Sensitivities of the Rayleigh and Love Phase Velocities and Attenuation Coefficients

Abstract

In situ characterization of dynamic soil characteristics by means of surface wave tests frequently involves the determination and inversion of dispersion and attenuation curves. The inverse problem is formulated as a non-linear least-squares problem minimizing the misfit between theoretical and experimentally obtained dispersion and attenuation curves, which is often solved using gradient-based techniques. A new analytical and computationally efficient methodology is presented for the determination of the sensitivities of the Rayleigh and Love phase velocities and attenuation coefficients with respect to the shear wave velocity, the dilatational wave velocity, the material damping ratios in volumetric and shear deformation, and the thickness of the layers. The expressions are based on the direct stiffness method for elastodynamic wave propagation. The proposed analytical method requires only a fraction of the calculation cost of the dispersion and attenuation curves. Sensitivities of Rayleigh dispersion and attenuation curves are computed for four soil profiles, including two shallow soil profiles, a very deep profile, and an inverse profile with a soft layer trapped in between two stiffer layers. Results obtained with the proposed method are shown to be in perfect correspondence with sensitivities reported in the literature and obtained with a finite difference method.