A high speed algorithm for computation of frequency-wavenuniber (f-k) spectra is developed, and two real-time infrasonic data processing techniques that it makes possible, are described: (1) Signal detection by a search of f-k space. This process is compared to the N-4 correlator, a broad-band signal detector. The f-k search with a Fisher detector has a theoretical advantage, which we verify in practice.(2) An f-k filter technique for calculating ' best beam ' estimates. This technique traces the beam containing maximum power, from frequency to frequency through f-k space, and thus allows for wandering of signal velocity and arrival azimuth. This maximum power function is taken as the frequency spectrum of the best beam. In our programs the Fisher statistic of the signal estimate, and the velocity and azimuth, are computed and displayed as functions of frequency. Examples from real data for both processing techniques are discussed.
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An entirely analytic single-station surface-wave processor is developed that analyzes long-period seismic records two orders of magnitude faster than real time on an IBM 360/44.coaputer. In processing four days of continuous synthetic data the algorithm detected 85% of the 170 signals of S/N -½, with false alarm rate of one per day. A novel detectioi~ theory is in--troduced that exploits the consistency of the azimuthal estimates associated with a sequence of detections .
Two-dimensional cross-sections of finite frequency-wavenumber spectra can easily be misinterpreted, since leakage of energy occurs along lines of constant wavenumber. In particular, the signal phase velocity determined from measurements on cross-sections normal to the frequency axis can be incorrect. We discuss an algorithm which corrects this situation. Examples using real and synthetic data are given.
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