Evaluation of Caldera Hosted Geothermal Potential during Volcanism and Magmatism in Subduction System , NE Japan

Deep-seated geothermal reservoirs beneath calderas have high potential as sources of renewable energy. In this study, we used an analysis of melt inclusions to estimate the amount of water input to the upper crust and quantify the properties of a deep-seated geothermal reservoir within a fossil caldera, the late Miocene Fukano Caldera (formation age 8–6Ma), Sendai, NE Japan. Our research shows that Fukano Caldera consists of the southern part and northern part deposits which differ in the age and composition. The northern deposits are older and have higher potassium and silica contents than the southern deposits. Both the northern and southern deposits record plagioclase and plagioclase–quartz differentiation and are classified as dacite– rhyolite. The fossil magma chamber underlying the caldera is estimated to have a depth of ~2–10 km and a water content of 3.3–7.0 wt.%, and when the chamber was active it had an estimated temperature of 750C–795C. The water input into the fossil magma chamber is estimated at 2.3–7.6 t/yr/m arc length based on the magma chamber size the water content in the magma chamber and the length of volcanism periods of Fukano Caldera, NE Japan arc. The total amount of water that is stored in the chamber is ~10 kg. The chamber is saturated in water and has potential as a deep-seated geothermal reservoir. Based on the shape of the chamber, the reservoir measures ~10 km× 5 km in the horizontal dimension and is 7–9 km in vertical extent. The 0th estimate shows that the reservoir can hold the electric energy equivalent of 33–45GW over 30 years of power generation. Although the Fukano reservoir has great potential, commercial exploitation remains challenging owing to the corrosive nature of the magmatic fluids and the uncertain permeability network of the reservoir.


Introduction
The supercritical geothermal potential that is located near or below the brittle-ductile transition zone has attracted much research interest in recent years [1] because such a supercritical geothermal system could yield high well productivity owing to a higher fluid enthalpy of >150-225 °C [2][3][4].Increasing the enthalpy of fluid could improve the energy productivity of a power plant; e.g., in Iceland, it has been numerically estimated that a supercritical reservoir could produce about tenfold the amount of energy of currently producing wells [1,5].In Japan, an attempt to drill to supercritical conditions was made in the Kakkonda Geothermal Field in 1994-1995 [6].Well WD-1a was drilled to a depth of 3729 m with a bottom-hole temperature of 500 °C [1,7].The brittle-ductile transition in this well was indicated by an inflection in the temperature profile at ~380 °C [8].This attempt has opened up the possibility of drilling into crust with supercritical conditions.
However, the extraction of energy from supercritical geothermal systems remains challenging on account of the permeability of the host materials and the characteristics of the fluids.Initial studies suggested that permeability shows a marked decrease at the brittle-ductile transition (BDT) [9][10][11].However, later investigations showed that sufficient permeability is maintained at the BDT, with evidence being found from outcrops [12,13], laboratory experiments [14,15], and geophysical studies [16].The primary limiting factor is the properties of the fluids produced in supercritical geothermal systems, which are dominated by magmatic fluids.Such fluids are corrosive, meaning that fluid extraction using current technologies is challenging.Therefore, more in-depth research needs to be performed to overcome this problem.Although commercial utilization is not yet possible, an understanding of the properties of supercritical geothermal systems, including the evaluation and estimation of the energy potential, should provide us with a better picture of this prospective energy source.
At a large scale, water supply and budget are essential aspects of a subduction system as they affect the productivity of the arc magma, the cycling of volatiles in the mantle, and the rheology of the mantle [17].The transportation and distribution of a large volume of water beneath an arc affect the seismicity, rheology, ore deposits, and geothermal energy of the overlying arc crust [18].Knowledge of magmatic processes is essential to understanding deep-seated geothermal reservoirs and to estimate water inputs to the upper crust.Melt inclusions (MIs) in caldera-fill sediments provide petrological evidence of magmatic processes in the crust.As these inclusions formed at high pressure and are contained within a relatively uncompressible mineral host, MIs preserve the pre-eruption volatile composition of the magma [19].
Extensive studies of silicate MIs have been conducted to understand petrogenetic processes such as assimilation [20] and fractional crystallization [21].The characteristics of silicate MIs and the methods used for their analysis have been summarized in reviews [19,22].Silicate MIs contain information on the dissolved volatile concentrations of igneous rocks.A variety of analytical and thermobarometric methods can be used to study MIs, leading to a better understanding of magma volatile concentrations, the compositions of exsolved magmatic fluids, and the pressure-temperature conditions under which magmas crystallize [19].Silicate MIs from a single phenocryst (when analyzed for volatile content) might represent the composition of the melt at the time of crystallization and help determine whether variations in volatile concentrations are consistent with a specific physical-chemical magmatic process [22].A recent study [23] of silicate MIs in deposits of the Shirasawa caldera, NE Japan, showed that MIs could be useful for the assessment of geothermal resources.
NE Japan (Tohoku District) contains ca.45% of the geothermal potential of the entire country [24,25].The ductile zone is relatively shallow around active volcanic fronts (<3 km) [10], and at least 80 caldera collapse structures are recognized in NE Japan, with these structures having a close genetic relationship with the occurrence of granitic plutons [26].The mass balance analysis of crust-melt reaction zones [13] indicates that the original >5.0-5.6 wt.% of H 2 O within the arc magma is partitioned into ≤3.7 wt.% H 2 O consumed by the hydration of local crustal material and ≥1.3-1.9 wt.% H 2 O expelled to the overlying upper crust.The ascent of magmatic water may increase pore fluid pressure, thereby reducing the strength of the crust, or it may generate hydrothermal fluids that could produce ore deposits [27] and/or deep geothermal resources within the crust [13].
In this study, MIs were used to evaluate the properties of a potential geothermal reservoir (magma chamber) in Fukano Caldera, NE Japan, including (1) the magmatic processes that occurred within the magma chamber, (2) the distribution of the geothermal reservoir, and (3) estimations of the water input to the upper crust and of the geothermal energy.

