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Published October 1976 | Published
Journal Article Open

Velocity dispersion due to anelasticity; implications for seismology and mantle composition


The concept of a relaxation spectrum is used to compute the absorption and dispersion of a linear anelastic solid. The Boltzmann after-effect equation is solved for a solid having a linear relationship between stress and strain and their first time derivatives, the 'standard linear solid', and having a distribution of relaxation times. The distribution function is chosen to give a nearly constant Q over the seismic frequency range. Both discrete and continuous relaxation spectra are considered. The resulting linear solid has a broad absorption band which can be interpreted in terms of a superposition of absorption peaks of individual relaxation mechanisms. The accompanying phase and group velocity dispersion imply that one cannot directly compare body wave, surface wave, and free oscillation data or laboratory and seismic data without correcting for absorption. The necessary formalism for making these corrections is given. In the constant Q regions the correction is the same as that implied in the theories of Futterman, Lomnitz, Strick and Kolsky.

Additional Information

Copyright © 1976 The Royal Astronomical Society. Received 1976 May 17; in original form 1976 April 1. The authors wish to thank M. J. Randall, whose criticism of the authors' (D. L. Anderson and H.-P. Liu) earlier assumption that anelasticity can be modelled by a perturbation in the imaginary part of the elastic moduli alone led to the present construction of an acoustic attenuation-dispersion theory based on physical relaxation mechanisms. We also thank C. B. Archambeau and J.-B. H. Minster for discussions and A. C. R. Livanos for assistance with the numerical computations. This work is supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract No. F44620-72-C-0078. Contribution No. 2737.

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Published - Geophys._J._Int.-1976-Liu-41-58.pdf


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August 22, 2023
October 18, 2023