A numerical tour of wave propagation

Computation strategies and boundary saving

There are several possible ways to do RTM computation. The simplest one may be just storing the forward modeled wavefields on the disk, and reading them for imaging condition in the backward propagation steps. This approach requires frequent disk I/O and has been replaced by wavefield reconstruction method. The so-called wavefield reconstruction method is a way to recover the wavefield via backward reconstructing or forward remodeling, using the saved wavefield shots and boundaries. It is of special value for GPU computing because saving the data in device variables eliminates data transfer between CPU and GPU. By saving the last two wavefield snaps and the boundaries, one can reconstruct the wavefield of every time step, in time-reversal order. The checkpointing technique becomes very useful to further reduce the storage (Dussaud et al., 2008; Symes, 2007). It is also possible to avert the issue of boundary saving by applying the random boundary condition, which may bring some noises in the migrated image (Liu et al., 2013b; Clapp, 2009; Liu et al., 2013a; Clapp et al., 2010).

Yang et al. (2014) proposed an effective boundary for regular and staggered-grid finite differences. In the case of regular grid finite difference of order $2N$ , we need to save $N$ points on each inner side in the model zone to reconstruct the wavefield. For staggered grid finite difference of order $2N$ , we need to save $2N-1$ points on each inner in the model for perfect reconstruction. The concept of effective boundary saving does not depends on C or GPU implementation. However, it is of special value for GPU implemenation, because it eliminates the CPU-GPU data transfer for boundary saving. An example of effective boundary saving for regular grid finite difference is given in Figure 10. The imaging examples using effective boundary saving with staggered-grid finite difference can be found in the next section.

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Figure 10. The forward modeled wavefield can be exactly reconstructed using effective boundary saving.

A numerical tour of wave propagation