Introduction

Crustal fluids are critical for energy and material transfer (e.g., ore deposits) from the Earth’s interior towards its surface, and the dynamic behavior of the crust (e.g., crustal deformation, earthquakes, and volcanic activity)1,2,3,4,5,6. The main source of crustal fluids is aqueous fluids released by the slab dehydration at subduction zones1,2,7,8,9,10. The migration of these fluids in the overlying mantle and crust controls the long-term stability of the ocean, generation of arc magmas, and earthquakes (both at plate margins and within the plate)1,2,8,10. The aqueous fluid-bearing areas in the crust are generally demarcated as high-conductivity regions by magnetotelluric measurements6,9, and/or low-velocity zones by seismic tomographies3,10. These areas are frequently located beneath the seismogenic zones of the arc crust3,6,9. Quartz veins in exhumed crustal materials also suggest highly channelized flow paths in the crust. Traces of repeated fracturing in the crack-seal veins support that aqueous fluids accumulate in the crust; thereby, raising the fluid pressure to near lithostatic pressure, and activate fractures in the rocks. Subsequently, the fluid flows until its pressure drops, and/or the newly formed fracture is entirely sealed by quartz precipitation5,11,12. Such fault-valve behavior may control the recurrence of tremors and earthquakes at the plate margin and within the plate4,13, which may be linked to hazardous earthquakes. Fluid storage in the crust and their subsequent release during earthquakes are further supported by the migration of hypocenters during earthquake swarms14,15, which are sometimes accompanied by the eruptions of fluids16. Elemental transport by fluid flow along the crustal faults and under volcanoes generates epithermal–mesothermal gold5,17 and porphyry copper deposits18,19, which are geological manifestations of episodic fluid flow in the lower crust5,20. Fluid volume and flux govern the dynamic and static behaviors of the various geological processes. Geophysical studies have revealed the macroscopic distribution of fluid in the subduction zone3, while geochemical studies have estimated long-term fluid flux from subducting plates1,2,7 and volcanoes, solidifying magmatic chambers and dikes8,21,22,23. However, the absolute amounts and flow rates of the crustal fluids are highly uncertain, owing to the limited resolution of those approaches in the lower crust. Such deep crust fluids principally originate from the dehydration of the subducting slab1,7. Hydrous magmas generated in the subarc mantle carry aqueous fluids that are released into the lower and middle crust8. These fluids then migrate to the bottom of the upper crust and deep geothermal reservoirs3,10,22,24.

However, dehydration of the subducting slab and release of fluids from hydrous magmas is a slow process, governed by the velocity of the subducting slab and cooling of a pluton, respectively, and there is a huge time gap between the Ma-scale geological fluid flux and the seismogenic fluid flux, the duration of which ranges from seconds to years. Thus, there has been no means of knowing the dynamic behavior of slab-derived fluids beyond the geologic spatiotemporal time resolution, though it could connect intense seismogenic activities.

The 2011 M9 Tohoku earthquake in Japan triggered numerous swarms14,15,25 and provided a unique opportunity to directly constrain the crustal fluid volume using seismological data. Integrating the insights from a recent and detailed study of the injection-induced seismicity fields26,27,28 with those of the swarm observations, we present the first estimate of the fluid volume stored in the crust before the M9 Tohoku earthquake. Critical comparisons with background geologic fluid flux revealed the episodic nature of fluid storage and release in the arc crust within a period of 102–104 y.

