Compressional Behavior of Hydrous Orthoenstatite: Insight into the Nature of LVZ under Continental Plate

: A suite of hydrous orthoenstatite crystals were synthesized at 5–7 GPa and 1100–1300 ◦ C, corresponding to the mid upper mantle conditions in continental regions. The synthetic crystals presented a clear, inclusion-free, and euhedral form with a size range from 100 to a few hundred microns. The Al- and water content of crystals were less than 2 wt. % and ranging from ~500 ppm to 1000 ppm, respectively, characterized by Raman and IR spectroscopy, electron microscopy, and SIMS. The analysis shows that the capability of water incorporation for this suite of hydrous orthoenstatite is correlated to the Al-content in the crystal structure. To understand how the detailed crystal structure reﬂects the inﬂuence of water and Al, single crystal X ray di ﬀ raction analysis was performed for this suite of hydrous orthoenstatite. By comparing the results obtained at ambient conditions, we ﬁnd that for low-level of Al-content, < 2 wt. %, the Al 3 + cation tends to occupy one of tetrahedral sites (TB) only. Analysis of the X ray di ﬀ raction results under high pressure indicates that the elasticity of orthoenstatites is insensitive to the presence of low-level water and Al. We use this ﬁnding to evaluate the velocity proﬁle at the mid upper mantle of continental regions to compare with seismic observation. The comparison indicates that the cause of the low velocity zone in continental regions originates from the geotherm proﬁle rather than the e ﬀ ect of water on the elasticity of mantle phases.


Introduction
The Mg-rich orthoenstatite (OEn) phase is one of the major mineral phases in lherzolite and harzburgite xenoliths, which put constraints on the composition of the lithosphere in continental regions [1]. To shed light on the physical state of the upper mantle, the elasticity of the anhydrous OEn phase has been investigated under high pressure and high temperature [2][3][4][5][6][7][8][9][10]. In terms of crystal chemistry, the pyroxene phase is a "nominally anhydrous mineral (NAM)". Field evidence shows that the OEn phase often contains some amount of "water" within the crystal structure, up to 600-800 ppm, usually incorporated as hydroxyl, OH − [11][12][13]. It is well-known that the crystal chemistry (e.g., H + concentration and minor elements) of mineral phases could have a different influence on the physical properties (e.g., [14][15][16][17][18]). Recent experiments indicate that the phase boundary of monoclinic enstatite (low-pressure phase to high-pressure phase) is noticeably shifted by the water content [19,20]. On the other hand, the phase transition in the hydrous orthoenstatite with low water-content at high pressure is only shifted by less than 1 GPa (from Pbca to P2 1 /c) [21].
The experimental results also indicate that the presence of high Al-content in the synthetic orthoenstatite can enhance the water concentration up to 7500 ppm at low-pressure, but the Al content presented in orthopyroxene structure is depressed by the pressure effect [22][23][24]. The results of X-ray single-crystal diffraction experiments suggest that the site occupancy of H + varies with the concentration of Al 3+ , as the H + is located at the Si 4+ site when the Al-content is fairly low. In contrast, H + is located at both M and Si 4+ sites when the Al-content was high in orthoenstatite [23,25]. To shed light on the effect of H + incorporation in different crystallographic sites on elasticity, the compressional behavior of the hydrous OEn phase has to be investigated.
In the upper mantle, a low-velocity zone (LVZ) is characterized by low seismic velocity, high seismic attenuation and high electrical conductivity. Some potential causes of LVZ have been proposed, including: (1) change of geothermal gradient, (2) the presence of small amounts of the melt, and (3) the hydrogen present in the structure of NAMs [22,[26][27][28][29][30]. In the wet mantle, the "water" can either be incorporated into the mantle phases to affect the elasticity, or exist as a hydrous fluid, which reduces the solidus of rock and may produce melt if the geotherm intersects with solidus [27,31,32]. The above factors have an effect on each other in the wet upper mantle. Among the mantle phases, the pyroxene phase is capable of carrying the highest water content at the mantle conditions [13,33]. As mentioned above, previous measurements on orthoenstatite were focused on anhydrous orthoenstatite. In order to evaluate the possible causes of LVZ in the continental regions, it is important to have access to the physical properties of hydrous pyroxene around the depth of LVZ. In this study, we investigated the compressional behavior of the orthoenstatite phase with crystal chemistry (Al 3+ and water contents) under the mid upper mantle conditions.

