Introduction

Water is a key substance not only on Earth’s surface but also in its interior. The oceanic plate and overlying sediments contain free water in pore spaces and bound water (or in the form of hydroxyl OH) in hydrous minerals1. In subduction zones, water contained in subducting slabs is expelled by compaction and dehydration processes, constituting a deep water cycle that is pivotal for earthquake occurrence as well as arc magmatism2,3,4. Based mainly on seismic data analyses, many studies have revealed the involvement of deep fluids in nonvolcanic earthquakes5,6, and some of them interpret deep fluids as slab-derived7,8,9,10. However, in the case of an earthquake swarm for the years preceding the main shock of the 2024 Noto Peninsula earthquake (Mw7.5) that struck Japan on New Year’s Day, it is controversial whether the origin of such fluids (and water) was a slab11, uppermost mantle12, or hidden magma13. Moreover, while progress has been made in quantifying the amount of water transported to the mantle by subducting slabs, the mechanism and location of water release from the slabs as well as the amount and flow paths of the released water remain unclear14.

Here, we target nonvolcanic hot springs at Arima, a renowned spa area with a history of more than a millennium, in western Japan (Fig. 1, Supplementary Table 1). The hot spring water called ‘Arima-type (deep) brine’, which is characterized by unique H and O isotopic signatures (expressed as δ2H and δ18O) that are clearly distinct from those of meteoric water and a high Cl content of more than twice that of seawater15,16, is considered to contain slab-derived water17,18. In addition, Arima is situated only 30 km northeast of the epicenter of the 1995 Kobe earthquake, and historical records have shown sudden temperature increases after earthquakes in this area19. We recently acquired the latest isotope data while compiling past data of more than half a century to identify meteoric and lithospheric components in hot spring waters and then verified that the lithospheric component is slab-derived water by comparing its isotopic signatures with numerical predictions. Finally, we show secular variations in the fraction of slab-derived water and quantify its amount replenished in conjunction with the earthquake.

Fig. 1: Location and tectonic setting of Arima hot springs.
figure 1

a Index map showing western Japan and Nankai Trough with contours to top of the Philippine Sea slab25 (black dashed lines). b Map showing locations of the epicenter of 1995 Kobe earthquake (yellow star), monitoring sites of precursory changes in Cl33 (yellow circle) and Rn34 (yellow square), and active faults53 (purple lines). c Map showing sampling sites of hot springs (red circles; AR1-AR7) and cold springs/rivers (blue crosses) with divides for nearby rivers (white dashed lines), active53/nonactive54 faults (thick/thin purple lines), and negative Bouguer anomaly domain30 (pink ellipse). (a) and (b) were created using the ArcGIS Pro 3.1.2 (Esri Inc.) with digital elevation model of the ETOPO 2022 15 Arc-Second Global Relief Model55 (in a) and the Japan Flow Direction Map56 (in b). (c) was created by editing GSI Tiles (elevation) at Geospatial Information Authority of Japan website (https://maps.gsi.go.jp/vector/#13.048/34.7846/135.219595/&ls=vstd%7Crelief%7Crelief_free&disp=101&d=l&reliefdata=35G0000FFGAG0095FFGFAG00EEFFG12CG91FF00G1F4GFFFF00G3E8GFF8C00GGFF4400).

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Results

Two end-members of hot spring water

As shown by previous studies15,16,18, the δ18O-δ2H relationships in the seven selected hot spring waters are almost linear (Fig. 2, Supplementary Table 2), and the slope (=1.345 ± 0.070) of the regression line is far smaller than the slope (=8.552) of the local meteoric water line (LMWL). Since such a linear correlation is found for the relationship between the Cl- concentration and δ2H or δ18O15,16,18 (Eqs. (2) and (3) in “Methods”, Supplementary Table 3), the regression line (Eq. (1) in “Methods”) for hot spring waters in the δ18O-δ2H space is regarded as the mixing line (MXL) between two end-members rather than the trend in the isotope shift from meteoric water20. Both the δ2H (= −52.1‰) and δ18O (= −8.12‰) values of the meteoric end-member coincide with those of cold mineral (carbonated and Rn-containing) springs and are slightly lower than those of nearby rivers (Supplementary Table 2), indicating that the mean recharge elevation of the meteoric component of the springs is greater than the catchment mean elevation of the rivers21. On the other hand, the nonmeteoric end-member is regarded as lithospheric water (including slab-derived water), and its isotopic signature is determined to be δ2H = −29.0 and δ18O = +8.93 as the intersection point of the MXL and the ocean-origin lithospheric water curve (OLWC)22. This newly determined isotopic signature of the lithospheric end-member is similar to but updates past estimates for δ2H (−25 to −30‰15, −32‰16, and −33‰18) and δ18O (+8‰15, +10‰16, and +6‰18).

