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A (Rayleigh) dispersion curve consists of phase velocities at different frequencies that represent theoretically possible propagation modes of (Rayleigh) surface waves. For a given frequency, there are multiple phase velocities at which surface waves can travel; the slowest velocity is called the fundamental mode (M0), the next higher velocity is called the 1st higher mode (M1), the next higher one is called the 2nd higher mode (M2), and so on. Collection of such phase velocities of the same mode is called the fundamental-mode (M0) dispersion curve, the first higher mode the (M1) dispersion curve, and so on. In theory, the ultimate governing equation that predicts possible phase velocities at a given frequency is the elastic-wave equation (Sheriff and Geldart, 1982). A derived formulation predicts that phase velocities are determined by solving a characteristic equation (also called "dispersion function") of a layered-earth model that consists of shear-wave velocity (Vs), compressional-wave velocity (Vp), and density (rho) parameters assigned to horizontally homogeneous layers of different thicknesses (h's). In practice, however, numerical approaches are taken to find the closest values ("roots") to the theoretical solutions. According to Schwab and Knopoff (1972), roots to the dispersion function are searched by continuously changing the possible phase velocity for a given frequency until the function becomes the opposite sign—a numerical method called the bisection (Press et al., 1992).
This module of the ParkSEIS calculates Rayleigh-wave dispersion curves based on the FORTRAN IV program presented in Schwab and Knopoff (1972).