This paper presents a theoretical comparison of the backazimuth and velocity estimation performance of arrays and three-component stations in severe noise conditions. Theoretical estimates of performance for low signal-to-noise ratios (SNRs) are validated through simulation. The high SNR limits of array performance are determined through an empirical study of 23 events at a single source location. Theory and simulation indicate a gradual and uniform deterioration in three-component station performance as the SNR is decreased, beginning at relatively high SNR. At very low SNR, the signal is overwhelmed by the noise, and the performance reaches an asymptotic plateau determined by a priori physical limitations on the velocity of incident waves. By contrast, arrays exhibit a sharp transition between a high SNR performance floor determined, presumably, by scattering effects in the signal, and a low SNR plateau. The SNR threshold for the transition in array performance is low enough that a band of SNRs exist for which arrays have usefully small direction and velocity errors, but three-component stations do not.

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