Interval gravity‐gradient determination concepts

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 828-832 ◽  
Author(s):  
Dwain K. Butler
Keyword(s):  
Finite Difference ◽  
Gravity Data ◽  
Vertical Gradient ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
Tower Structure ◽  
Gravity Measurements ◽  
Vertical Gradients

Considerable attention has been directed recently to applications of gravity gradients, e.g., Hammer and Anzoleaga (1975), Stanley and Green (1976), Fajklewicz (1976), Butler (1979), Hammer (1979), Ager and Liard (1982), and Butler et al. (1982). Gravity‐gradient interpretive procedures are developed from properties of true or differential gradients, while gradients are determined in an interval or finite‐difference sense from field gravity data. The relations of the interval gravity gradients to the true or differential gravity gradients are examined in this paper. Figure 1 illustrates the concepts of finite‐difference procedures for gravity‐gradient determinations. In Figure 1a, a tower structure is illustrated schematically for determining vertical gradients. Gravity measurements are made at two or more elevations on the tower, and various finite‐difference or interval values of vertical gradient can be determined. For measurements at three elevations on the tower, for example, three interval gradient determinations are possible: [Formula: see text]; [Formula: see text]; [Formula: see text]; where [Formula: see text] and [Formula: see text] etc. For a positive downward z-;axis, these definitions for [Formula: see text] and [Formula: see text] will result in positive values for the vertical gradient. Relations of the interval gradients to each other and to the true or differential gradient are examined in this paper.

Relative precision of vertical and horizontal gravity gradients measured by gravimeter

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 99-101 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Survey Data ◽  
Hilbert Transform ◽  
Gravity Data ◽  
Gradient Methods ◽  
Vertical Gradient ◽  
Gravity Gradients ◽  
Relative Precision ◽  
The Hilbert Transform ◽  
Vertical Gradients ◽  
Vertical Gradient Of Gravity

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.

scholarly journals Research Article. A new gravity laboratory in Ny-Ålesund, Svalbard

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
K. Breili ◽  
R. Hougen ◽  
D. I. Lysaker ◽  
O. C. D. Omang ◽  
B. Tangen
Keyword(s):  
Noise Level ◽  
Gravity Data ◽  
Ocean Tide ◽  
Gravity Gradients ◽  
Svalbard Archipelago ◽  
Ocean Tide Loading ◽  
Lower Elevation ◽  
Gravity Measurements ◽  
Space Geodetic Techniques ◽  
Under Construction

AbstractThe Norwegian Mapping Authority (NMA) has recently established a new gravity laboratory in Ny-Ålesund at Svalbard, Norway. The laboratory consists of three independent pillars and is part of the geodetic core station that is presently under construction at Brandal, approximately 1.5 km north of NMA’s old station. In anticipation of future use of the new gravity laboratory, we present benchmark gravity values, gravity gradients, and final coordinates of all new pillars. Test measurements indicate a higher noise level at Brandal compared to the old station. The increased noise level is attributed to higher sensitivity to wind.We have also investigated possible consequences of moving to Brandal when it comes to the gravitational signal of present-day ice mass changes and ocean tide loading. Plausible models representing ice mass changes at the Svalbard archipelago indicate that the gravitational signal at Brandal may differ from that at the old site with a size detectable with modern gravimeters. Users of gravity data from Ny-Ålesund should, therefore, be cautious if future observations from the new observatory are used to extend the existing gravity record. Due to its lower elevation, Brandal is significantly less sensitive to gravitational ocean tide loading. In the future, Brandal will be the prime site for gravimetry in Ny-Ålesund. This ensures gravity measurements collocated with space geodetic techniques like VLBI, SLR, and GNSS.

THE ANOMALOUS FREE‐AIR VERTICAL GRADIENT IN BOREHOLE EXPLORATION

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 441-443 ◽  
Author(s):  
Stephen Thyssen‐Bornemisza
Keyword(s):  
Observation Interval ◽  
Vertical Gradient ◽  
Gravitational Effects ◽  
Free Air ◽  
Gravity Measurements ◽  
Source Of Error ◽  
Vertical Gradients ◽  
Interpretation Of Results

Hammer (1950) and Smith (1950), in discussions about gravity measurements in vertical shafts and boreholes, have pointed out that gravitational effects originating in zones or layers above or below the gravity‐meter observation interval may easily produce anomalous free‐air vertical gradients. These anomalous gradients cannot well be corrected without the proper density information and, therefore, would represent a possible source of error in the interpretation of results.

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.

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.

Operating an industry-grade quantum differential gravimeter

2020 ◽  
Author(s):  
Camille Janvier ◽  
Vincent Ménoret ◽  
Jean Lautier ◽  
Bruno Desruelle ◽  
Sebastien Merlet ◽  
...  
Keyword(s):  
Accurate Determination ◽  
Vertical Gradient ◽  
Physical Principle ◽  
Gravity Gradient ◽  
Vertical Acceleration ◽  
Short Term ◽  
Gravity Measurements ◽  
Vertical Accelerations ◽  
The Stability ◽  
Absolute Quantum