Materials and Methods
Single-crystal synthesis was carried out in a multi-anvil large volume high pressure apparatus installed at National Cheng Kung University (Tainan, Taiwan). The stoichiometry of the starting mixture of oxides, SiO 2 , MgO, Mg(OH) 2 , and Al(OH) 3 , was chosen to correspond to the composition of pure end-member or aluminous orthopyroxene. The MgSiO 3 glass was used to synthesize anhydrous orthoenstatite, hereafter "OEn", (R638). The synthesis was carried out at the pressure of 5-7 GPa and temperature of 1100-1300 • C. Experimental details are compiled in Table 1. The synthesized single crystals presented clear, inclusion-free and euhedral form ( Figure 1). To identify the synthesized phase and verify the presence of [OH − ] bonds, Raman spectroscopy measurements were carried out with the wavenumber range extended up to 4000 cm −1 . The detailed characterization of [OH − ] bands were performed by FTIR carried out at the Magmas and Volcanoes Laboratory of Clermont Auvergne University (Clermont-Ferrand, France). Figure 2 shows the Raman and IR spectra in the [OH − ] vibrational region, collected from two crystals from runs R623 and R624 in this study. Water content was measured using the SIMS technique, with Cameca IMS-1280 ion microprobe installed at School of Ocean and Earth Science and Technology, University of Hawaii at Manoa (Honolulu, HI, USA), with the calibration curves constructed using standards employed in previous studies [34,35]. Chemical composition analyses were carried out by the electron microprobe in energy dispersive mode with FEI Quanta 250 electron microscopy installed at the Department of Earth Sciences, National Cheng Kung University.   X-ray single-crystal diffraction was performed at ambient conditions and at high pressure on a Bruker D8 Venture diffractometer equipped with IµS 3.0 Microfocus Source with Ag Kα radiation and a fixed-chi type goniometer installed at X-ray Atlas lab of the University of Hawaii at Manoa (Honolulu, HI, USA). Diffraction images were collected using PHOTON II detector. The tilting and rotation of the detector and the sample-to-detector distance were calibrated using NIST standard LaB 6 powder. BX90 diamond anvil cells equipped with two 400-µm diameter culet diamonds were used for high pressure experiments. Rhenium gaskets were preindented to~40 µm thicknesses and then~180 µm diameter holes were laser-drilled at the center of gasket as sample chamber. Methanol-ethanol (4:1) mixture was loaded into the chamber as a pressure medium. Two~10 µm ruby spheres were also loaded into the sample chamber to measure the pressure.
Diffraction images were analyzed using the APEX3 software package (v2018.1, Bruker AXS, Madison, WI, USA), including XPREP and SHELXL. Diffraction data were integrated using SAINT+ (Bruker-AXS) after exclusion of the non-sample diffraction spots and then corrected for absorption using the ABSORB software. Crystal symmetry and space group were determined by XPREP. Crystal structures were refined from the intensity data using the SHELXL software (2014/7, Bruker AXS, Madison, WI, USA). The cation occupancy parameters were constrained according to chemical analysis and charge balance. The balance formulas are shown in the following: X obs = X M1 +X M2 (chemical analysis) where X is molar number in chemical formula and X obs is the value based on the chemical analysis. The instrumental errors were corrected according to NIST standard LaB 6 powder following previous described procedure [21,36]. For high pressure experiments, the positions and intensities of~400-600 unique peaks were extracted from the raw diffraction patterns at each pressure point. Dynamic masks were employed to correct for the regions on the detector shaded by the diamond-anvil cell. The rest of the data processing was carried out in a similar fashion to the data processed at ambient conditions.

