Sensitivity analysis of leaky-mode dispersion curves for horizontal stratified models

SUMMARY The leaky-mode dispersion extracted from seismograms and noise cross-correlation functions has gained lots of attention in recent years. It has been reported that leaky modes can provide constraints for subsurface structures, especially for P-wave velocities, which may compensate for the limits of traditional surface wave methods. For stable and reliable dispersion-curve inversion, the quantitative analysis of leaky-mode sensitivity is of great importance, which, however, has rarely been studied systematically. Limited by the forward modelling methods, the previous methods for calculating leaky-mode sensitivity are usually hindered by issues of mode skipping, low efficiency, etc. To this end, we propose an effective method that can calculate the leaky-mode sensitivity for various types of models based on the previously proposed forward modelling method named the semi-analytical spectral element method (SASEM). Using the intermediate results of SASEM, we derive analytical expressions for the sensitivity kernels with only matrix operations, which endows the sensitivity calculation procedure with high accuracy and reliability identical to the SASEM. In addition, we suggest a novel modal classification scheme to distinguish different kinds of leaky modes based on the sensitivity features. This scheme facilitates the stable identification of the most attractive guided-P modes from numerous normal and leaky modes, which removes obstacles in the dispersion-curve inversion using guided-P modes to constrain P-wave velocities. Several numerical tests are performed to demonstrate the high accuracy of the sensitivity calculation method and the effectiveness of the modal classification method. To assess the roles of leaky modes in the retrieval of underground structures, we perform comprehensive sensitivity analyses of leaky modes using both crust-scale and near-surface models. Besides the general conclusion that the joint inversion using normal and leaky modes can effectively retrieve P- and S-wave velocities, the feasibility of constraining models with the apparent Σ modes and the split guided-P mode dispersion curves has been demonstrated.