A Revised Adiabatic Temperature Profile for the Mantle

This study reevaluates the adiabatic temperature profile of the Earth's mantle. The global average temperature at the 410‐km discontinuity is estimated to be 1839 (38) K by comparing the globally averaged depths of the 410‐km discontinuity with the previously determined phase diagram of the olivine‐wadsleyite transition in the system (Mg,Fe)2SiO4 at two temperatures. The temperature at the 410‐km discontinuity is extrapolated to shallower and deeper regions using the adiabatic temperature gradient, which is estimated from the pressure‐volume‐temperature relations and heat capacities of the major mantle minerals, namely, olivine, wadselyite, ringwoodite, and bridgmanite. The experimental temperatures and pressures in the original studies used in these evaluations are recalculated using the recently proposed pressure correction on EMF of the W97Re3‐W75Re25 thermocouple. The uncertainties are evaluated by the Monte Carlo simulation. The temperatures on the adiabatic temperature profile are found to be 1646 (35), 1994 (40), 1960 (40), and 2587 (60) K, respectively, at a 50‐km depth, just above the 660‐km discontinuity, just below the 660‐km discontinuity, and at 2,800‐km depth. The lower mantle temperatures in the current estimation are lower than those given by Katsura et al. (2010), https://doi.org/10.1016/j.pepi.2010.07.001. The 50‐km depth temperature is slightly higher but generally agrees to that estimated from the melting of depleted peridotite.

KATSURA 10.1029/2021JB023562 2 of 11 et al., 2004). Then, they estimated the temperatures above and below the D410 using the formula of the adiabatic temperature gradient with depth as: where T is the temperature, z is the depth, α is the thermal expansivity of the constituent, g is the gravitational acceleration, and Cp is the isobaric heat capacity per weight of the constituent (Turcotte and Schubert, 2014). In their calculation, the mantle rocks were approximated by the Mg endmembers of olivine, wadsleyite, ringwoodite, and bridgmanite. The P-V-T relations of these minerals were determined using the multianvil in situ X-ray diffraction experiments by (Katsura, Yokoshi, et al., 2004;Katsura, Yokoshi, et al., 2009;Katsura, Shatskiy, Manthilake, Zhai, Fukui, et al., 2009;). The Cp for olivine, wadsleyite, and ringwoodite were taken from Saxena et al. (1993), and that for bridgmanite was calculated using the Debye model.
This paper presents a revised average adiabatic temperature profile in the mantle by integrating the above-mentioned new data and using a newly made calculation program.

Methods
The current study estimates an adiabatic temperature profile in the mantle by the procedure very similar to Katsura et al. (2010). Namely, it first estimates the temperature at D410, then estimates the temperature gradient, finally calculates the temperature profile from the D410 temperature using the estimated temperature gradient. Details of the procedure are explained below.

