In this work the authors propose an approximation to calculate the RTM migration (and the FWI gradient), without having to store in memory or write to disk the forward wavefield that must be correlated with the reverse propagated wavefield, avoiding significant input/output (I/O) cost.
Their approach boils down to the following equation:
where
and
In RTM, is a source wavefield forward propagated using a smooth velocity model, whereas
equals the weighted sum of the forward
and the backward
wavefields
Whe wavefield is calculated by depropagating the forward wavefield
which must be carefully stored on the boundaries of the model at each time step and together with the correct initial conditions, it is possible to reconstruct the direct wavefield within machine precision. When this happens, the remaining term in equation above (
), the residual propagation, gives the approximation to the RTM after scaled by
. According to Figure 5 of the paper, the best alpha value depends on the image condition used.
In the examples shown here the following image condition was used:
The difference between conventional RTM and RWII migration can be seen in the example for a layered model for double precision and for the marmousi model for single precision.