Absorption Band Q Model for the Earth

Abstract

Body wave, surface wave, and normal mode data are used to place constraints on the frequency dependence of Q in the mantle. With a simple absorption band model it is possible to satisfy the shear sensitive data over a broad frequency range. The quality factor Q_s (ω) is proportional to ω^α in the band and to ω and ω^(−1) at higher and lower frequencies, respectively, as appropriate for a relaxation mechanism with a spectrum of relaxation times. The parameters of the band are Q(min) = 80, α = 0.15, and width, 5 decades. The center of the band varies from 10^1 seconds in the upper mantle, to 1.6×10^3 seconds in the lower mantle. The shift of the band with depth is consistent with the expected effects of temperature, pressure and stress. High Q_s regions of the mantle are attributed to a shift of the absorption band to longer periods. To satisfy the gravest fundamental spheroidal modes and the ScS data, the absorption band must shift back into the short-period seismic band at the base of the mantle. This may be due to a high temperature gradient or high shear stresses. A preliminary attempt is also made to specify bulk dissipation in the mantle and core. Specific features of the absorption band model are low Q in the body wave band at both the top and the base of the mantle, low Q for long-period body waves in the outer core, an inner core Q_s that increases with period, and low Q_P/Q_S at short periods in the middle mantle. The short-period Q_s increases rapidly at 400 km and is relatively constant from this depth to 2400 km. The deformational Q of the earth at a period of 14 months is predicted to be 463.

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