Random boundary condition for low-frequency wave propagation

Introduction

A random boundary condition (Clapp, 2009) is attractive in Reverse Time Migration (RTM) imaging, since it generates time-reversible wavefields that scatter incoherently from boundaries. The advantage of the random boundary condition is that the receiver wavefield can be first propagated from max-time to 0 , then simultaneously propagated with the source wavefield from 0 , to max-time. This eliminates the need to either store the entire wavefield on disk, or use checkpointing schemes at the cost of an extra propagation. Such reduction in memory requirement is particularly suitable for implementation on novel hardwares such as GPUs (Micikevicius, 2008). The incoherent nature of the reflections off the random boundary creates random correlations when the imaging condition is applied, resulting in little to no degradation of the final image.

In theory, this random boundary condition can be easily extended to wavefields at all temporal frequency ranges. However, due to memory and computational requirements, overly large boundary regions are unfavorable. Therefore, problems arise when we move to low frequencies. In that case, increased spatial wavelengths mandate larger boundary regions if we are to use the same random boundary scheme. For low-frequency applications such as waveform inversion, if we can keep the size of the random boundary approximately the same as that used in RTM, computational efficiency will be greatly improved, especially in 3D by avoiding extra computation of waves propagating in the boundary domain. In this paper, we introduce a scheme of perturbing the grain shape of the random boundary condition to keep the boundary region small but still effective with low frequency wave propagation. The same random boundary is also effective for high-frequency wave propagation. We briefly discuss the theory and illustrate the method using synthetic examples.

Random boundary condition for low-frequency wave propagation