Results and discussion

Earthquake swarm associated with the M9 Tohoku earthquake

Earthquake swarm in the crust is a sequence of earthquakes without a clear mainshock, and thought to be a natural version of injection-induced seismicity. They typically show clear spatial migration over time and are interpreted to be caused by fluid migration18,19,26. For instance, the slab-derived fluids were the probable cause of the earthquake swarm near the Yamagata–Fukushima border in Japan14,15 (Fig. 1a). This earthquake swarm activated approximately a week after the 2011 M9 Tohoku earthquake, which had occurred hundreds of kilometers away, even though the strain energy was reduced by the Tohoku earthquake14,. The activation of this swarm can be attributed to the increase in pore pressure due to upward fluid migration following the Tohoku earthquake14 (Fig. 1b). A low-velocity region10 and a paleo-caldera were found to exist just below and above the swarm region, respectively, suggesting the existence of an upward path for fluids. Indeed, during the swarm activity, the earthquake hypocenters moved from deep to shallow levels through multiple faults14 (Fig. 1c). Additionally, various features of seismic activity were similar to those of injection-induced seismicity14,29. After the Tohoku earthquake, similar earthquake swarms occurred in various parts of eastern Japan15, but the one near the Yamagata–Fukushima border was the largest.

Fig. 1: Field overview including location and seismic activity.
figure 1

a Study area (red triangle) in the Japan volcanic arc. Black triangles represent the Quaternary volcanoes. The star marks the epicenter of the Tohoku earthquake, and its slip distribution is also shown. b Hypocenter distribution of the swarm near the Yamagata-Fukushima border12. The swarm has been classified into four clusters12, shown with different color schemes and their respective occurrence times. c Cross-sectional time migration patterns of the swarm hypocenters for each cluster.

Estimation of fluid volume

We employed two representative models for the injection-induced seismicity studies to connect seismic activity and causal fluid volume. The cumulative seismic moment of the swarm was used to estimate the fluid volume using McGarr’s model27 (see “Methods”). The estimated fluid volume that led to the swarm activation was 8.0 × 105 m3. We also utilized the seismogenic index (SI) model based on pore pressure diffusion28 (see “Methods”). We estimated the fluid volume (Supplementary Figs. 3 and 4) with previously observed SI sets (ranging from −2.0 to 1.0)28,30 from geothermal reservoirs in crystalline rocks. The estimated fluid volume is in the order of 0.082–82 × 106 m3.

In addition to injection-induced seismicity, hydrological models were also adopted to estimate the fluid volume that caused the earthquake swarm. We modeled the spatiotemporal migration of the swarm as a proxy for fluid flow using Darcy’s law or the cubic law (see Methods). This law allows the estimation of the flow rate and its time integral, i.e., the fluid volume when the flow zone and hydraulic parameters (diffusivity or permeability) are available. We modeled the flow zone and diffusivity from the time-series migration of the hypocenters31. The resultant fluid volume estimated using Darcy’s law ranged from approximately 5.1 × 106–1.4 × 108 m3, while that using the cubic law was approximately 2.8 × 105–7.6 × 106 m3 for the pressure difference (ΔP = 10–270 MPa) (Supplementary Figs. 615).

In summary, the possible range of fluid volume estimated using four different methods was in the order of 105–108 m3 (Supplementary Fig. 16). All the models suggest that a large portion of the fluid was released in the early part of the swarm sequence (Supplementary Figs. 2, 3, 5, 14, and 15), which coincides with the very intense early seismic swarm activity14. The fluid volume estimated for each cluster (Supplementary Figs. 2, 3, 5, 14, and 15), indicated differences among the clustered swarms depending on the scale and amount of seismic activity. All four models were based on different physical processes, and this multidisciplinary approach was utilized to evaluate the values that denote the dynamics of slab-derived fluids in swarm sequences.

Considering the methodology, the estimate from McGarr’s model can be denoted as the lower limit of the fluid volume27 and is nearly the same value of lower limit of the SI model with the representative value of SI = 0.5 (Basel, EGS field). Therefore, we can constrain the lower bound of fluid volume as 106 m3. The SI model presented the widest range of fluid volume up to 108 m3, for the lowest SI value −2 (Soultz, EGS field)28,30. Darcy’s law also estimated as a large fluid volume, similar to that of the SI model. One well reasoned estimate of ΔP = 140 MPa (pore pressure at source: lithostatic, pore pressure at the edge of swarm region: hydrostatic) presented a similar value to the upper bound of the SI model. Consequently, fluid volume estimates from four different models fall in the range of two orders; 106–108 m3, considering the overlapped values of well reasoned cases from each method (Fig. 2). The upper range of fluid volume might be overestimated. The seismo-tectonic activity level (SI value) of our study area in the mobile belt is unlikely to be the same as that in Europe, such as −2 (Soultz, EGS field)28,30, which led to the upper limit of fluid volume estimation. In addition, very intense swarm activity in the first 50 days makes it difficult to estimate the reasonable apparent diffusivity or permeability in that period. Possible overestimation in SI model and in Darcy’s law might be present in higher fluid volume estimates. Indeed, we defined this order range of the fluid volume (106–108 m3) as the plausible range and explicate following multidisciplinary discussions based on this range.

