The rest of this chapter is organized in the following manner:

- The first order wave equation is presented.
- The wave equation is developed from first principles.
- Model results for a one dimensional problem are used to illustrate the reflection coefficient.
- A matrix formulation for computing difference weights is reviewed.
- The seismic source is presented as a numerical method to produce realistic seismic waves with a finite duration in time and limited in bandwidth.
- A geological model is defined and two methods are presented which reduce unwanted reflections from the model boundaries.
- The exploding reflector model is introduced as a method to generate a synthetic seismogram.
- The ``reverse'' time imaging concept is presented to process the synthetic seismic data.
- The seismic modeling and imaging codes are introduced with
operating instructions and several example models.

The seismic data are too complex to visualize as numbers so visualization tools are provided to help in understanding the modeling and imaging process.