Abstract：Multiple scattering effect of elastic waves propagating in rocks with defects is studied theoretically and numerically. First, a double elliptical model is established to describe the multiple scattering paths of elastic wave between two elliptical defects. Second, the wave equations and boundary conditions on the defect interface governing opening displacement generating scattering field are derived based on the basic solution of Green function and the boundary integral method. The opening displacement of the defect boundary induced by the interaction of waves and defects are characterized in terms of a "stiffness matrix" that depends on both the incident harmonic and material properties. The problem of multiple scattering of elastic wave propagation in rocks is then analyzed for the dispersion and attenuation in order to evaluate the multiple scattering effect on the wave speed and amplitude. The calculation results show that compared with the single elliptical defect model, the dispersion and attenuation of the elastic wave are stronger due to the effect of multi-scattering. Moreover, the affected region of a defect is given quantitatively about six times of characteristic scale of the defect, which is basically consistent with the macro porosity limit of multiple scattering. This scale separates the multiple scattering strong interaction from the linear superposition of the single scattering effect. The multi-scale effect of elastic wave propagation is further discussed. It is found that the frequency of Rayleigh peak, Mie peak on the dispersion curve and attenuation peak has a definite quantitative relationship with the ratio of the long axis of the ellipse to the incident wavelength. The corresponding numerical simulation results show that the interaction between elastic wave and defect induces the interface wave at the defect interface, and the frequency dependence of these interface waves affects the dispersion and attenuation characteristics of the macroscopic propagation of elastic wave. Within this double defect model, the multiple scattering for interaction of the elastic waves and the defect can enhance dispersion and attenuation.
2022, Vol. 43 