Fig. 2: Fluid volume estimation.
figure 2

Each line corresponds to the well-reasoned upper and lower case for each model. Vertical arrows indicate the plausible range of fluid volume estimation (green) and all possible range of that (gray).

It is surprising that such an amount of free aqueous fluid exists beneath the swarm region of the mid-crustal level since the apertures (cracks/pores/openings) in the grain boundary are extremely small (~10−9 m)32. The maximum length of mechanically stable cracks in granite under crustal condition had been estimated as <20 m33, where their aspect ratios would be <10−2–10−334, showing that a voluminous body of water is mechanically unstable in the deep crust. However, other geological evidence, such as mineral veins and mineral deposits, support past massive fluid flows.

As the amount of fluids in the crust has been discussed for different timescales ranging from years to millions of years5,8,17,20,21,23, this finding would promote a comprehensive understanding in the field of slab-derived fluids, while simultaneously achieving a breakthrough in the geological calculations of fluid budgets since they have not previously been quantified to understand their dynamic behavior.

Duration of fluid storage

The constrained fluid volume (106–108 m3) allows us to evaluate the duration of fluid storage in the crust prior to the swarm. The upward movement of the swarm (Fig. 1c) strongly suggests that the fluids were supplied from the deeper crust and were stored near the swarm zone. The swarm is located near the Bandai-Azuma-Adatara volcanic clusters35 below the Miocene Otoge volcanic caldera36 (Fig. 3a). The uppermost mantle and the lower crust are characterized by low Vs and high Vp/Vs ratio10,37 indicating the presence of melt or partial melting zones (Supplementary Fig. 1 and Fig. 3a)38. These volcanic clusters were supplied with highly hydrous magma (H2O = ~5 wt.%)21,39,40, which would release a large amount of H2O during solidification in the lower and/or upper crust22. In the NE Japan arc, many seismic reflectors exist beneath volcanic regions in the upper crust (<18 km), suggesting the existence of aqueous fluids in the planar fractures or cracks41,42. Therefore, we suggest that the fluids supplied to the base of the swarm originated from the partial melting zones in the lower crust and were stored in the upper crust within fractures or cracks (Fig. 3a).

Fig. 3: Conceptual summarization of this study.
figure 3

a Schematic model of fluid supply below swarm regions. The seismic velocity structure10 is interpreted based on ref. 38. The Miocene Otoge caldera is from ref. 36, the depths of the magma chambers of the Miocene fossil caldera in NE Japan are from refs. 21, 39. Earthquake (EQ) swarm is from ref. 14. b Estimation of periods of fluid accumulation. Fluid supply from the lower crust is based on refs. 8, 21, 39. Blue bars indicate the ranges of fluid volume estimated by each method. MG McGary’s model, SI seismogenic index, CL cubic law, DL Darcy’s law.

The background H2O flux under the NE Japan arc is predominantly supplied from hydrous melt (~13 t/yr/m of the arc length)8, consistent with the H2O fluxes observed in the upper crustal fossil magma chambers (4–17 t/yr/m)21,39, which corresponds to an average H2O flux of 10−4–10−3 m3/m2/yr. Assuming the area of the swarm region to be 10 × 10 km2, the estimated fluid volume (106–108 m3) corresponds to the accumulation of fluids over 10–104 years (Fig. 3b). These fluid accumulation periods are much longer than the interval between the Tohoku earthquake and the beginning of the swarm (~7 days), suggesting that fluids had been stored in the crust prior to the Tohoku earthquake in the form of mobile fluid. Additionally, the Japan Meteorological Agency (JMA) catalog (since 1919) and modern seismic records from the 1970s do not suggest any seismic activity in this region. Thus, the accumulation periods have been longer than ~90 y and possibly ranged from hundreds to tens of thousands of years. This range included the last M9 Jogan earthquake (869 AD) at least, suggesting the possibility that such seismic swarms occur periodically accompanying the M9 class earthquakes.

