Comparison of wave-propagation simulations in fractured domains using discrete fractures and equivalent media

Fractures largely control reservoir permeability and, therefore, it is of immediate importance to know the geometrical parameters of fracture sets and their effects on seismic data. To understand the interaction between the fractures and seismic wavefield, we performed numerical simulations of elastic wave propagation in fractured digital rocks (FDRs) using the discontinuous Galerkin method, the linear-slip model and sets of randomly distributed fractures. We compared the results with those obtained using Hudson's equivalent media theory (HEM) and observed that, when the fracture density is 0.08 or less, there is no statistical difference between the FDR and HEM results; however, when the fracture density is higher than 0.08, the results of HEM diverge from those of FDR. Furthermore, HEM accuracy depends not only on the fracture density but also on the P- to S-wave velocity ratio. The P-wave anisotropy induced by the fractures is observed as a delay, which can be due to fracture density, length or a mixture of both. The Pwave is delayed in all directions, but mostly in the direction perpendicular to the fractures' orientation.