THE GRAVITATIONAL ATTRACTION OF A RIGHT RECTANGULAR PRISM

Geophysics ◽  
1966 ◽  
Vol 31 (2) ◽  
pp. 362-371 ◽  
Author(s):  
Dezsö Nagy
Keyword(s):  
Gravity Field ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Vertical Component ◽  
Gravitational Effect ◽  
Rectangular Prism ◽  
Gravitational Attraction ◽  
Closed Expression ◽  
Building Element ◽  
Terrain Corrections

The derivation of a closed expression is presented to calculate the vertical component of the gravitational attraction of a right rectangular prism, with sides parallel to the coordinate axis. As any configuration can be expressed as the sum of prisms of various sizes and densities, the computation of the total gravitational effect of bodies of arbitrary shapes at any point outside of or on the boundary of the bodies is straightforward. To calculate the gravitational effect of the “unit” building element a subroutine called Prism has been developed, tested, and incorporated, in one program to calculate terrain corrections, and in another program for three‐dimensional analysis of a gravity field.

scholarly journals Thickness and Basal Configuration of Lower Blue Glacier, Washington, Determined by Gravimetry

1965 ◽  
Vol 5 (41) ◽  
pp. 637-650 ◽  
Author(s):  
Charles E. Corbató
Keyword(s):  
Gravity Field ◽  
Three Dimensional ◽  
Successive Approximations ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Gravity Measurements ◽  
Computational Errors ◽  
Terrain Corrections ◽  
Seismic Reflections ◽  
Regional Gravity

AbstractGravity measurements at 146 stations on lower Blue Glacier were used to determine the subglacial bedrock configuration. The gravity values, station elevations and density contrast were carefully measured, and terrain corrections thoroughly evaluated to insure accuracy of the Bottguer anomalies. A series of successive approximations results in evaluation of the regional gravity field and a three-dimensional model of the glacier whose gravimetric effects fit the range of the observational and computational errors. Comparison with bore holes and seismic reflections indicates no significant errors in the model and accuracies of 5–10 per cent in the calculated thicknesses of the glacier.

On: “THE GRAVITATIONAL ATTRACTION OF A RIGHT RECTANGULAR PRISM,” BY DEZSÖ NAGY (GEOPHYSICS, APRIL, 1966, PP. 362–371)

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 987-987 ◽  
Author(s):  
Charles E. Corbató
Keyword(s):  
Vertical Component ◽  
Rectangular Prism ◽  
Gravitational Attraction ◽  
Gravitational Effects ◽  
Rectangular Parallelopiped

You might be interested to note that the results obtained by Nagy (1966) and published in Geophysics concerning the vertical component of the gravitational attraction of a right rectangular prism not only had been published previously by Sorokin and Haáz but also were derived and published (in English) 136 years ago by Everest (1830, p. 94–97). Everest calculated closed expressions which are equivalent to that of Nagy for the horizontal and vertical gravitational effects of a rectangular parallelopiped and used these equations to estimate the topographic deflection of the plumb bob due to the Satpura Range in India.

Gravitational attraction of a rectangular prism with depth‐dependent density

Geophysics ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 470-473 ◽  
Author(s):  
J. García‐Abdeslem
Keyword(s):  
Cross Sections ◽  
Integral Method ◽  
Three Dimensional ◽  
Density Contrast ◽  
Gravitational Attraction ◽  
Two Dimensional ◽  
Gravity Effect ◽  
Line Integral ◽  
Closed Expression ◽  
Dependent Density

The gravity effect produced by two and three‐dimensional bodies with nonuniform density contrast has been treated by several authors. One of the first attempts in this direction made by Cordell (1973), who developed a method to compute the gravity effect due to a two‐dimensional prism whose density decreases exponentially with depth. A different approach was proposed by Murthy and Rao (1979). They extended the line‐integral method to obtain the gravity effect for bodies of arbitrary cross‐sections, with density contrast varying linearly with depth. Chai and Hinze (1988) have derived a wavenumber‐domain approach to compute the gravity effect due to a vertical prism whose density contrast varies exponentially with depth. Recently, Rao (1990) has developed a closed expression of the gravity field produced by an asymmetrical trapezoidal body whose density varies with depth following a quadratic polynomial.

TERRAIN CORRECTIONS FOR GRAVIMETER STATIONS

Geophysics ◽  
1939 ◽  
Vol 4 (3) ◽  
pp. 184-194 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Gravitational Effect ◽  
Relative Accuracy ◽  
Terrain Correction ◽  
Gravitational Attraction ◽  
Gravity Station ◽  
Terrain Corrections ◽  
Instrumental Precision

In this paper the correction for the gravitational attraction of the topography on a gravity station is considered as consisting of two parts; (1) the restricted but conventional “Bouguer correction” which postulates as a convenient approximation that the topography consists of an infinite horizontal plain, and (2) the “Terrain correction” which is a supplementary correction taking into account the gravitational effect of the undulations of the terrain about the plane through the gravity station. The paper illustrates the necessity of making terrain corrections if precise gravity surveys are desired in hilly country and presents terrain correction tables with which this quantity may be determined to a relative accuracy of one‐tenth milligal. This accuracy is required to fully utilize the high instrumental precision of modern gravimeters.

scholarly journals Thickness and Basal Configuration of Lower Blue Glacier, Washington, Determined by Gravimetry

1965 ◽  
Vol 5 (41) ◽  
pp. 637-650 ◽  
Author(s):  
Charles E. Corbató
Keyword(s):  
Gravity Field ◽  
Three Dimensional ◽  
Successive Approximations ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Gravity Measurements ◽  
Computational Errors ◽  
Terrain Corrections ◽  
Seismic Reflections ◽  
Regional Gravity

AbstractGravity measurements at 146 stations on lower Blue Glacier were used to determine the subglacial bedrock configuration. The gravity values, station elevations and density contrast were carefully measured, and terrain corrections thoroughly evaluated to insure accuracy of the Bottguer anomalies. A series of successive approximations results in evaluation of the regional gravity field and a three-dimensional model of the glacier whose gravimetric effects fit the range of the observational and computational errors. Comparison with bore holes and seismic reflections indicates no significant errors in the model and accuracies of 5–10 per cent in the calculated thicknesses of the glacier.

In situ investigation of the primary recrystallization of alpha titanium in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 634-635
Author(s):  
S. Naka ◽  
R. Penelle ◽  
R. Valle
Keyword(s):  
Dimensional Analysis ◽  
Texture Evolution ◽  
Cold Work ◽  
Three Dimensional ◽  
Primary Recrystallization ◽  
Thin Foils ◽  
In Situ Investigation ◽  
Grain Growth Model ◽  
Alpha Titanium

The in situ experimentation technique in HVEM seems to be particularly suitable to clarify the processes involved in recrystallization. The material under investigation was unidirectionally cold-rolled titanium of commercial purity. The problem was approached in two different ways. The three-dimensional analysis of textures was used to describe the texture evolution during the primary recrystallization. Observations of bulk-annealed specimens or thin foils annealed in the microscope were also made in order to provide information concerning the mechanisms involved in the formation of new grains. In contrast to the already published work on titanium, this investigation takes into consideration different values of the cold-work ratio, the temperature and the annealing time.Two different models are commonly used to explain the recrystallization textures i.e. the selective grain growth model (Beck) or the oriented nucleation model (Burgers). The three-dimensional analysis of both the rolling and recrystallization textures was performed to identify the mechanismsl involved in the recrystallization of titanium.

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