Fig. 2: Measured isotope data in the δ18O-δ2H space.
figure 2

LMWL, local meteoric water line; MXL, mixing line; OLWC, ocean-origin lithospheric water curve. Shaded zone represents uncertainty range of OLWC22.

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Origin of lithospheric end-members

Some past studies have inferred that the lithospheric component of Arima hot springs consists of slab-derived fluids. This inference is grounded in the unique δ2H and δ18O values that resemble those of magmatic water, 3He/4He ratios equivalent to those of mantle helium18, Li/Cl ratios reflecting high-temperature reactions23, and extraordinarily low δ88/86Sr values24. However, the H isotopic signature of the lithospheric component has not evidently matched the numerical prediction for water derived from the Philippine Sea slab at depths >60 km (i.e., the depths estimated for Arima25); rather, it has matched that for the Pacific slab at the same depths18.

Unlike the previous study, comparisons between the H and O isotopic signatures of lithospheric end-members and those of slab-derived water numerically predicted by our improved model of water isotope evolution under conditions of Philippine Sea slab subduction22 show very good agreement (Fig. 3). The predicted temperature range (500–600 °C) of the slab top beneath Arima corresponds to temperatures suitable for dehydration by metamorphic processes1,26. These results show that the lithospheric component contained in the Arima hot springs was indeed derived from the Philippine Sea slab. In addition, it is confirmed that the ascending water from the slab through wedge mantle is not affected by isotopic re-equilibration with mantle peridotites, probably owing to the water/rock ratio (i.e., the total mass of water successively flowing through preferential paths versus the limited mass of rock that reacts with the flow) being large enough to fully adjust the isotopic signature of the rock to that of the water27,28.

Fig. 3: Comparison between isotopic signatures of the lithospheric end-member and those predicted for water in subducting Philippine Sea slab.
figure 3

a, b The δ2H (a) and δ18O (b) versus the depth (below sea level) of Philippine Sea slab top. c Predicted depth profile of the slab top temperature. Red diamonds (error bars) represent isotopic signatures (uncertainties) of the lithospheric end-member of the Arima hot spring waters. Prediction results shown as red-shaded zones are from the Monte Carlo simulation (1000 runs in each panel) considering uncertainties in model parameters22. Gray lines represent predictions in a previous study18.

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Secular variation in the slab-derived water fraction

The latest isotopic signatures of the hot springs are closer to the meteoric end-member than they were in the past (Fig. 2). In six out of seven hot springs, the fraction of slab-derived water (Fsdw), which is estimated from mixing analysis using isotope data (including those converted from Cl data using Eqs. (2) and (3); Supplementary Table 4), shows exponential decay during period I (1960–1993) before the 1995 earthquake (Fig. 4a). This suggests that semi-finite amounts of slab-derived water are gradually diluted by meteoric water over time after deep borehole drilling (more than 200 m deep) for the current hot springs was performed in the 1940–1960s. At the same time, Fsdw tends to approach a constant value (not always zero), indicating a small steady supply of slab-derived water. The inconsistency in the values of Fsdw and their temporal variation among the springs imply the existence of multiple reservoirs with less water interchange. Seismic data support a high crack density at depths of ~18 km beneath the Arima area29, and at more local scales, negative Bouguer anomalies are observed around the study springs30 (Fig. 1c), supporting abundant cracks with large void spaces.

