The theory of Love-and Rayleigh-wave dispersion for plane-layered earth models has undergone a number of developments since the initial work of Thomson and Haskell. Most of these were concerned with computational difficulties associated with numerical overflow and loss of precision at high frequencies in the original Thomson-Haskell formalism. Several seemingly distinct approaches have been followed, including the delta matrix, reduced delta matrix, Schwab-Knopoff, fast SchwabKnopoff, Kennett's Reflection-Transmission Matrix and Abo-Zena methods. This paper analyses all these methods in detail and finds explicit transformations connecting them. It is shown that they are essentially equivalent and, contrary to some claims made, each solves the loss of precision problem equally well. This is demonstrated both theoretically and computationally. By extracting the best computational features of the various methods, we develop a new algorithm (see Appendix A5), called the fast delta matrix algorithm. To date, this is the simplest and most efficient algorithm for surface-wave dispersion computations (see Fig. 4).The theory given in this paper provides a complete review of the principal methods developed for Love-and Rayleigh-wave dispersion of free modes in plane-layered perfectly elastic, isotropic earth models and puts to rest controversies that have arisen with regard to computational stability.

Summary This paper is concerned with the dispersion of Love and Rayleigh waves in multilayered models with smooth and weakly non‐parallel boundaries. Perturbation formulae for the phase, frequency, wavenumber, phase velocity, group velocity and amplitude are derived from first‐order perturbation theory of Whitham’s equation for dispersive waves in non‐uniform media. Derivation of the average Lagrangian for Love and Rayleigh waves is obtained as required by the perturbation formulae. Explicit formulae are given for Love waves in the long‐wavelength limit and comparisons with related studies are made. In order to demonstrate the results, numerical calculations for the perturbation in frequency, wavenumber, amplitude and phase are performed. The models consist of non‐uniform media of one and two layers over a half‐space. The perturbed parameter is the layer depth, sampled at different locations.

No abstract

No abstract

No abstract