Stratification effects on nonlinear elastic surface waves

Details Stratification effects on nonlinear elastic surface waves Stratification effects on nonlinear elastic surface waves

Jan 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988pepi...50...16p&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 50, Issue 1, p. 16-25.

Physics

5

Scientific paper

On a homogeneous elastic half-space, linear surface waves are nondispersive. In each direction, waves having any profile travel without distortion. Nonlinearity causes intermodulation between the various wavelengths so that the signal distorts. Even when nonlinearity is small, sinusoidal profiles do not remain approximately sinusoidal. The absence of dispersion means that profiles suffer cumulative distortion, until the surface slope and strain become locally unbounded. Although this behaviour is typical of many signals, there are some signals for which intermodulation is constructive. These signals can travel coherently over large distances.
For seismological applications, it is important to study the effects due to stratification. Dependence of the material constants on depth modifies the nonlinear evolution equations previously derived for homogeneous media. It has a smaller effect on higher frequencies than on lower frequencies. An approximate theory for short wavelength (high frequency) signals is introduced. Calculations show that when nonlinearity is no more important than dispersion, initially sinusoidal profiles propagate with surface slope remaining finite. When dispersion is small compared to nonlinearity, certain sharp peaked profiles can travel large distances while suffering little distortion.

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