Perturbational and nonperturbational inversion of Love-wave velocities

We describe a set of MATLAB codes to forward model and invert Love-wave phase or group velocities. The forward modeling is based on a finite-element method in the frequency-wavenumber domain, and we obtain the different modes with an eigenvector-eigenvalue solver. We examine the issue of parasitic modes that arises for modeling Love waves, in contrast to the Rayleigh wave case, and how to discern parasitic from physical modes. Once the matrix eigenvector-eigenvalue problem has been solved for Love waves, we show a straightforward technique to obtain sensitivity kernels for S-wave velocity and density. In practice, the sensitivity of Love waves to density is relatively small and inversions only aim to estimate the S-wave velocity. Two types of inversion accompany the forward-modeling codes: One is a perturbational scheme for updating an initial model, and the other is a nonperturbational method that is well-suited for defining a good initial model. The codes are able to implement an optimal nonuniform layering designed for Love waves, invert combinations of phase and group velocity measurements of any mode, and seamlessly handle the transition from guided to leaky modes below the cutoff frequency. Two software examples demonstrate use of the codes at near-surface and crustal scales.