Numerical Modelling of Elastic Waves based on the Asymmetric Wave Equations

Abstract

It is a trend in the development of geophysics to seek wave theory closer to the physical reality and derive corresponding wave equations to achieve the high accurate forward modelling, imaging, and inversion of complex structures. The generalized continuum mechanics (GCM) theory enriches the context of the conventional continuum mechanics theory by introducing the additional characteristic length scale parameters to represent the microstructural properties of the medium, and the asymmetric elastic wave equations derived from GCM theory can handle the influence of heterogeneity of medium caused by the microstructure interactions on propagation of seismic waves. Up to the present stage, there are few researches on the numerical and analytical solutions of the elastic wave equations derived from the GCM theory, especially in the frequency band of seismic exploration. In addition, there are few studies in the existing literature that incorporate multiple theories and methods of the GCM theory into an integrated frame. In this paper, we introduce the concept of the multi-scale microstructure interactions and construct quantitative relationship between the characteristic length scale parameter and the characteristic length scale parameter of the micropore reflects the micropore structures, and then integrate the modified couple stress theory and the one-parameter second strain gradient theory into the unified framework for numerical modelling and analysis.