A finite-element algorithm with a perfectly matched layer boundary condition for seismic modelling in a diffusive-viscous medium

Seismic numerical modelling involved in each stage of seismic exploration process is aimed at predicting seismograms in an assumed subsurface medium. The energies and phases of waves vary with the presence of fluids, while the frequency-dependent seismic reflections in a reservoir with hydrocarbons was explained using the diffusive-viscous wave (DVW) equation. We proposed a Galerkin finite-element method (FEM) to numerically study the propagation properties of the DVW in fluid-filled media to ascertain the influences of saturated fluids on characteristics of the wavefield. We also theoretically analysed the numerical dispersion and stability condition of the FEM algorithm, which indicated that a minimum of six nodes per wavelength is recommended to achieve more accurate results. In numerical simulation, we presented a non-split perfectly matched layer (NPML) boundary condition for the DVW equation to absorb the artificial reflections in finite-element modelling, using a homogeneous model to demonstrate the effectiveness of the NPML boundary condition through comparisons with the results without the PML condition. Moreover, we modelled the DVW propagation in a fluid-saturated (gas, oil and water) medium with sharp edges and curved interfaces using the proposed method and compared the results with those pertaining to acoustic waves. The numerical results indicated significant amplitude damping and phase variation in the DVW when it propagates across the fluid-saturated layers compared with those of acoustic waves. Furthermore, we compared the numerical results in the fluid-saturated model calculated via the FEM with those calculated via FCT-FDM (flux corrected transport-finite-difference method) to demonstrate the validity of the former.