Frictional slip wave solutions for dynamic sliding between a layer and a half-space

Abstract

Interfacial waves propagate along the interface between two elastic solids, and are the subject of basic interest to diverse scientific fields, like, seismology, geophysics, material science and composite structures. The focus of the present work is to analyse the interfacial waves arising due to frictional slipping between an elastic layer and an elastic half-space having dissimilar elastic properties, wherein the deformations are confined to the plane of the solids. The interfacial friction is modelled by employing a slip-dependent friction law. The elastodynamic relations between the displacement discontinuities across the fractured interface and the associated traction components of stress for pure slip events (no crack opening along the interface) are obtained. This allows us to derive a secular dispersion relation governing the interfacial wave solutions. The dispersion relation relating the phase velocity and wavenumber is analysed numerically. A family of solutions are shown to exist depending on the critical slip distance, δc, a parameter governing the interfacial friction law, and on the contrast in material properties. We demonstrate the existence of a number of wave modes, all being dispersive in nature. The fundamental wave mode with the lowest phase velocity exists over the largest range of wavenumbers, while other wave modes exist only at sufficiently high non-dimensional wavenumber. The dispersion curves for the frictional slip waves are found to lie between the dispersion curves for the cases of the smooth and the bonded interface. As a case study, the present model is used to study the dispersion of slip waves propagating in Earth's crust-mantle geophysical model. The field observations of surface wave dispersion appear to be in good agreement with that of the frictional slip waves studied here. Based on our results, we suggest an alternative explanation for the observed surface wave dispersion at the regional and global scales. It is suggested that frictional slip waves at the crust-mantle interface could propagate with phase velocities similar to the Rayleigh and Love surface waves.