Mean amplitudes of the signal in the seasonal and shorter period length of day time series computed by the frequency-dependent autocovariance

<p>The frequency-dependent autocovariance (FDA) function is defined in this paper as the autocovariance function of a wideband oscillation filtered by the Fourier transform bandpass filter (FTBPF). It was shown that the FDA estimation is a useful algorithm to detect mean amplitudes of oscillations in a very noisy time series. In this paper the least-squares polynomial harmonic model was used to remove the trend, low frequency as well as the annual and semi-annual oscillations from the IERS eopc04R_IAU2000_daily length of day (LOD) time series to compute their residuals. Next, the mean amplitudes of the signal as a function of frequency were determined from the difference between the FDA of LOD residuals and FDA of power-law noise model similar to the noise present in LOD residuals.  Several power-law noise model data were generated with a similar spectral index and variance as the noise in LOD data to estimate the mean amplitude spectrum in the seasonal and shorter period frequency band.  It was shown that the mean amplitudes of the oscillations in LOD residuals are very small compared to the noise standard deviation and do not depend on the filter bandwidth of the FTBPF. These small amplitudes explain why LOD prediction errors increase rapidly with the prediction length.</p>

Detection of millihertz quasi-periodic oscillations in the X-Ray binary 1RXS J180408.9−342058

ABSTRACT Millihertz quasi-periodic oscillations (mHz QPOs) observed in neutron-star low-mass X-ray binaries (NS LMXBs) are generally explained as marginally stable thermonuclear burning on the neutron star surface. We report the discovery of mHz QPOs in an XMM–Newton observation of the transient 1RXS J180408.9−342058, during a regular bursting phase of its 2015 outburst. We found significant periodic signals in the March observation, with frequencies in the range 5–8 $\, \mathrm{mHz}$, superimposed on a strong ∼1/f power-law noise continuum. Neither the QPO signals nor the power-law noise were present during the April observation, which exhibited a 2.5 × higher luminosity and had correspondingly more frequent bursts. When present, the QPO signal power decreases during bursts and disappears afterwards, similar to the behaviour in other sources. 1RXS J180408.9−342058 is the eighth source known to date that exhibits such QPOs driven by thermonuclear burning. We examine the range of properties of the QPO signals in different sources. Whereas the observed oscillation profile is similar to that predicted by numerical models, the amplitudes are significantly higher, challenging their explanation as originating from marginally stable burning.

Impacts on Noise Analyses of GNSS Position Time Series Caused by Seasonal Signal, Weight Matrix, Offset, and Helmert Transformation Parameters

The noise characteristics of the Global Navigation Satellite System (GNSS) position time series can be biased by many factors, which in turn affect the estimates of parameters in the deterministic model using a least squares method. The authors assess the effects of seasonal signals, weight matrix, intermittent offsets, and Helmert transformation parameters on the noise analyses. Different solutions are obtained using the simulated and real position time series of 647 global stations and power law noise derived from the residuals of stacking solutions are compared. Since the true noise in the position time series is not available except for the simulated data, the authors paid most attention to the noise difference caused by the variable factors. First, parameterization of seasonal signals in the time series can reduce the colored noise and cause the spectral indexes to be closer to zero (much “whiter”). Meanwhile, the additional offset parameters can also change the colored noise to be much “whiter” and more offsets parameters in the deterministic model leading to spectral indexes closer to zero. Second, the weight matrices derived from the covariance information can induce more colored noise than the unit weight matrix for both real and simulated data, and larger biases of annual amplitude of simulated data are attributed to the covariance information. Third, the Helmert transformation parameters (three translation, three rotation, and one scale) considered in the model show the largest impacts on the power law noise (medians of 0.4 mm−k/4 and 0.06 for the amplitude and spectral index, respectively). Finally, the transformation parameters and full-weight matrix used together in the stacking model can induce different patterns for the horizontal and vertical components, respectively, which are related to different dominant factors.

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series

A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized ‘events’. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate. Finally, an expression for an event’s ‘region of influence’ within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events. Signals can then be reconstructed based on a small number of isolated points on the time/scale plane. This method, termed element analysis , is applied to the identification of long-lived eddy structures in ocean currents as observed by along-track measurements of sea surface elevation from satellite altimetry.