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A model of Q−1 based on Walsh's theory for attenuation in partially melted rock is proposed for the upper mantle of western North America. The asthenosphere (or low-Q zone), in which attenuation is attributed to a superposition of thermally activated relaxation processes, is 300 km thick in the model and must be vertically inhomogeneous. The lithosphere (or high-Q lid) is 60 km thick. The model is consistent with a wide assortment of attenuation and velocity data, in all spanning approximately three decades in frequency. Both the shear modulus and Q−1 for shear waves are frequency dependent in the asthenosphere. The viscosity and volume concentration of melt can be estimated from the relaxation parameters. Further, if lateral changes in these parameters, determined from the differential attenuation and travel-time delays of P and S waves, are attributed to horizontal temperature variations, then these temperature differences in the asthenosphere need be no larger than 100 to 200°K at a depth of several hundred kilometers. The highest temperatures determined in this fashion are beneath the Rocky Mountain and Pacific border regions.
Sean C. Solomon (Fri,) studied this question.