Guided elastic waves produced by a periodically joined interface in a rock mass

Abstract

Mining-induced seismic events pose a serious risk to workers in deep mines. Accurate numerical simulations are useful in analyzing the problem and developing mitigation strategies. Here we tackle the problem of guided interfacial elastic wave propagation in a periodically joined interface of two half spaces. The problem is viewed as a mixed boundary-condition plane strain problem and a displacement discontinuity model is used to model the boundary condition. The coupled set of first order linear differential equations for stress and velocity for an elastic continuum are replaced by an explicit finite difference scheme that is implemented on a regular rectangular staggered grid. Phase velocity dispersion curves for the guided interfacial wave modes are obtained via a phase spectra analysis method. The analysis reveals that longer wavelengths travel faster than shorter ones and that the phase velocity dispersion curve is a function of many model parameters including: source type (shear or dilatation), source time function, inherent periodicity at the model interface and size of periodic strips joining the interface. Lastly, we observe that the medium acts like some sort of “soft” frequency filter.