Wave-equation migration velocity analysis by residual moveout fitting

Computational cost

The computational cost and storage overheads for evaluating terms II and III in the gradient expression 16 are limited because only operations on the prestack image are required. On the contrary, the computation of term I is computationally more demanding. It requires the forward propagation and backward propagation of wavefields. The application of ${\bar{{\bf P}}_{s} }'$ and ${\bar{{\bf P}}_{g} }'$ requires the storage, and retrieval, of the source wavefield and receiver wavefield. Furthermore, to apply $\frac{\partial {{\bf P}_{s} }}{\partial {\bf {s}}}'$ and $\frac{\partial {{\bf P}_{g} }}{\partial {\bf {s}}}'$ we need to correlate the source and receiver wavefields with the wavefields generated by the image derivatives. In summary, the computational cost of one gradient computation of the proposed method can be roughly estimated to be twice the computational cost of one gradient computation of a full-waveform inversion algorithm. The factor of two occurs because two propagations are needed to backproject the image perturbations into the slowness model along both the source wavepaths and the receiver wavepaths.

The data-handling task could be simplified if the frequency-domain downward-continuation migration is used instead of reverse-time migration, because computations can be performed independently for each frequency. The adaptation of the theory presented in this paper to downward-continuation migration is fairly straightforward. It would only require to exchange expressions 1 and A-4 with the corresponding frequency-domain expressions.

Wave-equation migration velocity analysis by residual moveout fitting