Markov modulated Poisson processes for stochastic modelling of background seismicity

2021 ◽  
Author(s):  
Elisa Varini ◽  
Antonella Peresan ◽  
Amel Benali
Keyword(s):  
Poisson Process ◽  
Case Studies ◽  
Nearest Neighbor ◽  
Statistical Tests ◽  
Central Italy ◽  
Space Time ◽  
Poisson Processes ◽  
Suitable Alternative ◽  
Background Seismicity ◽  
Markov Modulated

<p>We investigate the statistical properties of declustered catalogs as obtained from the application of two different data-driven declustering algorithms, namely the nearest-neighbor method and the stochastic declustering method (Benali et al., Stoch. Environ Res Risk Assess, 2020). The nearest-neighbor method partitions earthquakes into background and clustered components, based on nearest-neighbor distances between earthquakes in the space-time-magnitude domain (Zaliapin and Ben-Zion, J Geophys Res, 2013); the stochastic declustering method classifies earthquakes into background and clustered components through a probabilistic procedure based on the estimation of the space-time ETAS model (Zhuang et al., J Geophys Res, 2004).</p><p>Two Italian case studies are considered: North-Eastern Italy (data from OGS Bulletins) and Central Italy (data from ISIDe catalog). For both case studies, the time series of background seismicity are obtained from the two declustering methods. Then we investigate the general assumption according to which the temporal sequence of background seismicity is suitably modelled by the stationary Poisson model. For this purpose, several features and statistical tests are considered to verify the main properties that characterize Poisson processes (e.g. events are independent, exponential inter-arrival times, etc.). </p><p>Whenever the Poissonian hypothesis is rejected, we get evidence of certain heterogeneity in the background sequence, which leads us to rule out the simple Poisson process for background seismicity modeling. As a simple and more suitable alternative, we consider here the Markov Modulated Poisson Process (MMPP model), which allows the Poisson seismicity rate to change over time according to a finite (unknown) number of states of the system. The MMPP model turns out suitable for identifying and quantifying heterogeneities in background seismicity, as well as for comparing them against the two considered declustering algorithms.</p>

Enahancing the detail on low-level seismicity and swarms in central-southern Italy by template matching

2021 ◽  
Author(s):  
Luca Carbone ◽  
Rita de Nardis ◽  
Giusy Lavecchia ◽  
Laura Peruzza ◽  
Enrico Priolo ◽  
...  
Keyword(s):  
Template Matching ◽  
Nearest Neighbor ◽  
Matched Filter ◽  
Central Italy ◽  
Total Duration ◽  
Space Time ◽  
Risk Area ◽  
Low Level ◽  
Seismic Catalogue ◽  
Completeness Magnitude

<p> </p><p>During the seismic sequence which followed the devastating L’Aquila 2009 earthquake, on 27 May 2009 the OGS (Istituto Nazionale di Oceanografia e di Geofisica Sperimentale) and the GeosisLab (Laboratorio di Geodinamica e Sismogenesi, Chieti-Pescara University) installed a temporary seismometric network around the Sulmona Basin, a high seismic risk area of Central Italy located right at SE of the epicentral one. This area of the central Apennines is generally characterized by low level seismicity organized in low energy clusters, but it experienced destructive earthquakes both in historical and in early instrumental time (Fucino 1915 =XI MCS, Majella 1706 =X-XI MCS, Barrea 1984 =VIII MCS).</p><p>From the 27 May 2009 to 22 November 2011, the temporary network provided a huge amount of continuous seismic recordings, and a seismic catalogue covering the first seven months of network operation (-1.5≤M<sub>L</sub>≤3.7, with a completeness magnitude of 1.1) and a spatial area that stretches from the Sulmona Basin to Marsica-Sora area. Aiming to enhance the detection of microearthquakes reported in this catalogue, we applied the matched-filter technique (MFT) to continuous waveforms properly integrated with data from permanent stations belonging to the national seismic network. Specifically, we used the open-source seismological package PyMPA to detect microseismicity from the cross-correlation of continuous data and templates. As templates we used only the best relocated events of the available seismic catalogue. Starting from 366 well located earthquakes<strong> </strong>we obtain a new seismic catalogue of 6084 new events (-2<M<sub>L</sub><4) lowering the completeness magnitude to 0.2. To these new seismic locations, we applied a declustering method to separate background seismicity from clustered seismicity in the area. All the seismicity shows a bimodal behaviour in term of distribution of the nearest-neighbor distance/time with the presence of two statistically distinct earthquake populations. We focused the attention on two of these clusters (C1 and C2) that numerically represent the 60% of the catalogue. They consist in 2619 and 995 events, respectively, with magnitude -2.0<M<sub>L</sub><3.6 and -0.5<M<sub>L</sub><3.2 occurred in Marsica-Sora area. C1 shows the typical characteristics of a seismic swarm, without a clear mainshock, but with 8 more energetic events (3.0≤M<sub>L</sub>≤3.5); the temporal evolution is very articulated with a total duration of one month with different bursts of seismicity and characteristic time extension of approximately one week. C2 instead has a different space-time evolution and consists of different swarm-like seismic sequences more discontinuous in comparison with C1. These swarms are described in greater detail to investigate the influence of overpressurized fluids and their space-time distribution.</p>

On some characterizations of the poisson process

1989 ◽  
Vol 26 (01) ◽  
pp. 176-181
Author(s):  
Wen-Jang Huang
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Arrival Time ◽  
Random Variables ◽  
Poisson Processes

