Estimation of fracture-strike azimuth by QVOA analysis validated by simulated seismic data of physical modeling

Abstract

Vertical fractures cause azimuthal anisotropy. To predict the fractures’ azimuth, we use anisotropy analysis of the seismic attribute QVOA. The QVOA means “Q Versus Offset (θ) and Azimuth (φ)”. Q is a quality factor. The inverse (or the reciprocal) of the quality factor (Q-1) is a measure of the attenuation of the seismic-wave energy. When analysing the azimuthal variation of attenuation, 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). We derive an updated QVOA method to achieve the highest accuracy in estimation of the fracture-strike angle. The method is based on a new formula for the Q-1(θ,φ)-attenuation function, which gives the highest accuracy in estimating the azimuth of fractures by the least-squares method (LSM). As a sought-for parameter, we consider the fractures’ azimuth (φ0). In the former version of QVOA method, we used a simplified approximation formula of the attenuation function in the form A + Bx + Cx2 (where x = sin2θ cos2(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 the attenuation function, which gives the best accuracy of 0.25 degrees, which is validated by simulated seismic data of physical modelling. To test our QVOA method we use seismic data simulated by ultrasonic experiment. An artificial sample of fractured rock is built in the form of a four-layer cake model, which is immersed in water. Inside this layer cake there is an insert with artificial vertical aligned cracks. The Q-data on the attenuation are estimated along three seismic lines with 3 azimuths of the source-receiver line, φ = 0°, φ = 45°, and φ = 90°. To estimate the fracture-strike φ0-azimuth, we use the least squares method (LSM), namely, we minimize the functional of the difference between the theoretical function Q-1(θ,φ) and the real attenuation estimated from seismic data. The canonical formula results in the smallest and the most stable error (compared to the older versions of QVOA-method). The maximal attenuation is obtained at the φ = 0°-azimuth, which is the direction orthogonal to the fracture strike; and the minimal attenuation is at the φ0 = 90°, which is the fracture-strike. Thus, the experiment fully confirms the QVOA-method.