Efficient wavefield reconstruction at half the Nyquist rate

We have developed a simple method to halve the memory required to store the forward wavefield for the imaging condition in adjoint-state methods such as reverse time migration and full-waveform inversion. It stores the wavefield at only half the Nyquist rate, and it uses the wave equation to calculate the second time derivative, allowing approximate reconstruction of the forward wavefield at the required Nyquist rate. We have determined that the method produces an image with the Marmousi model that is not visibly different compared to a traditional (full Nyquist) implementation.