Permutation Entropy of Weakly Noise-Affected Signals

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.

Features of time variations of microseismic noise at seismic stations in Tajikistan

The spectral structure of microseismic noise in the frequency range of 0.01-40 Hz at different times of the day and year, recorded by broadband equipment at eight IRIS group seismic stations in Tajikistan in 2005-2020, was analyzed. Two disjoint frequency ranges are distinguished, which we conditionally call "high-frequency" (2-40 Hz) and "low-frequency" (0.01-0.75 Hz) noise, separated by a natural drop in the noise amplitude to 20-30 Db. It is assumed that the high-frequency range of noise has a local nature, due to exogenous sources of natural origin in the form of wind gusts, concussions from powerful watercourses and fluctuations in the level of large reservoirs, as well as man-made in-terference due to road and quarry explosions, the work of large industrial enterprises and concussions from road traffic. Low-frequency noise is most likely caused by global storm microseisms. High-frequency noise has a well-defined daily frequency, which is completely absent in low-frequency noise. At the same time, in both frequency ranges, the existence of a clearly pronounced seasonal peri-odicity has been established, the amplitude of which reaches 6-7 Db for high-frequency noise and about half as much for low-frequency noise. However, at the same time, the seasonal frequency of high frequency and low-frequency noise turns out to be antiphase, which indicates in favor of the different genesis of these two components of microseismic noise. The amplitude of the diurnal periodicity in variations of the high-frequency noise level is maximal during the daytime, remaining approximately constant for 8-10 hours. At the same time, the decline in the noise amplitude in the evening lasts longer than the steeper morning growth. The time intervals of a sharp increase and decrease in the intensity of the discussed daily extreme are quite well correlated, respectively, with morning and evening twilight at different times of the year. This is reflected in the wider flat part of the maximum noise level in summer compared to winter and the differences in its level up to 6 Db in favor of summer time. This observation can be considered as a manifestation of the deep influence of the Sun on the oscillatory processes that generate high-frequency microseismic noise.

Wind-induced seismic noise at the Princess Elisabeth Antarctica Station

Icequakes are the result of processes occurring within the ice mass or between the ice and its environment. Studying icequakes provides a unique view on ice dynamics, specifically on the basal conditions. Changes in conditions due to environmental or climate changes are reflected in icequakes. Counting and characterizing icequakes is thus essential to monitor them. Most of the icequakes recorded by the seismic station at the Belgian Princess Elisabeth Antarctica Station (PE) have small amplitudes corresponding to maximal displacements of a few nanometres. Their detection threshold is highly variable because of the rapid and strong changes in the local seismic noise level. Therefore, we evaluated the influence of katabatic winds on the noise measured by the well-protected PE surface seismometer. Our purpose is to identify whether the lack of icequake detection during some periods could be associated with variations in the processes generating them or simply with a stronger seismic noise linked to stronger wind conditions. We observed that the wind mainly influences seismic noise at frequencies greater than 1 Hz. The seismic noise power exhibits a bilinear correlation with the wind velocity, with two different slopes at a wind velocity lower and greater than 6 m s−1 and with, for example at a period of 0.26 s, a respective variation of 0.4 dB (m −1 s) and 1.4 dB (m −1 s). These results allowed a synthetic frequency and wind-speed-dependent noise model to be presented that explains the behaviour of the wind-induced seismic noise at PE, which shows that seismic noise amplitude increases exponentially with increasing wind speed. This model enables us to study the influence of the wind on the original seismic dataset, which improves the observation of cryoseismic activity near the PE station.

Change of the Most Probable Escape Path in a Fast-Slow Insect Outbreak System Under Different Noise Amplitude Ratios

In the present paper, noise-induced escape from the domain of attraction of a stable fixed point of a fast-slow insect outbreak system is investigated. According to Dannenberg's theory(Dannenberg PH, Neu JC, 2014)[1], different noise amplitude ratios μ lead to the change of the Most Probable Escape Path(MPEP). Therefore, the research emphasis of this paper is to extend their study and discuss the changes of the MPEPs in more detail. Firstly, the case for μ=1, wherein the MPEP almost traces out the critical manifold, is considered. Via projecting the full system onto the critical manifold, a reduced system is obtained and the quasi-potential of the full system can be partly evaluated by that of this reduced system. In order to test the accuracy of the computed MPEP, a new relaxation method is then presented. Then, as μ converges to zero, an improved analytical method is given, through which a better approximation for the MPEP at the turning point is obtained. And then, in the case that the value of μ is moderate, wherein the MPEP will peel off the critical manifold, to determine the changing point of the MPEP on the critical manifold, an effective numerical algorithm is given. In brief, in this paper, a complete investigation on the structural changes of the MPEPs of a fast-slow insect outbreak system under different values of μ is given, and the results of the numerical simulations match well with the analytical ones.

