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.

We present a multitaper algorithm to estimate the polarization of particle motion as a function of frequency from three‐component seismic data. This algorithm is based on a singular value decomposition of a matrix of eigenspectra at a given frequency. The right complex eigenvector truezˆ corresonding to the largest singular value of the matrix has the same direction as the dominant polarization of seismic motion at that frequency. The elements of the polarization vector truezˆ specify the relative amplitudes and phases of motion measured along the recorded components within a chosen frequency band. The width of this frequency band is determined by the time‐bandwidth product of the prolate spheroidal tapers used in the analysis. We manipulate the components of truezˆ to determine the apparent azimuth and angle of incidence of seismic motion as a function of frequency. The orthogonality of the eigentapers allows one to calculate easily uncertainties in the estimated azimuth and angle of incidence. We apply this algorithm to data from the Anza Seismic Telemetered Array in the frequency band 0 ≤ ƒ ≤ 30 Hz. The polarization is not always a smooth function of frequency and can exhibit sharp jumps, suggesting the existence of scattered modes within the crustal waveguide and/or receiver site resonances.

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We present a new method for estimating the frequencies of the Earth's free oscillations. This method is an extension of the techniques of Thomson (1982) for finding the harmonic components of a time series. Optimal tapers for reducing the spectral leakage of decaying sinusoids immersed in white noise are derived. Multiplying the data by the best K tapers creates K time series. A decaying sinusoid model is fit t o the K time series by a least squares procedure. A statistical F-test is performed to test the fit of the decaying sinusoid model, and thus determine the probability that there are coherent oscillationsin the data. The F-test is performed at a number of chosen frequencies, producing a measure of the certainty that there is a decaying sinusoid at each frequency. We compare this method with the conventional technique employing a discrete Fourier transform of a cosine-tapered time-series. The multiple-taper method is found t o be a more sensitive detector of decaying sinusoids in a time series contaminated by white noise.