On: “Method of Computing Residual Anomalies from Bouguer Gravity Map by Applying Relaxation Technique” by M. K. Paul (GEOPHYSICS, August 1967, p. 708–719)

Geophysics ◽  
1970 ◽  
Vol 35 (1) ◽  
pp. 160-161
Author(s):  
N. F. Uren
Keyword(s):  
Gravity Field ◽  
Theoretical Basis ◽  
Two Dimensions ◽  
Relaxation Technique ◽  
Bouguer Gravity ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Regional Gravity ◽  
Gravity Map

Dr. M. K. Paul suggests that further investigation of this method may be necessary. The theoretical basis for this method is that [Formula: see text] i.e., that the regional gravity field obeys Laplace’s equation in two dimensions over the plane of observation.

A METHOD OF COMPUTING RESIDUAL ANOMALIES FROM BOUGUER GRAVITY MAP BY APPLYING RELAXATION TECHNIQUE

Geophysics ◽  
1967 ◽  
Vol 32 (4) ◽  
pp. 708-719 ◽  
Author(s):  
M. K. Paul
Keyword(s):  
Linear Function ◽  
Linear Equations ◽  
Point Of View ◽  
Relaxation Technique ◽  
Bouguer Gravity ◽  
Left Hand ◽  
Analytical Point ◽  
Residual Values ◽  
The Right ◽  
Gravity Map

A new method of computing residual anomalies for gravity prospecting data from a Bouguer gravity map has been evolved. In arriving at the proposed method, we have at first examined the behavior of the regional gravity field from an analytical point of view. With the concepts acquired therefrom in mind, we consider the case of square grids with such separation of stations that in an elementary area, formed by joining the four nearest stations around a central station, the regional field may be represented by a linear function of the Cartesian coordinates in the horizontal surface of observation. Making use of the formal relationship between the residual, regional, and Bouguer gravity values, we have been able to formulate in this case a set of simultaneous linear equations—one for each station of observation—with the residual values at the grid corners as the unknowns in the left hand sides of these equations and some linear function of the Bouger values at the grid corners as the known quantities in the right hand sides. With some plausible estimates of the residual values at the stations on the boundaries at hand, these equations can be solved efficiently with the aid of the relaxation technique as has been exemplified in the cases of theoretical model as well as field data.

On: “A Method of Computing Residual Anomalies from Bouguer Gravity Map by Applying Relaxation Technique” by M. K. Paul (GEOPHYSICS, vol. 32, no. 4, p. 708–719, August, 1967)

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 357-357
Author(s):  
H. A. Meinardus
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Relaxation Technique ◽  
Bouguer Gravity ◽  
Entire Region ◽  
Degree Polynomial ◽  
Entire Area ◽  
Bouguer Map ◽  
Polynomial Formula ◽  
Gravity Map

On page 711 the author, after reference to previous users of the least‐squares method for estimating residuals in a Bouguer gravity map, states, “All of them have used the method for estimating the residual field over the entire area under consideration, while in this case the method will be applied to obtain the same on the boundaries only.” He then proceeds to compute residuals on the boundaries from the second degree polynomial [Formula: see text], (10) representing the regional field over the entire region. However, by this procedure the residuals on the boundaries are influenced by all the gravity observations inside the region, as implied by equation (16) where the vector A is a function of the Bouguer map values over the whole area. In fact, equation (12) could be solved for the vector b, and the condition [Formula: see text] arising from [Formula: see text] (A) could be introduced. The following expression for the regional over the entire area results: [Formula: see text], and there is no need for additional computations by the relaxation technique described.

An alǵebraic technique for the solution of Laplace's equation in three dimensions

1970 ◽  
Vol 67 (2) ◽  
pp. 383-389 ◽  
Author(s):  
K. S. Kunz
Keyword(s):  
Conformal Mapping ◽  
Analytic Functions ◽  
Euclidean Plane ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Complex Numbers ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Real Linear ◽  
Algebraic Technique

In obtaining a solution of Laplace's equation in two dimensions by the method of conformal mapping, one first maps the points (x, y) of the Euclidean plane R2 into the algebra of complex numbers C by means of the real-linear function g: R2→C using the prescription g(x, y) = x + iy ≡ z. One then obtains solutions of Laplace's equation by allowing those mappings of C into itself that are expressed by analytic functions.

scholarly journals Delineation of subsurface features by gravity technique in parts of Shivpuri District, M.P.

MAUSAM ◽  
2021 ◽  
Vol 72 (3) ◽  
pp. 661-668
Author(s):  
RAJAN KUMAR ◽  
ANIL KUMAR SINGH
Keyword(s):  
Gravity Anomaly ◽  
Physical Property ◽  
Shear Zones ◽  
Residual Soil ◽  
Bouguer Gravity ◽  
Contour Map ◽  
Gravity Station ◽  
The North ◽  
Regional Gravity ◽  
Gravity Map

This research paper represents the search of faults/ fractures/ shear zones/ altered zones, to find out mineral target zones in part of Shivpuri district, M.P. Geologically, the study area is represented by Vindhyan Supergroup of Meso to Neoproterozoic age. The area is mainly covered by alluvium which is characterized river gravels, sand and residual soil. The gravity survey was carried out with a station density of 1 gravity station per 2.5 sq km along with elevations of each gravity stations covered 2800 sq km. The rock samples have been collected from different litho-units of the study area for measurement of physical property (Density) which are useful for understanding & evaluating of geological response. The general trend of contour pattern of Bouguer gravity is NW-SE directions. Bouguer gravity anomaly contour map is characterized by broad gravity ‘high’ in southern part whereas ‘low’ in northern part which inferred depression of basement toward the north. The nosing in aligned approximately NW-SE direction is recorded in central part which may be interpreted as inferred lineament and it is clearly reflected on residual gravity map. The regional gravity anomaly aligned in NW-SE is characterized by broad gravity ‘high’ in southern part whereas ‘low’ in northern part which reflects basement deepening towards north. The majority of Euler 3D solutions are falling on linear bodies (inferred lineament) with varying depths from 0.5 to 2.5 km.

On: “A Method of Computing Residual Anomalies from Bouguer Gravity Map by Applying Relaxation Technique,” by M. K. Paul (GEOPHYSICS, August 1967, p. 708–719)

Geophysics ◽  
1969 ◽  
Vol 34 (3) ◽  
pp. 480-483
Author(s):  
K. Biesheuvel
Keyword(s):  
Digital Computer ◽  
High Speed ◽  
New Method ◽  
Relaxation Technique ◽  
Bouguer Gravity ◽  
Gravity Map

The following comments on this new method indicate some limitations of the technique as well as a more practical means of solving the equations involved by high‐speed digital computer.

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