Time-reversal checkpointing methods for RTM and FWI

Time-domain seismic simulation can form the basis of reverse time depth migration and full-waveform inversion. These applications need to temporally crosscorrelate a forward simulation state with an adjoint simulation state and therefore need to be able to access each time step of a forward simulation in time-reverse order. This requires saving all forward states for all times (which can require more memory than is typically available on a computer system for many problems of interest), or the ability to checkpoint information and rapidly recompute forward simulation states as needed. Prior work has suggested how to do the latter by optimally choosing which forward simulation time steps to checkpoint, thereby enabling the most efficient reuse of memory buffers and minimizing recomputation. The optimal trade-off between memory usage and recomputation can be further improved under the assumption that the information needed to do temporal crosscorrelation is smaller than the information required to restart a simulation from a given time step. This assumption is true for many geophysical problems of interest. The modification can yield a reduction in the memory requirement and recomputation time. The tested examples applied to isotropic elastic reverse time migration and anisotropic viscoelastic full-waveform inversion.