A note on formulas for the Rayleigh wave speed in elastic solids

Area of Science:

• Geophysics
• Seismology
• Wave Propagation

Background:

• Rayleigh waves are crucial for understanding seismic wave behavior.
• Accurate determination of Rayleigh wave speed is essential in geophysics.
• Existing methods for calculating wave speed have limitations.

Purpose of the Study:

• To present new analytical, numerical, and approximate methods for determining Rayleigh wave speed.
• To provide exact expressions for Rayleigh wave roots in isotropic media.
• To enhance the accuracy of Rayleigh wave speed calculations in both isotropic and anisotropic media.

Main Methods:

• Lagrange's method for exact root expressions in isotropic media.
• A non-iterative quadrature method for numerical determination in isotropic and anisotropic media.
• Discrete least squares approximation using Chebyshev-Gauss-Lobatto nodes for improved approximations.

Main Results:

• Exact expressions for Rayleigh wave roots in isotropic media were derived.
• Numerical methods were successfully applied to determine wave speeds in isotropic and anisotropic media.
• An approximate method demonstrated improved accuracy in Rayleigh wave speed calculations.

Conclusions:

• The presented methods offer accurate and efficient ways to determine Rayleigh wave speed.
• These techniques are applicable to both isotropic and anisotropic geological media.
• The study contributes to advancing seismic wave analysis and geophysical modeling.