Modelling of two-dimensional seismic waves in double-porosity media using the frequency-domain finite-element method

We present a frequency-domain finite-element (FDFE) method for simulating PSV-mode seismic waves (including two slow compressional waves) in 2-D double-porosity media. A functional, whose extremum corresponds to the governing equations with boundary conditions for 2-D PSV waves, is constructed. Solving the boundary value problem of the governing equations is thus equivalent to finding the extremum of the associated functional. We use structured rectangular elements to discretize the computational domain and employ perfectly matched layers (PMLs) to absorb the seismic waves. The FDFE method is validated by comparing the results with those from a semi-analytic method. Numerical simulations are conducted to investigate the propagation of seismic waves in double-porosity media. Assuming a non-viscous pore fluid, we simulate the propagation of slow P waves (P2 and P3 waves) in a two-layer model consisting of double-porosity media. We observe the reflection and transmission of the P2 and P3 waves at the interface. Additionally, we simulate the propagation of seismic waves in a model with irregular interfaces. Seismic signals collected from horizontal and vertical receiver arrays have demonstrated that the P1 wave experiences higher attenuation in a double-porosity medium.