scholarly journals Analytical expressions and distributions of vertical gradient of gravity caused by model bodies symmetry with respect to a vertical axis, and characteristics of these maps

2006 ◽  
Vol 59 (2) ◽  
pp. 193-210
Author(s):  
Toshio Hiroshima ◽  
Masahiko Makino
Geophysics ◽  
1966 ◽  
Vol 31 (4) ◽  
pp. 816-820 ◽  
Author(s):  
Thomas A. Elkins

The recent interest in borehole gravimeters and vertical gravity gradient meters makes it worthwhile to analyze the simple case of the vertical gravity gradient on the axis of a hollow cylinder, simulating a borehole. From the viewpoint of potential theory the results are interesting because of the discontinuities which may occur when a vertical gradient profile crosses a sudden change in density. Formulas for the vertical gradient effect are given for observations above, inside, and below a hollow cylinder and a solid cylinder. The special case of an infinitely large outer radius for the cylinders is also considered, leading to formulas for the vertical gradient effect inside a borehole on its axis and inside a horizontal slab. Some remarks are made on the influence of the shape of a buried vertical gradient meter on the correction factor for changing the meter reading to density.


Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 99-101 ◽  
Author(s):  
Sigmund Hammer

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.


Geophysics ◽  
1981 ◽  
Vol 46 (11) ◽  
pp. 1609-1610 ◽  
Author(s):  
Sigmund Hammer

The maximum gradient which can be caused by a simple mass is that of a spherical body. The equation for the vertical gradient at the point P above the center of a spherical mass of density contrast σ (see insert on Figure 1) can be written in the form [Formula: see text] where G is the universal gravity constant [Formula: see text] Expressing the gradient in the Eötvös units, we have [Formula: see text] In terms of percentage of the earth’s normal vertical gradient, the anomaly is [Formula: see text] of 3086 E°. At the surface of the sphere (h = 0), we have the maximum value [Formula: see text] of 3086 E° which is independent of the radius R.


Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1505-1508 ◽  
Author(s):  
T. R. LaFehr ◽  
Kwok C. Chan

In his reply to C. J. Swain’s (1984) discussion Karl states that no one has disagreed with his proposed (0.265 mGal/m) “average value” for the normal gravity gradient and that his global terrain model can be used to challenge the validity of the traditional approach to data reduction. Our investigations show that Karl is in error on both counts, and we hope that the following analyses will help toward a clearer understanding of this question.


Geophysics ◽  
1971 ◽  
Vol 36 (1) ◽  
pp. 216-216
Author(s):  
Sigmund Hammer

The foregoing discussion by Dr. Thyssen‐Bornemisza calls attention to interesting extensions of the rather simplified theoretical analysis in my paper. Dr. Thyssen‐Bornemisza has published extensively on the subject of the vertical gradient of gravity and its applications in exploration. My paper was limited to a very specific topic, namely the variability of the vertical gradient along a vertical profile above an anomalous mass.


2021 ◽  
Vol 6 ◽  
pp. 116-124
Author(s):  
Ivan A. Inzhevatov

In connection with the need to use the vertical gradient in the processing of the results of gravimetric measurements and their interpretation when solving problems of geology, geophysics, geodesy, geodynamics and navigation, in addition to the urgent problems of improvement, socalled indirect methods of measuring the vertical gradient, there is an equally urgent task of developing methods for determining the vertical gradient of gravity, using dependencies between different physical fields. The article presents the development and study of a method for determining the vertical gradient from gravity anomalies using the relationship between gravity anomalies and altitude based on field data obtained in the area of the Tashtagol field on Mount Boulanger in 2019 and 2020.


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