Reply to comment by Williams on "spatial changes in inclusion band spacing as an indicator of temporal changes in slow slip and tremor recurrence intervals".

Our recent paper (Nishiyama et al. in Earth Planets Space 73:126, 2021) suggested that the sealing time of a crack-seal event recorded in quartz-filled shear veins in the Makimine mélange may temporally increase or decrease. Nishiyama et al. (Earth Planets Space 73:126, 2021) describes the optical estimates of the vapor–liquid ratio of primary two-phase fluid inclusions between solid inclusion bands in shear veins. The variation in vapor–liquid ratio was used as an indicator of fluid pressure conditions at the time of trapping of fluid inclusions during a crack-seal event. Comment on our paper (Williams in Earth Plantes Space 10.1186/s40623-022-01599-1 2023) raised the issue that our paper neglected the error in fluid pressure associated with the uncertainties in the optical estimate of the vapor–liquid ratio of fluid inclusions. Williams (Earth Plantes Space 2023 10.1186/s40623-022-01599-1) claimed that, if a certain uncertainty in the optical estimate of the vapor–liquid ratio is considered, there is a large error in the fluid pressure. The argument by Williams (Earth Plantes Space 2023 10.1186/s40623-022-01599-1) is based on the assumption that the uncertainty of the vapor–liquid ratio can be determined accurately. An accurate estimate of the uncertainty of the vapor–liquid ratio is possible if the homogenization temperature of the fluid inclusion is measured. However, it has been a challenging issue to measure the homogenization temperature of fluid inclusions between inclusion bands in a crack-seal vein, because the spacing of inclusion bands is too small (typically, a few tens of microns or less) to measure the homogenization temperature. Therefore, it is difficult to provide a confidential discussion regarding the error in the fluid pressure during a crack-seal event. Nishiyama et al. (Earth Planets 73:126, 2021) showed the sealing time of a crack-seal vein for a wide range of fluid pressure drops and discussed that the sealing time is comparable to the slow slip and tremor recurrence intervals when the fluid pressure drop is large. We consider that such a presentation and discussion are appropriate rather than discussing the error in fluid pressure based on the ambiguous uncertainty in the optical vapor–liquid ratio estimate. [ABSTRACT FROM AUTHOR]