Reverse time migration (RTM) requires that fields computed in forward time be accessed in reverse order. Such out-of-order access, to recursively computed fields, requires that some part of the recursion history be stored (checkpointed), with the remainder computed by repeating parts of the forward computation. Optimal checkpointing algorithms choose checkpoints in such a way that the total storage is minimized for a prescribed level of excess computation, or vice versa. Optimal checkpointing dramatically reduces the storage required by RTM, compared to that needed for nonoptimal implementations, at the price of a small increase in computation. This paper describes optimal checkpointing in a form which applies both to RTM and other applications of the adjoint state method, such as construction of velocity updates from prestack wave equation migration.

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