Abstract: A method of prestack reverse-time migration of seismic data that yields significant gains in computer storage and memory bandwidth efficiency is disclosed. The values only of the source wave incident on the boundaries of a simulation domain are saved, rather than all of the values of the wavefield throughout the entire simulation domain. This data allows an accurate and robust approximation of the forward propagated source wave for all finite-difference approximation orders of the acoustic wave equation. The method reduces the amount of data storage required by an order of magnitude and overcomes the present challenge of requiring special large memory hardware while allowing for the implementation of 3D prestack reverse-time migration on off-the-shelf platforms.