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CHANGES OF SHAPE OF SEISMIC IMPULSES IN HOMOGENEOUS VISCOELASTIC MEDIA
Author(s) -
POSTMA G. W.
Publication year - 1958
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1958.tb01666.x
Subject(s) - viscoelasticity , superposition principle , relaxation (psychology) , correspondence principle (sociology) , simple (philosophy) , pulse (music) , nonlinear system , attenuation , seismogram , basis (linear algebra) , mathematics , statistical physics , physics , geology , mathematical analysis , optics , geometry , seismology , thermodynamics , quantum mechanics , psychology , social psychology , philosophy , epistemology , detector , economics , market economy
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 et al. (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.