Detecting harmonic signals in a noisy time series: The z-domain AutoRegressive (AR-z)spectrum
Detecting harmonic signals in a noisy time series: The z-domain AutoRegressive (AR-z)spectrum
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DOI：
10.1093/gji/ggv077
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发表时间：
2015-06
影响因子：
2.8
通讯作者：
H. Ding;B. Chao
中科院分区：
文献类型：
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作者：
H. Ding;B. Chao
对Chao&Gilbert的AR方法进行了扩展，提出了一种检测含噪时间序列中含有指数衰减/增长的谐波信号的AR-z谱方法。该方法包括：(I)对于任何选择的频率，无论是否真的存在信号，都将一个二阶ARfit‘盲目地’强加于频域中的信号内容；(Ii)在复z域中对对应的AR(复共轭对)极点进行fi；(Iii)通过Prony关系将极点位置转换为相应的谐波信号的复频率，以及(Iv)构造z域中的洛伦兹功率谱，概念上构成从(实)频域到复数z域的频谱的解析延拓，其中真正的谐波信号表现为洛伦兹峰值。AR-Z谱可以通过根据可用的多个记录形成产品谱来进一步增强。我们应用AR-z谱方法，利用近期大地震后的超导重力仪记录，检测和估计了地球自由振动简正波的复频率。具体地，我们给出了探测和精确估计0 S 2、2 S 1、1 S 2和0 S 0的分裂单态频率和Q值的例子，并报道了0 T2、0 T3和0 T4环状模的重力仪记录所表现出的模耦合。与传统的傅立叶谱相比，AR-z谱对衰减正弦波的谐波信号具有很高的灵敏度，特别是在信号较弱和需要高频谱分辨率的情况下。
We develop a new method referred to as the AR-z spectrum for detecting harmonic signals with exponential decay/growth contained in a noisy time-series by extending the autoregressive (AR) method of Chao & Gilbert. The method consists of (i) ‘blindly’ forcing one 2nd-order AR fit to the signal content in the frequency domain for any chosen frequency whether or not there is truly a signal; (ii) finding the corresponding AR (complex-conjugate pair of) poles in the complex z -domain; (iii) converting the pole locations into the corresponding complex frequencies of the harmonic signals via the Prony’s relation and (iv) constructing the Lorentzian power spectrum in the z -domain, conceptually constituting the analytical continuation of the spectrum from the (real) frequency domain to the complex z -domain, where a true harmonic signal is manifested as a Lorentzian peak. The AR-z spectrum can be further enhanced by forming the product spectrum from multiple records as available. We apply the AR-z spectral method to detect and to estimate the complex frequencies of the Earth’s normal-modes of free oscillation using superconducting gravimeter records after recent large earthquakes. Specifically we show examples of detection and precise estimation of the frequencies and Q values of the split singlets of the spheroidal modes 0 S 2 , 2 S 1 , 1 S 2 and 0 S 0 , and report the mode couplings manifested by the gravimeter recording of the toroidal modes 0 T 2 , 0 T 3 and 0 T 4 . The AR-z spectrum proves to be highly sensitive for harmonic signal of decaying sinusoids in comparison to the conventional Fourier-based spectrum, particularly when the signal in is weak and where high spectral resolution is desired.