Temperature at the 410-km Discontinuity
The current study first considers the most probable global average of the D410 depth. Chambers et al. (2005), Shearer (1998, 1999), Houser et al. (2008Houser et al. ( , 2016, and Huang et al. (2019) mapped the D410 depths globally and suggested the averaged depths of 418, 418, 409, 410, 411, and 416.8 km, respectively. Very recently, Waszek et al. (2021) reported the average D410 km depths of 410.0 and 414.4 km based on the SS and PP precursors. We use these eight depths for the estimation of the adiabatic temperature profile.
The current study employs the data given by Katsura, Yamada, et al. (2004) for the phase relations of the olivine-wadsleyite transition in (Mg,Fe) 2 SiO 4 . They synthesized coexisting olivine and wadsleyite in a multi-anvil press with temperatures measured by W 97 Re 3 -W 75 Re 25 thermocouples and pressures estimated from MgO volumes by in situ X-ray diffraction using the P-V-T relations of MgO suggested by Matsui et al. (2000). Then, Katsura, Yamada, et al. (2004) measured the compositions of recovered olivine and wadsleyite grains using an electron probe microanalyzer (EPMA). In the current study, the temperatures in Katsura, Yamada, et al. (2004) are corrected using Nishihara et al. (2020) pressure correction of the EMF-temperature relations. The pressures in Katsura, Yamada, et al. (2004) are recalculated using these new temperatures and the two MgO equations of state (EOS) based on the third-order Birch-Murnaghan EOS and Vinet EOS by Tange et al. (2009).
The recalculated olivine-wadsleyite phase-relation data are fitted to Strixrude's (1997) equations to express the binary loops at the above two temperatures. One essential parameter in his equations is the Fe-Mg partition coefficients between olivine and wadsleyite, K D where X j i is the mole fraction of component i in phase j, and Π is the reduced pressure using the transition pressures of the endmembers of Mg 2 SiO 4 and Fe 2 SiO 4 , P Mg2SiO4 and P Fe2SiO4 , respectively as: where P is the experimental pressure. The mole fraction of wadsleyite, f Wd , is expressed as a function of Π with the parameter K D Mg−Fe as: where x bulk is the bulk mole fraction of the Fe 2 SiO 4 component. Fitting the experimental data to Equations 2-4 yields K D Mg−Fe , P Mg2SiO4, and P Fe2SiO4 . Although Katsura et al. (2010), Katsura, Yamada, et al. (2004) assumed that the difference in the endmember transition pressures, P Mg2SiO4 -P Fe2SiO4 , is independent of the temperature, this assumption is not adopted in the current study.
Similar to Katsura et al. (2010), the current study assumes that the upper mantle comprises Hawaiian pyrolite, namely, X Mg = 0.89 (X Mg = Mg/(Mg + Fe)) (Green & Falloon, 1998). Stixrude (1997) suggested that the D410 depth corresponds to the pressure where the olivine-to-wadsleyite ratio is 1:2, namely, f Wd = 2/3. The current study follows this idea to obtain the olivine-wadsleyite transition pressure in Hawaiian pyrolite (P Ol-Wd, Py ) as a function of temperature. Comparing the pressure corresponding to the D410 depth with P Ol-Wd, Py allows estimating the D410 temperature.
The uncertainties in the above estimations are evaluated using the Monte Carlo simulation by producing 1,000 replica sets of the phase relation data. This procedure produces the replica sets' data points, including pressure and compositions of olivine and wadsleyite, as:  (4) Note. The initial data are from Katsura, Yamada, et al. (2004). where x j i is the ith data values in the jth replica data set, x 0 i and σx 0 i are the average and standard deviation of the ith datum in the original data set, and p is the normally distributed random number. Assuming the D410 depths of 409 and 411 km, the D410 temperatures are calculated for each replica set. The average and uncertainty of the D410 temperature are obtained from the mean value and standard deviation of the 1,000 replica sets at the two D410 depths.

