Some properties of partial derivatives of the Love wave dispersion function

Abstract

The paper is systematically presents how, by applying the implicit function theorem, the problem of determining partial derivatives of the phase and group velocities of the Love surface wave is reduced to the derivation of the dispersion function with respect to independent variables. In addition to that, two relations are derived which are valid among the partial derivatives of the dispersion function of the Love wave phase velocity in a n+1 layered solid medium according to independent variables. It is shown that these relations serve to check the numerical values of the partial derivatives, and they can be used for checking computer programmes of the linear inversion structure calculation.