Storage of the source wavefield during reverse-time migration and full-waveform inversion can be avoided by reconstructing that wavefield during reverse-time stepping along with the receiver wavefield. With absorbing boundary conditions, this requires the final states of the source wavefield and a strip of boundary values at all times. The width of the stored boundary strip, positioned in between the interior domain and the absorbing boundary region, usually equals about half that of the finite-difference stencil. The required storage in 3D with high frequencies can still adversely affect computational efficiency, despite the huge reduction in data volume compared to storing the source wavefields at all or appropriately subsampled time steps.

A method is proposed that requires a boundary strip with a width of just one point. Stored boundary values over time enable the computation of the second and higher even derivatives normal to the boundary, which together with extrapolation from the interior provides stability and accuracy. Numerical tests show that the use of only the boundary values provides at most fourth-order accuracy for the reconstruction error in the source wavefield. With the higher even normal derivatives, higher orders can be reached as is demonstrated by examples up to order 26.


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