In this article we give some characterizations of Poisson processes, the model which we consider is inspired by Kimeldorf and Thall (1983) and we generalize the results of Chandramohan and Liang (1985). More precisely, we consider an arbitrarily delayed renewal process, at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the ith new atom assigned to the process Di, i = 1, ···, k. We shall show that the existence of a pair of uncorrelated processes Di, Dj, i ≠ j, implies the renewal process is Poisson. Some other related characterization results are also obtained.

scholarly journals Failure Analysis of Apennine Masonry Churches Severely Damaged during the 2016 Central Italy Seismic Sequence

Buildings ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 58 ◽  
Author(s):  
Francesco Clementi
Keyword(s):  
Case Studies ◽  
Central Italy ◽  
Numerical Data ◽  
Sensitivity Study ◽  
Nonlinear Material ◽  
Seismic Sequence ◽  
Nonlinear Approach ◽  
Nonlinear Static ◽  
Masonry Churches ◽  
Global And Local

This paper presents a detailed study of the damages and collapses suffered by various masonry churches in the aftermath of the seismic sequence of Central Italy in 2016. The damages will first be analyzed and then compared with the numerical data obtained through 3D simulations with eigenfrequency and then nonlinear static analyses (i.e., pushover). The main purposes of this study are: (i) to create an adequately consistent sensitivity study on several definite case studies to obtain an insight into the role played by geometry—which is always unique when referred to churches—and by irregularities; (ii) validate or address the applicability limits of the more widespread nonlinear approach, widely recommended by the Italian Technical Regulations. Pushover analyses are conducted assuming that the masonry behaves as a nonlinear material with different tensile and compressive strengths. The consistent number of case studies investigated will show how conventional static approaches can identify, albeit in a qualitative way, the most critical macro-elements that usually trigger both global and local collapses, underlining once again how the phenomena are affected by the geometry of stones and bricks, the texture of the wall face, and irregularities in the plan and elevation and in addition to hypotheses made on the continuity between orthogonal walls.

scholarly journals A bivariate two-state Markov modulated Poisson process for failure modeling

2021 ◽  
Vol 208 ◽  
pp. 107318
Author(s):  
Yoel G. Yera ◽  
Rosa E. Lillo ◽  
Bo F. Nielsen ◽  
Pepa Ramírez-Cobo ◽  
Fabrizio Ruggeri
Keyword(s):  
Poisson Process ◽  
Failure Modeling ◽  
Markov Modulated Poisson Process ◽  
Markov Modulated

Radial generation of n-dimensional poisson processes

1984 ◽  
Vol 21 (03) ◽  
pp. 548-557
Author(s):  
M. P. Quine ◽  
D. F. Watson
Keyword(s):  
Poisson Process ◽  
Poisson Processes ◽  
Three Dimensions ◽  
Simulation Studies ◽  
Simple Method ◽  
Efficient Simulation ◽  
Nearest Neighbours

A simple method is proposed for the generation of successive ‘nearest neighbours' to a given origin in ann-dimensional Poisson process. It is shown that the method provides efficient simulation of random Voronoi polytopes. Results are given of simulation studies in two and three dimensions.

Convergence to equilibrium in a traffic model with restricted passing

1979 ◽  
Vol 16 (4) ◽  
pp. 881-889 ◽  
Author(s):  
Hans Dieter Unkelbach
Keyword(s):  
Poisson Process ◽  
Limit Theorems ◽  
Point Processes ◽  
Road Traffic ◽  
Poisson Processes ◽  
Traffic Model ◽  
Cluster Point ◽  
Convergence To Equilibrium ◽  
Constant Intensity

A road traffic model with restricted passing, formulated by Newell (1966), is described by conditional cluster point processes and analytically handled by generating functionals of point processes.The traffic distributions in either space or time are in equilibrium, if the fast cars form a Poisson process with constant intensity combined with Poisson-distributed queues behind the slow cars (Brill (1971)). It is shown that this state of equilibrium is stable, which means that this state will be reached asymptotically for general initial traffic distributions. Furthermore the queues behind the slow cars dissolve asymptotically like independent Poisson processes with diminishing rate, also independent of the process of non-queuing cars. To get these results limit theorems for conditional cluster point processes are formulated.

On interpoint distances for planar Poisson cluster processes

1983 ◽  
Vol 20 (3) ◽  
pp. 513-528 ◽  
Author(s):  
Richard J. Kryscio ◽  
Roy Saunders
Keyword(s):  
Lebesgue Measure ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Indicator Function ◽  
Poisson Processes ◽  
Interpoint Distance ◽  
Poisson Cluster ◽  
Cluster Processes

For stationary Poisson or Poisson cluster processes ξ on R2 we study the distribution of the interpoint distances using the interpoint distance function and the nearest-neighbor indicator function . Here Sr (x) is the interior of a circle of radius r having center x, I(t) is that subset of D which has x ∊ D and St(x) ⊂ D and χ is the usual indicator function. We show that if the region D ⊂ R2 is large, then these functions are approximately distributed as Poisson processes indexed by and , where µ(D) is the Lebesgue measure of D.

A characterization of the Poisson process

1974 ◽  
Vol 11 (1) ◽  
pp. 72-85 ◽  
Author(s):  
S. M. Samuels
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Poisson Processes ◽  
Renewal Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Proof ◽  
Necessary And Sufficient

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

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