Fracture-direction estimation by QVOA analysis: Validation by physical modeling

We study anisotropy of P-wave attenuation that is Q-anisotropy, and develop an approach named QVOA (seismic quality factor Q versus offset and azimuth) to estimate the fracture-strike direction identified by the azimuth ?0. We derive QVOA formula Q^-1(?, ?) for the P-wave attenuation Q^-1 as a function of the polar angle ? and azimuth ?, and test Q^-1(?,?) using physical modeling data. Our testing consists of fitting a function Q^-1(?, ?) to the data from the physical modeling, using the method of least squares. The QVOA-formula gives the most accurate estimation of the direction ?0 of the HTI-symmetry axis in comparison with other approximation formula. The values of velocity and attenuation are, in some sense, reciprocals of each other: the attenuation is greatest in the direction of the HTI-symmetry axis ?0=0°, where the velocity is least, and vice versa at the orthogonal direction ?=90°, which is the fracture-strike direction. That is, the azimuth of the minimal attenuation ?=90° coincides with the direction of the fracture strike (?=90°), where the velocity is maximal.