Mathematically, the simplest hyperbolic partial differential equation is the constant density acoustic wave equation. The basis for using this particular wave equation [2] will be developed further. Because the computational effort of solving three dimensional problems ([16] Chapter 10 and [15] Chapter 1) exceeds most computing environments, this study will primarily focus on one and two dimensional problems. All the techniques and algorithms presented here can be directly extended to three dimensions.

The constant density assumption simplifies model representation: only a sound speed is required. The earth density variation is important for modeling and imaging. However, neglecting density variation will still provide a useful wave equation. One additional comment about earth parameters: surface measurements using physical methods use potential fields, gravity for example. These physical measurements are of a different scale compared to reflection seismology. The seismic data wavelength has sufficient resolution for structural imaging. Resolution of the seismic experiment is a direct function of the wavelength; the shorter the wave length the higher the resolution.