Fig. 4: Secular variation in slab-derived water.
figure 4

a Variation in the fraction of slab-derived water (Fsdw) in the seven hot springs (AR1-AR7). Colored symbols outlined (non-outlined) in black show estimations from isotope (Cl) data. Approximated, exponential asymptotic curves (excluding AR7) are given as colored solid lines. Open symbols represent two outliers that are not used for the approximation. Error bars represent non-systematic uncertainties given by Eq. (9) in “Methods”, and dashed vertical line shows the year of the Kobe earthquake occurrence. Colored dotted-lines represent the maximum estimated Fsdw after the earthquake as the lower limits of interpolated Fsdw at the former part of period III. Figures for each spring are given as Supplementary Fig. 1. b Variation of total outflow of slab-derived water through seven hot springs. Components of steady inflow, pre-existing (computed using Eq. (13) with the reservoir capacity, V, for Period I), and episodic replenishment (as residual) are shown. Dotted line represents the lower limits of the estimated total outflow.

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In period II (1994–1999; i.e., immediately before and after the earthquake), the Fsdw temporarily increases and then declines again exponentially in the subsequent period III (2000–2024). All these temporary surges in Fsdw are attributable to episodic replenishment of slab-derived water to the reservoirs, while the magnitude, timing of initiation, and duration of the increase differ among the springs. Historical documents have mentioned sudden increases in water temperature at Arima hot springs after intense earthquakes in 1596, 1854, 1899, and 191619. In particular, it is estimated that the water temperature increased from approximately 40 to 90 °C after the 1596 earthquake. In addition, the temperature increase after the 1899 earthquake was accompanied by doubled outflow in the subsequent months. These facts suggest that earthquakes can episodically replenish very hot, slab-derived water into reservoirs, although the temperature increase due to earthquakes became unobvious after the deep borehole drilling because the ordinary temperature nearly reached the boiling point.

At the exceptional hot spring AR7, an increase in Fsdw in conjunction with the earthquake is also found, while it does not show obvious exponential decay and remains relatively high. This implies that at AR7, the steady inflow of slab-derived water to the reservoir (Isdw) is relatively large compared to the capacity of the reservoir (V) and/or spring outflow (O) as mixtures of meteoric and slab-derived components.

Quantifying episodically replenished water

Assuming constant V and O during a period in question, the decay constant of Fsdw corresponds to the turnover time (=V/O)31,32. The estimated turnover time from a ‘mixing reservoir’ model (see “Methods”) with curve fitting by an asymptotic exponential function for each spring (AR1-AR6) is 31.3 (±8.3) years on average (±SD) in period I and then decreases to 7.4 ( ± 4.7) years in period III (Supplementary Table 5, Supplementary Fig. 1). Using the mean O throughout all the periods at each of the springs (because no obvious change in O is observed between the two periods), the total capacity of the reservoirs is estimated to be approximately 3.3 × 106 m³ in period I and 7.6 × 105 m³ in period III. Assuming the reservoir capacity of 106 m3, horizontal cross-sectional area of 104 m2 and average porosity of 0.1 as rough estimates yields their average depth of about 1000 m. The decrease in the reservoir capacity likely reflects either a reduction in void space or shrinkage of the depth zone where slab-derived water mixes with meteoric water (in other words, expansion of the zone that is saturated with slab-derived water) or both. Despite a constant O, the outflow of slab-derived water increased to nearly twice the amount at the 1993 level due to episodic replenishment (Fig. 4b). In total, 4.2 × 105 m³ of slab-derived water is estimated to have been episodically replenished in conjunction with the earthquake. However, the approximated (or extrapolated) Fsdw at the former part of period III may be somewhat overestimated. If we assume the maximum estimated Fsdw after the earthquake as the lower limits of approximated values at the period, the total amount of the episodic replenishment is reduced to 2.6 × 105 m³. In either case, although these amounts are relatively small compared to the slab-derived fluid storage (106−108 m3) involved in the earthquake swarm associated with the 2011 Tohoku earthquake (Mw9.0)10, the spatiotemporal density of the flow is considerably high at Arima.