Evaluation of the Parameters for the Adiabatic Temperature Gradient
The adiabatic temperature gradient with pressure is given as: where ρ c is the density of the constituent (Turcotte and Schubert, 2014). Therefore, evaluating the adiabatic temperature gradient requires the thermal expansivity, density, and isobaric heat capacity of the constituents as a function of pressure and temperature.
Following Katsura et al. (2010), the current study approximates the mantle constituents by the Mg-endmembers of olivine, wadsleyite, ringwoodite, and bridgmanite at depth ranges of 50-410, 410-520, 520-660, and 660-2,800 km, respectively. Wolf et al. (2015) found that the adiabatic temperature gradients of MgSiO 3 and (Mg 0.83 Fe 0.17 ) SiO 3 bridgmanite are very similar, supporting the above approximation. On the other hand, although some studies suggested that the mantle transition zone contains weight percent levels of H 2 O (Fei et al., 2017;Pearson et al., 2014), Houser (2016) predicted that the mantle transition zone is generally dry by combining the global analysis of long-period seismic data and the mineral physics data. Hence, we primarily assume that the Earth's mantle is essentially dry. In the latter part of this paper, we argue a possible effect of H 2 O incorporation on estimating the adiabatic temperature profile.
The data sets for the density and thermal expansivity of olivine, wadsleyite, and ringwoodite are taken from (Katsura, Shatskiy, Manthilake, Zhai, Fukui, et al., 2009;and Katsura, Yokoshi, et al., 2004, respectively. Those of bridgmanite are taken from Katsura, Yokoshi, et al., 2009 andTange et al. (2012). The temperatures of these data sets are recalculated using Nishihara et al. (2020) pressure correction on the thermocouple EMF. The pressures are then recalculated based on these new temperatures using the two MgO EOS's given by Tange et al. (2009).
The P-V-T data set of each mineral is fitted to the Mie-Grüneisen-Debye EOS (Jackson & Rigden, 1996) with the third-order Birch-Murnaghan EOS (Katsura & Tange, 2019). At the standard temperature of T 0 = 300 K, the third-order Birch-Murnaghan EOS is expressed as: where P (V, T 0 ) is the pressure at volume V and the standard temperature of T 0 , K T0 is the isothermal bulk modulus at the temperature of T 0 , K T0 ' is its pressure derivative, and V P0,T0 and V P,T0 are the volume at the standard pressure of P 0 = 0 and at the pressure of P, respectively, under the temperature condition of T 0 . The Mie-Grüneisen-Debye EOS is: where P (V, T) is the pressure at the volume V and temperature T, γ is the Grüneisen parameter, and E th is the thermal energy. The volume dependence of the Grüneisen parameter is expressed using the constant q as: where γ 0 is the Grüneisen parameter at the standard pressure P 0 and temperature T 0 . The thermal energy, E th , is given by: where θ is the Debye temperature at the volume V, n is the number of atoms per formula unit, and R is the gas constant. The Debye temperature at the volume V is expressed as: where θ 0 is the Debye temperature at the standard volume V 0 .
The uncertainties of the fitting results of K T0 ', γ 0 , and q are evaluated using the Bootstrap method as follows. First, 1,000 bootstrap data sets are produced by randomly choosing data points from the original data set with allowing duplication. Then, uncertainties multiplied by the normally distributed random numbers are added to the individual data points using Equation 5. The three parameters of K T0 ', γ 0 , and q are obtained by fitting the individual bootstrap data sets to Equations 7-11. The averages and standard deviations of the three parameters are obtained from the mean values and standard deviations of the 1,000 bootstrap data sets. Note that the Bootstrap method is not adopted in modeling the phase relations because the number of the data points for the phase relations is too small for the bootstrap method (3 pairs of olivine and wadsleyite compositions at each temperature).
The density at given pressure and temperature is evaluated from the ambient density divided by the relative volumes given by Equations 7-10. The thermal expansivity is obtained from the differentiation of the relative volumes with respect to the temperature.
It is assumed that the isochoric heat capacity, C V , of olivine is independent of the pressure because of the high temperatures. Therefore, the isobaric heat capacity at high pressure, C P , can be obtained using the isobaric heat capacity of olivine at ambient pressure, C P 0 as: where α and α 0 are the temperature-dependent thermal expansivities of olivine at high and ambient pressures, respectively. The isobaric heat capacity of olivine at ambient pressure is taken from Saxena et al. (1993), which was also adopted in Katsura et al. (2010).
The isobaric heat capacities of wadsleyite, ringwoodite, and bridgmanite are obtained by multiplying the Debye heat capacity by 1 + αγT.

Evaluation of Adiabatic Temperature Profile in the Earth's Mantle
The adiabatic temperature gradient to the depth (z) in the mantle is written as:  Isaak et al. (1989). b Mao et al. (2008). c Watanabe et al. (1982). d converted from K S given by Sinogeikin et al. (2003). e Tange et al. (2012). f Akaogi and Ito (1993). where ρ m and g are the density and gravity acceleration at a certain depth of the Earth's mantle given by PREM (Dziewonski & Anderson, 1981).
Note that the ρ m in this equation is different from ρ c in Equation 6. The former is the density of the Earth's mantle, which consists of Fe-bearing peridotite. On the other hand, the latter is that of the Fe-free endmembers of the major mantle minerals. Katsura et al. (2010) did not consider this difference and simply obtained the adiabatic temperature gradient to the depth using Equation 1, which is the major error source of Katsura et al. (2010).
Using Equation 13, the temperatures at depths are obtained by 10-km increments and decrements from the D410 depth to deeper and shallower depths, respectively. It is well-known that the latent heat associated with the phase transition of olivine to wadsleyite, wadsleyite to ringwoodite, and ringwoodite to bridgmanite + ferropericlase abruptly changes the temperature profile (Ito & Katsura, 1989;Katsura et al., 2010). Following Katsura et al. (2010), the current study assumes the temperature change of +60, +43, and −34 K by these transitions. Since the D410 is taken as the depth where the olivine and wadsleyite have a volume ratio of 1:2 (Stixrude, 1997), the temperature changes of +20 and −40 K are delivered above and below the D410, as Katsura et al. (2010) did. The wadsleyite to ringwoodite and ringwoodite to bridgmanite + ferropericlase transitions are assumed to occur at fixed depths of 520 and 660 km, respectively.

