Surface Wave Dispersion

One of the important characteristics of surface wave arises from the way in which they disperse. The figure below shows two different waves with the same total energy, but the longer wavelength has its energy spread out over a larger interval.

If earth materials’ elastic parameters yield higher velocities with depth, longer wavelength surface waves will travel faster than those with shorter wavelengths. The variation of velocities with wavelength makes it possible to infer critical information about the subsurface. We recognize two different velocity in the study of wave dispersion: group velocity and phase velocity.

Phase and group velocity are both dependent on wavelength and are related by the equation.

We usually use phase velocities in surface wave inversion as it is easier to construct a dispersion curve of phase velocities that group velocities. The properties derived from the inversion are the Lame parameters which will be used to to relate stress to strain.