
Transient Waves in Visco-Elastic Media
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Developments in Solid Earth Geophysics 10: Transient Waves in Visco-Elastic Media deals with the propagation of transient elastic disturbances in visco-elastic media. More specifically, it explores the visco-elastic behavior of a medium, whether gaseous, liquid, or solid, for very-small-amplitude disturbances. This volume provides a historical overview of the theory of the propagation of elastic waves in solid bodies, along with seismic prospecting and the nature of seismograms. It also discusses the seismic experiments, the behavior of waves propagated in accordance with the Stokes wave equation, and wavelet functions and their polynomials. The book explains the laws of propagation of seismic wavelets and seismic ray paths, as well as the equations of wavelet propagation, the velocity-type seismic wavelet, and the spectrum of the wavelet. It discusses the motion of a mechanical seismograph disturbed by extraneous forces or motions. It also provides information on the differential equation describing the motion of a galvanometer, laboratory studies of wavelet contraction, and characteristics of a wavelet-contractor amplifier. Furthermore, the book explains the experimental studies of the primary seismic disturbance and internal friction. This monograph is a valuable source of information for physicists, students who want to pursue a career in geophysics or selenophysics, and those who actively working in these fields.
Table of Contents
Preface
Acknowledgements
Chapter 1. Historical Introduction
Classical elastic waves
Early seismic prospecting
The problem
The attack
Chapter 2. The Nature of Seismograms
The failure of classical elastic-wave propagation theory
The effect of selective absorption
Seismic wavelets
Experimental studies
Chapter 3. The Equation of Wave Propagation for an Elastic Medium with Viscous Absorption
The Stokes wave equation
The solution of the Stokes wave equation for continuous sinusoidal waves
Numerical distance and numerical time
Chapter 4. Wavelet Functions and Polynomials
Solutions of the Stokes wave equation
Wavelet functions
The wavelet polynomials
Chapter 5. Wavelet-Form Functions and The Laws of Propagation of Seismic Wavelets
Wavelet-form functions
Laws of propagation of seismic wavelets
Chapter 6. Very-Near-Shot Wavelet and the Nature of the Shot Pulse
Problems in the neighborhood of the explosive source
Series solutions developed about the point at infinity
Integral representations of the functions
Recapitulation and the nature of the shot pulse
The unit impulse shot pulse and delta functions
The nature of the detonation process
Chapter 7. Seismic Ray Paths
Search for an area for fundamental seismic studies
The Pierre shale of eastern Colorado
Earth with a uniform velocity gradient
Chapter 8. Some Characteristics of Seismic Disturbances
Two aspects of wavelet propagation
Changes in wavelet shape
Wavelet broadening
Wavelet attenuation
The illusory first kick
Chapter 9. Wavelet Complexes and Seismic Resolving Power
Wavelet complexes
Seismic resolving power
Chapter 10. Distortionless Wavelet Transmission
The velocity-type seismic wavelet
The spectrum of the wavelet
Distortionless transmission of wavelets
Definition of a wavelet contractor
Wavelet contraction
Chapter 11. The Seismograph
The differential equation of motion of a mechanical seismograph
Solutions of the differential equation
Conditions for low wavelet distortion in the seismograph
Chapter 12. The Galvanometer
The differential equation of motion for a galvanometer
Solutions of the differential equation
Conditions for low wavelet distortion by the galvanometer
Galvanometer output forms calculated with the aid of Hermite functions
Chapter 13. Laboratory Studies of Wavelet Contraction
Experimental wavelet propagation studies
Wavelet contractors and wavelet generators
Chapter 14. Field Studies with the Wavelet Contractor
Preliminary field studies
The wavelet-contractor evaluation programme
Characteristics of the wavelet-contractor amplifiers
The wavelet-contracting seismograph used in the field evaluation programme
Creative imagination
Chapter 15. Experimental Studies of the Primary Seismic Disturbance
Plans for the studies
The experimental equipment
The shot holes
The seismograms
The measurements
Wave surfaces in the Pierre shale
Wavelet shapes and wavelet breadths
The frequency spectrum of the disturbance
Decay in amplitude of the disturbance with increasing travel time
The effect of depth of shot on seismic punch
Transition-frequency measurements
The overall seismic behavior of the Pierre shale
Effect of charge size on amplitude of the disturbance
Results of the studies in Pierre shale
Addendum: On the determination of the misalignment of deep instrument holes with the vertical
The low-velocity layer
Chapter 16. Shooting in Sand
Plans for the studies
Putting plans into practice
The seismograms
Wave-surface charts
The velocity—depth function
Breadth of the disturbance versus travel time
Seismic amplitude studies
Laboratory studies of sand crushing
The mechanism of sand crushing by a detonating charge
Chapter 17. The Nature of Internal Friction
In retrospect
The internal-friction studies of S.L. Quimby
The author's work on internal friction
The Stokes wave equation and the equation for the conduction of heat
Gases and liquids
Epilogue
Interpretations
Appendix A. Extension to large Charges and large Distances
The results of the experimental studies of the primary seismic disturbance
The graphs extended to large charges and large distances
Appendix B. Symbols - Nomenclature - Formulae
Integral representation of the functions
Appendix C. Prologue to the Tables and Computer-Drawn Curves
Tables of Ricker's wavelet integrals: evaluation and use
Use of the tables
Bibliography
Subject Index
Product details
- No. of pages: 288
- Language: English
- Copyright: © Elsevier 1977
- Published: January 1, 1977
- Imprint: Elsevier
- eBook ISBN: 9780444601698
About the Author
Norman Ricker
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