Geological Setting
Fukano Caldera is located ~10 km east of the present volcanic front, near Sendai City, NE Japan (Figure 1).The most recent period of volcanic activity in NE Japan is an island-arc stage (13-0 Ma), which can be divided into submarine volcanism, late Miocene caldera formation, Pliocene caldera formation, and a compressional volcanic arc phase (the present active volcanic front).These changes in the mode of igneous activity are correlated with the stress regime, which is controlled mainly by Eurasia and Pacific plate motion, and with the evolutionary path typical of arc magmatism.Fukano Caldera is classified within the late Miocene Caldera Group, which has a close genetic relationship with granitic plutons [26].This caldera was chosen because of the proximity to the city compared with the present/recent volcanic front and the availability of geophysical data.
Fukano Caldera contains two calderas: Fukano Caldera itself (the northern part) and Tenjin Caldera (the southern part).In plain view, Fukano and Tenjin calderas have elliptical shapes, elongate N-S (Figure 1).The major and minor axes of these elliptical shapes are 10 and 5 km long, respectively.Fukano Caldera has been active since ~8-7 Ma, with activity in Tenjin Caldera commencing later at ~7-6 Ma.The timing of these events is based on the local stratigraphy and fossil data [28][29][30].The Akiu Group (including the Fukano and Tenjin formations) unconformably overlies the Natori Group (Tsunaki Formation; 10.0-8.3Ma) and is overlain unconformably by the Sendai Group (~6.4 Ma), as determined by fission track dating, planktonic foraminifera, and diatom analyses [29].
In this study, Fukano and Tenjin calderas are termed the northern and southern parts of Fukano Caldera, respectively, based on the regions in which sampling was conducted (Figure 1).The Sakunami Fault bounds the western margin of the two-caldera structure.This fault comprises two parallel fault systems.One trends N-S and dips 40 °-80 °to the west, and it forms the boundary between the Aone Formation (to the west) and the Sakunami Formation (to the east).A second fault, which dips 60 °-80 °to the east, marks the boundary between the Sakunami Formation and the caldera volcanic rocks (the Fukano Formation and the Tenjin Tuff Member).Pumice tuffs in a fine-grained matrix and laminated sandy tuffs are distributed near the Sakunami Fault.In contrast, the eastern margin of the caldera structure is overlain by cross-laminated sandy tuffs that dip gently to the west [31].