Note that we excluded two data points (i.e., at AR5 in 2006 and at AR3 in 2019; represented by open symbols in Fig. 4a) from the curve fitting of the Fsdw decay. The former is accompanied by an extraordinarily low temperature (45.1 °C) compared to the ordinary temperature at AR5 (>90 °C) due to partial clogging of the permeable borehole wall by precipitates that inhibit the inflow of slab-derived water but not meteoric water inflow. In contrast, the latter is accompanied by a higher temperature (100.5 °C) and several times greater outflow than ordinary values (Supplementary Table 4). This irregular surge in Fsdw occurred immediately after dredging inside the borehole, indicating an enhanced inflow of slab-derived water that had been inhibited. These two cases suggest that changes in the borehole condition affect only short-term changes in Fsdw.

Discussion

The most interesting and debatable point in our results is that increases in Fsdw in the hot springs of AR1, AR6, and AR7 preceded the occurrence of the earthquake. It has been reported that the concentrations of Cl (20 km northeast of the epicenter and 10 km southwest of Arima; yellow circle in Fig. 1b)33 and Rn (30 km northeast of the epicenter and 10 km southeast of Arima; yellow square in Fig. 1b)34 in deep groundwater increased 3 to 5 months prior to the earthquake. H and O isotopic changes in groundwater as precursors to earthquakes have also been reported in other regions, for instance, Hafralækur in northern Iceland35 and Tottori in western Japan36. Overpressurized fluids are often considered potential triggers for fault movement4,5. Therefore, it is highly likely that increases in Fsdw were also the precursors to the 1995 Kobe earthquake although we cannot specify when Fsdw started to increase because of the coarse measurement intervals. On the other hand, increases in Fsdw at AR2, AR3, and AR5 lag one or more years behind the main shock. Such large and variable time lags are distinct from those of other hydrogeochemical precursors and postseismic responses37,38.

We infer that the earthquake and episodic replenishment of slab-derived water (as well as precursory changes in groundwater Cl and Rn) were both induced by a flood-like release of water from the slab (>60 km deep) or by bursting of clogged flow paths from the slab to the hypocenter (~18 km deep). Increase in water flow can propagate faster than the actual flow velocity by the piston-like flow (or called translatory flow; i.e., upstream waters push out downstream waters). Water inflow and accumulation at the source region including the hypocenter reduced the apparent friction coefficient and thus the fault strength, resulting in the earthquake; then, the seismicity facilitated further upwards migration of the slab-derived water (Figs. 5 and 6). If there had been no flooding, the earthquake might have occurred later. The slab-derived water and meteoric water are mixing in a network of the cracks (down to ca. 1000 m) as well as in boreholes. Isotope data suggest that the mean recharge elevation of the meteoric component of the hot springs is greater than the catchment mean elevation for adjacent rivers, as mentioned at “Two end-members of hot spring”, suggesting that the hydraulic head of meteoric water is higher than the ground surface at the hot spring sites. In addition, as mentioned at “Water budget analysis using the mixing reservoir model” in Methods, the hot springs are naturally or artificially gas-lifted, and static water level in the borehole is not always above the ground surface. Therefore, meteoric waters can mix with slab-derived waters. Before 1940s, hot springs were naturally flowing (without borehole drilling), and the meteoric component was dominated in shallower depth zones. On the other hand, the fraction of hot, slab-derived component was kept high in deeper zones. In 1950–60s the drilling of deep boreholes enabled outflow of waters having high temperature and high fraction of slab-derived component, making static level lower within the boreholes. This enlarged the influx of the meteoric water and diluted slab-derived water during 1970–80s. Flooding of slab-derived waters in the former 1990s replenished the mixing reservoirs with new slab-derived waters, and then they are still being diluted (Fig. 6).

Fig. 5: Conceptual model of the flooding of slab-derived water.
figure 5

This was created using the Surfer 24.3.218 (Golden Software, LLC) with the data of the land surface elevation55, the Moho depth57, and the slab top depth25.

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Fig. 6
figure 6

Conceptual model of slab-derived water upwelling and mixing.

