"Analysis of Rayleigh Waves and Surface Ellipticity: A New Numerical Approach for Comparing Existing Formulas in Literature"

Résumé

Rayleigh waves are also fundamental in geophysics, seismology and material science, e.g. when studying the behaviour of surface waves in anisotropic and orthotropic materials. Surface ellipticity, which is one of the main features of Rayleigh waves, is a vital property of the latter that can be applied in applications such as seismic inversion and subsurface imaging. A novel numerical approach to the comparison between the discrete least squares approximation (DLSA) of Chebyshev-Gauss-Lobatto (CGL) nodes and the already known aspect ratio formulas of Rayleigh wave surface ellipticity are given in this work.

We also use the numerical approximations in DLSA in order to test a number of analytical formulations in the literature in a systematic way and to establish their accuracy. The CGL node usage also decreases numerical stability and interpolation error by refining numerical inaccuracies in the approximation of surface ellipticities functions. The results indicate that there are significant variations among the existing formulas and there is a need to have the better models in special material conditions. Moreover, the suggested numerical solution provides a sound methodology of testing analytical equations of Rayleigh wave ellipticity in various waves propagation conditions.

This work demonstrates the effectiveness of DLSA in CGL nodes to the problem of wave mechanics and provides new insights into the comparative effectiveness of existing equations. The findings are used to add to the predictive modeling of surface wave behavior to be used in material science, engineering and geophysics.