A total of 106–108 m3 of fluids sourced from the lower crustal partial melting zones were accumulated beneath the swarm region within 102–104 y, thereby increasing the pore pressure. However, the flow pathway connecting it to the swarm region was sealed by the fault-valve behavior. The Tohoku earthquake probably broke the sealed parts of the fractures and dynamically increased the permeability43. Consequently, pore pressure migration caused the fluids to reach the swarm zone after 7 days. Seismological observations suggest that the pore pressure was as high as the minimum principal stress (lithostatic stress in this case) during the early stage of the swarm sequence29. Thus, our estimates of fluid volume and duration of fluid storage add more precise and detailed explanation for the scenario of swarm activity (Fig. 3a).

Assuming a geothermal gradient of 28–38 °C/km beneath the swarm region38,44,45, the migration of estimated fluid volume induced SiO2 precipitation46 of 1.4 × 102–106 kg (see “Methods”) that manifested as quartz veins, which are often observed in crustal rocks and deep-level ore deposit formations47. The majority of the ores (Au, Ag, Cu) in the arc crust precipitate at a temperature range of 450–100 °C18. The estimated fluid volume provides a key link between the geological observations (mineral veins and ore deposits) with periodic swarm activity. Contrary to the typical duration of ore formation in sub-million to a few million years18, our observations suggest that smaller duration earthquake swarms (~2 years) can also produce detectable mineral veins and/or ore deposits.

The Yamagata-Fukushima swarm witnessed the release of crustal fluids that accumulated in the crust for 102–104 y. This study provides the first quantitative seismological evidence of fluid accumulation in the crust and its influence in causing earthquake swarm. The flux and periods of fluid accumulation obtained in this study, which covers the recurrence periods of M9 earthquakes, can be tested in future, whether the swarm recurrence time is consistent with the predicted fluid accumulation period. Further, we can discover the links between the swarm and M9 earthquakes by correlation between swarm recurrence and future M9 earthquakes. Furthermore, our approach provides a different perspective for understanding fluid-related phenomena in subduction zones and expands horizons for tracing the spatiotemporal evolution of slab-derived fluids in the crust. Based on fluid volume, we provided a temporal linkage between the dynamic crustal seismicity and geological features, such as mineral precipitation. Further application in studying earthquake swarm sequences in other parts of volcanic arcs or other geological settings around the world will provide information on any heterogeneous behavior of slab-derived fluids, as well as its connection to the various fluid-related processes in subduction zones, such as episodic earthquakes, slow earthquakes, inland earthquakes, and volcanic activity.

Methods

Fluid volume estimation with injection-induced seismicity model McGarr’s theory

McGarr27 presented a theory to connect the injected fluid volume and the corresponding seismic moment released by elastic deformation. The relationship between the injected fluid volume and the cumulative seismic moment is described as:

$$\Sigma {{{{{\rm{Mo}}}}}}=\frac{2\mu (3\lambda +2G)}{3}\triangle V,$$
(1)

where Mo is the seismic moment, μ is the friction coefficient, λ and G are Lame’s elastic parameters, and ΔV is the injected volume. Commonly, we assume λ = G and μ = 0.6. The simplified form of Eq. (1) is:

$$\Sigma {{{{{\rm{Mo}}}}}}=2G\triangle V$$
(2)

This model is widely used to estimate the maximum magnitude of induced seismicity associated with fluid injection in this form or other extended forms28.