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A previous study on Arima hot springs argued that slab-derived fluid is originally under supercritical condition39. If that is correct, it will make it easier to explain the rapid and widespread movement of slab-derived fluid. However, some other studies suggested that the fluid at depths >83 km40 or at temperatures >650 °C41 is under supercritical condition. In our computation, predicted temperatures at the slab top beneath Arima (67.4 km depth) ranges from 500 to 600 °C. In addition, slab-derived fluid that reaches near the Earth’s surface does not retain its original chemical composition (Supplementary Table 6), unlike fluid inclusions in minerals. Therefore, we cannot conclude whether slab-derived fluid that is contained in Arima hot spring waters was originally under supercritical condition or not. Even without assuming a supercritical fluid, rapid flood propagation can be explained by piston-like flow.

Our results indicate that large earthquakes do not strike anywhere7,8 and anytime but they are more likely to occur at the time and place where the flooding of slab-derived water happens. A situation similar to the 1995 Kobe earthquake can be found in the 1965–1967 earthquake swarm (the highest Mw = 5.4) at Matsushiro, central Japan, where more than 700,000 earthquakes were observed together with a vast volume of enhanced outflows (~107 m3/yr) of saline water oversaturated with CO2 at a hot spring42,43. Although the saline water involved in this swarm has been postulated to be of magma origin43,44, our recent study22 showed that it is also derived from the Philippine Sea slab (in the original paper, Na2 and Na3 correspond to hot springs at Matsushiro). The similarity between Arima and Matsushiro highlights the importance of hot springs as outlets of slab-derived water. Exploring such hydrologically slab-connected hot springs across subduction zones and their long-term, frequent monitoring will deepen and broaden our understanding of the ultradeep water cycle and its causal relationship with earthquakes.

Methods

Sampling, isotopic analysis, and data compilation

At Arima, there are more than forty source springs, including hot and/or mineral springs, for spas. We collected water samples from seven typical hot springs and two cold mineral springs as well as from two nearby rivers in August 2019 and/or January 2024 (Supplementary Table 1). Hydrogen and oxygen stable isotope ratios in the water samples were measured by cavity ring-down laser absorption spectroscopy (CRDS) using an L2130-i instrument (Picarro Inc., Santa Clara, CA, USA) at the Center for Research in Radiation, Isotopes, and Earth System Sciences (CRiES), University of Tsukuba. Two working standards, calibrated against three international standards (Vienna Standard Mean Ocean Water, Standard Light Antarctic Precipitation, and Greenland Ice Sheet Precipitation), were analyzed with samples for validation (or calibration if necessary). The measurement errors are ±0.25‰ for δ2H and ±0.05‰ for δ18O. We also assembled a previously measured dataset of both δ2H and δ18O (with accuracy of ±1‰ and ±0.1‰, respectively) in the studied hot springs (Supplementary Table 3). Additionally, to increase the temporal resolution of the isotopic data, Cl data (with accuracy of about ±100 mg/kg) as proxies were compiled based on previous studies45,46,47,48,49 and those provided by spring owners (Supplementary Tables 4 and 6; the analysis of Cl content is conducted in accordance with the guidelines established by the Japanese government). The regression lines for the δ18O-δ2H, Cl-δ2H, and Cl-δ18O relationships in the hot springs are given as

$${\delta }^{2}{{{\rm{H}}}}=1.345\times {\delta }^{18}{{{\rm{O}}}}-41.15\,({r}^{2}=0.937)$$
(1)
$${\delta }^{2}{{{\rm{H}}}}=5.011\times {10}^{-4}\times {{{\rm{Cl}}}}-51.81\,({r}^{2}=0.870)$$
(2)
$${\delta }^{18}{{{\rm{O}}}}=3.483\times {10}^{-4}\times {{{\rm{Cl}}}}-7.26\,({r}^{2}=0.985)$$
(3)

where Cl is the chloride ion concentration (mg/kg). The regression lines for the δ18O-δ2H relationships in the cold mineral springs and rivers, which represent the local meteoric water line (LMWL) at Arima, are expressed as follows.

$${\delta }^{2}{{{\rm{H}}}}=8.552\times {\delta }^{18}{{{\rm{O}}}}+17.32\,({r}^{2}=0.660)$$
(4)

Although Eq. (4) is derived from limited data (n = 4) and its determination coefficient (r2) is not high enough, it is close to the LMWL (\({\delta }^{2}{{{\rm{H}}}}=8\times {\delta }^{18}{{{\rm{O}}}}+17\)) at Okayama (120 km west of Arima)50 and thus considered confident.