Olivine-Wadsleyite Transition in (Mg,Fe) 2 SiO 4
Table 1 presents the recalculated pressures and temperatures with the olivine and wadsleyite compositions from Katsura, Yamada, et al. (2004) experiments. Figure 1 shows the recalculated phase relations of the olivine-wadsleyite transitions in (Mg,Fe) 2 SiO 4 . The Nishihara et al. (2020) pressure correction of thermocouple EMF has increased from 1600 and 1900 K to 1644 and 1962 K, respectively. This correction has accordingly increased the pressures by 0.22 and 0.32 GPa at these temperatures, respectively. The fitting yields K D Mg−Fe = 0.517 ± 0.036, P Mg2SiO4 = 14.11 ± 0.14 GPa, and P Fe2SiO4 = 3.6 ± 1.1 GPa at 1962 K and K D Mg−Fe = 0.599 ± 0.035, P Mg2SiO4 = 15.42 ± 0.18 GPa, and P Fe2SiO4 = 4.6 ± 1.1 GPa at 1962 K. Consequently, the Clapeyron slopes of the Mg and Fe endmember transitions are 4.1 ± 0.5 and 3.4 ± 3.6 MPa/K, respectively. The uncertainties of P Fe2SiO4 estimation (1.0 and 1.0 GPa) are 6-8 times larger than those of P Mg2SiO4 (0.13 and 0.17 GPa). This is because Katsura, Yamada, et al. (2004) conducted the experiments with the bulk compositions around X Mg = 0.9. The estimated P Mg2SiO4 and P Fe2SiO4 are anticorrelated, as expected ( Figure S1 in Supporting Information S1). Yagi et al. (1987) determined the fayalite-ahrensite transition in Fe 2 SiO 4 using in situ X-ray diffraction with a multi-anvil press. Their data suggested P Fe2SiO4 's of 7.0 ± 0.1 and 6.2 ± 0.1 GPa at 1644 and 1962 K, respectively, which are significantly higher than those estimated in the current study. Hence, the binary loop should have an old-crescent shape. However, these curvatures should be insignificant for the current study because the compositional range of Katsura, Yamada, et al. (2004) already covers the mantle composition (X Mg = 0.89 (Green & Falloon, 1998; Figure 1).

Temperature at the 410-km Discontinuity
The olivine-wadsleyite transition pressures in Hawaiian pyrolite, P Ol-Wd, Py , are found to be 13.09 ± 0.07 and 14.34 ± 0.08 GPa at temperatures of 1644 and 1962 K, respectively. The smaller uncertainties in P Ol-Wd, Py than P Mg2SiO4 are because Katsura, Yamada, et al. (2004) conducted the experiments with the bulk compositions around X Mg = 0.9 and not at X Mg = 1.0 or equivalently because the P Mg2SiO4 and P Fe2SiO4 are anticorrelated.
The temperature dependence of P Ol-Wd, Py is dP Ol-Wd, Py /dT = 3.9 ± 0.3 MPa/K. This temperature dependence is significant because the temperature increase by 100 K causes the olivine-wadsleyite transition pressure to increase by 9.8 ± 0.7 km. In other words, 1-km variation of D410 depths should correspond to a temperature variation of 10.2 ± 0.7 K. Comparing P Ol-Wd, Py with the pressures of the D410 depths suggests the temperature at D410 to be 1839 ± 38 K. This temperature is identical to that estimated by Katsura et al. (2010), 1830 ± 48 K within the errors. This agreement has been made by the cancellation of the D410 depths, the used MgO equation of state, and the thermocouple correction. Katsura et al. (2010) adopted 409 km as the D410 depth, whereas the current study uses 8 reported depths, whose average depth is 413 ± 4 km. This increase in depth has raised the temperature by 40 K. Katsura et al. (2010) used Matsui et al. (2000 P-V-T relations of MgO in addition to Tange et al. (2009) EOS's. Matsui et al. (2000 data provided 80 and 40 K lower temperatures than Tange et al. (2009) Vinet-and Birch-Murnaghan EOSs. The thermocouple correction raises not only temperatures but also pressures of the experimental data points. The ratio of the pressure increase to the temperature increase is equal to the thermal pressure of MgO, which is 6.4 MPa/K at around 13 GPa and 1900-1600 K based on Tange et al. (2009). On the other hand, the temperature dependence of P Ol-Wd, Py is smaller, i.e., 3.9 ± 0.3 MPa/K. As a result, the required temperature for the olivine-wadsleyite transition becomes 50 K lower by the thermocouple correction. Also, note that the uncertainty in the temperature estimation is smaller in the current study than in Katsura et al. (2010). This smaller uncertainty is because Katsura et al. (2010) did not consider the anticorrelation of P Mg2SiO4 and P Fe2SiO4 .

