Remarks on infinite towers of gravitational memories

An infinite tower of gravitational memories was proposed in \cite{Compere:2019odm} by considering the matter-induced vacuum transition in the impulsive limit. We give an alternative realization of the infinite towers of gravitational memories in Newman-Penrose formalism. We also demonstrate that the memories at each order can be associated to the same supertranslation instead of infinite towers of supertranslations or superrotations.