Materials and Methods
3.1.Analyzed Samples.Caldera-fill samples from the southern and northern parts of Fukano Caldera were obtained 2 Geofluids from 20 locations on the caldera from the margin to the center (Figure 1).The five samples taken from the southern part of the caldera (Tenjin Tuff Member of the Fukano Formation and the Motoisago Formation) consist of fine tuff and pumice tuff, with mineral assemblages of quartz, plagioclase, biotite, and magnetite.Apatite occurs as inclusions in quartz.Zircon crystals have been identified in the deposits of the Fukano and Tenjin formations through heavy liquid separation (R. Takashima, Tohoku University; pers.comm.).The 15 samples taken from the northern part of the caldera (the Fukano, Shirasawa, and Imotoge formations) consist of pumice tuff, welded tuff, fine tuff, muddy fine tuff, volcanic breccia, and pyroclastic breccia, with mineral assemblages of quartz, plagioclase, alkali feldspar, biotite, hornblende, and magnetite.Apatite occurs as inclusions in quartz.
The MIs examined in this study were all hosted in quartz crystals.MI diameters range from <1 to 200 μm, and they commonly occur as homogeneous glassy inclusions.However, bubbles and daughter minerals are also present in some samples and are termed "crystalline inclusions" (Figure 2; Table 1).The crystalline inclusions were not suitable for electron probe and water content analyses owing to the inhomogeneous nature of the inclusions.The crystalline inclusions therefore underwent homogenization treatment using a Linkam TS1500 heating stage with a maximum temperature of 1500 °C and maximum quenching rates of 100 °C/min.So-called "hourglass" inclusions also appear in some samples (Figure 2(b)).An hourglass inclusion is a melt inclusion that consists of glass or crystallized melt connected to the exterior of the host crystal by a canal or capillary [33],    1 and Table 2).(b) Quartz crystals from the southern part showing rounded, dark crystalline inclusions in sample 160411-1a (Table 1 Table 2).The hourglass-type inclusions observed in the samples were not analyzed (see text for details).
3 Geofluids  4 Geofluids allowing volatiles and other elements to diffuse at the time of crystallization.Therefore, this type of inclusion was not analyzed in the present study.

