Detecting harmonic signals in a noisy time-series: the z-domain Autoregressive (AR-z) spectrum

Abd El-Gelil, 2010, Normal mode detection and splitting after Sumatra–Andaman earthquake, J. Geodyn., 50, 49, 10.1016/j.jog.2010.02.003

Buland, 1978, Improved resolution of complex eigenfrequencies in analytically continued seismic spectra, Geophys. J. Int., 52, 457, 10.1111/j.1365-246X.1978.tb04243.x

Buland, 1979, Observations from the IDA network of attenuation and splitting during a recent earthquake, Nature, 277, 358, 10.1038/277358a0

Burg, 1967, Maximum Entropy Spectral Analysis, Paper presented at 37th Annual International Soc. Expl. Geophys. Meeting

Carlin, 2011, Bayesian Methods for Data Analysis, 3rd edn

Chao, 1990, On the use of maximum entropy / autoregressive spectrum in harmonic analysis of time series, Pure appl. Geophys., 134, 303, 10.1007/BF00877003

Chao, 1990, Comment on “A new method of spectral analysis and its application to the Earth's free oscillation: the “Sompi” method” by Hori et al., J. geophys. Res., 95, 19 789, 10.1029/JB095iB12p19789

Chao, 2014, Spherical harmonic stacking for the singlets of Earth's normal modes of free oscillation, Geophys. Res. Lett., 41, 10.1002/2014GL060700

Chao, 1980, Autoregressive estimation of complex eigenfrequencies in low frequency seismic spectra, Geophys. J. R. astr. Soc., 63, 641, 10.1111/j.1365-246X.1980.tb02643.x

Churchill, 1974, Complex Variables and Applications

Deuss, 2011, Splitting function measurements for Earth's longest period normal modes using recent large earthquakes, Geophys. Res. Lett., 38, L04303, 10.1029/2010GL046115

Ding, 2013, Search for the Slichter modes based on a new method: optimal sequence estimation, J. geophys. Res., 118, 10.1002/jgrb.50344

Ding, 2013, Determination of the complex frequencies for the normal modes below 1mHz after the 2010 Maule and 2011 Tohoku earthquakes, Ann. Geophys., 56

Dziewonski, 1981, Preliminary reference Earth model, Phys. Earth planet. Int., 25, 297, 10.1016/0031-9201(81)90046-7

Efron, 1986, Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Statist. Sci., 1, 54, 10.1214/ss/1177013815

Froberg, 1969, Introduction to Numerical Analysis, 2nd edn

Häfner, 2013, Signature of 3-D density structure in spectra of the spheroidal free oscillation 0S2, Geophys. J. Int., 192, 285, 10.1093/gji/ggs013

Hamming, 1962, Numerical Methods for Scientists and Engineers

Hinderer, 2007, Gravimetric methods—superconducting gravity meters, Treatise on Geophysics, 65, 10.1016/B978-044452748-6.00172-3

Hori, 1989, A new method of spectral analysis and its application to the Earth's free oscillation: the “Sompi” method, J. geophys. Res., 94, 7535, 10.1029/JB094iB06p07535

Hu, 2006, Wavelet filter analysis of atmospheric pressure effects in the long-period seismic mode band, Phys. Earth planet. Int, 154, 70, 10.1016/j.pepi.2005.09.003

Kay, 1981, Spectrum analysis—a modern perspective, Proc. IEEE, 69, 1380, 10.1109/PROC.1981.12184

Lacoss, 1971, Data adaptive spectral analysis methods, Geophysics, 36, 661, 10.1190/1.1440203

Lindberg, 1987, Multiple-taper spectral analysis of terrestrial free oscillations: part II, Geophys. J. R. astr. Soc., 91, 795, 10.1111/j.1365-246X.1987.tb01669.x

Makhoul, 1975, Linear prediction: a tutorial review, Proc. Inst. Electr. Electron. Eng., 63, 561, 10.1109/PROC.1975.9792

