Abstract

This paper is concerned with detection of seismic phases and refining arrival times of phases in noise using seismic array data. The first problem is treated as testing hypotheses about statistical properties of seismic signal and noise. The optimal detector is designed for the case where the signal-to-noise ratio is small. The detecting algorithm includes a generalized version of the Capon optimal beamforming procedure, computation of a quadratic form from several first values of the sample beam trace autocovariance function, and a triggering when the quadratic form exceeds a threshold. The practical implementation of the detector can yield a significant increase in detection reliability for the case where seismic noise has high coherence, provided the noise matrix power spectral density (MPSD) is known or is periodically estimated by a special adaptation procedure. A computationally efficient and statistically precise estimate of MPSD is developed on the basis of multidimensional autoregression modeling. The signal-to-noise ratio gain of optimal beamforming procedure and its adaptive version are compared with the gain of conventional beamforming by a theoretical study and by Monte-Carlo simulation. The capability of adaptive optimal beamforming to refine seismic signal from noise is confirmed by processing of seismic noise and earthquake $P$-wave data recorded at NORSAR array.