Q factors estimated with spectral ratios describe the attenuation experienced by seismic arrivals in their travel from the source(s) to the receiver(s). When Q is not the same along the travel path of each arrival, the formulation must incorporate two Q factors making the problem indeterminate. Here we show that by assuming that Q is a random variable, the parameters of its probability distribution can be recovered through a mapping workflow using the spectral ratios. An advantage of such a workflow is that uncertainties in source location and velocity model can also be incorporated by representing these elements as random variables. We apply such a methodology to an acoustic emission (AE) data set from a laboratory experiment of hydraulic fracturing in a Colton sandstone block. We assume that the probability distribution of Q is normal. Anisotropic mean (μQ) values correlate with the triaxial stress conditions imposed at the boundaries of the block, with higher stress corresponding with less attenuation. The μQ values estimated within time intervals in the direction perpendicular to the hydraulic fracture plane correlate with stress buildup at the borehole during fracture propagation and borehole pressure relaxation or drop during fracture closure. The standard deviations (σQ) reflect the attenuation heterogeneity within the sampled regions. An increase in heterogeneity is correlated with pressure buildup at the borehole, which we interpret to reflect a dynamic stress gradient formed from the hydraulic fracture toward the surroundings.
- acoustic emissions
- hydraulic fracturing