Transient Waves in Visco-Elastic Media

Transient Waves in Visco-Elastic Media

1st Edition - January 1, 1977

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  • Author: Norman Ricker
  • eBook ISBN: 9780444601698

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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


    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



    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


    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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