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Linear viscoelasticity and dispersion in seismic wave propagation
Author(s) -
Brennan B. J.,
Smylie D. E.
Publication year - 1981
Publication title -
reviews of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.087
H-Index - 156
eISSN - 1944-9208
pISSN - 8755-1209
DOI - 10.1029/rg019i002p00233
Subject(s) - viscoelasticity , impulse response , isotropy , dispersion (optics) , linear system , impulse (physics) , wave propagation , physics , mathematical analysis , geology , geophysics , acoustics , mechanics , optics , classical mechanics , mathematics , thermodynamics
The theoretical background to the application of linear viscoelasticity in describing the anelastic behavior of rocks is developed in this review. The constraints imposed on the behavior of the impulse response and system function of a linear system by the requirements that the system be causal and passive are examined. These include the existence of dispersion relations for the system function for causal systems and the role of the concepts of positive reality and minimum phase in passive systems. The uses of these linear system concepts in linear viscoelasticity and in the propagation of plane waves in an isotropic viscoelastic medium are considered. Finally, applications to seismology are presented, in particular the significance of the dispersion associated with a quality factor Q that is constant or varies as a power of frequency in comparisons of seismic data for different frequency ranges and in the evolution of the shape of propagating pulses.