A fast, accurate method for computing group-velocity partial derivatives for Rayleigh and Love modes

Abstract

Abstract A method for quickly and accurately calculating Rayleigh- and Love-mode group-velocity partial derivatives with respect to model parameters (m) is developed. The method requires computer codes that calculate C, U, and ∂C∂m|ω and employs numerical differentiation of ∂C∂m|ω to yield ∂U∂m|ω. The method is fast because ∂C∂m|ω and ∂U∂m|ω for all the model parameters can be obtained at a given frequency from only two solutions of the period equation. The accuracy of the method is established with two examples. For Love waves, the group-velocity partials computed by this method agree exactly with those obtained analytically by Novotny (1970). For Rayleigh waves, comparison with a “brute force” calculation of group-velocity partials showed agreement to the order of 0.00002. Systematic inversion of group-velocity data separately or in combination with phase-velocity data is computationally feasible using this method.