Masters, 1983, Attenuation in the earth at low frequencies, Phil. Trans. R. Soc. Lond., A, 308, 479, 10.1098/rsta.1983.0016

Munk, 1964, Super-resolution of tides, Studies on Oceanography, 339

Oppenheim, 1975, Digital Signal Processing, 585

Park, 1990, Radial mode observations from the 5/23/89 MacQuarie Ridge Earthquake, Geophys. Res. Lett, 17, 1005, 10.1029/GL017i007p01005

Park, 1987, Multiple-taper spectral analysis of terrestrial free oscillations: part I, Geophys. J. R. astr. Soc., 91, 755, 10.1111/j.1365-246X.1987.tb01668.x

Riedesel, 1980, Stacking for the frequencies and Qs of 0S0 and 1S0, Geophys. J. R. astr. Soc., 62, 457, 10.1111/j.1365-246X.1980.tb04867.x

Rosat, 2007, Optimal Seismic source mechanisms to excite the Slichter mode, Proceedings of the IAG Symposia, Dynamic Planet, 571, 10.1007/978-3-540-49350-1_83

Rosat, 2003, First observation of 2S1 and study of the splitting of the football mode 0S2 after the June 2001 Peru earthquake of magnitude 8.4, Geophys. Res. Lett., 30, 10, 10.1029/2003GL018304

Rosat, 2005, High-resolution analysis of the gravest seismic normal modes after the 2004 Mw = 9 Sumatra earthquake using superconducting gravimeter data, Geophys. Res. Lett, 32, L13304, 10.1029/2005GL023128

Rosat, 2007, Geographical variations of the 0S0 normal mode amplitude: predictions and observations after the Sumatra-Andaman earthquake, Earth Planets Space, 59, 307, 10.1186/BF03353109

Rosat, 2008, Application of a non-linear damped harmonic analysis method to the normal modes of the Earth, J. Geodyn., 45, 63, 10.1016/j.jog.2007.06.001

Rosat, 2012, Correction to “High-resolution analysis of the gravest seismic normal modes after the 2004 Mw = 9 Sumatra earthquake using superconducting gravimeter data”, Geophys. Res. Lett., 39, L22601, 10.1029/2012GL054248

Roult, 2006, New determinations of Q quality factors and eigenfrequencies for the whole set of singlets of the Earth's normal modes 0S0, 0S2, 0S3 and 2S1 using superconducting gravimeter data from the GGP network, J. Geodyn., 41, 345, 10.1016/j.jog.2005.08.020

Roult, 2010, Observation of split modes from the 26th December 2004 Sumatra-Andaman mega-event, Phys. Earth planet. Int., 179, 45, 10.1016/j.pepi.2010.01.001

Sailor, 1978, Measurements and interpretation of normal mode attenuation, Geophys. J. R. astr. Soc., 53, 559, 10.1111/j.1365-246X.1978.tb03760.x

Smylie, 1993, The product spectra of gravity and barometric pressure in Europe, Phys. Earth. planet. Int., 80, 135, 10.1016/0031-9201(93)90044-A

Thomson, 1982, Spectrum estimation and harmonic-analysis, Proc. IEEE, 70, 1055, 10.1109/PROC.1982.12433

Ulrych, 1975, Maximum entropy spectral analysis and autoregressive decomposition, Rev. Geophys. Space Phys., 13, 183, 10.1029/RG013i001p00183

Van den Bos., 1971, Alternative interpretation of maximum entropy spectral analysis, IEEE Trans. Inform. Theory, 17, 493, 10.1109/TIT.1971.1054660

Widmer-Schnidrig, 2007, Theory and observations—normal modes and surface wave measurements, Treatise on Geophysics, 373

Wilkinson, 1965, The Algebraic Eigenvalue Problem

Xu, 2008, Amplitude and Q of 0S0 from the Sumatra earthquake as recorded on superconducting gravimeters and seismometers, Seismol. Res. Lett., 79, 797, 10.1785/gssrl.79.6.797