Elastic Wave Propagation in Geological Media Embedded With Discrete Fractures Following Power Law Length Scaling

This paper studies the behaviour of elastic waves in fractured geological media. The length distribution of natural fractures is characterized by a power law whose exponent defines the relative proportion of large and small fractures in the system. A series of two-dimensional discrete fracture networks (DFNs) associated with a fixed length exponent of 2.5 but different fracture density values is generated to represent various connectivity states of fracture networks. Each discrete fracture is then represented using a rectangular-shaped thin layer associated with equivalent elastic properties in the context of a continuum-based numerical framework and an unstructured mesh discretization. The wave propagation and scattering processes in the fractured rocks are simulated using the finite element method. The numerical model is validated against analytical solutions of the reflection and transmission coefficients of elastic waves for a single fracture. By further sending and receiving elastic wave signals in DFNs, the relationship between wave parameters (e.g. amplitude, wavefield and waveform) and fracture properties (percolation parameter and fracture normal/shear stiffness) is explored. The research findings of this paper have important implications for geophysical engineering practice of interpreting in-situ wave data and detecting subsurface geological structures.