A Caltech Library Service

Importance of physical dispersion in surface wave and free oscillation problems: Review

Kanamori, Hiroo and Anderson, Don L. (1977) Importance of physical dispersion in surface wave and free oscillation problems: Review. Reviews of Geophysics, 15 (1). pp. 105-112. ISSN 8755-1209. doi:10.1029/RG015i001p00105.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


Physical dispersion resulting from anelasticity is investigated from the point of view of linear viscoelastic models and causality relations. It is concluded that inasmuch as Q in the earth's mantle is nearly independent of frequency, at least in the seismic frequency band, a dispersion relation in the form of C(ω) = C(ω_r)[1 + (1/πQ_m) In (ω/ω_r)] must be used for correcting the effect of physical dispersion arising from anelasticity. (Here C(ω) is the phase velocity of either body waves, surface waves, or free oscillations, ω is the angular frequency, ωr is the reference angular frequency, and Q_m is the path average Q for body waves or Q of a surface wave or a mode of angular frequency ω; for surface waves and free oscillations, C(ω_r) should be understood as the phase velocity at ω computed by using the elastic moduli at ω = ω_r.) The values of Q outside the seismic frequency band affect mainly the absolute value of the phase velocity but do not affect significantly the relative dispersion within the seismic frequency band. Even if the microscopic mechanism of attenuation is nonlinear, this dispersion relation can be used if departure from elasticity is relatively small, so that the signal can be approximated by a superposition of propagating harmonic waves. Since surface wave and free oscillation Q is 100–500 for fundamental modes, a correction of 0.5–1.5% must be made for joint interpretation of body wave and surface wave data. This correction is nearly 1 order of magnitude larger than the uncertainties associated with these data and are therefore very significant. When this correction is made, the discrepancy between the observed surface wave phase velocities and free oscillation periods and those predicted by the Jeffreys or Gutenberg model becomes much smaller than has previously been considered.

Item Type:Article
Related URLs:
URLURL TypeDescription
Kanamori, Hiroo0000-0001-8219-9428
Additional Information:Copyright © 1977 by the American Geophysical Union. (Received August 23, 1976; accepted August 31, 1976.) Paper 6R0680. This research was 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 F44620-72-C-0078. Contribution 2799 of the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125.
Funding AgencyGrant Number
Advanced Research Projects Agency (ARPA)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F44620-72-C-0078
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Caltech Division of Geological and Planetary Sciences2799
Issue or Number:1
Record Number:CaltechAUTHORS:20141105-093502267
Persistent URL:
Official Citation:Kanamori, H., and D. L. Anderson (1977), Importance of physical dispersion in surface wave and free oscillation problems: Review, Rev. Geophys., 15(1), 105–112, doi:10.1029/RG015i001p00105.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51283
Deposited By: George Porter
Deposited On:05 Nov 2014 18:38
Last Modified:10 Nov 2021 19:08

Repository Staff Only: item control page