F-K Characteristics of the Seismic Response to a Set of Discrete Parallel Fractures

Abstract

We model seismic wave propagation in a reservoir with discrete fracture zones using a finite difference scheme, which implements the Coates-Schoenberg formulation for fractured media. We study the variation of scattered energy in the direction perpendicular and parallel to the fracture strike. In the modeled data, we observe variations in the coherence of seismic energy and interference between backward and forward scattered energy. We then sorted data from the Emilio field in Italy in azimuthal gathers. These panels show a striking qualitative resemblance to the modeled data. We conclude that, in this case, a discrete representation of the fractures in the reservoir predicts the observation in the field data well. This supports the idea that fractures can cluster into fracture zones that scatter seismic energy. We then analyze the seismic energy on a profile in the direction perpendicular to the fracture strike. First we use estimated scattered energy in a window around the target zone to estimate the spacing between large fracture zones. The scattered energy in a later time window is shown to consist of mainly P to S scattered energy. For the estimation of smaller spacings, we rely on the smaller wavelength of these converted waves to illuminate finer structure. The result of spacing estimation is not very sensitive to the time window from which we estimate the scattered energy, because, in f-k domain, the wavenumber values of the dominant backscattered energy within successive time windows are almost the same, but frequency content drops gradually. Finally we apply this analysis to field data from Emilio Oil Field, and estimate a fracture spacing of about 40 m.