Results and Discussion
In this study, we intended to synthesize anhydrous OEn by using mixed oxides (MgO and SiO 2 ) and MgSiO 3 glass for high pressure study. However, the Raman measurements showed that these "anhydrous phase" specimens (R626 and R638, starting with oxides and MgSiO 3 glass) contained [OH − ] signals. By comparing the integrated area of [OH − ] bands of specimen R624, the water content of which was measured by SIMS, we estimated the crystals from R626 and R638 runs to contain~300 ppm of water. Therefore, the specimens synthesized in this study are all hydrous phases. Chemical analysis of synthetic OEn is summarized in Table 2 and indicates that the synthetic pure Mg end-member specimens incorporated a small amount of aluminum (less than 0.34 Al 2 O 3 wt. %), which were contaminated during the preparation of starting powder. This suite of low-Al content specimens, including R545, R598, R623, R626, and R638, will be referred to as Mg#100. The other two specimens, R608 and R624, contain Al 2 O 3 at around 1.5-1.9 wt. % and will be referred as the Al-bearing OEn. The SIMS results indicate that the Al-bearing group contains about 800-1000 ppm of H 2 O, in contrast to Mg#100, which H 2 O content was around 400-500 ppm or less ( Table 2). Figure 3a presents the relation of Al-and H 2 O-content of synthetic OEns in this study and [23], illustrating the Al-content having a strong influence of water incorporation in OEn structure, with higher Al concentration resulting in higher water content. The following discussion of water-dependence of the crystal structure will be highlighted by the influence of Al-replacement in the hydrous phase. Furthermore, based on the chemical analysis of Al-bearing OEn and the crystal-structure refinement, we observed that with less than 2 wt. % of Al 2 O 3 , the Al 3+ cation only substitutes for Si 4+ in tetrahedral site and prefers to occupy the SiB (i.e., TB) sites rather than the SiA (i.e., TA) sites, which is indicated as "AlB" occupancy in Supplementary Table S2 (R624 and R608). * Both R626 and R638 were intended to be the anhydrous OEn, but obvious OH − bands were observed by Raman and IR measurements. The concentration of water was estimated by comparing the area of OH − bands with those of R608. The details were described in text.

Figure 3.
The relations between Al-content (a), cell volume (b) and water content among the investigated OEn crystals from this study and [23]. The half-filled and filled blue symbols are hydrous pure and Al-bearing OEn from this study, respectively; the black symbol is higher-aluminous OEn from the study of [23]. The error bars are smaller than the size of symbols. The details were described in text.
The X-ray diffraction result on the synthetic enstatite crystals clearly indicated orthorhombic symmetry with space group Pbca. X-ray diffraction measurements at ambient conditions were performed on six synthetic OEn specimens. Detailed refinement information is listed in Supplementary Tables S1 and S2. The cell volumes of the synthetic OEn investigated in this study (shown in Figure 3b, blue and half-filled blue circles) are distributed into two groups, corresponding to a detectable volume reduction caused by the Al-content incorporating in the structure. Compared with the anhydrous OEn from Ref. [37] (V 0 = 831.4 Å 3 ), the cell volumes of low-level water content OEn (less than 500 ppm, half-filled blue symbols in Figure 3b) are comparable within uncertainty, between 830.5 and 831.5 Å 3 . At higher water-content (~800-1000 ppm, blue symbols in Figure 3b), the measured cell volumes show systematically lower value (<830 Å 3 ), compared with those of the hydrous Mg#100 (>830 Å 3 ) specimens. The trend of the cell volume of hydrous OEn reduced by the water content observed in this study fits the earlier observation of high water-content Al-bearing specimen (11.7 wt. % of Al 2 O 3 with 7500 ppm of water) presented by [23] (shown as black circle in Figure 3b). The relation of lengths of crystallographic axes and Al-content is illustrated in Figure 4. Within 2 wt. % Al 2 O 3 , the b-axial length presents a systematic decrease by more than 0.3%. In contrast, the aand c-axial lengths remain roughly unchanged. When the OEn contains high Al 2 O 3 content (~11.7 wt. %) as shown in [23], the b-axial length is dramatically shortened by 1%, while a and c-axes change only by ±0.1% (black symbols in Figure 4). Examination of the changes in unit cell parameters as a function of Al-content clearly shows that the reduction of cell volume is controlled by the shortening of b-axial length.  