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”

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