Reading wavefield checkpoints from disk is quickly becoming the bottleneck in Reverse Time Migration. We eliminate the need to write the wavefields to disk by creating an increasingly random boundary around the computational domain when propagating source function. The wave-field that encounters the boundary region is pseudo-randomized. Reflections off the random layer have minimal coherent correlation with the receiver wave-field but can be reformed by running the wave equation in the reverse direction. This allows the source to first be propagated to the maximum recording time and then to be backward propagated simultaneously with receiver wave-field significantly reducing memory and IO requirements. We demonstrate the methodology on the Sigsbee synthetic and show that it it significantly reduces coherent correlations.
Reverse Time Migration (RTM) (Baysal et al., 1983) is quickly becoming the standard for high-end imaging. At the core of the RTM algorithm is a modeling kernel. The simplicity of the the modeling kernel has led to high-performance implementation on Field Programmable Gate Arrays (FPGA) (Nemeth et al., 2008), General Processing Graphics Processing Units (GPGPU) (Micikevicius, 2008), and conventional processors. Of growing significance is the problem that the source field must propagated from t = 0 to t = maxtime while the receiver wavefield must be propagated from t = maxtime to t = 0 yet the fields must be correlated at equivalent time positions. As a result, one propagation must be stored either completely or in a check-pointed manner to disk.
Symes (2007) and Dussaud et al. (2008) discuss checkpointing methods to handle the different propagation directions. Dussaud et al. (2008) and Clapp (2008) suggest an alternate approach of propagating the source wavefield to the maximum recording time and then reversing the propagation to make it consistent with the receiver propagation direction. The use of damping schemes around the boundary result in the need to inject energy from the non-damped, forward propagated wavefield, inside the boundary region. The RAM requirement with this scheme is less than conventional checkpointing approaches but still imposes significant disk IO requirements.
In this paper, we discuss an alternate approach. We replace the conventional damped region with an increasingly random velocity region. Rather than eliminate reflections we distort them to minimize coherent correlations with the receiver wavefield. We begin by describing the construction of the random boundary. We then demonstrate the amplitude behavior of the time reversed wavefield. We conclude by showing the methodology applied to a 2-D synthetic.
The basic idea behind RTM is to propagate a source function within the computational domain from time t = 0 to t = maxtime, storing the wavefield s(t,
) at time steps consistent with the time sampling of the data dt. The recorded data is injected into a second computational domain and propagated from t = maxtime to t = 0 and stored in r(t,
). The final image I is constructed or some similar imaging condition. The problem is that s(t,
) and r(t,
) are too large to store in memory and often too large store on disk.