Tables S2 and S3), we note that the trend of tetrahedral volume of B-chain (V TB , diamond symbol) as function of Al-content presents a positive change (Figure 5a), whereas that of A-chain (V TA , circle symbols) remains unchanged, including the results of high Al-content OEn from the study of [23] (black symbols). In the case of the octahedral volumes of M1 and M2 sites (V M1,2 ), a decreasing trend presents as the Al-containing OEn is increasing in general, shown in Figure 5b. Furthermore, in the high Al-content OEn [23], the reduction of V M1 (the black circle in Figure 5b) is almost two times as large as that of V M2 (black diamonds in Figure 5b). The observed volume change as a function of Al-content can be explained by the analysis of crystal chemistry and the refined structural parameters obtained in this study and [23] (Supplementary Tables S2 and S3). When the Al-content is as low as <2 wt. % Al 2 O 3 , the larger Al 3+ cation (ionic radius 0.53Å) tends to occupy the TA site rather than the TB site by replacing small Si 4+ cation (ionic radius 0.40Å) (see item "AlB" in Supplementary  Table S2). In contrast, when the Al-content is as high as~11.7 wt. % of Al 2 O 3 [23], the Al 3+ cation occupies not only the tetrahedral site (TA) but also octahedral M1 site, replacing larger cation, like Mg 2+ (ionic radius 0.72Å), resulting in M1 volume reduction by~3.5%. On the other hand, the observation of minor volume reduction (~1%) in M1 and M2 sites for the low Al-content specimens in this study (<2.0 wt. %, blue filled symbols) is related to the introduction of vacancies in both sites, noted in Supplementary Table S2. The M2 volume reduction observed in [23] (black diamond in Figure 5b) is also caused by the vacancy incorporation. Figure 5. The relative difference of tetrahedral (TA and TB sites, (a)) and octahedral (M1 and M2 sites, (b)) volumes among investigated hydrous OEn as a function of Al-content. The half-filled colored symbols represent Mg#100 and full colored to be Al-bearing composition. The black symbols are the data from [23]. The polyhedral volumes in this figure were compared to those of anhydrous OEn presented in [37]. The error bars are smaller than the size of symbols.
Two high-pressure X ray diffraction experiments were performed on hydrous Mg#100 OEn (R598, 515 ppm of water) and hydrous Al-bearing OEn (R608, 1.56 wt. % of Al 2 O 3 with 978 ppm of water) up to 15 GPa. The diffraction data were successfully indexed using the orthorhombic Pbca unit cell up to 13.2 and 10.0 GPa for Mg#100 OEn and Al-bearing OEn, respectively (Supplementary Table S4). The refinement details for Al-bearing OEn at high pressure are listed in Supplementary Table S5. Beyond the pressures mentioned above, the data became difficult to resolve for both runs due to a known phase transition at high pressure, from the Pbca phase to the P2 1 /c phase, which was confirmed in previous studies [36,38]. Our high-pressure diffraction data suggest that the transition pressure for the Mg#100 phase and the Al-bearing phase were above 13.0 and 10.0 GPa, respectively. Figure 6 shows the volume compression behavior of hydrous Mg#100 and Al-bearing OEn from this study, compared with previous studies on anhydrous Mg#100 [37] and hydrous Mg#100 with 600 ppm H 2 O [21]. All four datasets show similar compression behavior in orthoenstatite structure within Pbca stability field. This indicates that, below 1000 ppm, water/low Al-content in OEn has a small effect on the compression behavior of volume. As for the axial compressibility (Figure 7), all four OEn crystals with different crystal chemistry show the b-axis to be the most compressible, decreasing by about 3.5% at 12 GPa, while those aand c-axes shorten between 