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

Abstract

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.

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