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.

Upper mantle anisotropy from long‐period P polarization

“…A singular value decomposition of the eigenspectra matrix produces, in the presence of a well-polarized signal, one large singular value which is associated with a complex vector defining the direction and phase of particle motion. Multitaper spectral analysis has been applied to complex surface wave and regional body wave signals [Laske et at., 1994;Park et at., 1987a]. In our study, the measurements were performed on P onsets with a high signal-to-noise ratio, which are very simple and linearly polarized, so that some of the characteristics of multitaper analysis (stability with respect to incoherent noise and minimization of spectral leakage) are unneccessary; still, it provides an advantage over simpler techniques [Vitiate, 1986;Jurkevics, 1988] in that it gives a measure of the uncertainty associated with each measurement [Park et at., 1987a].…”

“…We used a multitaper frequency domain technique [Park et at., 1987a] to measure the direction of particle motion within one cycle of the P onset (Figure 1).…”

Attenuation tomography in the western central Andes: A detailed insight into the structure of a magmatic arc

“…Amplitude spectra of 2.56 s time windows following and preceding the first break of the P waves of each seismogram (signal and noise) were calculated using the multitaper approach [Park et al, 1987]. Figure 3 shows the observations of an arbitrary event.…”

The development of enhanced ripple-fire identification methods using high frequency data from Pinedale

“…We chose to focus on the program developed by researchers at UCSD (Hedlin et al, 1989(Hedlin et al, ,1990. In doing their research, Hedlin et al used techruques from previous papers (Baumgardt and Ziegler, 1988;Park et al, 1987) that they felt were valuable, such as using an adaptive multitaper algorithm for spectral estimates to help minimize leakage from outside a pre-specified bandwidth. They also introduced the use of a binary sonogram (Figure l), which may be a first step toward automating the discrimination process.…”

“…Events that look similar and come from a similar direction could be grouped. But the method that has the most promise looks for modulations in the spectrum that result from a technique usedin quany blasting called "ripple-fire" (park et al, 1987;Baumgardt and Ziegler, 1988;Smith, 1989;Hedlin et al, 1989Hedlin et al, , 1990Kim et al, 1994). Ripple fire is a technique that maximizes the amount of rock and product (i.e.…”