Summary
Vertical fractures cause azimuthal anisotropy. To predict the fractures’ azimuth, we use anisotropy analysis of four seismic attributes: NMOA, AVOA, QVOA and Shear-Wave-Splitting (SWS). Namely: the first NMOA-attribute means "Normal-Move-Out velocity versus Azimuth". The second attribute AVOА stands for "Amplitude Versus Offset and Azimuth". The amplitude is understood as the reflection coefficient of the longitudinal (PP) wave. In the SWS analysis, we separate two shear waves from each other (S1 and S2). The S1 -wave has its polarization vector parallel to the plane of the fractures, and the other (S2) is perpendicular. The delay time Δt between the S1-wave and the S2 -wave is proportional to the fracture concentration. Regarding the NMOA, the unequal time of arrival of the PP-wave in different azimuths is due to the velocity anisotropy induced by fractures. The azimuthal variation of the NMO velocity is described by the NMO ellipse. The spatial time-field surface for the reflected PP-wave can be represented as a hyperboloid with an elliptical section, which is the so-called NMO ellipse. The minor axis of the ellipse points to the fractures’ azimuth (α0). In addition, the AVOA attribute is used for fracture characterization. The azimuthal variation of the AVO gradient can be represented as an ellipse, whose minor axis (Bmin) shows the fracture direction azimuth. We can estimate the concentration of fractures by the value of its major axis (Bmax). We apply an integrated approach, that is, the analysis of four anisotropy attributes: NMOA, AVOA, SWS and QVOA. The QVOA-attribute means "Q Versus Offset and Azimuth". Q is a quality factor. The inverse (the reciprocal) of the quality factor 1/Q is a measure of the attenuation of the seismic-wave energy. When analyzing the azimuthal variation of an anisotropy attribute, it is considered that a fractured reservoir can be represented as a model of a transversely isotropic medium with a horizontal axis of symmetry (HTI). With regard to the latter QVOA method, we come to the conclusion that in order to achieve the highest accuracy in the angle of the fracture-direction estimation, it is best to use our new "canonical" formula derived for the Q−1(θ, φ)-attenuation function, which gives the highest accuracy in estimating the azimuth of the fracture direction compared to its former approximations. In the former version of QVOA method, we used a simplified approximation formula of the attenuation (Q−1(θ, φ)) in the form A + Bx + Cx2, (where x = sin2θcos2(φ − φ0), as well as its truncated approximation A + Bx. However, to achieve the highest accuracy in estimating fracture direction, it is best to use our new "canonical" formula of Q−1(θ, φ)-function, which gives the best accuracy in estimating the azimuth angle of fractures’ direction compared to those simple approximations. Thus, our improved QVOA method gives an excellent absolute accuracy of more than 0.25 degrees.
