In fractured reservoir development, azimuthal AVO (AVOaz) properties of reflected PP waves from reservoir tops are often used to infer fracture properties. The fracture parameter inversion is based on either effective media model (EMM) or discrete fracture model (DFM). We address the differences in fracture properties that may be inferred by AVOaz based on the two models. We focus on fractures whose length and spacing are comparable to the seismic wavelength. First, we compute the elastic parameters describing the fractured reservoir. Then we synthesize seismic data using a finite-difference program for both sets of elastic parameters. By performing AVOaz analysis, we find that EMM and DFM predict different optimal offsets for maximal magnitudes of AVOaz. The DFM results show larger AVOaz magnitude with farther offsets. Phase changes at offsets larger than 35 degrees may indicate compliant fractures in a reservoir. Fracture strike determined using AVOaz based on EMM may be normal to the true strike. DFM may be better suited for modeling wavelength-scale fractures.
Geophysicists commonly use effective media theory to delineate seismic properties of formations with vertically aligned fractures to interpret the seismic amplitude and velocity variations with azimuth and offset (Lynn, 2004). The azimuthal AVO (AVOaz) properties of reflected PP waves have been used to identify fracture orientation (Shen et al., 2002). However, the effective media model (EMM) is valid for media with small fractures -- relative to the seismic wavelength (Lynn, 2004, Liu et al., 2000). For fractures whose lengths are comparable to seismic wavelength, discrete fracture models (DFM) are more realistic (Coates and Schoenberg, 1995). Willis et al. (2004) used the DFM and scattered seismic energy to determine spatial orientation and distribution of reservoir fractures. They applied their method to synthetic and field data and showed robust and high quality results consistent with log data. They computed their synthetic data using DFM. In this study, we compare the AVOaz characteristics of a fractured medium characterized by (1) small fractures (EMM) and (2) discrete fractures (DFM). We use finite difference modeling to calculate the synthetic seismograms.
We generate the 3-D full-azimuth, synthetic seismograms using finite-difference calculation. The finite-difference code uses a rotated staggered grid (RSG) (Saenger, 2004). The RSG method can represent accurately large contrast of elastic moduli between the fracture and surrounding formation. We also apply the perfectly matched layer absorbing boundary condition to minimize boundary reflections (Marcinkovich and Olsen, 2003). Figure 1 shows the schematics of the physical model: a soft formation with Vp = 2460 m/s, Vs = 1230 m/s, and density= 2300 kg/m3 with an embedded 100 meter thick fractured layer. The fractured layer can be represented as an equivalent transversely isotropic medium with a horizontal symmetry axis. We assume the same fracture density, aperture, and fluid inclusion for EMM and DFM. For EMM, we use the method of Liu et al. (2000) to calculate the media properties. For DFM, we compute the elastic constants using the method of Coates and Schoenberg (1995). We create four different fracture spacing models: 20m, 30m, 40m, and 50m.
