Colored Noise in DOA Estimation from Seismic Data: an Empirical Study

Estimation of the direction of arrival (DOA) of a seismic signal is required for accurate localization of seismic events, such as earthquakes and human-made explosions. Currently, seismic DOA estimation algorithms are based on the assumption that the additive seismic noise is uncorrelated between sensors. However, in this paper we show by analyzing real data sets that seismic sensors exhibit noise correlation. We calculate a robust estimator of the noise covariance matrix from off-line real data. Then, we present three estimators: 1) the seismic-wave DOA maximum likelihood estimator (MLE) that acknowledges the correlated noise between sensors; 2) the MLE for uncorrelated noise with spherical covariance matrix; and 3) the beamforming Bartlett estimator, which is the method used in seismic applications. We show by numerical simulations on real-data statistics that DOA estimates that do not consider these correlations depart from the true direction and have significantly higher values of mean-squared-error and bias.