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The statistical theory of signal detection and estimation has been applied to problems in large array seismology. Using this theory the structure of the optimum detector for a known signal and long observation time in additive Gaussian noise is derived. The array processing filter employed by the optimum detector is known as the maximum-likelihood filter. This filter also has the property that it provides a minimum-variance unbiased estimate for the input signal when it is not known, which is the same as the maximum-likelihood estimate of the signal if the noise is a multidimensional Gaussian process. A series of experiments was performed using data from the large aperture seismic array to determine the effectiveness of the maximum-likelihood method relative to simpler methods such as beam-forming. These results provide significant conclusions regarding the design and processing of data from large seismic arrays. The conventional and high-resolution estimation of the frequency-wavenumber spectrum of the background microseismic noise is also presented. The diffuse structure of this spectrum is shown to aid in explaining the relative performance of array processing methods.