Analysis of Noise and Velocity in GNSS EPN-Repro 2 Time Series

This study evaluates the EUREF Permanent Network (EPN) station position time series of approximately 200 GNSS stations subject to the Repro 2 reprocessing campaign in order to characterize the dominant types of noise and amplitude and their impact on estimated velocity values and associated uncertainties. The visual inspection on how different noise model represents the analysed data was done using the power spectral density of the residuals and the estimated noise model and it is coherent with the calculated Allan deviation (ADEV)-white and flicker noise. The velocities resulted from the dominant noise model are compared to the velocity obtained by using the Median Interannual Difference Adjusted for Skewness (MIDAS). The results show that only 3 stations present a dominant random walk noise model compared to flicker and powerlaw noise model for the horizontal and vertical components. We concluded that the velocities for the horizontal and vertical component show similar values in the case of MIDAS and maximum likelihood estimation (MLE), but we also found that the associated uncertainties from MIDAS are higher compared to the uncertainties from MLE. Additionally, we concluded that there is a spatial correlation in noise amplitude, and also regarding the differences in velocity uncertainties for the Up component.

Cyclone Signatures in the South-West Indian Ocean from Two Decades of Microseismic Noise

Tropical Cyclones (TC) represent the most destructive natural disaster affecting the islands in the South-West Indian Ocean (SWIO) each year. Monitoring ocean activity is therefore of primary importance to secure lands, infrastructures and peoples, but the little number of oceanographic instruments makes it challenging, particularly in real time. Long-term seismological records provide a way to decipher and quantify the past cyclonic activity by analyzing microseisms, seismic waves generated by the ocean activity and propagating through the solid Earth. In the present study, we analyze this microseismic noise generated by cyclones that develop in the SWIO basin between 1999 and 2020, using broadband seismic stations in La Réunion. The power spectral density (PSD), together with the root mean square (RMS) analyses of continuous seismic data recorded by the permanent Geoscope RER seismic station, indicate the intensification of the microseismic noise amplitude in proportion to the cyclone intensity. Thus, we establish a relationship between the cyclone intensity and the PSD of the Secondary Microseisms (SM) in frequency band ∼0.14 to 0.25 Hz (4 to 7 s period). The Pearson coefficient between the observed and estimated TC intensity are >0.8 in the presence of a cyclone with mean wind speeds >75 km/h and with a seismic station distance-to-storm center D < 3000 km. A polarization analysis in the time and frequency domains allows the retrieval of the backazimuth of the SM sources during isolated cyclone events and well-polarized signal, i.e., CpH > 0.6. We also analyzed the RMS of the Primary Microseisms (PM frequency between ∼0.05 and 0.1 Hz, i.e., for 10 to 20 s period) for cyclones passing nearby La Réunion (D < 500 km), using the available temporary and permanent broadband seismic stations. We also found high correlation coefficients (>0.8) between the PM amplitude and the local wave height issued from the global hindcast model demonstrating that the PM amplitude can be used as a robust proxy to perform a real-time wave-height monitoring in the neighboring ocean. Transfer functions are calculated for several cyclones to infer wave height from the seismic noise amplitude recorded on land. From the analysis of two decades of data, our results suggest that it is possible to quantify the past ocean activity for as long as continuous seismic archives are available, emphasizing microseismic noise as a key observable for quantifying and understanding the climate change.

Influence of non-tidal atmospheric and oceanic loading deformation on the stochastic properties of over 10,000 GNSS vertical land motion time series

&lt;p&gt;Over the past two decades, numerous studies demonstrated that the stochastic variability in GNSS position time series &amp;#8211; often referred to as noise &amp;#8211; is both temporally and spatially correlated. The time correlation of this stochastic variability can be well approximated by a linear combination of white noise and power-law stochastic processes with different amplitudes. Although acknowledged in many geodetic studies, the presence of such power-law processes in GNSS position time series remains largely unexplained. Considering that these power-law processes are the primary source of uncertainty for velocity estimates, it is crucial to identify their origin(s) and to try to reduce their influence on position time series.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;Using the Least-Squares Variance Component Estimation method, we analysed the influence of removing surface mass loading deformation on the stochastic properties of vertical land motion time series (VLMs). We used the position time series of over 10,000 globally distributed GNSS stations processed by the Nevada Geodetic Laboratory at the University of Nevada, Reno, and loading deformation time series computed by the Earth System Modelling (ESM) team at GFZ-Potsdam. Our results show that the values of stochastic parameters, namely, white noise amplitude, spectral index, and power-law noise amplitude, but also the spatial correlation, are systematically influenced by non-tidal atmospheric and oceanic loading deformation. The observed change in stochastic parameters often translates into a reduction of trend uncertainties, reaching up to -75% when non-tidal atmospheric and oceanic loading deformation is highest.&lt;/p&gt;