Analytical Procedures.
Quartz phenocrysts were handpicked, washed ultrasonically in water, and dried overnight at room temperature.The quartz was then mounted in resin and polished until the MIs were exposed at the surface.The samples were analyzed in the following order to avoid damage and element loss during measurement: Fourier transform-infrared (FT-IR) spectroscopy, secondary electron microscopy-energy-dispersive spectroscopy (SEM-EDS), and laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS).
Major element compositions (SiO 2 , TiO 2 , Al 2 O 3 , MnO, MgO, CaO, Na 2 O, K 2 O, and P 2 O 5 ) for MIs were determined using a JEOL JSM-7001F SEM-EDS at the Department of Earth Science, Tohoku University, Japan.The analytical conditions were an accelerating voltage of 15 kV, a probe current of 1.4 nA, a magnification of 5000x, and a working distance of 10.00 mm.Sodium loss associated with alkali migration during electron bombardment was prevented by using a low probe current and low magnification.
Trace element concentrations were measured for 10 MIs in two samples from the southern part of the caldera and for 3 MIs in one sample from the northern part.Trace element (Cs, Rb, Ba, Th, U, Nb, Ta, La, Ce, Pb, Pr, Sr, Nd, Sm, Zr, Hf, Eu, Gd, Tb, Dy, Y, Ho, Er, Tm, Yb, and Lu) concentrations were determined using an Analyte Excite excimer laser and a PerkinElmer ELAN 9000 Quadrupole ICP-MS at the Graduate School of Environmental Studies, Tohoku University, Japan.These analyses used a laser wavelength of 193 nm, a laser spot diameter of 50 μm, 80% power, a repetition rate of 20 Hz, and an ablation time of 15 s.Standard samples (NIST 611, 612, and 614) were used to determine the detection limits of the instrumental measurements.MIs with diameters of >100 μm were chosen for analysis to accommodate the laser spot diameter and to prevent ablation of the surrounding quartz.
Water and CO 2 contents were determined using a Thermo Scientific Nicolet iN10 transmission FT-IR at the Department of Earth Science, Tohoku University, Japan.These analyses used an aperture of 30 μm × 30 μm and wave numbers of 675-6000 cm −1 .Infrared absorption bands were assigned as 1630 cm −1 for the bending mode of H 2 O, 3600 cm −1 for the stretching mode of H 2 O and OH, and 5230 and 4500 cm −1 for the combination of the stretching and bending modes of H 2 O and OH [34], respectively.Given that the 3600 cm −1 peak was oversaturated in this study, the 5230 and 4500 cm −1 absorption bands were used.
The major element compositions of MIs were also used to calculate the crystallization pressures of the host quartz.The pressure was estimated using the DERP (determining rhyolite pressure) [37] geobarometer.This geobarometer is based on the pressure dependence of the cotectic curve separating the quartz and feldspar stability fields in the rhyolite system Qtz-Ab-Or(-An-H 2 O).DERP is calibrated for pressures in  [36] showing the compositions of MIs from the northern and southern parts of Fukano Caldera, compared with data for Shirasawa Caldera [23].Ol: olivine; Q: quartz.6 Geofluids the range 50-500 MPa and takes into account the effect of normative An content as well as of water content in melt [37].As the geobarometer was applied to MIs that were in direct contact with one mineral only (i.e., quartz), we crosschecked the congruence of the resulting pressure determination with the water saturation pressure (discussed in Magma Chamber Depth).DERP was used to calculate pressures from the data of 313 melt inclusions.As the pressure estimation is dependent on the water content in the melt, we varied the water content from the lowest measured water content (3 wt.%) to the highest (7 wt.%) to estimate the uncertainty, which was determined to be ±25 MPa.The pressure calculated using this method varied from 0.7 to 450 MPa for the northern samples and from 0.7 to 511 MPa for the southern samples.Assuming that pressure follows the lithostatic gradient with a crustal density of 2.7 g/cm 3 , the crystallization depth ranged from 0.02 to 17 km and from 0.02 to 19 km for the northern and southern samples, respectively.
Histograms of quartz crystallization pressure were constructed for the northern and southern parts of the caldera (Figure 4(a)) to reveal the vertical distribution of pressure calculated using the MI data.The magma chamber model (Figure 4(b)) was based on the vertical distribution of the MIs (Figure 4(a)), with higher frequencies of crystallization pressure corresponding to wider sections of the magma chamber for each part of the caldera.The inferred depth of the magma chamber for the southern part of the caldera (~7 km) is slightly greater than that for the northern part (~5 km).However, given the uncertainty of the data (±25 MPa; ~1 km), both chambers are placed at a similar depth and might have formed a single magma chamber.The deposits of the northern part of the caldera (Fukano Formation, 8-7 Ma) are older and have a higher potassium content than the deposits of the southern part (Tenjin Tuff Member, 7-6 Ma) [28].This may indicate the input of lessevolved magma into the chamber during the formation of the southern part deposits.

