This paper investigates Q-anisotropy for characterizing fractured reservoirs — specifically, the variation of the seismic quality factor Q versus offset and azimuth (QVOA). We derive an analytical expression for P-wave attenuation in a transversely isotropic medium with horizontal symmetry axis (HTI) and provide a method (QVOA) for estimating fracture direction from azimuthally varying Q in PP-wave reflection data. The QVOA formula is similar to Rüger's approximation for PP-wave reflection coefficients, the theoretical basis for amplitude variation with angle offset (AVOA) analysis. The technique for QVOA analysis is similar to azimuthal AVO analysis. We introduce two new seismic attributes: Q versus offset (QVO) gradient and intercept. QVO gradient inversion not only indicates fracture orientation but also characterizes Q-anisotropy. We relate the Q-anisotropy parameter to fractured-medium parameters and invert the QVO gradient to estimate . The attenuation parameter and Thomsen-style anisotropy parameter are found to be interdependent. The attenuation anisotropy magnitude strongly depends on the host rock's parameter, whereas the dependence on fracture parameters is weak. This complicates the QVO gradient inversion for the fracture parameters. This result is independent of the attenuation mechanism. To illustrate the QVOA method in synthetic data, we use Hudson's first-order effective-medium model of a dissipative fractured reservoir with fluid flow between aligned cracks and random pores as a possible mechanism for P-wave attenuation.