Multitaper spectral analysis of high‐frequency seismograms

Abstract

Spectral estimation procedures which employ several prolate spheroidal sequences as tapers have been shown to yield better results than standard single‐taper spectral analysis when used on a variety of engineering data. We apply the adaptive multitaper spectral estimation method of Thomson (1982) to a number of high‐resolution digital seismic records and compare the results to those obtained using standard single‐taper spectral estimates. Single‐taper smoothed‐spectrum estimates are plagued by a trade‐off between the variance of the estimate and the bias caused by spectral leakage. Applying a taper to reduce bias discards data, increasing the variance of the estimate. Using a taper also unevenly samples the record. Throwing out data from the ends of the record can result in a spectral estimate which does not adequately represent the character of the spectrum of nonstationary processes like seismic waveforms. For example, a discrete Fourier transform of an untapered record (i.e., using a boxcar taper) produces a reasonable spectral estimate of the large‐amplitude portion of the seismic source spectrum but cannot be trusted to provide a good estimate of the high‐frequency roll‐off. A discrete Fourier transform of the record multiplied by a more severe taper (like the Hann taper) which is resistant to spectral leakage leads to a reliable estimate of high‐frequency spectral roll‐off, but this estimate weights the analyzed data unequally. Therefore single‐taper estimators which are less affected by leakage not only have increased variance but also can misrepresent the spectra of nonstationary data. The adaptive multitaper algorithm automatically adjusts between these extremes. We demonstrate its advantages using 16‐bit seismic data recorded by instruments in the Anza Telemetered Seismic Network. We also present an analysis demonstrating the superiority of the multitaper algorithm in providing low‐variance spectral estimates with good leakage resistance which do not overemphasize the central portion of the record.