Trace Elements. The trace element concentrations of 10
MIs in two samples from the southern part of the caldera and for 3 MIs in one sample from the northern part were measured to determine the differentiation of the magma beneath Fukano Caldera and to estimate the magma chamber temperature.The concentrations were normalized to a basaltic andesite sample (ZA1011) from Zao Volcano [38] (see Supplementary Table St-2).This sample is expected to be compositionally similar to the parental magma of Fukano Caldera samples on account of its relatively close spatial proximity.To determine the differentiation patterns of the samples, the normalized concentrations were plotted on a spider diagram (Figure 5).
Except for two samples from the northern part of the caldera, which show higher concentrations of trace elements compared with the other samples, samples from both the northern and southern parts of the caldera have a close correlation to those of the Zao basaltic andesite with marked depletions and enrichment.Strontium and europium are depleted relative to the Zao basaltic andesite.Apart from europium and strontium, the trace elements in the Fukano Caldera samples are enriched relative to the Zao basaltic andesite (Figure 5).
The partition coefficients of strontium and europium are higher in plagioclase compared with other elements.As such, strontium and europium concentrations in magma decrease with plagioclase crystallization.Those elements with concentrations higher than the Zao basaltic andesite are presumed to have been affected by the crystallization of minerals such as quartz.Such elements are not compatible in quartz, meaning that their concentrations in the melt increase during quartz crystallization as SiO 2 decreases.
Zircon saturation temperatures were calculated using a solubility model [39].The calculations were conducted on six MIs from the northern and southern parts of the caldera (Supplementary Table St-4).The existence of zircon was confirmed to ensure that the samples were saturated in this phase.Because the zircon saturation thermometer [39] is calibrated only for subaluminous and peraluminous melt compositions, only the samples that fell within this compositional range were selected for the calculations.The results show no systematic difference in the zircon saturation temperature between the northern and southern part samples.The calculated temperatures vary from 750 °C to 795 °C, with an average magma temperature of ~774 °C ± 18 °C.

Water Contents.
Water content was measured for 5 MIs from the northern part of the caldera and for 3 MIs from the southern part.MIs that were heated using the heating stage were avoided because of the potential loss of volatiles.The total water contents of MIs in the northern part vary from 4.2 to 7.0 wt.%, and those in the southern part from 3.3 to 7.0 wt.% (Figure 6(a), Supplementary Table St-3).CO 2 absorbance could not be determined from either set of samples and was therefore presumed to be 0 ppm (Figure 6(b)).
The CO 2 -H 2 O saturation pressure is determined by the pressure of water saturation based on the measured water content in MIs using the formula provided by Liu et al. [40].The formula expresses the temperature-and pressuredependent H 2 O and CO 2 solubility of rhyolite based on synthetic haplogranitic and natural rhyolitic melt experiments.In general, the water-saturated pressures range from 60 to 250 MPa (see Supplementary Table St-3), and the pressures calculated from major element data vary from 0.7 to 511 MPa but are clustered in the range 25-275 MPa.These data indicate that the samples from Fukano Caldera are mostly water-saturated.
4.4.Magma Chamber Depth.The depth of the magma chamber in this study, as described above, was estimated using the DERP geobarometer.Based on this method, magma chamber pressure estimates ranged from 0.7 to 511 MPa with an uncertainty of ±25 MPa.However, this method has a limited calibration that is restricted to the range 50-500 MPa (~2-18 km), so the pressures below and above this range were discarded.Although the samples fell within a wide range of pressure, the histogram (Figure 4) shows a cluster      Geofluids at pressures between 50 and 275 MPa (Figure 4), with ~2-10 km being the inferred depth range of the magma chamber.
