Passive surface microseismic monitoring as a statistical problem: location of weak microseismic signals in the presence of strongly correlated noise

In this paper, we treat passive surface microseismic monitoring as a predominantly statistical problem of location sources of weak seismicity recorded in the presence of strongly correlated noise using dense seismic arrays. We introduce two statistically optimal algorithms (adaptive maximal likelihood algorithm and statistically optimal phase algorithm) and show that the traditional semblance-based microseismic processing algorithm (Seismic Emission Tomography) is just an extreme case of the maximal likelihood algorithm for Gaussian white noise (i.e., noise that is stationary and uncorrelated in time and space). We evaluate location uncertainties of all three microseismic algorithms for different types of noise patterns and signal-to-noise ratios. For Gaussian white noise, the Seismic Emission Tomography algorithm performs well, demonstrating even slightly better location accuracy than statistically optimal techniques. Actual noise affecting seismic sensors during hydraulic fracturing is non-stationary. It is correlated in time and space, and varies greatly in power and spectral content for different sensors of the array. We use Monte Carlo simulation to show that the location accuracy of statistically optimal algorithms can be 20 to 40 times better than for the Seismic Emission Tomography algorithm in the presence of man-made surface noise during hydraulic fracturing.