Among many improvements on phase velocity computation of Rayleigh waves in a layered Earth model, the methods based on reflection and transmission (R/T) coefficients produce stable and accurate phase velocities for both low and high frequencies and are appropriate for viscoelastic and anisotropic media. The generalized R/T coefficient methods are not the most efficient algorithms. This paper presents a new, more efficient algorithm called the fast-generalized R/T coefficient method to calculate the phase velocity of surface waves for a layered Earth model. The improvements include (1) computation of the generalized R/T coefficients without calculation of the modified R/T coefficients, and (2) presentation of an analytic solution for the inverse of the 4×4 layer matrix E. Compared with the traditional generalized R/T coefficient method, the fast-generalized R/T coefficient method, when applied on Rayleigh waves, significantly improves the speed of computation, cutting the computational time at least by half while keeping the stability and accuracy of the traditional method.

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