma and northeastern Texas is an ideal example of an aulacogen, the result of the tectonic evolution of a failed rift of the North American continent during the Palaeozoic era (540–360 Ma). The Wichita Province forms the uplifted basement portion of this Southern Oklahoma Aulacogen (SOA). The major fault zones to its north and south are clearly evident in gravity gradient maps produced by the recently constructed Earth Gravitational Model 2008 (EGM2008). Fault parameters, such as the dip angle, location and density contrasts have been estimated from profiles of seismic data and local gravimetry in the 1990s. On the other hand, gravitational gradients that are derived from EGM2008 and then combined to form the differential field curvature are particularly indicative of linear structures such as dip-slip faults. They are used here exclusively, that is, without additional geophysical constraints, in an optimal, least-squares estimation based on the Monte Carlo technique of simulated annealing to determine dip angle and location parameters of the major faults that border the Wichita Uplift region. Results show that these faults have small dip angles, in basic agreement with the low-angle faults inferred from seismic studies. The EGM2008 gradients also appear in some cases to provide an improved map of the major faults in the region, thus offering a strong constraint on their location.

Tesseroids: Forward-modeling gravitational fields in spherical coordinates

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. F41-F48 ◽  
Author(s):  
Leonardo Uieda ◽  
Valéria C. F. Barbosa ◽  
Carla Braitenberg
Keyword(s):  
Gravitational Potential ◽  
Computation Time ◽  
Forward Modeling ◽  
Gravity Gradient ◽  
Maximum Relative Error ◽  
Gravitational Acceleration ◽  
Spherical Coordinates ◽  
Gravity Gradients ◽  
Gravitational Fields ◽  
Adaptive Discretization

We have developed the open-source software Tesseroids, a set of command-line programs to perform forward modeling of gravitational fields in spherical coordinates. The software is implemented in the C programming language and uses tesseroids (spherical prisms) for the discretization of the subsurface mass distribution. The gravitational fields of tesseroids are calculated numerically using the Gauss-Legendre quadrature (GLQ). We have improved upon an adaptive discretization algorithm to guarantee the accuracy of the GLQ integration. Our implementation of adaptive discretization uses a “stack-based” algorithm instead of recursion to achieve more control over execution errors and corner cases. The algorithm is controlled by a scalar value called the distance-size ratio ([Formula: see text]) that determines the accuracy of the integration as well as the computation time. We have determined optimal values of [Formula: see text] for the gravitational potential, gravitational acceleration, and gravity gradient tensor by comparing the computed tesseroids effects with those of a homogenous spherical shell. The values required for a maximum relative error of 0.1% of the shell effects are [Formula: see text] for the gravitational potential, [Formula: see text] for the gravitational acceleration, and [Formula: see text] for the gravity gradients. Contrary to previous assumptions, our results show that the potential and its first and second derivatives require different values of [Formula: see text] to achieve the same accuracy. These values were incorporated as defaults in the software.

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