P-V-T Relations of Major Mantle Minerals
Tables S1-S4 in Supporting Information S1 show the recalculated P-V-T data of the four minerals. Table 2 presents the optimized values together with the assumed parameters. Figures S2-S5 in Supporting Information S1 show the comparisons of pressures obtained using the Tange et al. (2009) MgO EOSs and the EOS of each mineral in the current study.
The obtained K' of the four minerals are identical within the uncertainties (Table 2). A higher-pressure mineral has a larger γ 0 . This is reasonable because, according to the definition, γ 0 is the rate of the pressure increase to the thermal energy increase at constant volume and ambient pressure. Since the thermal expansivity of minerals vastly increases with decreasing pressure below their stability fields, the pressure increase rate caused by the energy increase should be more significant at ambient pressure in higher-pressure minerals.
However, the relation between the stability field and q among different minerals is unclear due to the significant uncertainties. Although ringwoodite apparently has a larger q than wadsleyite (2.4 ± 0.7 and 1.5 ± 1.1), this difference is within the uncertainties. As expected, the γ 0 and q are strongly correlated, especially for wadsleyite and ringwoodite due to their narrow experimental pressure ranges ( Figure S6 in Supporting Information S1). Consequently, the uncertainty in q has a relatively small effect on the estimations of density and thermal expansivity. Table 3 shows the adiabatic temperature profile in the mantle at depths from 50 to 2,800 km obtained in the current study. Although the temperature profile in the real mantle should not be adiabatic in the lower-most region due to the thermal boundary layer, the present profile is constructed by ignoring the presence of the thermal boundary layer. Table S5 in Supporting Information S1 shows various thermoelastic parameters at depths from 50 to 2,800 km with a 10-km step. Among the shown parameters in Table S5 in Supporting Information S1, the density, gravitational acceleration, and pressure are taken from PREM (Dziewonski & Anderson, 1981). The other parameters are obtained through the procedure described above. The thermal expansivity, adiabatic temperature gradient, and adiabatic temperature profile are plotted in Figures 2-4.
Since the other parameters for the adiabatic temperature gradient given by Equation 13 other than the thermal expansivity do not vary significantly, the adiabatic temperature gradient varies similarly to the thermal expansivity (Figures 2 and 3). The adiabatic temperature gradient continuously decreases with depth without a phase transition, whereas it increases when a phase transition occurs. In the olivine stability field, the adiabatic gradient decreases from (0.54 ± 0.03) to (0.36 ± 0.02) K km −1 down to 410-km depth. In the wadsleyite and ringwoodite stability fields, it decreases from 0.36 ± 0.02-0.35 ± 0.01 and from 0.39 ± 0.02-0.37 ± 0.01 K km −1 , respectively, at 410-520 and 520-660 km depths. In the bridgmanite stability field, it decreases from 0.41 ± 0.01-0.23 ± 0.02 K km −1 to 2800-km depth. As expected, the current adiabatic gradient is smaller than Katsura et al. (2010), similar to the thermal expansivity. On the other hand, the adiabatic gradient in the lower mantle from the current study agrees very well to those estimated by Wolf et al. (2015), which has gradients of 0.35-0.39 K/km at the top of the lower mantle and decrease to 0.25-0.27 K/km at 2,300-km depth. Turcotte and Schubert (2014) suggested an adiabatic temperature gradient of 0.3 K km −1 in the mantle. This value may be a good approximation in the regions from the bottom of the upper mantle to the mid-mantle, but it may be underestimated for the uppermost mantle and overestimated for the deeper regions of the lower mantle.
According to the above argument, the temperatures are 1799 ± 39 and 1860 ± 38 K, respectively, just above and below the D410, 1899 ± 39 and 1942 ± 39 K, respectively, just above and below 520-km depth, and 1994 ± 40 and 1960 ± 40 K, respectively, just above and below 660-km depth (Table 2 and Figure 4). The temperature at 50-km depth is 1646 ± 35 K, whereas that at 2800-km depth is 2587 ± 60 K. An extrapolation of the temperature at 50-km depth to the surface using the temperature gradient at 50-km depth (0.54 K km −1 ) yields the mantle potential temperature of 1619 K (1350°C). The upper mantle temperatures essentially have no change from Katsura et al. (2010). On the other hand, the lower mantle temperatures are becoming lower with depth compared to Katsura et al. (2010). The 2800-km depth temperature in the current study is about 80 K lower than that of Katsura et al. (2010). The reason for this discrepancy is that Katsura et al. (2010) miscalculated the thermal expansion coefficients of bridgmanite at shallower depths (Figure 2), leading to overestimation of the adiabatic temperature gradient in the lower mantle. Wolf et al. (2015) reported an adiabatic temperature profile in the lower mantle down to 2400-km depth. He suggested a temperature of 2390 K at 2400-km depth, which is 100 K lower than the current study (2490 K). This is because Wolf et al. (2015) arbitrarily assumed the temperature at 670-km depth of 1873 K, which is ca.   Wolf et al. (2015); green: Mg 0.87 Fe 0.13 SiO 3 bridgmanite lower mantle by Wolf et al. (2015). The solid and dashed curves show the most probable and 68% confidence intervals, respectively. 9 of 11 90 K higher than the present estimation (1960 K) (Figure 4). Brown and Shankland (1981) estimated the adiabatic temperature profile and reported 140 K lower temperature at 2070 km depth (2410 K) than the current study (Figure 4), which is also caused by the assumption of 1873 K at the top of the lower mantle in Brown and Shankland (1981). Sarafian et al. (2017) determined the solidus temperature of mantle peridotite with 140 wt. ppm of H 2 O at a pressure of 1.5 GPa, corresponding to 50 km depth. Their solidus temperature was 1590 ± 10 K, which is slightly lower than that of the present profile, 1646 ± 35 K. The peridotite melting may start at slightly deeper regions than 50-km depth, and the melt finally may separate from the source rocks at around 50 km depth beneath mid-oceanic ridges.

