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.

Reply by the author to Th. Krey

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1807-1807
Author(s):  
Peter Hubral
Keyword(s):  
Short Note ◽  
Normal Wave ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Geometrical Spreading ◽  
The Subject ◽  
Amplitude Reflection

I am grateful to Th. Krey for his derivation of formula (14) which is valid for the two‐dimensional case and which clearly shows what is actually obtained when subjecting primary reflections in neighbouring shot records to, what I called in the subject note, the process of normal wave stacking. Krey’s formula (14) confirms that the amplitude loss of primary shot record reflections, that is due to geometrical spreading, is removed by the normal wave stack as I stated in my short note. However, the formula also shows that the resulting event in the normal wave stack section does not, as I implied, provide a true amplitude reflection, which was correctly defined in my previous paper (Hubral, 1983) and in Krey’s short note (Krey, 1983). I am satisfied to see that Krey’s formula (14) however indicates that primary reflections in a normal wave stack section can very easily be transformed to the desired accurate true amplitude reflections with two simple corrections only.

Fictional Illustration Language with Reference to M. C. Escher and Istvan Orosz Examples

2017 ◽  
Vol 4 (11) ◽  
pp. 156-163
Author(s):  
Banu Bulduk Turkmen
Keyword(s):  
Visual Perception ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Technical Aspects ◽  
New Approaches ◽  
Alternative Approaches ◽  
The Subject ◽  
Three Dimensional Images

Alternative approaches in illustration language have constantly been developing in terms of material and technical aspects. Illustration languages also differ in terms of semantics and form. Differences in formal expressions for increasing the effect of the subject on the audience lead to diversity in the illustrations. M. C. Escher’s three-dimensional images to be perceived in a two-dimensional environment, together with mathematical and symmetry-oriented studies and the systematic formed by a numerical structure in its background, are associated with the notion of illustration in terms of fictional meaning. Istvan Orosz used the technique of anamorphosis and made it possible for people to see their perception abilities and visual perception sensitivities in different environments created by him. This study identifies new approaches and illustration languages based on the works of both artists, bringing an alternative proposition to illustration languages in terms of systematic sub-structure and fictional idea sketches. Keywords: Perception, illusion, illustration, fictional illustration, illustration languages, visual perception.

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.

Divided by a Common Language: Political Theory and the Concept of Power

Politics ◽  
1997 ◽  
Vol 17 (1) ◽  
pp. 45-52 ◽  
Author(s):  
Colin Hay
Keyword(s):  
Political Theory ◽  
Three Dimensional ◽  
Fundamental Concept ◽  
Common Language ◽  
Two Dimensional ◽  
Dimensional Approach ◽  
Political Analysis ◽  
Heated Debate ◽  
The Subject ◽  
Definition Of

Power is probably the most universal and fundamental concept of political analysis. It has been, and continues to be, the subject of extended and heated debate. In this article I critically review the contributions of Bachrach and Baratz, and Lukes to our understanding of the multiple faces of power. I suggest that although the former's two-dimensional approach to power is ultimately compromised by the residues of behaviouralism that it inherits from classic pluralism, the latter's three-dimensional view suggests a potential route out of this pluralist impasse. To seize the opportunity he provides, however, requires that we rethink the concept of power. In the second half of the paper I advance a definition of power as context-shaping and demonstrate how this helps us to disentangle the notions of power, responsibility and culpability that Lukes conflates. In so doing I suggest the we differentiate clearly between analytical questions concerning the identification of power within social and political contexts, and normative questions concerning the critique of the distribution and exercise of power thus identified.

scholarly journals Sinusoidal: An Exploration of Mathematics and Movement

2019 ◽  
Vol 21 (1) ◽  
Author(s):  
Caroline Grace Lockwood
Keyword(s):  
Three Dimensional ◽  
Sine Wave ◽  
Two Dimensional ◽  
Musical Score ◽  
Work Of Art ◽  
Dance Movement ◽  
Single Tone ◽  
The Subject ◽  
Three Dimensional Models ◽  
Aesthetic Understanding

Mathematic theory often takes place in two-dimensional forms. Whether hand-drawn graphs, or three-dimensional models on a screen, the presentation of the subject often lacks the length, breadth, and depth it deserves. Through four phases of research, I explored how one can model mathematic concepts through movement and music, both demonstrably and abstractly. I began my research by basing small dance/movement phrases in simple trigonometric concepts and giving my dancers tasks exploring related subjects. I then examined how other choreographers, both past and present, employed mathematic approaches in their work. To accompany my choreographic work and complete my project, I created a musical score using only single-tone sine wave frequencies. Finally, I interviewed my dancers, as well as other dancers and engineers, to understand how the piece was perceived as both a work of art and an informative display. Through my research, I hope to further the embodied and aesthetic understanding of applied simple and complex mathematic concepts.