Mixing analysis of hot spring water

The isotopic evolution of ocean-origin lithospheric waters (including not only slab-derived water but also so-called fossil seawater, metamorphic water, and magmatic water, as found in subseafloor pore water, submarine mud volcano pore water, coastal oil-field brine and volcanic steam) in the δ18O-δ2H space can be approximated by the ocean-origin lithospheric water curve (OLWC)22, as expressed by

$${\delta }^{2}{{{\rm{H}}}}=60/({\delta }^{18}{{{\rm{O}}}}-{\delta }^{18}{{{{\rm{O}}}}}_{{{{\rm{fin}}}}})+{\delta }^{2}{{{{\rm{H}}}}}_{{{{\rm{off}}}}}$$
(5)

where δ18Ofin = 11 ± 1 and δ2Hoff = 0 ± 10. The isotopic signature of the lithospheric end-member can be obtained as the coordinate of the intersection point of the OLWC and the mixing line (MXL) in the δ18O-δ2H space as follows:

$${\delta }^{18}{{{\rm{O}}}}= \left[-i+{\delta }^{2}{{{{\rm{H}}}}}_{{{{\rm{off}}}}}+s{\delta }^{18}{{{{\rm{O}}}}}_{{{{\rm{fin}}}}} \right. \\ \left.- \sqrt{{\left(1-{\delta }^{2}{{{{\rm{H}}}}}_{{{{\rm{off}}}}}-s{\delta }^{18}{{{{\rm{O}}}}}_{{{{\rm{fin}}}}}\right)}^{2} \! -4s \left(-i{\delta }^{18}{{{{\rm{O}}}}}_{{{{\rm{fin}}}}}+{\delta }^{18}{{{{\rm{O}}}}}_{{{{\rm{fin}}}}}{\delta }^{2}{{{{\rm{H}}}}}_{{{{\rm{off}}}}}-60\right)}\right] \!/2s$$
(6)
$${\delta }^{2}{{{\rm{H}}}}=s{\delta }^{18}{{{\rm{O}}}}+i$$
(7)

where s and i are the slope and intercept of the MXL (i.e., Eq. (1)), respectively. Similarly, the coordinates of the intersection points of the LMWL and MXL indicate the isotopic signature of the meteoric end-member. The fraction of slab-derived water (i.e., the most likely lithospheric component in the present study) is obtained as

$${F}_{{{{\rm{sdw}}}}}=({\delta }_{{{{\rm{hs}}}}}-{\delta }_{{{{\rm{mw}}}}})/({\delta }_{{{{\rm{lw}}}}}-{\delta }_{{{{\rm{mw}}}}})$$
(8)

where δ is δ2H or δ18O and the subscripts hs, mw, and lw denote the hot spring, meteoric end-member, and lithospheric end-member, respectively. We adopted the mean of the δ2H-based and δ18O-based values, even when the Cl data were converted to δ2H and δ18O using Eqs. (2) and (3). Expected errors in Fsdw (εF) is given as

$${\varepsilon }_{F}={\varepsilon }_{\delta }/({\delta }_{{{{\rm{lw}}}}}-{\delta }_{{{{\rm{mw}}}}})$$
(9)

where εδ is the measurement errors in δ2H (=1‰) or δ18O (=0.1‰). In case where δ values are converted from Cl, the εδ is given as

$${\varepsilon }_{\delta }=\sqrt{{({\varepsilon }_{{{{\rm{Cl}}}}}\cdot a)}^{2}+{({{{\rm{Cl}}}}\cdot {\varepsilon }_{a})}^{2}+{{\varepsilon }_{b}}^{2}}$$
(10)

where εCl is the measurement errors in Cl concentrations (=100 mg kg−1), a is the slope of the Cl-δ regression lines, εa and εb are the standard errors of a and b (the intercept of the regression lines), respectively. The Cl concentrations in the meteoric end-member can vary, resulting in uncertainties in the Cl-δ regression lines and thus errors in Fsdw estimation. Such an effect as well as errors in Cl measurements can be considered by Eq. (10).

