Numerical Modeling of Wave Equations Derived from the Generalized Continuum Mechanics Theory

摘要

A trend in the development of geophysics is to seek wave theory closer to the physical reality and derive corresponding wave equations to achieve highly accurate forward modeling, 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 a medium caused by the microstructural interactions on the propagation of seismic waves. To date, there are few studies 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 microstructural interactions and construct the quantitative relationship between the characteristic length scale parameter of the medium and the characteristic length scale parameter of the micro-pore reflecting the micro-pore structures, and then integrate the modified couple stress theory and the one-parameter second strain gradient theory into a unified framework for numerical modeling and analysis.