Seismic sources usually excite a continuous spectrum of surface-wave periods.  Each harmonic component has a velocity     c(ω), called a phase velocity where ω=2πf (radian frequency) that depends on the medium parameters (layer thickness, P and/or S velocities, etc.). Wave disturbances with a wide spectrum of periods interfere with each other producing constructive and destructive patterns.  Constructive patterns travel along the surface as wave packets with well-defined group, U(ω), that depend on the medium parameters and the variation in phase velocity with frequency.  Group velocity curves often have a local minimum at 20 and 200 seconds period known as an Airy phase and results from a large amount of energy arriving at the same time.  The techniques for these measurements will be discussed in greater detail on the phase velocity and group velocity pages

Geometric spreading produced by earth structure is the main reason for using dispersion as a tool.  It allows the dispersive nature of surface waves to be compared to theoretical models to try and understand what the best fitting structure is beneath an area of interest.

Here are the equations for group and phase velocities: