Accuracy of adaptive maximum likelihood algorithm for determination of micro earthquake source coordinates using surface array data in condition of strong coherent noise

In the paper (Kushnir et al., Int J Geomath 4(2):201–225, 2013) we offered the mathematically rigorous justification of the adaptive algorithm for statistical estimation of parameters of micro-earthquake source based on data recorded by a surface array of seismic receivers. The algorithm exploits the popular statistical Maximum Likelihood approach for determination of unknown parameters of probability distribution of a multichannel data generated by micro-earthquake source and registered by the surface array in the presence of strong noise. In this paper we consider unique properties of the mentioned adaptive maximum-likelihood estimator (AMLE) in conditions when the noise affecting the surface array receivers contains strong time-spatially correlated (coherent) component of man-made origin. These conditions are typical when AMLE algorithm is implemented for location of the micro-earthquakes caused by the medium hydraulic fracturing at hydrocarbon deposit sites. In the mentioned conditions AMLE algorithm demonstrates capability to suppress coherent noise component and hence to significantly improve the accuracy of determination of the coordinates of micro-earthquake sources. In the paper we theoretically investigate the signal-to-noise ratio (SNR) of AMLE statistic and show that this SNR tends to infinity while seismic noise becomes purely coherent. We have undertaken also the computer simulation of the micro-earthquake location with the help of AMLE algorithm using deployment of the 150 seismic receivers which corresponds geometry of a real USA surface seismic array. For this array we computed the model multidimensional realizations of the micro-earthquake signal, the coherent man-made noise component and the natural noise component. The results of this computer simulation have shown that in conditions when the power of the coherent man-made component of the modeled noise significantly exceeds the power of the natural component of this noise the errors of micro-earthquake source position determination become negligible.