A note on calculating Rayleigh wave velocity and the derivative of the Rayleigh determinant in elastic media

There are many approximate and exact formulae to calculate surface wave velocity in an elastic medium. An analytical expression for Rayleigh wave velocity in volume wave velocity values has been obtained. A formula which determines the remainder in the excitation and diffraction of surface acoustic waves in a homogeneous isotropic elastic half-space involving solutions for the strain and stress fields in the form of quadratures is worked out. The values of the Rayleigh wave velocity and the derivative of the Rayleigh determinant for different media according to the reference data were obtained. The results can help in obtaining analytic expressions and reducing the calculation time of numerical solutions of the diffraction and excitation of acoustic waves.