2.0% and 2.5%, respectively. Taking a close look of the axial compression behavior (Figure 7), one can notice that the trends of b/b 0 and c/c 0 of the hydrous phases from this study (Mg#100 and Al-bearing) and [21] (Mg#100) follow those of anhydrous Mg#100 of [37] (empty symbols). The trends for the a-axis compressibility for the hydrous Al-bearing phase (with~1000 ppm water) in this study and the hydrous Mg#100 (with~620 ppm water) from [21] (red dashed line in Figure 7a) present a detectable difference from our hydrous Mg#100 (with~520 ppm water) and the anhydrous Mg#100 from [37] (black dashed line in Figure 7a). The minor difference of compressibility in a-axis measured from our Al-bearing phase and Mg#100 in [21] does not affect the volume compressibility shown in Figure 6. At ambient conditions, the polyhedral volumes of the investigated Al-bearing OEn show a minor difference from those of anhydrous OEn from [37] (V TB , M1 and M2; Supplementary Table S3b). Under high pressure, the compressibility of tetrahedral voids (TA and TB) and octahedral voids (M1 and M2) of Al-bearing phase are comparable to those of anhydrous phase within uncertainty (Figure 8a,b). The half-filled and filled orange symbols represent the hydrous #Mg100 and Al-bearing OEn from this work, respectively; the empty hexagonal symbols for data of anhydrous OEn from [37]; the filled hexagonal symbols for data of hydrous OEn from [21]. The dashed line is the third-order Birch-Murnaghan equation of state (EoS) fit from anhydrous OEn from [37]. The error bars of the data points are smaller than the size of symbols. and Al-hydrous OEn from this work; the empty symbols for data of anhydrous OEn from [37]; the black symbols for data of hydrous OEn from [21]. The dashed black line is the fit of third-order Birch-Murnaghan equation of state (EoS) from [37] and the red dashed line in (a) represents the fit of Al-bearing OEn from this work and [21]. The error bars of the data points are smaller than the size of symbols. We investigated the synthetic OEn single crystals with less than 2 wt. % of Al 2 O 3 incorporating water content from~500 ppm to near 1000 ppm, corresponding to the upper limit of hydration at mid-upper mantle conditions (depth of 150-250 km). The results of single-crystal X ray diffraction indicate that the detailed crystal structure of hydrous Al-doped OEn shows only minor difference from the anhydrous Mg#100 OEn at ambient conditions, and that compressional behavior for this series studied OEn is insensitive to current crystal chemistry (Figures 6-8). The P-V results of this study suggest that the derived bulk modulus of hydrous low Al-bearing OEn is similar to that of anhydrous Mg#100 phase ( Figure 6). The analysis of [39] indicated that the major elastic moduli, Cij (i = j, i = 1-6), of pyroxene are strongly correlated to the distortion of M1 and M2 octahedra. Our results on the compression of tetrahedra and octahedra do not show much difference from those of anhydrous Mg#100 phase. Therefore, we draw a conclusion that the elasticity of the studied OEn is insensitive to this level of Al-and water-content.

Geophysical Implications
In this study, the water content in our synthetic OEn phases was within the range of 500-1000 ppm, close to that observed in natural samples [33] and experimental values observed at the pressure of 5-7 GPa, temperature of 1100-1400 • C [22,24], corresponding to the depth of 200 ± 50 km. The OEn phase is a major mineral phase in addition to olivine, in continental petrological models. Here, we employ the current findings to explore the velocity profile of continental regions, where the LVZ is observed around 200-250 km depth [40]. For simplicity, we model by using only olivine and OEn phases in the weight ratios from 60:40 to 80:20, respectively, for the petrological compositions ranging from harzburgite to lherzolite. In the following illustration, the water content of the olivine phase is set to be at a maximum level of 1200 ppm, equilibrating with~900 ppm H 2 O in Al-bearing OEn phase using the partitioning model of [24] (D water~0 .78) at conditions of 7.5 GPa, 1175 • C (Supplementary  Table S6).
