Relationship between Singular Spectrum Analysis and Fourier analysis: Theory and application to the monitoring of volcanic activity

Bozzo, Enrico; Carniel, Roberto; Fasino, Dario

doi:10.1016/j.camwa.2010.05.028

Cited by 65 publications

(47 citation statements)

References 8 publications

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“…However, the dimension f of the embedding manifold is unknown and for an experimental time series the sampling period τ s is already determined; for this reason in all the method of delays it is commonest to concentrate on the choice of m [Packard et al, 1980]. Both previous examples of an analysis of an experimental time series of a volcanic tremor [Carniel and Di Cecca, 1999] and numerical experiments [Bozzo et al, 2010] suggest that m=20 is a reasonable choice, which is the figure we adopt in this study.…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

Volcanic tremors: Good indicators of change in plumbing systems during volcanic eruptions

Tárraga

Martı́

Abella

et al. 2014

Journal of Volcanology and Geothermal Research

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Geophysical and geochemical signals recorded during episodes of unrest preceding volcanic eruptions provide information on movements of magma inside the lithosphere and on how magma prepares to reach the surface. When the eruption ensues continuous volcanic monitoring can reveal the nature of changes occurring in the volcano's plumbing system, which may be correlated with changes in both eruption behaviour and products. During the 2011-2012 submarine eruption of El Hierro (Canary Islands), the seismic signal, surface deformation, a broad stain on the sea surface of the eruption site, and the occasional appearance of floating lava balloons and pyroclastic fragments were the main observable signs. A strong continuous tremor in the vent accompanied the eruption and varied significantly in amplitude, frequency and dynamical parameters. We analysed these variations and correlated them with changes in the distribution of earthquakes and in the petrology of the erupting magma. This enabled us to relate variations in tremors to changes in the (i) stress conditions of the plumbing system, (ii) dimensions of the conduit and vent, (iii) intensity of the explosive episodes, and to (iv) rheological changes in the erupting magma. The results obtained show how the tremor signal was strongly influenced by stress changes in the host rock and in the rheological variations in the erupting magma. We conclude that the tracking of real-time syneruptive tremor signals via the observation of variations in plumbing systems and magma physics is a potentially effective tool for interpreting eruption dynamics, and suggest that similar variations observed in pre-eruptive tremors will have a similar origin.

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Section: Accepted M Manuscriptmentioning

confidence: 99%

Volcanic tremors: Good indicators of change in plumbing systems during volcanic eruptions

Tárraga

Martı́

Abella

et al. 2014

Journal of Volcanology and Geothermal Research

Self Cite

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“…Obtaining the desired components through an unsupervised grouping of the elementary components is not trivial since each elementary component reflects the signal behavior into a narrow band of nearly K/L cycles per sample [36]. Hence, the correlation between the elementary components of a nonstationary signal component is quite weak.…”

Section: The Sliding Ssa Method: An Emd-like Toolmentioning

confidence: 99%

“…The question here is: for given L and N , what is the minimum gap required between two frequencies in order to separate them? It has been shown theoretically and validated experimentally [36] that each singular value of the trajectory matrix can be approximated by averaging a suitable portion of the periodogram of the analyzed time series. More precisely, let s = {s n , n = 1 .…”

Section: A Separation Of Two Sinusoidsmentioning

confidence: 99%

See 1 more Smart Citation

The Sliding Singular Spectrum Analysis: A Data-Driven Nonstationary Signal Decomposition Tool

Harmouche

Fourer

Auger

et al. 2018

IEEE Trans. Signal Process.

110

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Singular Spectrum Analysis (SSA) is a signal decomposition technique that aims at expanding signals into interpretable and physically meaningful components (e.g. sinusoids, noise, etc.). This article presents new theoretical and practical results about the separability of the SSA and introduces a new method called sliding SSA. First, the SSA is combined with an unsupervised classification algorithm to provide a fully automatic data-driven component extraction method for which we investigate the limitations for components separation in a theoretical study. Second, the detailed automatic SSA method is used to design an approach based on a sliding analysis window which provides better results than the classical SSA method when analyzing non-stationary signals with a time-varying number of components. Finally, the proposed sliding SSA method is compared to the Empirical Mode Decomposition (EMD) and to the synchrosqueezed Short-Time Fourier Transform (STFT), applied on both synthetic and real-world signals.

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“…In the field of periodic pattern recognition of time series, various methods have been proposed [4,26,28], such as the complete periodic pattern, partial periodic pattern, period association rule, synchronous periodic pattern, and asynchronous periodic pattern. In [26], Loh et al proposed an efficient method to mine temporal patterns in the popularity of web items, where the popularity of web items is treated as time series and a gap measurement method was proposed to quantify the difference between the popularity of two web items.…”

Section: Related Workmentioning

confidence: 99%

A periodicity-based parallel time series prediction algorithm in cloud computing environments

Chen

Rong

et al. 2019

Information Sciences

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In the era of big data, practical applications in various domains continually generate large-scale time-series data. Among them, some data show significant or potential periodicity characteristics, such as meteorological and financial data. It is critical to efficiently identify the potential periodic patterns from massive time-series data and provide accurate predictions. In this paper, a Periodicity-based Parallel Time Series Prediction (PPTSP) algorithm for large-scale time-series data is proposed and implemented in the Apache Spark cloud computing environment. To effectively handle the massive historical datasets, a Time Series Data Compression and Abstraction (TSDCA) algorithm is presented, which can reduce the data scale as well as accurately extracting the characteristics. Based on this, we propose a Multi-layer Time Series Periodic Pattern Recognition (MTSPPR) algorithm using the Fourier Spectrum Analysis (FSA) method. In addition, a Periodicity-based Time Series Prediction (PTSP) algorithm is proposed. Data in the subsequent period are predicted based on all previous period models, in which a time attenuation factor is introduced to control the impact of different periods on the prediction results. Moreover, to improve the performance of the proposed algorithms, we propose a parallel solution on the Apache Spark platform, using the Streaming real-time computing module. To efficiently process the large-scale time-series datasets in distributed computing environments, Distributed Streams (DStreams) and Resilient Distributed Datasets (RDDs) are used to store and calculate these datasets. Logical and data dependencies of RDDs in the P-TSDCA, P-MTSPPR, and P-PTSP processes are considered, and the corresponding parallel execution solutions are conducted. Extensive experimental results show that our PPTSP algorithm has significant advantages compared with other algorithms in terms of prediction accuracy and performance.

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Relationship between Singular Spectrum Analysis and Fourier analysis: Theory and application to the monitoring of volcanic activity

Cited by 65 publications

References 8 publications

Volcanic tremors: Good indicators of change in plumbing systems during volcanic eruptions

Volcanic tremors: Good indicators of change in plumbing systems during volcanic eruptions

The Sliding Singular Spectrum Analysis: A Data-Driven Nonstationary Signal Decomposition Tool

A periodicity-based parallel time series prediction algorithm in cloud computing environments

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