On: “Gravitational Attraction of a Circular Disc,” by Shri Krishna Singh (GEOPHYSICS, Feb. 1977, p. 111–113)

Geophysics ◽  
1977 ◽  
Vol 42 (4) ◽  
pp. 877-877
Author(s):  
T. R. Lafehr
Keyword(s):  
Mineral Resource ◽  
Short Note ◽  
Three Dimensional ◽  
Salt Dome ◽  
Circular Disc ◽  
Gravitational Attraction ◽  
Dimensional Problem ◽  
Gravity And Magnetic ◽  
The Subject ◽  
Classic Paper

It is unfortunate that in the Short Note no mention whatever is made of Nettleton’s classic paper on the subject: “Gravity and Magnetic Calculations”. (Geophysics, 1942, p. 308). Not only did Nettleton’s paper precede Singh by 35 years but it provides a more practical approach (stacked discs) to solving a difficult three‐dimensional problem. Nettleton’s method endured long and well until modern computers rendered it less efficient several years ago; his technique has been applied countless times to thousands of salt dome and mineral resource problems.

Reply by author to Dr. LaFehr

Geophysics ◽  
1977 ◽  
Vol 42 (4) ◽  
pp. 877-877
Author(s):  
Shri Krishna Singh
Keyword(s):  
Closed Form ◽  
Solid Angle ◽  
Short Note ◽  
Circular Disc ◽  
Closed Form Expression ◽  
Gravitational Attraction ◽  
Form Expression ◽  
Practical Usefulness ◽  
Solid Angles ◽  
Classic Paper

It is difficult to include all references when dealing with a subject so well studied as the gravitational attraction of a circular disc. Although the practical usefulness of Nettleton’s paper can not be denied by anyone, it nevertheless gives no details (except for some references) of the computation of solid angles subtended by a disc from which his graphs (Geophysics, 1942, Figure 4) result. My short note deals with (in what I consider an easy way of) obtaining a closed form expression for the solid angle. For applications of the result the reader would do well to look up Nettleton’s classic paper.

On: “Simulating true amplitude reflections by stacking shot records,” by P. Hubral (GEOPHYSICS, v. 49, p. 303–306, 1984).

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1806-1807
Author(s):  
Th. Krey
Keyword(s):  
Short Note ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Precise Result ◽  
Normal Waves ◽  
Analytical Derivation ◽  
The Subject ◽  
Line Survey ◽  
Zero Offset

Quite recently Peter Hubral published a short note in which he described a special, very perspicuous stacking method which, starting from the records of a line survey, produces true amplitude reflections for “normal waves,” as defined in his Introduction. In the following I want to supplement Hubral’s note by showing the analytical connection with Hubral’s earlier paper (Hubral, 1983) and the additional short note by Krey (Krey, 1983). My present investigation will be two‐dimensional (2-D) as is that in the subject paper; an extension to the three‐dimensional (3-D) case is conceptionally easy for the following analytical derivation as well as for Hubral’s note. Besides a basic confirmation of Hubral’s findings, I shall show that the result of Hubral’s method has still to be multiplied by [Formula: see text] in the 2-D case and by [Formula: see text] in the 3-D case in order to obtain the precise result. Here ω is the frequency. Moreover the angle of emergence α of the zero‐offset raypath has to be taken into account.

Geological Field Sketches and Illustrations

2019 ◽  
Author(s):  
Matthew J. Genge
Keyword(s):  
Cross Sections ◽  
Earth Science ◽  
Three Dimensional ◽  
Worked Examples ◽  
Scientific Publications ◽  
Thin Sections ◽  
Geological Features ◽  
Different Types ◽  
The Subject

