Algorithms for synthesizing seismic data abound. Here we will focus on four: ray-based, finite-difference, finite-element, and Fourier domain based methods. Of course, one can construct algorithms in various combinations of these domains so it is technically possible to develop approaches that work with finite-differences in frequency-space or even perhaps time and spatial frequency. Once the basic concepts for the four are fully developed, pursuing alternative domain combinations is relative straightforward.
To keep the discussion as simple as possible we will focus all of our attention on the two-dimensional versions of Equation 17 or the coupled system Equation 36.
