Introduction
In this study we build three numerical models based on the Discrete Fracture Model (DFM) method with the finite difference (FD) scheme for two purposes as follow: the azimuthal AVO analysis on the PP reflection of the top of the fractured layer, and the estimation of scattering attenuation of the reflection from the bottom of the fractured layer. These models include a vertical fracture model, an orthogonal fracture model, and an isotropic model, which is for comparison (referred as VFM, OFM and IM respectively). First we observe that the distribution pattern of coda waves from either wavefield snaps or shot sections, due to the presence of the fractures, changes with the azimuth and the spacial structure of the fractures in the two fractured models. Azimuthal AVO variation reveals that the compliant fractures lower the magnitude of the PP reflection amplitudes in the two fractured models compared with the IM, and in the VFM we find the magnitude of the reflection amplitudes is smaller in the normal direction of the fracture strike than in other direction, which may indicate the fracture strike. In the case of two or more vertical fracture sets, the magnitude is even smaller. Frequency analysis of the reflection from the bottom of the fractured layer shows that the dominant frequency shifts to lower frequency with the increase of the offset. However, the estimation of the scattering attenuation is very small in the two fractured models.
Two major effective theories of fracture models, the Effective Medium Model (EMM) and the Discrete Fracture Model (DFM), have been developed in the inversion of the properties of fractured medium since 20 years ago. The theory of the EMM is valid for the small penny-size cracks embedded in isotropic background medium (Hudson, 1981), and the seismic wavelength involved are assumed to be large compared with the size of the cracks and with the separation distance. With the EMM, a fractured/cracked medium is modeled as a homogenous anisotropic medium, which means it cannot simulate the behavior of an individual fracture in the host medium while the DFM can. The DFM deals with the compliant fractures which have vanishing thickness, and their spacing is comparable to the seismic wavelength (Schoenberg, 1980; Schoenberg & Sayers, 1995). Theoretically, the host medium for fractures with the DFM can be any kind of anisotropic medium (Coates & Schoenberg, 1995). The studies based on the DFM are very limited, especially in the case of the 3D medium with two of more sets of fractures. Only in recent years some studies have been carried out based the DFM to investigate wave propagation through fractures, such as wavefield signature, coda wave pattern, scattering attenuation, azimuthal AVO and anisotropy intensity. Vlastos et al. (2003) applied this scheme to study the effect of different fracture spatial distribution on the seismic response. And also Vlastos et al. (2003) had built three 2D fractured models to study scattering attenuation at the different stages of the fracture evolution.