The water saturation pressure ranges from 60 to 250 MPa (~2-9 km).These data agree with the quartz crystallization pressure of 50-275 MPa (~2-10 km) within the ±25 MPa error.The fact that most of the samples fall within the water saturation pressure indicates that the magma was saturated with water and may have been able to form a supercritical geothermal reservoir.
The ascent of water-saturated magma may promote the expulsion of supercritical water from the magma body into the overlying crust.The formation of a supercritical geothermal reservoir above the intrusion is controlled by the brittle-ductile transition temperature (T BDT ), host rock permeability, and magma emplacement depth [41].Increasing the T BDT (i.e., from 450 °C to 550 °C) creates a larger supercritical zone without dramatically changing the thermo-hydraulic conditions [41].The host rock permeability strongly affects the extent of supercritical temperature.Supercritical-temperature resources have smaller extents in highly permeable (10 −14 m 2 ) host rock compared within moderately permeable (10 −15 m 2 ) host rocks because the rate of convective water circulation surpasses the ability of the intrusion to heat most of the circulating water to supercritical temperatures [41].The location of magma emplacement influences whether the system above the intrusion exceeds the critical pressure.In Fukano Caldera, the emplacement of the magma chamber is estimated to be ~2-10 km (~50-275 MPa), above the critical pressure of water (~22 MPa).The brittle-ductile transition zone is observed at a temperature of ~380 °C [8], above the critical temperature of water (374 °C), and fluid migration at a depth of 4-6 km suggests the existence of an intermediate-permeability zone (10 −15 m 2 ) [14,16] in the NE Japan region.Therefore, it is possible that a supercritical geothermal reservoir has formed beneath Fukano Caldera.
The above-mentioned petrological data are also in agreement with the seismic tomography map of Nakajima et al. [42] (Figure 7).A region of low seismic velocity is observed at depths of 5 to 10 km [42] (Figures 7(a) and 7(b)) and is consistent with the depth range of the magma chamber identified in the present study (~2-10 km).The existence of melt-filled pores can reduce seismic velocity and increase Poisson's ratio independent of the shape of pores, whereas H 2 O-filled pores have a different effect on seismic velocity, especially on Poisson's ratio, which is affected by the shape of the pores, specifically the aspect ratio, which is defined as the ratio of the minor radius to the major radius of fluidfilled oblate spheroidal pores [42].H 2 O-filled pores with an aspect ratio of less than ~0.1 increase Poisson's ratio and decrease the seismic velocity, giving the same effect as melt-filled pores, whereas H 2 O-filled pores with an aspect ratio of greater than ~0.1 will reduce Poisson's ratio and decrease seismic velocity [43].The observed region of low seismic velocity with slightly higher Poisson's ratio at depths of ~5-10 km suggests the existence of melt-or H 2 O-filled pores [42].
4.5.Water Budget.Water plays an essential role in a subduction system, as it is a critical factor in the formation of magma and the storage of energy.Two studies that have investigated the amount of water subducted beneath the NE Japan arc [17,44] estimated the water budget by using a slab-water-dehydration model to determine the amount and rate of water released from the slab during dehydration.The rate of water release from the slab in the NE Japan arc during subduction is estimated to be ~34 t/yr/m arc length [44].Kimura and Nakajima [17] used the geochemical and petrological model Arc Basalt Simulator version 4 (ABS4) to calculate that about 38% of the ~34 t/yr/m (~13 t/y/m) migrates into the crust.In the present study, we estimated the amount of water input to the upper crust using MI data from the caldera system (Figure 8).

