## 4 Discussion
### Hydrothermal Deposit  
As above, the equilibrium and nonequilibrium assemblages can be mineralogically determined if the mineral composition and texture of veins can be clearly distinguished. When we distinguish equilibrium assemblage from nonequilibrium assemblage via the microscopic observation of veins, the oxygen isotope equilibrium temperature of mineral formation can be calculated using the mineral \(\delta^{18}\)O values. The \(\delta^{18}\)O values of the quartz and calcite of the equilibrium assemblage, E1020V-2 (Figure 6), from a vein of the Kushikino deposit are 6.6% and 4.7%, respectively, and the oxygen isotope equilibrium temperature is calculated to be 173 \({}^{\circ}\)C using the experimentally determined fractionation factors of quartz-water [20] and calcite-water [23]. The equilibrium temperature of 144 \({}^{\circ}\)C is calculated for the equilibrium assemblage, W222V-2 (Figure 6), in the same way. The \(\delta^{18}\)O value of the coexisting hydrothermal fluid is then calculated to be \(-7\)% using the \(\delta^{18}\)O value of quartz or calcite and the fractionation factor of quartz-water or calcite-water, respectively [22]. The following estimations of the oxygen isotope equilibrium temperatures of the mineral-pair formation were used as an oxygen isotope thermometer based on the isotopic equilibrium for the mineral-pair: a quartz-muscovite thermometer for tungsten-quartz vein deposits (Ohtani and Kaneuchi deposits [24]), quartz-wolframite and quartz-cassiterite thermometers for tungsten-quartz vein deposits (Takatori deposit [25]), and a quartz-calcite thermometer for gold-bearing quartz-calcite veins (Noya deposit [26]). The study on the Kamioka skarn-type Pb-Zn deposits is a good example to consider the kinetics-to-equilibrium transition in isotopes for the genesis and evolution of the overcoming hydrothermal fluid [27]. The crystalline limestone in the mining area suffered from the ore-forming hydrothermal fluid. The \(\delta^{13}\)C and \(\delta^{18}\)O values of the limestone had changed from the original to varying values depending on the degree of the water/rock ratio, reaction time, and temperature. Oppositely, the direct precipitation of calcite into veins from the hydrothermal fluid also occurred. The calcite was supposed to be equilibrated with the hydrothermal fluid, and the \(\delta^{13}\)C and \(\delta^{18}\)O values of calcite were the end-members of the mining area [27]. The \(\delta^{13}\)C and \(\delta^{18}\)O values of the isotopically reacted limestone are distributed in a wide range of isotope ratios between the original limestone and precipitated veins in a \(\delta^{13}\)C-\(\delta^{18}\)O graph [27]. This confirms that the isotope exchange kinetics in the limestone changed the \(\delta^{13}\)C and \(\delta^{18}\)O values to various degrees. The \(\delta^{13}\)C and \(\delta^{18}\)O values of the most reacted limestone are identical to those of the veins. This most reacted limestone can be considered to be near equilibrium with the hydrothermal fluid. We observed that the \(\delta^{18}\)O values of amorphous silica precipitated from low-temperature hydrothermal fluids were on the low-temperature side extrapolation line of the isotopic equilibrium fractionation between quartz and water obtained at high temperatures (Section 4.3). The isotope exchange reaction is slow for vein-type hydrothermal deposits at low temperatures, and minerals are taken away from the hydrothermal fluid because of subsequent mineral precipitation on the previously precipitated mineral layer. Nevertheless, minerals in many epithermal vein-type deposits have been shown to be in isotopic equilibrium with coexisting hydrothermal fluid (e.g., Figure 6). Minerals do not crystallize from fluid in perfect equilibrium. Therefore, crystal growth is essentially governed by kinetics; however, the precipitation in the vein-type deposit is extremely slow.