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Published August 1979 | Published
Journal Article Open

The frequency dependence of Q in the Earth and implications for mantle rheology and Chandler wobble


For most solids the 'high temperature background' attenuation dominates at low frequencies and temperatures greater than about one-half the melting temperature. It is likely to be important in the mantle at seismic frequencies. The same mechanism also contributes to transient creep at low stresses and low total strains. A relaxation spectrum is found which satisfies the frequency dependence of laboratory Q and the time dependence of transient creep data. This makes it possible to provide a physical interpretation of the parameters in Jeffrey's modified Lomnitz creep function. Q is predicted to increase as ω^α in the lower Q regions of the mantle. At high and low frequencies Q should increase as ω and ω^(−1), respectively. The location of the ω^α band depends on temperature and therefore shifts with depth. At high temperatures, seismic waves are on the low-frequency side of the absorption band and Q decreases with frequency. Far from the melting point and at sufficiently high frequencies Q should increase linearly with frequency. We use Chandler wobble, tidal and free oscillation data to estimate that α is ∼ 1/5 to 1/3, consistent with laboratory measurements of transient creep and internal friction at high temperature. A preliminary attempt is made to estimate the transient creep response of the mantle from Q measurements. The inferred viscosity agrees well with direct measurements. The effect of anelasticity is to lengthen the calculated period of the Chandler wobble by 5-20 days, depending on the Chandler wobble Q. A Q of 300 for the wobble, which is within the experimental uncertainty of recent determinations, gives the observed period after correcting for the effect of the oceans.

Additional Information

Copyright © 1979 The Royal Astronomical Society. Received 1978 December 29; in original form 1978 August 14. We thank Sir Harold Jeffreys for useful correspondence on the subject matter of this paper and Anton Hales and Richard O'Connell for critically reading the manuscript. F. A. Dahlen made some helpful suggestions. This research was supported by the Earth Sciences Section National Science Foundation Grant No. (EAR 77-14675). Contribution No. 3141, California Institute of Technology, Pasadena, California 91125, USA.

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August 19, 2023
October 18, 2023