<p>After three years of development in collaboration with LNE-SYRTE, we report on the development, the integration and the preliminary operation of an industry-grade absolute differential gravimeter. This new generation of instrument goes beyond the possibilities offered by existing gravity gradiometers, as one differential gravimeter measures simultaneously g and the vertical gradient of g [1]. Relying on atom interferometry with cold 87 Rb atoms, a single vertical laser beam simultaneously measures the vertical acceleration experienced by two sets of laser-cooled atoms free-falling from different heights. For each drop, the half-sum of the two vertical accelerations gives access to g and the half-difference to dg / dz. As far as technology is concerned, our differential gravimeter relies on a physical principle and a set of technologies that have already been validated for absolute quantum gravimeters [2].</p><p><br>Our demonstrator is operational since November 2019 and has shown the ability to run continuously for more 18 days without any human attendance.  We will present in detail the experimental results for the measurement of g and dg / dz. Regarding the measurement of the vertical gradient of g, we obtain a short-term sensitivity of 76 E/√t (1E = 10 -9 s -2 = 0.1 µGal/m) and a resolution of a 4 E when data is averaged over 1000 s. Regarding the measurement of g itself, we obtain a short-term sensitivity of 36 µGal/√t and a resolution of a few µGal when data is averaged over 500 s. These are preliminary results and options and future plan to improve the sensitivity and the stability of the measurements will be discussed.</p><p><br>Such quantum differential gravimeter is to our knowledge the only technology that allows for an absolute continuous drift-free monitoring of simultaneously gravity and gravity gradient over timescales from a few minutes to several months.</p><p> </p><p>This work has been supported by the DGA, the French Department of Defense.</p><p> </p><p>[1] R. Caldani <em>et al.</em>, "Simultaneous accurate determination of both gravity and its vertical gradient", Phys. Rev. A <strong>99</strong>, 033601 (2019)</p><p>[2] V. Ménoret <em>et al.</em>, "Gravity measurements below 10−9 g with a transportable absolute quantum gravimeter", Nature Scientific Reports, vol. 8, 12300 (2018)</p>

scholarly journals Analysis of Groundwater Decline and Land Subsidence by using of Microgravity and Vertical Gravity Gradient Over Time Method

2014 ◽  
Vol 15 (1) ◽  
pp. 7 ◽  
Author(s):  
Suhayat Minardi ◽  
Hiden Hiden ◽  
Daharta Dahrin ◽  
Mahmud Yusuf
Keyword(s):  
Gravity Anomaly ◽  
Land Subsidence ◽  
Gravity Data ◽  
Vertical Gradient ◽  
Time Lapse ◽  
Gravity Gradient ◽  
Vertical Gravity Gradient ◽  
Vertical Gravity ◽  
Groundwater Decline ◽  
Over Time

Studies have been conducted to identify the occurrence of subsidence, a decline of groundwater, and to model the causes of subsidence in areas of Jakarta based on response of microgravity anomaly and vertical gravity gradient over time. Based on the processing and interpretation of gravity data advance of the time concluded that by using a combination of time lapse microgravity and its vertical gradient have been able to localize the source of the gravity anomaly and the results are strongly support the results of filtering to separate the source of the anomaly. The subsidence that occurs predominantly due to resettlement (in West and North Jakarta), caused by the extraction of groundwater and resettlement (in Central and East Jakarta), and dominated due to the extraction of groundwater (in South Jakarta).Keywords : Groundwater, time lapse micogravity, time lapse vertical gradient, resettlement, subsidence

Curvature of a geometric surface and curvature of gravity and magnetic anomalies

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. G15-G26 ◽  
Author(s):  
Xiong Li
Keyword(s):  
Gravity Data ◽  
Vertical Cylinder ◽  
Equipotential Surface ◽  
Magnetic Anomalies ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
Theoretical Derivation ◽  
Vertical Gravity Gradient ◽  
Gravity And Magnetic ◽  
Geometric Surface

Curvature describes how much a line deviates from being straight or a surface from being flat. When curvature is used to interpret gravity and magnetic anomalies, we try to delineate geometric information of subsurface structures from an observed nongeometric quantity. In this work, I evaluated curvature attributes of the equipotential surface as functions of gravity gradients and analyzed the differences between the theoretical derivation and a practical application. I computed curvature of a synthetic model that consisted of representative structures (ridge, valley, basin, dome, and vertical cylinder) and curvature of the equipotential surface, gravity, and vertical gravity gradient (which is equivalent to the magnetic reduction-to-the-pole result) due to the same model. A comparison of curvature of such a geometric surface and curvature of different gravity quantities was then made to help understand these curvature differences and an indirect link between curvature of gravity data and actual structures. Finally, I applied curvature analysis to a magnetic anomaly grid in the Gaspé belt of Quebec, Canada, to illustrate its useful property of enhancing subtle features.

RECONNAISSANCE SURVEY USING AVERAGE HORIZONTAL GRADIENTS OF GRAVITY

Geophysics ◽  
1965 ◽  
Vol 30 (4) ◽  
pp. 661-664
Author(s):  
Stephen Thyssen‐Bornemisza
Keyword(s):  
Gravity Gradient ◽  
Gravity Gradients ◽  
The South ◽  
Horizontal Gradients ◽  
Experimental Profile ◽  
Reconnaissance Survey ◽  
Gradient Technique ◽  
Vertical Gradients ◽  
Reconnaissance Surveys

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.

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

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1588-1595 ◽  
Author(s):  
I. Marson ◽  
E. E. Klingele
Keyword(s):  
Gravity Data ◽  
Vertical Gradient ◽  
Three Dimensions ◽  
Gravity Gradient ◽  
Horizontal Gradient ◽  
Euler Deconvolution ◽  
Model Studies ◽  
Combined Use ◽  
Deconvolution Techniques ◽  
Vertical Gradient Of Gravity

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.

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