Improved approximations for the Rayleigh wave velocity in [-1, 0.5]

Abstract

In the present paper we derive improved approximations for the Rayleigh wave velocity in the interval $\nu \in$ [−1, 0.5] using the method of least squares. In particular: (i) We create approximate polynomials of order 4, 5, 6 whose maximum percentage errors are 0.035 %, 0.015 %, 0.0083 %, respectively. (2i) Improved approximations in the form of the inverse of polynomials of order 3, 5 are also established. They are approximations with very high accuracy. (3i) By using the best approximate second-order polynomial of the cubic power in the space $C$[0.474572, 0.912622], we derive an approximation that is the best, so far, of the approximations obtained by approximating the secular equation.