Numerical simulation of the propagation of P waves in fractured media

We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such probl ems is the ratio between crack length and incident wavelength. When the wav elength of the incident wavefield is close to or shorter than the crack len gth, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simu late the anisotropic behaviour of fractured media resulting from the scatte ring of seismic waves by the cracks through the time delay of the arrival o f the transmitted wave. The method of calculation used is a boundary elemen t method in which the Green's functions are computed by the discrete wavenu mber method. For simplicity, the 2-D elastodynamic diffraction problem is c onsidered. The rock matrix is supposed to be elastic, isotropic and homogen eous, while the cracks are all empty and have the same length and strike di rection. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order t o reduce the computation time. The attenuation factor Q(-1) of the direct w aves passing through a fractured zone is measured in several frequency band s. We observe that the attenuation factor Q(-1) of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, a nd decreases proportionally to (kd)(-1) in the high-wavenumber range. In th e long-wavelength domain, the velocity of the direct P wave measured for tw o different crack realizations is very close to the value predicted by Huds on's theory on the overall elastic properties of fractured materials.