Transient Waves in Visco-Elastic Media

1st Edition - January 1, 1977
Author: Norman Ricker
Language: English
eBook ISBN:
9 7 8 - 0 - 4 4 4 - 6 0 1 6 9 - 8

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… Read more

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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.

PrefaceAcknowledgementsChapter 1. Historical Introduction Classical elastic waves Early seismic prospecting The problem The attackChapter 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 waveletsChapter 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 seismographChapter 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 functionsChapter 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 liquidsEpilogue InterpretationsAppendix 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 distancesAppendix B. Symbols - Nomenclature - Formulae Integral representation of the functionsAppendix C. Prologue to the Tables and Computer-Drawn Curves Tables of Ricker's wavelet integrals: evaluation and use Use of the tablesBibliographySubject Index