On the sampling distribution of Allan factor estimator for a homogeneous Poisson process and its use to test inhomogeneities at multiple scales

Serinaldi, Francesco; Kilsby, C. G.

doi:10.1016/j.physa.2012.11.015

Cited by 14 publications

(25 citation statements)

References 28 publications

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“…If non-Poissonian processes are present over a significant range of timescales it will be possible to identify α > 0 and AF > 1. Serinaldi and Kilsby (2013) that cyclic, hence non-homogenous, Poisson processes show AF > 1 for timescales associated to cyclic components. It is therefore necessary to identify and separate the timescales at which clustering occurs from those at which the point process is Poissonian.…”

Section: Clustering Analysis Methodologymentioning

confidence: 91%

“…To this end it is necessary to compare the AF pattern found in the wave time series with that of a process of known properties. A cyclic Poisson process is generated here with the same integrate and fire (IF) technique used in Serinaldi and Kilsby (2013). The cyclic components are selected by looking at the dominant harmonic components obtained with the Fourier analysis.…”

Section: Clustering Analysis Methodologymentioning

confidence: 99%

“…The simplicity of the AF analysis made it popular in the study of time sequences of a number of physical processes such as earthquakes (Telesca et al, 2002;Cavers and Vasudevan, 2015), lightning (Telesca et al, 2008), rainfall (Telesca et al, 2007;García-Marín et al, 2008) or fires (Telesca and Pereira, 2010). However, the AF can also be larger than 1 for non-homogeneous Poisson processes, as shown in Serinaldi and Kilsby (2013). Hence it is important to distinguish clustering dynamics from cyclic Poisson processes.…”

Section: Introductionmentioning

confidence: 99%

“…Hence it is important to distinguish clustering dynamics from cyclic Poisson processes. Methodologies that are suitable to achieve this are presented in Serinaldi and Kilsby (2013) and Telesca et al (2012).…”

Section: Introductionmentioning

confidence: 99%

“…This analysis is validated and compared against the AF evaluated using the time series of wave measurements of the Italian national Sea Wave Measurement Network (Rete Ondametrica Nazionale, hereinafter RON). Subsequently we apply the methodology proposed in Serinaldi and Kilsby (2013) to gain an insight into the type of process that is described by the AF. The objective of this study is to identify the presence of time clustering of wave storms in the whole of the Mediterranean basin and examine the timescales at which events are correlated as well as the spatial distribution of the clustering.…”

Section: Introductionmentioning

confidence: 99%

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Time clustering of wave storms in the Mediterranean Sea

Besio

Briganti

Romano

et al. 2017

Nat. Hazards Earth Syst. Sci.

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Abstract. In this contribution we identify storm time clustering in the Mediterranean Sea through a comprehensive analysis of the Allan factor. This parameter is evaluated from a long time series of wave height provided by oceanographic buoy measurements and hindcast reanalysis of the whole basin, spanning the period 1979-2014 and characterized by a horizontal resolution of about 0.1 • in longitude and latitude and a temporal sampling of 1 h (Mentaschi et al., 2015). The nature of the processes highlighted by the AF and the spatial distribution of the parameter are both investigated. Results reveal that the Allan factor follows different curves at two distinct timescales. The range of timescales between 12 h to 50 days is characterized by a departure from the Poisson distribution. For timescales above 50 days, a cyclic Poisson process is identified. The spatial distribution of the Allan factor reveals that the clustering at smaller timescales is present to the north-west of the Mediterranean, while seasonality is observed across the whole basin. This analysis is believed to be important for assessing the local increased flood and coastal erosion risks due to storm clustering.

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Section: Clustering Analysis Methodologymentioning

confidence: 91%

Section: Clustering Analysis Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Time clustering of wave storms in the Mediterranean Sea

Besio

Briganti

Romano

et al. 2017

Nat. Hazards Earth Syst. Sci.

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On the relationship between the index of dispersion and Allan factor and their power for testing the Poisson assumption

Serinaldi

2013

Stoch Environ Res Risk Assess

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Comparing seismicity declustering techniques by means of the joint use of Allan Factor and Morisita index

Telesca

Lovallo²,

Golay

et al. 2015

Stoch Environ Res Risk Assess

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In this paper, we propose to compare different declustering methods on the basis of the time-correlation and the space-clustering of the residual earthquake catalog after the declustering techniques have been applied. To this aim, we applied two point process clustering measures, the Allan Factor and the Morisita Index, for the identification and quantification of temporal correlation and spatial clustering in point processes, respectively. We used our joint space-time approach to study the earthquake spacetime point processes of southern California and Switzerland with surrounding area, declustered by using the method of Gardner and Knopoff (with Grünthal and Uhmhammer window) and that of Reasenberg (with different setting parameters). Our results show that the residual declustered catalog is still characterized by timecorrelated structures at long timescales; however, the cutoff timescale that is the lowest timescale above which the time-correlation is visible is higher with the Reasenberg method while is smaller with the Gardner and Knopoff method with Grünthal window. The space-clustering analysis performed by means of the Morisita Index suggests that the declustering technique effectively reduces the spatial clustering of the seismicity of Switzerland, but does not change the spatial properties of the residual seismic catalogue of the southern California.

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On the sampling distribution of Allan factor estimator for a homogeneous Poisson process and its use to test inhomogeneities at multiple scales

Cited by 14 publications

References 28 publications

Time clustering of wave storms in the Mediterranean Sea

Time clustering of wave storms in the Mediterranean Sea

On the relationship between the index of dispersion and Allan factor and their power for testing the Poisson assumption

Comparing seismicity declustering techniques by means of the joint use of Allan Factor and Morisita index

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