Modified Thomson-Haskell Matrix Methods for Surface-Wave Dispersion-Curve Calculation and Their Accelerated Root-Searching Schemes

In this paper we introduce two modified Thomson–Haskell matrix (TH) methods for dispersion-curve calculation of the Rayleigh and Love waves: the doubled Thomson–Haskell matrix method (DTH) for the Rayleigh wave and the nor-malized Thomson–Haskell matrix method (NTH) for the Love wave. Both DTH and NTH keep the brevity of the original TH method. They remedy the high-frequency numerical instability of the dispersion-curve calculation of surface waves by compul-sorily setting some positive exponential terms to be zeros and doing some proper normalization. The validity of these methods is tested. The capability of these methods to calculate the dispersion curves in high frequencies is illustrated. We also introduce an auxiliary function to accelerate the calculation of the dispersion curves of the sur-face waves. Compared with the conventional root-searching scheme, our scheme apparently speeds up the root search. Both of the modified TH methods are deduced in vertical transversely isotropic (VTI) media. The impact of surface-wave disper-sion due to VTI anisotropy is investigated. The modified TH methods and their root-searching schemes are expected to be a useful tool for investigating the anisotropy and simulating complete seismograms of VTI media.