Seismic Characterization of Rock Fractures by Q-Anisotropy Analysis (QVOA) Validated by Numerical Simulation

We develop a seismic-exploration method based on the phenomenon of seismic anisotropy; namely we deal with the azimuthal anisotropy induced by vertical fractures. The network of aligned vertical fractures causes not only the anisotropy of seismic-wave velocity, but also the anisotropy of attenuation of the wave energy (i.e., the so-called Q-anisotropy). The task of estimating the fractures’ characteristics is very important both at the exploration stage and the oil recovery. In particular, in hydraulic fracturing, the sought-for fracture azimuth points the direction of maximum horizontal hydraulic permeability. To predict the fractures’ azimuth, we develop the anisotropy analysis of Q Versus Offset and Azimuth (QVOA). Q is the quality factor. The reciprocal of the quality factor (Q−1) is a measure of the attenuation. When analyzing the azimuthal variation of Q, it is considered that a fractured reservoir can be represented as a model of a transversally isotropic medium with a horizontal axis of symmetry (HTI). The azimuthal variation of Q is described by our updated QVOA equation, from which we estimate the fracture-strike azimuth φ0. To validate the newly upgraded QVOA-method we use synthetic seismic data for a 3D viscoelastic medium. From the synthetic seismic signatures, we estimate the Q−1-attenuation for five different azimuths (φ) of source-receiver lines, as a function of the wave-incidence angle θ. Based on our upgraded attenuation function Q−1(θ, φ) derived (which we will call the “Canonical” equation throughout the paper), we develop the least-squares method to estimate the φ0-azimuth of fractures. As a result, the Canonical equation gives high accuracy in the computation of the fractures’ azimuth φ0, with absolute error (Δφ0) of only one degree. In addition, we also perform the QVOA-testing for the data with the 10%-Gaussian noise added into the seismic signatures. In the case of noise, the Canonical formula is more stable than its older versions and yields very high accuracy Δφ0 =  \(0.24^{\circ }\) , while the old approaches give large errors, Δφ0 =  \(4^{\circ }\) (the complete equation), and Δφ0 =  \(3^{\circ }\) (its concise approximation).