1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 6, Issue 4
  5. Article
Volume 6 Number 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Changes of shape of seismic waves provide information on the properties of the material in which the waves propagate. Ricker (1953) has attempted to explain the changes of shape on the basis of a simple viscoelastic theory. His conclusions are at variance with those of others who find a dependence of the attenuation on frequency which could be explained only by a much more complicated linear theory or by nonlinear theories.

To provide a basis for discussion, the essentials of the theory of viscoelasticity are briefly reviewed. If a relaxation spectrum, rather than one or very few relaxation times, is admitted, a great variety of experimental results can be described by the linear theory of viscoelasticity. A linear theory is indicated when no obvious violations of the principle of superposition occur.

Ricker's theory is presented with some modifications which allow for a finite duration of the initial pulse and for the approximate character of his basic assumptions. There do not appear to be serious discrepancies between his theory and his experimental results. Some of the objections to his theory can be met by assuming a finite duration of the initial pulse. However, more direct measurements made under similar circumstances by McDonal (1958) at the same location lead to a conclusion on the nature of the material not in accordance with Ricker's. This casts doubt on the sensitivity of his method.

Laboratory measurements usually yield results which are not explainable in terms of simple viscoelastic models. Whether a linear theory with a relaxation spectrum or a nonlinear theory should apply depends much on the experimental conditions. We must also consider the possibility of nonlinear mechanisms which are active at small amplitudes. No stand is taken in this controversy, but it is pointed out that the question linear or nonlinear could be decided experimentally without considering the details of the theories.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.1958.tb01666.x
2006-04-27
2024-04-26

  • From This Site

    /content/journals/10.1111/j.1365-2478.1958.tb01666.x
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Alfrey, T., 1944, Nonhomogeneous Stresses in Viscoelastic Media, Quart. Appl. Math., 2, 113.
    [Google Scholar]
  2. Alfrey, T., 1945, Methods of Representing the Properties of Viscoelastic Materials, Quart. Appl. Math., 3, 143.
    [Google Scholar]
  3. Biot, M. A., 1954, Theory of Stress‐Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena, J. Appl. Phys., 25, 1385–1391.
    [Google Scholar]
  4. Biot, M. A., 1956, Thermoelasticity and Thermodynamics, J. Appl. Phys., 27, 240–253.
    [Google Scholar]
  5. Birch, F., and Bancroft, D., 1938, Elasticity and Internal Friction in a Long Column of Granite, Bull. Seis. Soc. Am., 28, 243.
    [Google Scholar]
  6. Born, W. T., 1941, The Attenuation Constant of Earth Materials, Geophysics, 6, 132.
    [Google Scholar]
  7. Bruckshaw, J. M., and Mahanta, P. C, 1954, The Variation of the Elastic Constants of Rocks with Frequency, Petroleum, 17, 14.
    [Google Scholar]
  8. Brune, O., 193031, Synthesis of a Finite Two‐Terminal Network, J. Math, and Phys., 3–191.
    [Google Scholar]
  9. Collins, F., and Lee, C. C, 1956, Seismic Wave Attenuation Characteristics from Pulse Experiments, Geophysics, 21, 16.
    [Google Scholar]
  10. Deresiewics, H., 1957, Plane Waves in a Thermoelastic Solid, J. Acoust. Soc. Am, 29, 204–209.
    [Google Scholar]
  11. Förtsch, O., 1956, Die Ursachen der Absorption Elastischer Wellen, Annali di Geofisica, 9, 469.
    [Google Scholar]
  12. Knopoff, L., 1956, The Seismic Pulse in Materials Possessing Solid Friction, Bull. Seis. Soc. Am., 46, 175.
    [Google Scholar]
  13. Macdonald, G. J. F., 1958, Attenuation of Small Amplitude Stress Waves in Solids, Revs. Mod. Phys., in press.
    [Google Scholar]
  14. Markham, I. J., Beyer, R. T., and Lindsay, R. B., 1951, Absorption of Sound in Fluids, Revs. Mod. Phys., 23, 353–411.
    [Google Scholar]
  15. McDonal, F. J.Angona, F. A., Mills, R. L., Sengbush, R. L., Van Nostrand, R. G., and White, J. E., 1958, Attenuation of Shear and Compressional Waves in Pierre Shale, Geophysics, 23, 421.
    [Google Scholar]
  16. Ricker, N., 1953, The Form and Laws of Propagation of Seismic Wavelets, Geophysics, 18, 10.
    [Google Scholar]
  17. Van Melle, F. A., 1954, Note on “The Primary Seismic Disturbance in Shale”, by N.Ricker and W. A.Sorge, Bull. Seis. Soc. Am., 44, 123.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.1958.tb01666.x
Loading
  • Article Type: Research Article

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error