Drawings, illustrations, and field sketches play an important role in Earth Science since they are used to record field observations, develop interpretations, and communicate results in reports and scientific publications. Drawing geology in the field furthermore facilitates observation and maximizes the value of fieldwork. Every geologist, whether a student, academic, professional, or amateur enthusiast, will benefit from the ability to draw geological features accurately. This book describes how and what to draw in geology. Essential drawing techniques, together with practical advice in creating high quality diagrams, are described the opening chapters. How to draw different types of geology, including faults, folds, metamorphic rocks, sedimentary rocks, igneous rocks, and fossils, are the subjects of separate chapters, and include descriptions of what are the important features to draw and describe. Different types of sketch, such as drawings of three-dimensional outcrops, landscapes, thin-sections, and hand-specimens of rocks, crystals, and minerals, are discussed. The methods used to create technical diagrams such as geological maps and cross-sections are also covered. Finally, modern techniques in the acquisition and recording of field data, including photogrammetry and aerial surveys, and digital methods of illustration, are the subject of the final chapter of the book. Throughout, worked examples of field sketches and illustrations are provided as well as descriptions of the common mistakes to be avoided.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

GRAVITY AND MAGNETIC INVESTIGATIONS AT THE GRAND SALINE SALT DOME, VAN ZANDT CO., TEXAS

Geophysics ◽  
1945 ◽  
Vol 10 (3) ◽  
pp. 376-393 ◽  
Author(s):  
Jack W. Peters ◽  
Albert F. Dugan
Keyword(s):  
Physical Properties ◽  
Quantitative Evaluation ◽  
Gravity Data ◽  
Salt Dome ◽  
Salt Mine ◽  
Geological Data ◽  
East Texas ◽  
Additional Information ◽  
Theoretical Mass ◽  
Gravity And Magnetic

During May, 1944, detailed gravity and magnetic surveys were made at the Grand Saline Salt Dome to secure additional information on the physical properties of this typical East Texas salt dome. The results of the surface gravity and magnetic surveys, and the subsurface gravity survey in the Morton Salt Mine are illustrated and discussed. Densities and the available subsurface data were compiled and were utilized in a quantitative evaluation of the observed gravity data. The theoretical mass distribution which was determined by this quantitative evaluation is not intended to represent the unique solution of the geophysical and geological data; instead, it is offered as a possible solution based on relatively simple assumptions.

Graphed equilibrium parameters of channels formed in sediment

1980 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
A.W. Peterson ◽  
T. Blench
Keyword(s):  
Subject Matter ◽  
Three Dimensional ◽  
Numerical Data ◽  
Reference List ◽  
Laboratory Measurements ◽  
Practical Applications ◽  
Circular Pipes ◽  
The Subject ◽  
Specialized Mathematics ◽  
Major Reference

This paper, for river engineers and their environmental counterparts, presents and explains the origin and potential of four-dimensional charts that smooth most of the world's numerical data obtained from the equilibrium dimensions of sand rivers, gravel rivers, and laboratory flumes. These charts aim to provide a practical service comparable with that provided by factual plots on the comprehensive classic three-dimensional Stanton friction-factor diagram for circular pipes and clean Newtonian fluid. In the river problems, especially, the existence of different phases (whose transitions are not susceptible to formulation), the inadequacies of textbook theories even for simple phases, and the unavoidable imperfections of both field and laboratory measurements combine to prevent responsible design. The remedy is a graphing of total information backed by references from which its reliability and practicability can be assessed.The references have been chosen to contain principal information in the forms of: (i) usable photos, graphs, and tables; (ii) explanations free from specialized mathematics and speculative arguments; and (iii) papers with discussions, authors' replies, and further useful references (since a major reference list would be too long for this paper). Because condensation has had to be extreme the authors will be glad to attempt answers to discussions and questions on the subject matter, its practical applications, and its implications in teaching and research.

Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces

2017 ◽  
Vol 73 (5) ◽  
pp. 387-402 ◽  
Author(s):  
Gregory S. Chirikjian ◽  
Sajdeh Sajjadi ◽  
Bernard Shiffman ◽  
Steven M. Zucker
Keyword(s):  
General Theory ◽  
Rigid Body ◽  
Three Dimensional ◽  
Molecular Replacement ◽  
Translation Group ◽  
Common Occurrence ◽  
Space Group ◽  
Space Groups ◽  
Relevant Case ◽  
The Subject

In molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension.

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