MULTITAPER SPECTRAL-ANALYSIS OF HIGH-FREQUENCY SEISMOGRAMS
MULTITAPER SPECTRAL-ANALYSIS OF HIGH-FREQUENCY SEISMOGRAMS
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DOI：
10.1029/jb092ib12p12675
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发表时间：
1987-11-10
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影响因子：
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通讯作者：
VERNON, FL
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作者：
PARK, J;LINDBERG, CR;VERNON, FL
在各种工程数据中，采用多个长球面序列作为锥度的光谱估计程序已被证明比标准的单锥度光谱分析产生更好的结果。我们将Thomson（1982）的自适应多锥度谱估计方法应用于许多高分辨率数字地震记录，并将结果与使用标准单锥度谱估计获得的结果进行比较。单锥度平滑谱估计受到估计方差和频谱泄漏引起的偏差之间权衡的困扰。应用渐变来减少偏差会丢弃数据，增加估计的方差。使用锥也不均匀取样记录。从记录的末端抛出数据可能导致频谱估计不能充分代表非平稳过程（如地震波形）的频谱特征。例如，对非锥形记录进行离散傅里叶变换（即，使用箱形锥度）可以对震源频谱的大振幅部分进行合理的频谱估计，但不能可靠地提供高频滚降的良好估计。记录的离散傅里叶变换乘以更严重的锥度（如汉恩锥度），可以抵抗频谱泄漏，从而得到高频频谱滚降的可靠估计，但这种估计对分析数据的权重不相等。因此，受泄漏影响较小的单锥度估计器不仅会增加方差，而且还会歪曲非平稳数据的光谱。自适应多锥度算法在这些极值之间自动调整。我们利用Anza遥测地震台网仪器记录的16位地震数据证明了它的优势。我们还提出了一项分析，证明了多锥度算法在提供低方差谱估计方面的优势，该算法具有良好的抗泄漏性，不会过度强调记录的中心部分。
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.