Adiabatic temperature profile in the mantle

Abstract

The temperature at the 410-km discontinuity is re-evaluated by comparing the depth of the discontinuity with the olivine–wadsleyite transition pressure obtained using in situ X-ray diffraction experiments by Katsura et al. (2004a) and equation of state (EoS) of MgO by Tange et al. (2009) (Tange scale) and Matsui et al. (2000). The newly estimated temperature is 1830 ± 48 K, 70 K higher than that by our previous estimation. The EoSes of the major mantle minerals (olivine, wadsleyite, ringwoodite and perovskite) are also recalculated using the Tange scale. The adiabatic temperature gradient is calculated using the thermal expansion coefficient obtained from these EoSes. The adiabatic temperature gradient gradually decreases with increasing depth without a phase transition, and abruptly increases in association with phase transitions. The adiabatic temperature gradients are found to be 04–0.5 and 0.3 K/km in the upper and lower parts of the mantle, respectively. The temperatures at a depth of 200 km, the bottom of the mantle transition zone, the top of the lower mantle and a depth of 2700 km are found to be 1720 ± 40, 2010 ± 40, 1980 ± 40, and 2730 ± 50 K. The mantle potential temperature is found to be 1610 ± 35 K.

Introduction

Temperature is an important parameter for modeling the dynamics of the Earth's interior. Estimation of the temperature distribution in the deep mantle is essential for solid Earth geophysics. However, here is no direct way to measure temperature in the Earth's deep interior. A combination of indirect methods is indispensable to estimate the temperature distribution in the deep mantle.

The olivine–wadsleyite transition, and dissociation of ringwoodite to perovskite + periclase are believed to be responsible for the 410-km and 660-km seismic discontinuities, respectively. The pressures of these phase transitions could depend on temperature. Hence, it is expected that the temperature at the discontinuity can be estimated by comparing the depth of the discontinuity with the transition pressure. Previously Ito and Katsura (1989) estimated the temperature at the 660-km discontinuity by comparing the pressure of the dissociation of ringwoodite given by Ito and Takahashi (1989) with depth of the 660-km discontinuity given by Nakanishi (1988). The recent studies on the dissociation of ringwoodite however, suggest that the temperature dependence of the pressure of the dissociation is very small (Katsura et al., 2003, Fei et al., 2004, Litasov et al., 2005). Therefore, temperature at the 660-km discontinuity is difficult to estimate in this strategy. On the other hand, Katsura et al. (2004a) showed that pressure of the olivine–wadsleyite transition depends significantly on temperature. If the 410-km discontinuity is caused by the olivine–wadsleyite transition, then the depth of the discontinuity varies by 0.1 km/K (Katsura et al., 2004a). Although there are a number of uncertainties, we may be able to estimate the mantle temperature by the olivine wadsleyite transition and 410-km discontinuity.

To obtain the temperature distribution of the mantle, the temperature at the 410-km discontinuity should be extrapolated to both the deeper and shallower regions. Conductive and radiative heat transfer is considered to be negligible because of the small thermal conductivity of mantle minerals, and heat should be mainly transported by convection in most part of the mantle. Therefore, the temperature gradient is considered to be nearly adiabatic in the Earth's mantle. The adiabatic temperature gradient, ( ∂ T/∂ z)_s, in the Earth is expressed as:

$${(\partial T/\partial z)}_s=\frac{\alpha gT}{C_p}$$

where T is temperature, z is depth, g is gravitational acceleration, and α and C_p are the thermal expansion coefficient and isobaric heat capacity of the constituent materials, respectively (Turcotte and Schubert, 2002). Gravitational accelerations in the mantle are reasonably estimated from the density. Isobaric heat capacity does not change significantly with increasing pressure and temperature at high temperatures. On the other hand, the thermal expansion coefficient depends largely upon pressure and temperature (Anderson, 1967). Hence, knowledge of the thermal expansion coefficients of the mantle minerals is essential for estimating the temperature distribution in the mantle. For this reason, we have been trying to measure precisely the volumes of important mantle minerals at realistic P-T conditions for the mantle [olivine: Katsura et al. (2009a), wadsleyite: Katsura et al. (2009b), ringwoodite: Katsura et al. (2004a), perovskite: Katsura et al. (2009c)] using an advanced multi-anvil apparatus for in situ X-ray diffraction (Katsura et al., 2004c).

The pressures in the above studies were calculated using the equation of state (EoS) of MgO given by Matsui et al. (2000) (Matsui scale). Recently, Tange et al. (2009) proposed a new EoS of MgO that is consistent with many series of experimental data (Tange scale). Here, we recalculated the pressures of the olivine–wadsleyite transition and evaluated the temperature at the 410-km discontinuity. The adiabatic temperature distribution in the mantle is constructed by extrapolating the estimated temperature at the 410-km discontinuity using Eq. (1) with the recalculated thermal expansion coefficient.