Geofluids
The northern and southern magma chambers of Fukano Caldera are estimated to occupy a depth range of 2-10 ± 1 km; that is, they have vertical extents of 7-9 km (Figure 4).To simplify the calculation, the northern and southern magma chambers were treated as a single large magma chamber.The extent of this magma chamber was estimated from the caldera rim structure, which extends for ~10 km N-S and ~5 km E-W.For a caldera with a roof aspect ratio of ≤1 (the ratio of the caldera diameter to the distance between the ground surface and the top of the magma chamber), the gravity-driven normal faults form as a border to the caldera and propagate from the surface to the magma chamber margin [46][47][48][49] with vertical or subvertical dips of ~60 °-90 ° [47,50,51].Therefore, the lateral extent of the magma chamber can be estimated at ~9.7-10.0km for the major axis and ~4.7-5.0 km for the minor axis.
The NE Japan arc extends N-S, and therefore, the length of the arc supplying water to the crust can be assumed as the width of the magma chamber in the N-S direction, which is 9.7-10 km.We assumed the water content of the magma chamber to be the same as those in the studied MIs (3.3-7.0 wt.%).We also assumed that the magma density is similar to the MI density, which was calculated using the formula of Okumura and Nakashima [34].The density of magma varied from 2254 to 2306 kg/m 3 (Supplementary Table St-3).To predict a yearly supply of water, we assumed that the accumulation period of the caldera was 3 Myr, based on the stratigraphic interval of the volcanic products [29] of the Akiu Group.
Using the above data and assumptions, the amount of water contained in the magma chamber is calculated to be 6.8 × 10 13 to 2.3 × 10 14 kg, which accumulated during a 3 Myr period along the 9.7-10 km arc length.Therefore, the yearly water input into the magma chamber is 2.3-7.6 t/yr/ m arc length (Supplementary Calculation Sc-1).In the study of Kimura and Nakajima [17], it was assumed that hydration and water input along the arc are uniform.In our study, the estimation is based on only one caldera (Fukano Caldera); however, multiple calderas are present along the NE Japan arc, which have varying sizes and water contents as well as patterns of spatial distribution [26].Throughout the NE Japan arc, calderas are dispersed in groups called "hot fingers" correlated to local hot regions within the mantle wedge [52], suggesting that conditions along the arc are heterogeneous.However, our estimate of the amount of water that 10 Geofluids is input into the upper-crustal magma chamber is of the same order as the subarc water input reported by Kimura and Nakajima [17] (13 t/yr/m).
Using the volume and temperature of the magma chamber, the probable geothermal energy can be estimated.The energy stored in the Fukano chamber reservoir was evaluated using the volumetric method [53,54].The calculation is based on the thermal energy in the rock and in the fluid that could be extracted based on the specified reservoir volume, reservoir temperature, and reference temperature (see Supplementary Calculation Sc-1 for details).The temperature of the magma chamber during crystallization was estimated above using the Zr saturation temperature (~774 °C).However, this is not the actual present-day temperature because the magma chamber may have cooled down over the millions of years that have elapsed since crystallization.Therefore, the geothermal gradient (70 °C/ km) [45] of Shirasawa Caldera and its surrounding which represents the geothermal gradient beneath the ancient caldera were adopted to predict the present-day temperature of the reservoir (Figure 8).
As the Fukano chamber is a high-enthalpy reservoir, the reference depth (Zr) was set to a depth corresponding to a temperature of 150 °C [2][3][4] using a geothermal gradient of 70 °C/km.The average annual temperature of Sendai was taken as 12 °C and set as the reference temperature (T ref ).The depth of the reservoir corresponding to a temperature of ~150 °C in Fukano Caldera is therefore 2 km (152 °C).This depth represents the high enthalpy reservoir.The maximum depth of the reservoir was set at 10 km (712 °C), corresponding to the bottom of the magma chamber.The volumetric density of rocks + water was set at 2.7 J/cm 3°C .The total reservoir energy (Qr) is calculated as 1.6 × 10 18 kJ, which, with a 25% rate of recovery of energy, gives a result of 4 × 10 17 kJ.To determine the energy that can be obtained from the reservoir, we first assumed that the depth of the borehole used for extracting the hot fluid is 3 km (220 °C).The hot fluid that rises from this depth does so against gravity, meaning that some energy loss may occur during extraction.Therefore, we calculate the available work (W a ) based on the enthalpy at the well source and the reference.Also, energy loss will occur because of conversion efficiency of the power plant.For water-dominated systems, it is set to be ~0.4.Using this method, the amount of electric energy can be calculated, including the upper and lower bounds on reservoir energy.We calculate that the electrical energy that could be obtained from Fukano Caldera is 3.16-4.25× 10 16 kJ, and the electric energy obtained over 30 years of power generation is 33-45 GW (Supplementary Calculation Sc-1).
The estimation of geothermal energy is approximate because of the many simplifying assumptions that are made, such as the continuity of the magma chamber and the treatment of the reservoir as a water-dominated system regarding energy recovery rate and efficiency.The geothermal gradient may not be valid in such a deep system, and the reservoir is assumed to have sufficient permeability.Although commercial exploitation is not yet possible, the deep-seated geothermal reservoir beneath Fukano Caldera has a huge potential as an energy source in the future.11 Geofluids

