Deployment of networks at the surface or/and in wells to monitor the seismicity induced in underground reservoirs is common. The goals are to better image and characterize the reservoir and to mitigate the seismic hazard. With low coverage network, however, event location using only observed arrival times is either poorly constrained or not constrained at all, and may not bring any value. This is typical from borehole monitoring of hydraulic fracturing operations that requires using the seismic wave polarization to indicate the event direction of arrivals.

Within a Bayesian framework, we propose a probabilistic formulation to integrate correctly the P-wave polarization for hypocentre determination. We take a single three-component sensor perspective and assume that the covariance matrix measured around the P-wave quantifies the polarization. This matrix contains all necessary axial information including uncertainties. Using directional statistics, we can define the so-called angular central Gaussian (ACG) likelihood that quantifies the probability density function associated with a modelled polarization vector given the observed covariance matrix.

The ACG formulation eliminates physical issues existing in current formulations. It is simple, easy to implement and offers an “all-in-one” solution including spatial dependencies and uncertainties that lead to smaller location uncertainties.


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