We inverted this relationship to estimate ΔV by inputting the cumulative observed seismic moments assuming G (modulus of rigidity) = 30 GPa28. As more detailed case, we also estimated λ = 26.5 GPa and G = 3.3 GPa with the method based on seismic velocity measurements of granite (see Darcy’s law section) to fully utilize Eq. (1). It turns out to be ΣMo = 58.43 ΔV, assuming μ = 0.6, which is nearly equivalent to Eq. (1), with G = 30 GPa: ΣMo = 60 ΔV. Considering our target depth, lithostatic pressure and pore pressure gradient (Supplementary Table 1), assuming a friction coefficient of 0.6 is also reasonable48. Even when we used μ = 0.85, the estimates of fluid volume were 0.7 times smaller. The fluid volume estimate by McGarr’s theory is currently 8.0 × 105 (Fig. 2) and can be reduced to 5.7 × 105 m3. It does not make a big difference as estimates of both cases are in an order of 105.

Supplementary Fig. 2 show the time-series of the estimated fluid volume from the entire sequence and each cluster. The output of this model is sensitive to the magnitude of the events as its definition. Thus, a large amount of fluid was released during the first 50 days and was accompanied by intense seismic activity and moderate magnitude events.

This model provides the upper limit of the cumulative seismic moment when the entire injected volume converts the elastic energy into a seismic moment that is released without any energy loss, such as fluid leakage or conversion. Therefore, we should consider the estimated fluid volume from this method as the lower limit that caused the swarm sequence.

Seismogenic index

Shapiro28 invented the seismogenic index (SI) model to assess the potential risk associated with fluid injection49,50. SI itself is a site-specific parameter representing the seismotectonic response to fluid injection. This model implicitly assumes that the induced seismicity value is related to the injected volume that migrates by diffusion. The SI model is defined as follows:

$$\Sigma ={\log }{N}_{M}\left(t\right)-{\log }V\left(t\right)+{bM}$$
(3)

where Σ is the SI, NM is the number of seismic events larger than M, M is the magnitude of the seismic event, V is the cumulative injected volume, and b is the b-value from the Gutenberg–Richter relationship. The SI becomes a function of the fluid volume and the Gutenberg–Richter parameter by introducing the Gutenberg–Richter law51: logNM = a(t) − bM.

$$\varSigma =a\left(t\right)-{\log }V(t)$$
(4)

We inverted this relationship to estimate the cumulative fluid volume, V. We estimated the a-values of the Gutenberg–Richter relationship from the swarm data using the maximum likelihood method52 with Mc = 2.0, which was used in a previous study on this swarm sequence29. We chose the SI value range aiming to model the similar seismo-tectonic features. We referred to the previously observed SI values28,30 from geothermal reservoirs in crystalline rock, where natural earthquake activity can be observed. We also considered the depth, rock type and b-value, then we set the upper bound to be 1.0, considering the Basel, Switzerland case (Σ = 0.5) and lower bound to be −2, considering the Soultz, France case (Σ = −2.0). We applied SI sets, from −2.0 to 1.0 with 0.5 increments, for fluid volume estimation and we regard SI = 0.5 (observed at Basel) as a representative case. A larger SI value denotes less fluid volume to explain the seismic sequence and vice versa.

We computed the Gutenberg–Richter parameters in the time series by expanding the time window for each cluster. In Supplementary Figs. 35, the fluid volume estimation results with the SI model for the whole swarm sequence and each cluster are presented.

Fluid volume estimation with a hydrology model

Darcy’s law

In addition to the injection-induced seismicity approaches, we directly modeled the spatiotemporal migration of a seismic swarm as a proxy of fluid flow using Darcy’s law or the cubic law. Darcy’s law is a well-accepted model in hydrology for describing fluid flow. In porous media, the hydraulic feature is characterized by the matrix permeability k [m2] and flow rate Q [m3/s] at cross-sectional area A [m2] invoked by the pressure difference ΔP [Pa] over the length of the flow path L [m] for the fluid with viscosity η [Pa·s], and can be described as follows:

$$Q=\frac{{kA}}{\eta L}\triangle P$$
(5)