Spherical Geometries and Multigroups

1950 ◽  
Vol 2 ◽  
pp. 100-119 ◽  
Author(s):  
Walter Prenowitz
Keyword(s):  
Three Dimensional ◽  
Spherical Geometry ◽  
Great Circle ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Elliptic Geometry ◽  
The Subject ◽  
Case Based

1. Introduction. The notion spherical geometry is suggested by the familiar geometry of the Euclidean 2-sphere in which the role of path is played by “arc of great circle”. The first postulational treatment of the subject seems to be that of Halsted [10] for the two-dimensional case. Kline [11] under the name double elliptic geometry, gave a greatly simplified foundation for the three-dimensional case based on the primitive notions point and order. Halsted and Kline study not merely descriptive (that is positional, non-metrical) properties of figures but also introduce metrical notions by postulating or defining congruence. Kline includes a continuity postulate designed to yield real spherical geometry.

The Aerodynamic Design of Swept Winged Aircraft at Transonic and Supersonic Speeds

1963 ◽  
Vol 67 (630) ◽  
pp. 325-337 ◽  
Author(s):  
R. C. Lock
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Aerodynamic Design ◽  
Wing Design ◽  
Swept Wing ◽  
Supersonic Speed ◽  
Speed Range ◽  
Section Design ◽  
The Subject ◽  
Dimensional Section

The idea of sweeping the wings of an aeroplane in order to delay or reduce the transonic drag rise is of course an old one, dating from at least 20 years ago. At subsonic speeds the art of swept wing design is now highly developed, largely due to research at the RAE under Küchemann on the three-dimensional aspects of the subject, and at the NPL, notably by Pearcey and Holder, on two-dimensional section design. It was soon realised that, at least in principle, the same ideas could be carried over some way into the supersonic speed range—how far still remains to be seen.

A three‐dimensional perspective on two‐dimensional dip moveout

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 604-610 ◽  
Author(s):  
David Forel ◽  
Gerald H. F. Gardner
Keyword(s):  
Line Segment ◽  
Constant Velocity ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Prestack Migration ◽  
Standard Normal ◽  
Ellipsoidal Surface ◽  
Zero Offset

Prestack migration in a constant‐velocity medium spreads an impulse on any trace over an ellipsoidal surface with foci at the source and receiver positions for that trace. The same ellipsoid can be obtained by migrating a family of zero‐offset traces placed along the line segment from the source to the receiver. The spheres generated by migrating the zero‐offset impulses are arranged to be tangent to the ellipsoid. The resulting nonstandard moveout equation is equivalent to two consecutive moveouts, the first requiring no knowledge of velocity and the second being standard normal moveout (NMO). The first of these is referred to as dip moveout (DMO). Because this DMO-NMO algorithm converts any trace to an equivalent set of zero‐offset traces, it can be applied to any ensemble of traces no matter what the variations in azimuth and offset may be. In particular, this three‐dimensional perspective on DMO can be used with multifold inline data. Then it becomes clear that velocity‐independent DMO operates on radial‐trace profiles and not on constant‐offset profiles. Inline data over a three‐dimensional subsurface will be properly stacked by using DMO followed by NMO.

scholarly journals Football, history, and the nation in Southeastern Europe

2016 ◽  
Vol 44 (6) ◽  
pp. 857-859 ◽  
Author(s):  
Catherine Baker
Keyword(s):  
National Identity ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Southeastern Europe ◽  
Cultural Boundaries ◽  
The Subject ◽  
Late Nineteenth

In October 2014, Serbia's European Championships qualifying match against Albania was abandoned after a drone flew onto the pitch in Belgrade with a banner showing Kosovo as part of a Greater Albania, provoking a fight between both teams and their fans. While the flight of the drone was a technologically novel reminder that the nation's territorial space is not two-dimensional but three-dimensional, the subject of a politics of verticality and volume (Weizman 2012,12; Elden 2013), the imagery of its invasive entry and violent ejection from the symbolic territory, and the battlefield of the nation underlined a point that could have been made at any point since the institutionalization of international sporting competition in the late nineteenth and early twentieth centuries: that controversies over sports, between and within nations, reveal the deeper conflicts about territorial and cultural boundaries that are the very process of constructing national identity. Yet all this has taken place within a framework of supposed internationalism and sporting fraternity; indeed, it is the very structure of organized, scheduled competition between nations that makes these sporting encounters regular and possible.

scholarly journals On three dimensional perceptions in the visual age

2015 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Melek Sahan
Keyword(s):  
Visual Perception ◽  
Visual Arts ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Related Literature ◽  
Visual Arts Education ◽  
Starting Point ◽  
The Subject ◽  
High Level ◽  
Document Review

Aim of the study is to examine the values of the three dimensional perception and collect information about that. Starting point is the observation of differences in two and three dimensional perception abilities of individuals having education in visual arts. It has been observed that some students, who have high level of competency in two dimensional perception, do not have the same competency in three dimensional perception. This is considered important since it creates two and three dimensional perceptions and differences of expression between them. We tried to emphasize the importance of the subject particularly in terms of visual arts education in the current visual age. The study is a document review. In this study we addressed the characteristics of the age we are living in, perception, visual perception, and two and three dimensional perception. We summarized the differences in visual perception and included three dimensional comprehension. By examining the related literature, we came to the conclusion that the two and three dimensional perception processes and their requirements are different.   Keywords: sculpture, three dimensional perceptions, visual perception, visual age.

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