Conclusions
The Fukano Caldera fossil magma chamber in NE Japan lies at depths of 2-10 ± 1 km and has a water content of 3.3-7.0wt.%.The rate at which water is supplied to the overlying crust during subduction in the NE Japan arc was used to estimate the amount of water accumulating in the fossil magma chamber, which is calculated to be 2.3-7.6 t/yr/m arc length.The magma chamber is saturated in water, and a 0-order estimation suggests that the energy potential is 33-45 GW over 30 years of power generation.
Our study shows that melt inclusion analysis is a useful tool in determining the magmatic processes and properties of a magma chamber as well as estimating the water budget within the crust.It is also reflecting the significance of deep-seated geothermal reservoir in the matter of energy potential.The energy potential of the deep-seated geothermal reservoir at Fukano Caldera is very high.However, the practical exploitation of this reservoir is not yet possible with current technology, given the challenges presented by the corrosive nature of the fluids and the uncertain permeability network of the reservoir.Further assessments of the Fukano reservoir and improvements in extraction technology will need to be made before its energy can be exploited.

Figure 1 :
Figure 1: Geological map of Fukano Caldera (modified from Kitamura et al. [32]) showing the distribution of formations and sampling points.The red square in then inset at the top right shows the location of Fukano Caldera.The open circles and triangles show the locations of northern and southern samples, respectively.The thick dashed lines indicate the distribution of the caldera rims.

Figure 2 :
Figure 2: Melt inclusions (MIs) from Fukano Caldera.(a) Quartz crystal from the northern part of the caldera showing large, round colorless glassy inclusions in sample 160804-5 (Table1 and Table 2).(b) Quartz crystals from the southern part showing rounded, dark crystalline inclusions in sample 160411-1a (Table1 Table 2).The hourglass-type inclusions observed in the samples were not analyzed (see text for details).

1 NP
= northern part of the caldera; SP = southern part of the caldera. 2 X = absent; Δ = exists; and O = abundant.

Figure 4 :
Figure 4: (a) Histograms showing quartz crystallization pressures (calculated from MI data) with depth in the northern (blue bars) and southern (yellow bars) parts of Fukano Caldera.The pressures were calculated based on an average water content in the samples (~5 wt.%).The vertical axis is the crystallization pressure, and the horizontal axis is the frequency of pressures in a specific class.(b) Model of the magma chambers based on the distribution of pressures in the histogram.The vertical axis indicates the depth corresponding to the crystallization pressures of the histogram vertical axis.

Figure 5 :
Figure 5: Trace element patterns of Fukano Caldera MIs normalized to Za1011 (Zao basaltic andesite) from Tatsumi et al. [38], showing the similar elemental concentrations of the samples.Depletions of strontium and europium resulting from plagioclase crystallization are evident.

Figure 6 :
Figure 6: Water content and CO 2 absorbance for the studied MIs.(a) Transmission FT-IR measurement results showing the spectrum of each measurement for the MIs.The 5230 and 4500 cm −1 peaks were used to determine the water content of the MIs.(b) CO 2 absorbance spectra show no evidence for CO 2 in the samples.

Figure 7 :
Figure 7: Seismic tomography maps showing (a) primary wave (P-wave) velocity perturbation (%), (b) secondary wave (S-wave) velocity perturbation (%), and (c) Poisson's ratio, modified from Nakajima et al. [42].A zone of low seismic velocity at depths of 5 and 10 km is observed in the study area (open square), indicated by a lighter shade.This zone is suggested to indicate the vertical extent of the magma chamber, in agreement with our study.The slightly higher Poisson's ratio observed at a depth of 5 km indicates the existence of melt-or H 2 O-filled pores.Black dots show earthquake swarms within ±2.5 km of the corresponding depth.

Figure 8 :
Figure8: Depiction of the estimated amount of water input to the magma chamber based on MI data from this study.The percentage of water in the magma chamber is 3.3-7.0wt.% (6.8 × 10 13 to 2.3 × 10 14 kg), which accumulated during a 3 Myr period along the ~10 km arc length of the chamber.The right-hand part of the diagram shows the geothermal gradient of Shirasawa Caldera (located immediately to the NE of Fukano Caldera), and its surrounds (70 °C/km)[45].

Table 1 :
Morphology of melt inclusions from Fukano Caldera.