NOTE ON THE EFFECT OF RANDOM ERRORS IN GRAVITY SECOND DERIVATIVE VALUES

Geophysics ◽  
1953 ◽  
Vol 18 (3) ◽  
pp. 720-724
Author(s):  
G. Ramaswamy
Keyword(s):  
Gravity Data ◽  
Prima Facie ◽  
Resolving Power ◽  
Magnetic Data ◽  
Second Derivative ◽  
Random Component ◽  
Random Errors ◽  
Prima Facie Case ◽  
Interesting Paper ◽  
Second Derivative Method

In an interesting paper “The Effect of Random Errors in Gravity Data on Second Derivative Values,” Thomas A. Elkins (1952) points out the need for eliminating the random component of gravity data before proceeding to interpret them with the aid of second derivative maps. There is a prima facie case for the elimination of random errors, if only to ensure reliability in results. The need, however, becomes more apparent if it is remembered: a. that the Second Derivative method of interpreting gravity (or magnetic) data is one of high resolving power, and b. that, therefore, errors creeping into those data may considerably vitiate the interpretation of those data.

THE SECOND DERIVATIVE METHOD OF GRAVITY INTERPRETATION

Geophysics ◽  
1951 ◽  
Vol 16 (1) ◽  
pp. 29-50 ◽  
Author(s):  
Thomas A. Elkins
Keyword(s):  
Horizontal Plane ◽  
Graphical Method ◽  
Gravity Data ◽  
Three Dimensional ◽  
Horizontal Cylinder ◽  
Resolving Power ◽  
Theoretical Formula ◽  
Second Derivative ◽  
Derivative Method ◽  
Second Derivative Method

The second derivative method of interpreting gravity data, although its use is justifiable only on data of high accuracy, offers a simple routine method of locating some types of geologic anomalies of importance in oil and mineral reconnaissance. The theoretical formula by which it is possible to compute the second (vertical) derivative of any harmonic function from its values in a horizontal plane is derived for both the two‐dimensional and the three‐dimensional cases. The graphical method of computing the second derivative is discussed, especially as to the sources of error. A numerical coefficient equivalent of the graphical method is also presented. Formulas and graphs for the second derivative of the gravity effect of such geometrically simple shapes as the sphere, the infinite horizontal cylinder, the semi‐infinite horizontal plane, and the vertical fault, are presented with discussions of their value in the interpretation of practical data. Finally, the gravity and second derivative maps of portions of some important oil provinces are presented and compared to show the higher resolving power of the second derivative.

A CONTRIBUTION TO THE COMPUTATION OF THE “SECOND DERIVATIVE” FROM GRAVITY DATA

Geophysics ◽  
1953 ◽  
Vol 18 (4) ◽  
pp. 894-907 ◽  
Author(s):  
Otto Rosenbach
Keyword(s):  
Gravity Data ◽  
Second Derivative ◽  
Practical Application ◽  
Arithmetic Means ◽  
Interesting Paper ◽  
Approximation Formulas ◽  
Series Development ◽  
Concentric Circles ◽  
Gravity Interpretation ◽  
Second Derivative Method

The theory and practical application of the second derivative method of gravity interpretation have been discussed by Elkins (1951) in a very interesting paper based partly on an earlier paper by Peters (1949). In this paper, Elkins shows how the second derivative may be computed at the center of a series of concentric circles using the arithmetic means of the gravity values, assumed to be continuous, around each circle. A method is here proposed which does not use a continuum of gravity values but instead requires only a series development. The approximation formulas needed for the routine calculations can be derived by a method different from that of Elkins and the least squares adjustments he used can be dispensed with. Two hypothetical examples using the formulas derived by the series method are given and the results are compared with those computed by Elkins’ formula.

AMBIGUITY IN GRAVITY INTERPRETATION

Geophysics ◽  
1947 ◽  
Vol 12 (1) ◽  
pp. 43-56 ◽  
Author(s):  
D. C. Skeels
Keyword(s):  
Gravity Data ◽  
Magnetic Data ◽  
Second Derivative ◽  
Two Dimensional ◽  
Wide Range ◽  
Geometrical Shapes ◽  
Unique Interpretation ◽  
Analytical Proof ◽  
Minimum Depth ◽  
Gravity Interpretation

It is shown that contrary to what is stated and implied in much of the literature, gravity data cannot, of themselves, be interpreted uniquely. It is shown by means of a two‐dimensional example that for a given anomaly and a given density contrast a wide range of possible interpretations can be made, at various depths, and that whereas there is a maximum depth for the solution the minimum depth is zero. Other examples are given to show that depth rules based upon the assumption of geometrical shapes may give results very much in error when applied to actual anomalies. Nor does the method of interpretation by vertical gradients allow us to make an unique interpretation, or to distinguish deep from shallow anomalies as has been claimed. It is shown that we do not escape the ambiguity by using second derivative quantities such as gradient and curvature, and that, in fact, gravity and its derivatives are related by a corollary of Green’s theorem. This theorem provides an analytical proof of ambiguity not only for the case of gravity data but for magnetic data as well.

THE EFFECT OF RANDOM ERRORS IN GRAVITY DATA ON SECOND DERIVATIVE VALUES

Geophysics ◽  
1952 ◽  
Vol 17 (1) ◽  
pp. 70-88 ◽  
Author(s):  
Thomas A. Elkins
Keyword(s):  
Random Error ◽  
Gravity Data ◽  
Second Derivative ◽  
Accurate Data ◽  
Random Errors ◽  
Second Derivatives ◽  
Normal Error

Two random error grids were prepared using a set of 111 balls marked according to the Gaussian normal error law. For these grids, considered as grids of errors in gravity data, the second derivative values were computed and contoured. The resulting maps show strikingly the dangers in uncritical interpretations of second derivative maps based on insufficiently accurate data. Statistical checks were applied both to the random error grids and to the computed second derivative values. The check on the latter necessitated the development of a theory of the correlation between second derivative values which is also applicable to many other quantities, besides second derivatives, which are computed by coefficients.

Computer Application in Geosciences: Imaging of the Subsurface by Structural Coupled Inversion of Potential Field Data

2014 ◽  
Vol 644-650 ◽  
pp. 2670-2673
Author(s):  
Jun Wang ◽  
Xiao Hong Meng ◽  
Fang Li ◽  
Jun Jie Zhou
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Gravity Data ◽  
Computer Application ◽  
Magnetic Data ◽  
Imaging Method ◽  
Inversion Algorithm ◽  
Constant Property ◽  
Near Surface ◽  
Potential Field Data

With the continuing growth in influence of near surface geophysics, the research of the subsurface structure is of great significance. Geophysical imaging is one of the efficient computer tools that can be applied. This paper utilize the inversion of potential field data to do the subsurface imaging. Here, gravity data and magnetic data are inverted together with structural coupled inversion algorithm. The subspace (model space) is divided into a set of rectangular cells by an orthogonal 2D mesh and assume a constant property (density and magnetic susceptibility) value within each cell. The inversion matrix equation is solved as an unconstrained optimization problem with conjugate gradient method (CG). This imaging method is applied to synthetic data for typical models of gravity and magnetic anomalies and is tested on field data.

scholarly journals Human Rights Law Without Natural Moral Rights

2015 ◽  
Vol 29 (2) ◽  
pp. 223-232
Author(s):  
Rowan Cruft
Keyword(s):  
Human Rights ◽  
Current System ◽  
Prima Facie ◽  
Modern Human ◽  
Moral Rights ◽  
International Human Rights Law ◽  
Human Rights Law ◽  
International Human Rights ◽  
Prima Facie Case ◽  
Human Rights Practice

In this latest work by one of our leading political and legal philosophers, Allen Buchanan outlines a novel framework for assessing the system of international human rights law—the system that he takes to be the heart of modern human rights practice. Buchanan does not offer a full justification for the current system, but rather aims “to make a strong prima facie case that the existing system as a whole has what it takes to warrant our support of it on moral grounds, even if some aspects of it are defective and should be the object of serious efforts at improvement” (p. 173).

Prima Facie Case

2018 ◽  
pp. 2796-2797
Author(s):  
Robert L. Heilbronner
Keyword(s):  
Prima Facie ◽  
Prima Facie Case
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