Estimation of Cp at HP and HT

• Ol, Wd & Rw
• • Their Cp’s were measured at HT and RP
  • • Ol: up to 1800 K
    • Wd: up to 700 K
    • Rw: up to 700 K
  • Cp = (1 + αγT) Cv
  • • Cp : isobaric heat capacity, or heat capacity at constant pressure
    • Cv : isochoric heat capacity, or heat capacity at constant volume
    • γ: Grueneisen parameter
    • α: thermal expansion coefficient
    • Cv is assumed to be independent from P
  • Only  (1 + αγT)  is corrected for HP
  • • Cp_HP = (1 + α_HPγ_HPT) / (1 + α_RPγ_RPT) Cp_RP
  •  α & γ  are taken from the present EoS’s.

Cp of Pv at HP and HT

• Akaogi & Ito [1993]
• • Cp was measured at LT and RP
  • • 140-295 K
    • • Pv breaks down at HT and LP
    • Regarded as Cv
    • Fitted to the Kiefer model
    • Calculate Cp = Cv + α²K_TVT
    • • α: Mao et al. [1991]
      • K_T: Yeganeh-Haeri et al. [1989]
• This study
• • Calculate Cv at HP and HT based on the Debye model
  • • θ_D = 1030 K above 700 K [Akaogi & Ito, 1993]
    • HP correction for θ_D
    • • γ(V) = γ₀(V/V₀)^q
      • θ = θ₀exp{[γ₀-γ(V)]/q}
  • Cp_HP = (1 + α_HPγ_HPT ) Cv_HP
  • • α & γ  are taken from the present EoS’s.

Thermal expansivity in the mantle

α generally decreases with depth where no phase transition

α increases at the phase transitions

Adiabatic temperature gradient

• The general features of (dT/dz)_s are the same as those of α.
• • Jumps associated with the phase transition
• (dT/dz)_s is not 0.3 but 0.4 K/km in the mantle transition zone.
• (dT/dz)_s decreases from 0.4 to 0.2 K/km in the lower mantle

Temperature profile in the mantle

• At the bottom of the transition zone: 1990 ± 50 K.
• At the top of the lower mantle: 1960 ± 50 K
• Just above the D” layer: 2630 ± 60 K

Estimation of viscosity in the mantle

If the viscosity profile from the post-glacial rebound (Peltier, 1998) is the case, the temperature gradient of the real mantle is slightly steeper than the adiabatic geotherm (0.4-0.5 K/km).
If that from the geoid and seismic profile (Mitrovica & Forte, 2004), the real temperature gradient of the real mantle is adiabatic up to 2200 km, and much steeper in the deeper region (~1 K/km).

Conclusion

• α decreases with depth, but increases at the mantle discontinuities.
• • α increases in association with the phase transitions
• (dT/dz)_S is about 0.4 K/km in the upper part of the mantle.
• (dT/dz)_S decreases to 0.2 K/km to the bottom of the lower mantle
• • Fairly shallow gradient