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H.-G. Scherneck, S. Bergstrand, M. Lidberg:

H.-G. Scherneck, S. Bergstrand, M. Lidberg: Fractals everywhere: Time series analysis and rate uncertainty NKG Working Group for Geodynamics Meeting in Ås, Norway, March 2006. We use: Unbiased autocovariance estimator (w.r.t. missing data) Window: Kaiser-Bessel

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H.-G. Scherneck, S. Bergstrand, M. Lidberg:

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  1. H.-G. Scherneck, S. Bergstrand, M. Lidberg: Fractals everywhere: Time series analysis and rate uncertainty NKG Working Group for Geodynamics Meeting in Ås, Norway, March 2006

  2. We use: • Unbiased autocovariance estimator (w.r.t. missing data) • Window: Kaiser-Bessel • A selection scheme for fit that avoids the spectral correlation due to windowing, and still gives a heavily overdetermined case. • We find: • Slope model fits almost always up to Nyquist • Disadvantage: Low-frequency part is not well resolved

  3. We use: • data from beg. 1998 to end 2004 • synth. fractal noise, 1,000-10,000 • masked by the real-world time series for breaks • Then we estimate a rate where (in white noise) we’d expect none. • ← shows histograms of these rates

  4. To specify the rate uncertainties, • We ought to use the fractal noise law • Next page: assumes Gauss-Markov

  5. From Johansson et al. 2002: ONSA.ra: -0.179 0.360 1.135 ONSW.ra: 4.077 0.483 2.274 OSKA.ra: 2.231 0.211 2.449 OSTE.ra: 8.331 0.209 3.290 OULU.ra: 10.761 0.199 2.010 OVER.ra: 9.020 0.226 1.520 POTS.ra: -1.389 0.176 4.195 RIGA.ra: 2.347 0.238 2.336 ROMU.ra: 7.566 0.268 3.313 SAAR.ra: 7.678 0.133 2.000 SKEL.ra: 10.527 0.217 4.126 SODA.ra: 11.143 0.217 1.692 SUND.ra: 9.926 0.206 2.614 SVEG.ra: 8.147 0.204 1.448 TROM.ra: 3.500 0.208 1.518 TUOR.ra: 6.062 0.158 1.807 UMEA.ra: 10.923 0.210 2.545 VAAS.ra: 10.750 0.187 1.607 VANE.ra: 4.132 0.209 4.322 VILH.ra: 8.508 0.210 2.508 VIRO.ra: 2.681 0.171 1.774 VISB.ra: 2.884 0.203 1.140 WETB.ra: 0.519 0.345 1.065 WETT.ra: -0.242 0.205 1.132 WTZR.ra: -0.232 0.216 0.000 GaussMarkov SITE co rate sigma sigmascale -------------------------------------------- ARJE.ra: 8.196 0.223 2.449 BORA.ra: 3.007 0.212 1.497 BRUS.ra: -1.624 0.172 1.797 HASS.ra: 1.008 0.205 1.898 HERS.ra: -1.286 0.087 22.761 JOEN.ra: 4.704 0.159 2.485 JONK.ra: 3.590 0.204 1.926 KARL.ra: 5.831 0.206 1.906 KEVO.ra: 5.437 0.253 4.795 KIRU.ra: 8.424 0.225 3.663 KIVE.ra: 8.469 0.245 2.981 KOSG.ra: -1.060 0.086 1.354 KUUS.ra: 12.200 0.264 5.649 LEKS.ra: 8.346 0.420 2.372 LOVO.ra: 5.964 0.212 1.465 MADR.ra: 0.983 0.247 1.870 MART.ra: 7.097 0.206 1.858 MATE.ra: -0.979 0.115 1.701 METS.ra: 5.242 0.234 1.355 NORR.ra: 4.898 0.211 1.376 NYAL.ra: 5.679 0.178 1.459 OLKI.ra: 8.516 0.171 1.768

  6. Conclusions • We think these considerations have a general notion; in GPS we have the advantage of long, regularly sampled time series • We find fractal noise with a non-integer power law  = ( 0.5 to 0.9) • Corresponding uncertainties for estimated rates must be scaled up with a factor of 4 to 15 w.r.t. white-noise results • This is more pessimistic than Gauss-Markov

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