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Author : Frank Hadsell
Publisher : Unknown
Page : 336 pages
File Size : 42,5 Mb
Release : 1999
Category : Algebras, Linear
ISBN : STANFORD:36105111425059
Author : Frank Hadsell
Publisher : SEG Books
Page : 257 pages
File Size : 50,7 Mb
Release : 1995
Category : Algebras, Linear
ISBN : 9781560800293
Author : Frank Hadsell,Richard Hansen
Publisher : SEG Books
Page : 328 pages
File Size : 53,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9781560800750
Author : Frank A. Hadsell
Publisher : Unknown
Page : 240 pages
File Size : 41,8 Mb
Release : 1995
Category : Algebras, Linear
ISBN : 0931830478
Author : Frank Hadsell
Publisher : Unknown
Page : 336 pages
File Size : 55,7 Mb
Release : 1999
Category : Algebras, Linear
ISBN : 0931830478
It is reasonable to present advanced concepts in undergraduate courses without rigor to make the courses more exciting and to give the students a preview of graduate research and education. Unfortunately, this strategy has its price. When these concepts are presented in the undergraduate environment, it is necessary to present them in such a superficial manner that they are often not viable, i.e., the student cannot build on the knowledge acquired without more help than is usually available. In this volume, the authors attempt to provide aspiring theoretical geophysicists some of that help. Some of this help is presented via generalized functions and more of it is presented via generic coordinate systems. Both of these recent mathematical developments are introduced in this volume, the second in a series of five Tensors of Geophysics volumes. The authors explain how generalized functions, or distributions, allow one to simplify some applied logic by providing the ability to treat singular functions beyond the intuitive level. They show how Fourier theory can be unified by means of distributions. The logic of 1D distributions is shown to be easily developed to that of N-D distributions. The theory of Cartesian views of tensors presented in Tensors of Geophysics for Mavericks and Mongrels is expanded to include all views, i.e., all coordinate systems. This leads to a lengthy study of the role of Hansen vectors in elastic wave theory. Cylinder functions, e.g., Bessel functions, are developed at some length. The discussion includes the Hankel transform, appropriate and convenient when the independent variable is offset. Curves and surfaces are viewed via tensors. Classical rules of spherical trigonometry are presented, and the reader is afforded a peek at some of the mathematics of relativity.
Author : Frank Hadsell
Publisher : Unknown
Page : 311 pages
File Size : 46,9 Mb
Release : 1999
Category : Algebras, Linear
ISBN : 0931830478
It is reasonable to present advanced concepts in undergraduate courses without rigor to make the courses more exciting and to give the students a preview of graduate research and education. Unfortunately, this strategy has its price. When these concepts are presented in the undergraduate environment, it is necessary to present them in such a superficial manner that they are often not viable, i.e., the student cannot build on the knowledge acquired without more help than is usually available. In this volume, the authors attempt to provide aspiring theoretical geophysicists some of that help. Some of this help is presented via generalized functions and more of it is presented via generic coordinate systems. Both of these recent mathematical developments are introduced in this volume, the second in a series of five Tensors of Geophysics volumes. The authors explain how generalized functions, or distributions, allow one to simplify some applied logic by providing the ability to treat singular functions beyond the intuitive level. They show how Fourier theory can be unified by means of distributions. The logic of 1D distributions is shown to be easily developed to that of N-D distributions. The theory of Cartesian views of tensors presented in Tensors of Geophysics for Mavericks and Mongrels is expanded to include all views, i.e., all coordinate systems. This leads to a lengthy study of the role of Hansen vectors in elastic wave theory. Cylinder functions, e.g., Bessel functions, are developed at some length. The discussion includes the Hankel transform, appropriate and convenient when the independent variable is offset. Curves and surfaces are viewed via tensors. Classical rules of spherical trigonometry are presented, and the reader is afforded a peek at some of the mathematics of relativity.
Author : Michael A Slawinski
Publisher : World Scientific Publishing Company
Page : 656 pages
File Size : 49,7 Mb
Release : 2014-12-15
Category : Science
ISBN : 9789814644211
The present book — which is the third, significantly revised edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves. The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices. In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols. Request Inspection Copy
Author : Michael A Slawinski
Publisher : World Scientific Publishing Company
Page : 616 pages
File Size : 44,6 Mb
Release : 2010-09-09
Category : Science
ISBN : 9789813107670
The present book — which is the second, and significantly extended, edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves. The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices. In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.
Author : Anonim
Publisher : Unknown
Page : 706 pages
File Size : 52,7 Mb
Release : 2002-05
Category : Geophysics
ISBN : STANFORD:36105111744269
Author : Society of Exploration Geophysicists
Publisher : Unknown
Page : 446 pages
File Size : 51,5 Mb
Release : 2000
Category : Geophysics
ISBN : UVA:X004440060
Author : Anonim
Publisher : Unknown
Page : 328 pages
File Size : 49,8 Mb
Release : 1996
Category : Geology
ISBN : UVA:X006010496
Author : Anonim
Publisher : Unknown
Page : 552 pages
File Size : 43,5 Mb
Release : 2007
Category : Elastic waves
ISBN : UOM:39015077133786
This volume contains 16 classic essays from the 17th to the 21st centuries on aspects of elastic wave theory.
Author : Anonim
Publisher : Unknown
Page : 464 pages
File Size : 49,6 Mb
Release : 1996-04
Category : Petroleum
ISBN : STANFORD:36105017487682
Author : Anonim
Publisher : Unknown
Page : 680 pages
File Size : 41,7 Mb
Release : 1996
Category : Petroleum
ISBN : CORNELL:31924077977381
Author : Rose Arny
Publisher : Unknown
Page : 3060 pages
File Size : 52,5 Mb
Release : 1996-06
Category : American literature
ISBN : UOM:39015023731261