Uncertainties Due to Possible Compositional Effects
Finally, we argue the chemistry effects on estimating the temperature profile, first the uniformity of constituting rocks, and second the H 2 O incorporation. Xu et al. (2008) examined a possibility that the mantle comprises a mechanical mixture of harzburgite and basalt (MM) rather than an equilibrium assemblage of pyrolitic composition (EA). If the Hawaiian pyrolite (Green & Falloon, 1998) and dunite/harzburgite (Afonso et al., 2008) represent pyrolite and harzburgite compositions, their X Mg are 0.89 and 0.93, respectively. Since the olivine-wadsleyite transition should not occur in the basaltic part but only in the harzburgite part in the MM mantle, the harzburgite composition controls the transition pressure with temperature. Due to the higher X Mg , the olivine-wadsleyite transition pressures in harzburgite (P Ol-Wd, Hz ) are higher than those in Hawaiian pyrolite: 13.47 and 14.72 GPa at 1644 and 1962 K, respectively. As a result, the D410 occurs at 10 km deeper depths at the same temperature. Consequently, the estimated D410 temperature is decreased by 100 K. The temperature profile with this D410 temperature is presented in Table S6 in Supporting Information S1 and depicted in Figure 5. In this profile, the temperature at a 50-km depth is 1559 ± 35 K. This temperature is slightly lower than the temperature required for the MORB magmatism given by Sarafian et al. (2017) (1590 ± 10 K), although the difference is still within the errors. Pearson et al. (2014) discovered a diamond inclusion of ringwoodite with 1.4 wt% of H 2 O. Therefore, the mantle transition is at least locally wet. Here, we examine the effect of 1.4 wt% H 2 O incorporation on the temperature profile. Chen et al. (2002) Table S7 in Supporting Information S1 and depicted in Figure 5. Since the solidus of H 2 O-saturated mantle peridotite is located at 1300 K at pressures of 5-11 GPa (Kawamoto and Holloway, 1997), however, this temperature profile is too high for the mantle to be solid. Hence, it is concluded that the mantle is globally dry.  Wolf et al. (2015); green: Mg 0.87 Fe 0.13 SiO 3 bridgmanite lower mantle by Wolf et al. (2015); gray: Brown and Shankland (1981). The solid and dashed curves show the most probably and 68% confidence intervals, respectively.

Data Availability Statement
The P-V-T data used in this study after the EMF correction using Nishihara et al. (2020) and the pressure calculation using Tange et al. (2009) are given at https://doi.org/10.5281/zenodo.5644426. The Matlab scripts to fit the P-V-T data to the equations of state, the temperature at the 410-km discontinuity, and calculate the adiabatic temperature profile are given at https://doi.org/10.5281/zenodo.5903286.