Subleading non linear gravitational memory effect

We apply the new method based on null geodesics for detecting gravitational memory and find the bulk memory in Newman-Unti gauge around the boundary of the conformally compactified space time. We show how we use the newly found conserved charges in the subleading orders of large-$r$ expansion of the BMS charges to define the gravitational memory at each order in the non-linearised gravitational theory. We also find the gravitational shift in the $r$ direction. It is shown that the longitudinal displacement at order $1/r$ is the relative radius change between two detectors derived by Strominger and Zhiboedov