Numerical prediction of the isotopic signature of slab-derived water

To identify the origin of the lithospheric component in hot spring waters, we numerically predicted the isotopic signature of water in the subducting Philippine Sea slab using a model of H and O isotope evolution22. Unlike the previous Rayleigh-type model18, our model computes the nonequilibrium exchange of hydrogen/oxygen isotopes among pools of pore water, interlayer water in clay particles (including adsorbed water on mineral surfaces), OH groups of hydrous minerals, and O atoms constituting mineral crystals. The temperature of the slab and the depth of the slab top surface along the horizontal distance from the Nankai Trough were given at every time step (=10,000 years) by empirical equations that approximate the simulation results for the subduction of the Philippine Sea slab26. To consider uncertainties in the model parameters, a Monte Carlo simulation result of 1000 runs was employed. To compare the prediction results and the isotopic signatures of lithospheric end-members, we estimated the depth of the Philippine Sea slab surface beneath the Arima area by interpolating depth contours from a previous study25 with ordinary kriging. Although there is little difference in geometry of Philippine Sea slab among literatures51, the difference in estimated slab-depths at Arima is within some 1 km.

Water budget analysis using the mixing reservoir model

The ancient hot springs in Arima are naturally flowing. Since the 1940s, deep wells for the current hot springs have been drilled, and they were originally the geysers due to a (natural CO2) gas-lift effect45. Then, inner pipes with enlarged diameters with deep ends were introduced into boreholes to increase the effect; hot water nearly continuously flows out (even if the static water level in the borehole is below the ground), while the intermittent nature of outflows with variable temperatures still persists (and in some springs, water is sometimes artificially gas-lifted using compressed air). Based on these characteristics, it has been inferred that slab-derived water moves from depth towards boreholes through a cluster of interconnected cracks, which form along faults and/or around intrusive bodies of igneous rock17,52.

The cluster of such cracks can be regarded as a water reservoir, where slab-derived water and meteoric water mix and a hot spring corresponds to its outlet. The temporal change in the storage amount of slab-derived water (Ssdw) within the mixing reservoir is expressed as

$${{{\rm{d}}}}{S}_{{{{\rm{sdw}}}}}/{{{\rm{dt}}}}={I}_{{{{\rm{sdw}}}}}-{{OF}}_{{{{\rm{sdw}}}}}$$
(11)

where t is the time, Isdw is the inflow of slab-derived water into the reservoir, and O is the outflow as a mixture of the slab-derived component and meteoric component. The temporal change in Fsdw as a spatial mean within a cluster of cracks is given as follows.

$${{{\rm{d}}}}{F}_{{{{\rm{sdw}}}}}/{{{\rm{d}}}}t=({I}_{{{{\rm{sdw}}}}}-{{OF}}_{{{{\rm{sdw}}}}})/V$$
(12)

Under the assumptions of a constant V, Isdw, and O during a period in question, integrating Eq. (12) yields

$${F}_{{{{\rm{sdw}}}}}=({F}_{0}-{I}_{{{{\rm{sdw}}}}}/O) \, {{{\mathrm{exp}}}}[-(O/V)t]+{I}_{{{{\rm{sdw}}}}}/O$$
(13)

where F0 is the initial (i.e., t = 0) value of Fsdw. If we approximate the temporal change in Fsdw by an exponential asymptotic function, Fsdw = c + b exp(at), we obtain Isdw = cO, F0 = b + c, τ = −a−1, and V = τO, where τ is the decay constant or the turnover time (Supplementary Table 5). In the present study, we assumed that Isdw and O remained constant throughout all the periods. For each spring, we obtained the value of Isdw/O that maximizes the sum of r2 for periods I and III using the logarithmic conversion of Eq. (13) and its linear regression. For period II, we reconstructed Fsdw values via linear interpolation as a first approximation (Supplementary Fig. 1). The use of parameters in period I for extrapolating the exponential decay in Fsdw (regardless of the occurrence of the earthquake) provides the hypothetical outflow of pre-existing slab-derived water. Thus, the difference between the actual and hypothetical outflows represents the outflow of the episodically replenished component (Fig. 4b).