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Published May 1987 | public
Journal Article

A Seismic Equation of State II. Shear properties and thermodynamics of the lower mantle


For most solids at normal conditions the effect of temperature on the elastic properties is controlled mainly by the variation of volume. Volume dependent extrinsic effects dominate at low pressure and high temperature. Under these conditions one expects that the relative changes in shear velocity, due to lateral temperature gradients in the mantle, should be similar to changes in compressional velocity. However, at high pressure, the extrinsic contribution is suppressed, particularly for the bulk modulus, and variations of seismic velocities are due primarily to changes in the rigidity. Seismic data for the lower mantle are used to estimate the two Grüneisen parameters and related parameters such as the temperature and pressure derivatives of the elastic moduli and thermal expansion. Standard assumptions about the volume dependence of the elastic moduli based on high temperature behavior of solids are shown to be inaccurate for the lower mantle. The Grüneisen-type parameters for the lower mantle are (∂ In K_s/∂ In P)_p=δ_s=1.8-1.0, (∂ In K_s/∂ In p)_s=3-3.8, (∂ In G/∂ In P)_p=5.8-7.0, (∂ In G/∂ In P)_s=2.4-2.6 and y=1.3-1.1 These are based on the radial and lateral variations of seismic velocity and density. The zero-pressure high-temperature values for the coefficient of thermal expansion and the Grüneisen ratio are estimated as α_0 = 3.8 × 10^(−5) K^(−1) and γ_0 = 1.4. The seismic data imply (∂ In y/∂ In P) = - 1+є and -(∂ In ɑ/∂ In P)_s = ~ 2-3. The effect of temperature on the pressure derivatives of the moduli is also estimated. The lattice conductivity, K_L, increases rapidly with depth, contributing to a lowering of the Rayleigh number in the lower mantle and a large thickness for deep thermal boundary layers. Temperature is less effective in altering density and seismic velocity at depth than assumed in geophysical modeling. Temperature induced phase changes are more important than temperature per se. These considerations cast doubt on the thermal interpretation of deep slab anomalies and, therefore, on the deep slab penetration hypothesis.

Additional Information

© 1987 Elsevier Science Publishers B.V. Received September 15, 1986; revision accepted October 7, 1986. I thank Huw Davies for initially calling my attention to the ∂V_p/∂V_s relation for the lower mantle and for reviewing the manuscript. Personal communications with Rob Clayton, John Woodhouse and Adam Dziewonski further convinced me that something needed explaining. I appreciate receiving these results in advance of publication. Mark Richards aroused my interest in the problem of δ_s for the lower mantle. The geoid-tomography correlation of Hager et al. (1984) is an important element of the present study. I appreciate the comments of Tom Duffy and F. Mulargia. Orson L. Anderson and Raymond Jeanloz provided extensive critiques of the preliminary draft and the present manuscript has benefited from their advice and preprints. This paper was completed in Erice, Sicily, thanks to the hospitality of Enzo Boschi. This research was supported by NSF grants EAR-8509350 and EAR-8317623. Contribution No. 4373, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, 91125.

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