A Mathematical Study of Voigt Viscoelastic Love Wave Propagation
A Mathematical Study of Voigt Viscoelastic Love Wave Propagation

Author: David Nuse Peacock

Publisher:

Published: 1966

Total Pages: 62

ISBN-13:

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"This research is a mathematical investigation of the propagation of a Love wave in a Voigt viscoelastic medium. A solution to the partial differential equation of motion is assumed and is shown to satisfy the three necessary boundary conditions. Velocity restrictions on the wave and the media are developed and are shown to be of the same form as those governing the elastic Love wave"--Abstract, leaf ii.

Wave Propagation in Viscoelastic and Poroelastic Continua
Wave Propagation in Viscoelastic and Poroelastic Continua

Author: Martin Schanz

Publisher: Springer Science & Business Media

Published: 2012-11-27

Total Pages: 176

ISBN-13: 3540445757

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Wave propagation is an important topic in engineering sciences, especially, in the field of solid mechanics. A description of wave propagation phenomena is given by Graff [98]: The effect of a sharply applied, localized disturbance in a medium soon transmits or 'spreads' to other parts of the medium. These effects are familiar to everyone, e.g., transmission of sound in air, the spreading of ripples on a pond of water, or the transmission of radio waves. From all wave types in nature, here, attention is focused only on waves in solids. Thus, solely mechanical disturbances in contrast to electro-magnetic or acoustic disturbances are considered. of waves - the compression wave similar to the In solids, there are two types pressure wave in fluids and, additionally, the shear wave. Due to continual reflec tions at boundaries and propagation of waves in bounded solids after some time a steady state is reached. Depending on the influence of the inertia terms, this state is governed by a static or dynamic equilibrium in frequency domain. However, if the rate of onset of the load is high compared to the time needed to reach this steady state, wave propagation phenomena have to be considered.

Viscoelastic Waves in Layered Media
Viscoelastic Waves in Layered Media

Author: Roger D. Borcherdt

Publisher: Cambridge University Press

Published: 2009-05-14

Total Pages: 323

ISBN-13: 0521898536

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This book is a rigorous, self-contained exposition of the mathematical theory for wave propagation in layered media with arbitrary amounts of intrinsic absorption. The theory, previously not published in a book, provides solutions for fundamental wave-propagation problems in the general context of any media with a linear response, elastic or anelastic. It reveals physical characteristics for two-and three-dimensional anelastic body and surface waves, not predicted by commonly used models based on elasticity or one-dimensional anelasticity. It explains observed wave characteristics not explained by previous theories. This book may be used as a textbook for graduate-level courses and as a research reference in a variety of fields such as solid mechanics, seismology, civil and mechanical engineering, exploration geophysics, and acoustics. The theory and numerical results allow the classic subject of fundamental elastic wave propagation to be taught in the broader context of waves in any media with a linear response, without undue complications in the mathematics. They provide the basis to improve a variety of anelastic wave propagation models, including those for the Earth's interior, metal impurities, petroleum reserves, polymers, soils, and ocean acoustics. The numerical examples and problems sets facilitate understanding by emphasizing important aspects of the theory for each chapter. Book jacket.

Wave Fields in Real Media
Wave Fields in Real Media

Author: José M. Carcione

Publisher: Elsevier

Published: 2014-12-08

Total Pages: 690

ISBN-13: 0081000030

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Authored by the internationally renowned José M. Carcione, Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media examines the differences between an ideal and a real description of wave propagation, starting with the introduction of relevant stress-strain relations. The combination of this relation and the equations of momentum conservation lead to the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. This book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may also find this text useful. New to this edition: This new edition presents the fundamentals of wave propagation in Anisotropic, Anelastic, Porous Media while also incorporating the latest research from the past 7 years, including that of the author. The author presents all the equations and concepts necessary to understand the physics of wave propagation. These equations form the basis for modeling and inversion of seismic and electromagnetic data. Additionally, demonstrations are given, so the book can be used to teach post-graduate courses. Addition of new and revised content is approximately 30%. Examines the fundamentals of wave propagation in anisotropic, anelastic and porous media Presents all equations and concepts necessary to understand the physics of wave propagation, with examples Emphasizes geophysics, particularly, seismic exploration for hydrocarbon reservoirs, which is essential for exploration and production of oil

Viscoelastic Waves and Rays in Layered Media
Viscoelastic Waves and Rays in Layered Media

Author: Roger D. Borcherdt

Publisher: Cambridge University Press

Published: 2020-10-22

Total Pages: 520

ISBN-13: 1108852246

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This second edition extends the rigorous, self-contained exposition of the theory for viscoelastic wave propagation in layered media to include head waves and general ray theory. The theory, not published elsewhere, provides solutions for fundamental wave-propagation and ray-theory problems valid for any media with a linear response, elastic or anelastic. It explains measurable variations in wave speed, particle motion, and attenuation of body waves, surface waves, and head waves induced at anelastic material boundaries that do not occur for elastic waves. This book may be used as a textbook for advanced university courses and as a research reference in seismology, exploration geophysics, engineering, solid mechanics, and acoustics. It provides computation steps for ray-tracing computer algorithms to develop a variety of tomography inferred anelastic models, such as those for the Earth's deep interior and petroleum reserves. Numerical results and problem sets emphasize important aspects of the theory for each chapter.

Wave Propagation in Viscoelastic Media
Wave Propagation in Viscoelastic Media

Author:

Publisher:

Published: 1979

Total Pages:

ISBN-13:

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The mathematical formulations of the wave propagation problem in a linear viscoelastic solid are reviewed from the point of view of constitutive equations and the theory of linear physical systems. Various general results from the theory of propagating singular surfaces and from the mathematical theory of hyperbolic equations are applied to the analysis of the wave propagation process. The impulse responses of three viscoelastic media are analyzed by use of asymptotic methods. The three material models are the standard linear solid, the standard linear solid with a continuous spectrum of relaxation times, and the power law solid. The standard linear solid with a continuous spectrum of relaxation times and the power law solid have a nearly constant quality factor, Q, over the seismic frequency band. The impulse responses of these two viscoelastic solids are compared. The results show significant and discernible features in the wave profile. It is concluded that differentiation of the models can be made by comparing wave shapes and that a complete knowledge of Q over the entire frequency range is required to determine the wave propagation problem when initiated by an impulsive process. 11 figures, 1 table.

Seismology and Plate Tectonics
Seismology and Plate Tectonics

Author: David Gubbins

Publisher: Cambridge University Press

Published: 1990-06-28

Total Pages: 352

ISBN-13: 9780521379953

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This introduction to seismological theory and the principles of plate tectonics also develops a practical approach to the interpretation of seismograms for physicists and mathematicians as well as geologists.