Yale University
Department of Statistics

Monday, October 9, 1995
Jonathan Lees, Department of Geology & Geophysics, Yale University

"Waveform Clustering and Spectral Analysis in Earthquake Seismology"

Seminar to be held in Room 107, 24 Hillhouse Ave at 4:15 pm

The nature of coherency between seismic signals recorded in tight arrays is investigated by reorganizing data via waveform cluster analysis. Multitaper spectral estimates and coherency functions suggest that pair-wise coherency between stations located only a few meters apart at Pinyon Flat, CA, is low above approximately 15 Hz. This observation is examined in detail by searching for clusters of similar waveforms using single link cluster analysis on suites of stations located in the high frequency, 60 station deployment of 1990. The analysis requires that noisy line spectra, introduced by instrument noise and shallow resonances be removed prior to analysis. This is accomplished by reshaping spectra to remove biases associated with smearing periodic signals in the frequency domain. Following Thomson's multi-taper methodology, an automated procedure for removal of periodic signals is presented. The technique is general and may be applied to other signal analysis problems where line spectra represent a significant biasing effect. Cluster analysis is performed on coherency and correlation scores derived from the multi-taper analysis of the 60 signals in the surface and borehole arrays. The cluster analysis shows that while simple pair-wise comparisons of coherency suggests that local scattering dominates the spectrum above 15 Hz, spatial clustering indicates that there is more structure in arriving waveforms than is apparent in the simple analysis. At Pinyon Flat, stations that are clustered together spatially also cluster in coherency score, at frequencies as high as 50 Hz. By re-arranging seismograms according to their associated clusters, signals along the north-south and east-west arms of the Pinyon Flat high frequency array are separable at frequencies ranging from 5-50 Hz. An additional cross-correlation score further manages to differentiate waveform clusters over time windows of length 0.5-1.0 seconds. After waveforms are re-organized by cluster the differences in waveforms across the array are apparent by visual examination. These observations have important implications for the use of high frequency seismic spectra in determination of source and path effects for small magnitude, local earthquake analyses.