We assumed that the fluid flow that caused the swarm could be modeled using Darcy’s law. We first estimated the diffusivity from the time-series hypocenter migration of the swarm based on Shapiro31. For each cluster and time step, the diffusivity is iteratively searched to fit 96% of the data (Supplementary Figs. 69). In Supplementary Figs. 69, we showed the example of time series evolution of seismic swarm front for each cluster. We checked the fits between the pressure front based on estimated diffusivity and observed seismic fronts. For cluster E and W (Supplementary Figs. 6 and 9), the pressure front did not describe the swarm event migration especially after 50 days. Very intense seismic activity in first 50 days after the Tohoku event presented very fast migration, so high diffusivity. Therefore, this caused the bias for the long-term diffusivity estimation as the algorithm tries to fit 96 % of whole events in the time window. For example, in Supplementary Fig. 6, time variable diffusivity surely covered most of the events, but triggering front lines did not fit the seismic front, even though time variable diffusivity decreased with time. So, to model the high (apparent) diffusivity at the early period of the swarm and to avoid overestimation of diffusivity later, we used two different ways to model diffusivity. For the first 50 days, we used the best fitted diffusivity and for the later period, we used the diffusivity of 0.2 m2/s, as shown in Supplementary Fig. 6. We visually checked the fit between the pressure front of 0.2 m2/s diffusivity and the data. For clusters N and S, we always used the best fitted diffusivity since we could confirm the reasonable fit on data.

Then, the diffusivity was converted to permeability, k, using Eq. (6) and the poroelastic modulus equation for crystalline rocks with low porosity (Eq. (7))31.

$$D={Nk}/\nu$$
(6)
$$N={\left[\frac{\phi }{{{{{{{\rm{K}}}}}}}_{{{{{{\rm{f}}}}}}}}+\frac{\alpha }{{{{{{{\rm{K}}}}}}}_{{{{{{\rm{g}}}}}}}}\right]}^{-1}$$
(7)

where D is the diffusivity [m2/s], N is the poroelastic modulus, ν is the dynamic viscosity of the fluid, ϕ is the porosity, Kf is the fluid bulk modulus, α = 1 − Kd/Kg, Kd is the dry-frame bulk modulus, and Kg is the grain material bulk modulus. Following Shapiro31, we considered Kd as the bulk modulus of the rock body, then Kd = 48.7 GPa based on seismic velocity measurements of granite under high PT conditions53 that were modeled by ref. 54. We estimated Kg = 58 GPa for granite with a modal abundance of 20 vol.% quartz, 54 vol.% plagioclase, 23 vol.% K-feldspar, and 3 vol.% biotite at ~320 MPa and 375 °C55. We used ϕ = 0.62% as the porosity of plutonic rocks under 250 MPa56 and Kf = 2.69 GPa57.

For viscosity (η), we used the value 1.24 × 10−4 Pa·s at 300 °C at 100 MPa58 (hydrostatic conditions at 10 km). Finally, we assumed that this permeability was the apparent (matrix) permeability in the flow region. We explained the dimensions of the flow regions (A and L) and ΔP in the different sections.

Cubic law

The cubic law is a hydrological formulation similar to Darcy’s law. When the fluid flow is assumed to occur in a single fracture, the flow rate in the fracture can be described using the cubic law Eq. (8). Instead of fracture permeability k, the fracture aperture d [m] is introduced to characterize the hydraulic features of the flow path.

$$Q=\frac{{d}^{3}}{12\eta }\frac{w}{L}\triangle P$$
(8)

We can convert d to k using Eq. (9).

$$k=\frac{{d}^{2}}{12}$$
(9)

We assumed that the fluid flow that caused the swarm could be modeled using the cubic law. We used 0.1 mm as fracture aperture59, equivalent to a fracture permeability of ~8.0 × 10−10. These values are consistent with the fracture permeability measured under experimental higher confining pressure conditions (100 MPa)60.

When we calculated the flow rate Q, we assumed that channeling flow occurred at ~20% of the entire fault area61, which was estimated from the hypocenter distribution. Therefore, we considered 20% of Q from Eq. (9) as the actual flow rate. From this analysis, we implicitly assumed that all fluid flows related to the swarm in multiple flow paths were modeled with fluid flow in one effective single fault.

