Transient Waves in Visco-Elastic Media

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.

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