Among the upper mantle phases, olivine has been investigated most extensively, regarding how the elasticity is affected by a wide range of water content within the structure [41]. The elasticity of the hydrate olivine, with~9000 ppm of water, are 0.6% and 0.4% for P and S waves, respectively, lower than those of anhydrous olivine. The water contents in our current investigated hydrous OEn phases is about the level of 1000 ppm, about one-ninth of samples in Ref. [41]. From the comparison of compressional behavior between anhydrous and hydrous OEn, we expect that the current water-content would not affect the elasticity too much. The compressibility study of hydrous diopside [42], with~600 ppm of water, provide some evidence for that. Without available elasticity measured by optic-acoustic measurements (i.e., Brillouin scattering or ultrasonic measurement) for hydrous OEn phase, we use the reduction factor established from the hydrous olivine phase summarized by [41] to scale down the elastic velocities of hydrous OEn investigated in this study. The tested P-T conditions are set at shallow upper mantle (less than 250 km depth), and thus, a linear relation of V S as function pressure and temperature is employed. Here, we only use the shear wave data to compare the S wave seismic models from [40], where V S(0) are S-wave velocity at ambient condition or high pressure-high temperature conditions, respectively, and dV S ⁄dP and dV S ⁄dT are the pressure and temperature derivatives of the velocity of olivine or enstatite, respectively. The thermoelastic parameters used in this study are presented in Table 3 [43][44][45]. Due to the measurements of the thermoelastic parameters for both hydrous olivine and OEn phases is incomplete, those parameters tabulated in Table 3 are from anhydrous phases. We tested the velocities of olivine and OEn under upper mantle conditions using the thermoelastic parameters in Table 3 along 100 Ma geotherm to compare with those calculated in [28]. The calculated S wave velocity profiles of olivine and OEn shared the same feature with those shown in Figure 4 of [28], displaying a velocity minimum around 150 km depth with Vs less 3% higher (the illustration is not shown in this study). This demonstrates that the simplified Equation (4) generates the same feature as reported in the previous study. We computed the pure olivine and OEn phases along the continental platform geotherm (solid black line in Figure 9, T p = 1350 • C, the mantle potential temperature). As clearly shown in Figure 10, the shear velocities of hydrous-olivine and -OEn (the blue dashed lines next to the green and orange lines, respectively) are insensitive to the water content at the level of 1000 ppm. The blue shed area is the resultant shear velocity profile of the continental petrological models (from harzburgite to lherzolite) calculated using a simple linear equation with different ratio in weight % of olivine and OEn. The calculated shear velocity profile for the continental area presents a broad low-velocity channel around the depth of 200 km, compared with the seismic models of Australia (yellow dashed line) and Canadian (red dashed line) areas where the LVZ presented below 200 km depth [40]. The difference of velocity minimum between our calculation and those seismic models is less than 1.7%, which can be reduced by introducing the low-velocity Ca-rich pyroxene into mineralogical assemblage models. The above modeling thermoelastic parameters are determined for end-member compositions, forsterite (Mg 2 SiO 4 ) and enstatite (MgSiO 3 ). To consider the iron effect on elasticity of olivine and OEn phases, the S wave velocity may reduce by~3% for the modeled mineral assemblies when the Mg number for both phases remain roughly the same at upper mantle condition, Mg# = 92 ± 2. Ref. [14] pointed out that the elastic velocities of Al-bearing (5 wt. %) OEn is approximately 3% faster than those of Mg#100. At the upper mantle, the Al-content in OEN is the function of depth. To consider the effect of Al-content on the S wave velocity in Figure 10, we expect the increase of the magnitude of velocity drop from the depth of 100 km to 200 km. However, we do not know the elasticity behavior of hydrous Al-bearing OEn, when high Al-content may contain higher water in the crystal structure at 'wet' mantle condition. Considering the ratio of OEn phase decreasing