Seismic imaging is a multibillion-dollar industry aimed at extracting information about the Earth interior from reflected seismic waves. Fundamentally, the task of reflection imaging is to take measured seismic waves from multiple experiments with moving sources and receivers on the surface and to extrapolate the waves numerically back in time and space to the moment of their reflection. This problem leads to novel partial-differential and pseudo-differential equations describing different parts of the imaging process. A constructive way for numerical wave extrapolation follows from a low-rank approximation of Fourier symbols.