Flow region

We detected the flow region from the time-variable hypocenter distribution of the swarm using 3D principal component analysis to extract the orientation and length of the cuboid flow region. Each of the three principal component orientations was compared with the time-series expansion of each cluster and was assigned a height, width, and length accordingly. The size of these cuboid dimensions was estimated as two factors of variance for each principal score, which means that 98% of the swarm events were included. We evaluated these parameters by expanding the time window for each cluster. The orientations and lengths of the three principal components are shown in Supplementary Figs. 1014 for each cluster. Thus, A and L for Darcy’s law, and w and L for the cubic law were estimated.

Pressure difference

We estimated the pressure difference in the driving force of the fluid flow from several observations. According to a previous study29 that analyzed the focal mechanisms, many swarm events occurred from sub-horizontal faults at the early stage of the swarm sequence in the reverse fault stress regime. This observation suggests that the pore pressure should have increased as high as the lithostatic pressure at around 10 km depth. Therefore, we assumed that the pore pressure at the inlet of the flow region, which corresponds to the initial point of the seismic swarm, was equal to the lithostatic pressure of 270 MPa (27 MPa/km × 10 km), which means 170 MPa overpressure from hydrostatic conditions (phyd = 100 MPa). We also assumed that the pore pressure at the inlet linearly decreased with time and equalized with the pore pressure at the outlet, because the pore pressure should decrease due to fluid flow once the seal of the fault valve is broken.

We prepared several pore pressure difference scenarios at the flow region outlet (the edge of the swarm region), and set the range of outlet pore pressure from 0 to 260 MPa, which led to a pressure difference of 10–270 MPa. The most realistic case is that the outlet pressure is hydrostatic pressure that varies in the range of 70–100 MPa, according to the depth of the time-varying swarm region. In this case, the initial pressure difference is 170 MPa. As an extreme case, we assumed that the seismic region was dry (no water). In this situation, the outlet pressure is 0 MPa, which leads to a pore pressure difference of 270 MPa. Another realistic case is that the outlet pressure is the critical pore pressure for a well-oriented fault for a given stress field, assuming a friction coefficient of 0.6. Our previous study found that the differential stress is approximately 20 MPa in this region62. We computed the critical pore pressure for a well-oriented fault to be 170.5 MPa, which is 100.5 MPa above the hydrostatic pressure at a depth of 7 km. This leads to a pore pressure difference of 69.5 MPa. We set the inlet pressure to linearly decrease with time and converge to the outlet pressure at 800 days. This is because the pore pressure source cannot maintain the initial pressure. Thus, we prepared various initial pressure difference cases, which provide a wide range of fluid volume estimation results using Darcy’s law and the cubic law. However, we consider that the outlet pressure is hydrostatic pressure as the most realistic case (initial pressure difference 170 MPa).

Estimation of the amount of quartz precipitation during the fluid flow

The migration of large amounts of aqueous fluids from the deep crust to the shallower crust induces mass transfer that would be comparable to geological observations. Adopting a geothermal gradient of 28–38 °K/km beneath the swarm region38,44,45, the solubility of SiO246 at the base of the seismic swarm is 1600–4700 ppm (i.e., 12 km, 330–450 °C), which decreases to 70–180 ppm (i.e., 4 km, 100–150 °C), resulting in the precipitation of SiO2 at 1.4 ×  102–106 kg. This predicts the precipitation of large amounts of quartz, which would correspond to quartz veins that are often observed in crustal rocks and deep ore deposit formations47. The amount of precipitation may be even larger if the source of the fluids is deeper. The temperature range of 450–100 °C corresponds to the precipitation of major ore metals (Au, Ag, Cu) in the arc crust18. Indeed, although not a present mineralization, the Otoge caldera hosts Pliocene Au-Ag-Pb-Zn ore deposits formed at ~250–340 °C63,64,65. The present seismic activity under the Otoge caldera may trace a similar fluid pathway for past mineralization.