upon the pressure increasing at upper mantle condition, the blue shaded zone in Figure 10 also gives the velocity trend, shifting towards left-side of area. The influence of crystal chemistry of NAM phases most likely is to show on the magnitude of velocity drop, not the depth of the velocity minimum channel and the width of the channel. The current geotherm model of the continental platform in Figure 9 would not satisfy the velocity minimum channel observed below 200 km depth, shown in the seismic models [40]. We also computed the shear velocity with harzburgite composition model (60 wt. % olivine: 40 wt. % OEn) along an averaged cratonic geotherm derived from heat flow of 40 mW/m 2 , suggested by [46], shown as black dashed line in Figure 9. The low-temperature geotherm results in a fast velocity drop (thick gray dashed line) and a deeper velocity minimum located at the depth of mantle adiabat, 250 km. By comparing different gradients of geotherms, we illustrate the depth of low-velocity channel strongly associated with the depth where the geotherm gradient turns from conductive mode (shallower than the empty red cross along the continental platform geotherm in Figure 9) to the condition of the mantle adiabat (at a depth of 250 km). Under the constraint of the seismic feature, the thermal gradient of the cratonic areas could be set between the continental platform and averaged cratonic regions in Figure 9, while considering the effect of thermal profile only.  . Solidus and thermal gradient as a function of depth discussed in this study. The continental geothermal gradient is from [32] and the averaged cratonic geotherm is from [46]. The dry and wet solidus are from [47,48], respectively. The geotherm above empty red cross represents the "conductive" geotherm and the mantle adiabat starts at a depth of 250 km at the upper mantle. The blue shaded area is the P-T conditions of synthetic orthoenstatite crystals in this study. The blue shaded zone represents the shear velocity computed from different mineralogical assembly using different weight ratios of olivine and OEn. The thick grey dashed line represents the shear velocity computed from the low-temperature geotherm [46]. The short-dashed lines are reprinted from the shear velocity model of [40], including Australia craton (yellow) and Canadian craton (red). The details are described in the text.
The water content of the measured OEn in this study (~1000 ppm) would be the upper bound under the upper mantle conditions according to the observation of natural mantle samples [13,33]. We use the amount of~1000 ppm water in the OEn phase as a constraint to model the water content in the olivine phase utilizing the partitioning coefficient at a pressure of 7.5 GPa, temperature of 1200 • C determined by [24], resulting in the estimated bulk water content to be 1000~1200 ppm for the petrology models employed in this study. As shown in Figure 9, the continental platform geotherm (solid black line) and the mantle solidus with 1000 ppm H 2 O (blue shaded area) could not intersect at the depth of 200 km or deeper. In this case, the origin of LVZ has little to do with partial melting at this depth, when the potential temperature was set around 1350 • C.
We demonstrated that the major influence of the depth and shape of LVZ in the continental area would be related to the character of the geothermal gradient, especially the depth segment from "conductive" mantle transforming to "adiabatic" mantle if the thermal effect is the major consideration. On the other hand, under such a cool continental geotherm, shown in Figure 9, if the cause of LVZ involves the melt, then the water content has to be higher than 1500 ppm at least in the mantle rock carried by the hydrous NAM minerals or free fluid. To investigate whether partial melting is involved in the origin of LVZ, the results of electrical conductivity measurements would need to provide additional constraints [49,50].
Supplementary Materials: The following are available online at http://www.mdpi.com/2075-163X/10/1/71/s1, Tables S1 to S6.  High-pressure facility at NCKU was partially supported by the grant of "Geochemical Precious Instrument Platform Project: Southern Branch Ministry of Science and Technology". X-ray diffraction work was conducted using the X-ray Atlas instrument at the University of Hawaii, funded by NSF grant EAR 1541516 (to P.D.).