SUMMARYThe measurements of fracture parameters, such as fracture orientation, fracture density and fracture compliance, in a reservoir is very important for field development and exploration. Traditional seismic methods for fracture characterization include shear wave birefringence Dok et al., 2001;Angerer et al., 2002;Vetri et al., 2003) and amplitude variations with offset and azimuth (AVOA) (Ruger, 1998;Shen et al., 2002;Hall et al., 2003;Liu et al., 2010;Lynn et al., 2010). These methods are based on the equivalent medium theory with the assumption that fracture dimension and spacing are small relative to the seismic wave length, so a fracture zone behaves like an equivalent anisotropic medium. But fractures on the order of seismic wave length are also very important for enhanced oil recovery, and they are one of the important subsurface scattering sources that generate scattered seismic waves. Willis et al. (2006) developed the Scattering Index method to extract the fracture scattering characteristics by calculating the transfer funtion of a fracture zone. Fang et al. (2011) proposed a modification of the SI method (the Fracture Transfer Function (FTF) method) that leads to a more robust fracture characterization. In this paper, we use both laboratory data and field data to explore the capability of the FTF method.
METHODOLOGYThe transfer function of a fractured layer is expressed as where O 1 (ω, θ ) and O 2 (ω, θ ), respectively, are the stacked data from above and below the fracture zone in azimuth θ , O 0 1 (ω) and O 0 2 (ω) are the averages of O 1 (ω, θ ) and O 2 (ω, θ ) over all azimuths, wl is water level.The spatial variation of the strength of fracture scattered waves shows characteristics related to fracture spacing due to interference (Willis et al., 2005;Grandi et al., 2007;Zheng et al., 2011). Fracture scattered waves are observed to be stronger at frequencieswhere FS is fracture spacing and V is velocity.f n is defined as the n-th eigen-frequency of the fracture zone in our study, and f 1 = V 2·FS is the base eigen-frequency. From both laboratory experiments and numerical simulations, we find that, in the direction normal to fracture strike, due to the disruptive nature of fracture scattered waves, notches can be found in FT F at the eigen-frequencies after stacking, in the fracture strike direction, the scattered waves can stack constructively, so peaks appear at the eigen-frequencies after stacking. So the azimuthal variation of FT F(ω, θ ) is larger at the eigen-frequencies given by Equation 2. The eigen-frequencies and the azimuthal variation of FT F after stacking give information about both fracture orientation and spacing.In order to quantify the azimuthal variation of FT F(ω, θ ), which can be used to determine the fracture orientation, we define the fracture orientation function aswhere θ is azimuth, [ω 1 , ω 2 ] is frequency window, the weighting function SDFT F(ω) is the azimuthal standard deviation of FT F, FT F(ω) is the mean of the FT F at frequency ω, N is the number of azimuth...