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Journal Article

Nonstationary Poisson model for earthquake occurrences

L.-L. Hong, S.-W. Guo
Published: 01 June 1995
Bulletin of the Seismological Society of America (1995) 85 (3): 814–824.
DOI: https://doi.org/10.1785/BSSA0850030814
...L.-L. Hong; S.-W. Guo Abstract A nonstationary Poisson model describing the occurrences of clustering earthquakes is developed. This model, characterized by a U-shape mean-occurrence-rate function, simulates the decreasing, nearly constant, and increasing variations of the mean occurrence rates...
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Journal Article

A two-state Poisson model for seismic hazard estimation

Bernice Bender
Published: 01 August 1984
Bulletin of the Seismological Society of America (1984) 74 (4): 1463–1468.
DOI: https://doi.org/10.1785/BSSA0740041463
... that are geologically similar, suggesting, on a local scale at least, temporal variations in seismicity. The simple two-state model presented here allows a region to have both seismically “active” and “inactive” states; in this model, earthquakes have a Poisson distribution during both states, but occur at a higher...
View PDF for article title, A two-state <span class="search-highlight">Poisson</span> <span class="search-highlight">model</span> for seismic hazard estimation
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Journal Article

The Seismic Hazard Implications of Declustering and Poisson Assumptions Inferred from a Fully Time‐Dependent Model

Edward H. Field, Kevin R. Milner, Nicolas Luco
Published: 05 October 2021
Bulletin of the Seismological Society of America (2022) 112 (1): 527–537.
DOI: https://doi.org/10.1785/0120210027
...Edward H. Field; Kevin R. Milner; Nicolas Luco ABSTRACT We use the Third Uniform California Earthquake Rupture Forecast (UCERF3) epidemic‐type aftershock sequence (ETAS) model (UCERF3‐ETAS) to evaluate the effects of declustering and Poisson assumptions on seismic hazard estimates. Although...
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View PDF for article title, The Seismic Hazard Implications of Declustering and <span class="search-highlight">Poisson</span> Assumptions Inferred from a Fully Time‐Dependent <span class="search-highlight">Model</span>
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Journal Article

An Updated Recurrence Model for Chilean Subduction Seismicity and Statistical Validation of Its Poisson Nature

Alan Poulos, Mauricio Monsalve, Natalia Zamora, Juan Carlos de la Llera
Published: 27 November 2018
Bulletin of the Seismological Society of America (2019) 109 (1): 66–74.
DOI: https://doi.org/10.1785/0120170160
... higher and lower than two of the previously reported models. Because one of the strongest assumptions in earthquake occurrence models is that they follow a homogeneous Poisson process, this hypothesis is statistically tested herein, finding that the declustered catalog only partially complies...
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View PDF for article title, An Updated Recurrence <span class="search-highlight">Model</span> for Chilean Subduction Seismicity and Statistical Validation of Its <span class="search-highlight">Poisson</span> Nature
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Voronoi residuals for (a) Null Poisson model, (b) Hawkes model estimated using isotropic MISD (equation 2), (c) Hawkes model estimated using anisotropic MISD (equation 5), and (d) Helmstetter et al. (2007). Striped shells indicate positive residuals, and solid cells indicate negative residuals, with lighter shading indicating larger absolute values of the residuals.

Voronoi residuals for (a) Null Poisson model, (b) Hawkes model estimated us...

Published: 18 May 2021
Figure D2. Voronoi residuals for (a) Null Poisson model, (b) Hawkes model estimated using isotropic MISD (equation  2 ), (c) Hawkes model estimated using anisotropic MISD (equation  5 ), and (d)  Helmstetter et al. (2007) . Striped shells indicate positive residuals, and solid cells indicate
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AALR values per grid point. (a) Poisson model. (b) G20sm_ab_6 ETAS conditional model. (c) G20sm_ab_6 ETAS unconditional model. Note that the color scale differs in panel (b).

AALR values per grid point. (a) Poisson model. (b) G20sm_ab_6 ETAS conditio...

Published: 01 February 2021
Figure 7. AALR values per grid point. (a) Poisson model. (b) G20sm_ab_6 ETAS conditional model. (c) G20sm_ab_6 ETAS unconditional model. Note that the color scale differs in panel (b).
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(a) A sequence of events generated by a Poisson model with μ=1. (b) A bursty sequence generated by the Weibull interevent‐time distribution with a=0.3, b=2. (c) An antibursty sequence generated by the Gaussian interevent‐time distribution with the mean m=1 and the standard deviation σ=0.1. The color version of this figure is available only in the electronic edition.

(a) A sequence of events generated by a Poisson model with μ = 1 . (...

Published: 14 April 2020
Figure 4. (a) A sequence of events generated by a Poisson model with μ = 1 . (b) A bursty sequence generated by the Weibull interevent‐time distribution with a = 0.3 , b = 2 . (c) An antibursty sequence generated by the Gaussian interevent‐time distribution with the mean m
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Zero-inflated Poisson model for collection events. All expected changes are...

Published: 01 August 2014
Table 3.— Zero-inflated Poisson model for collection events. All expected changes are significant except where marked by asterisk.
Journal Article

A rectangular-grid lattice spring model for modeling elastic waves in Poisson’s solids

Muming Xia, Hui Zhou, Hanming Chen, Qingchen Zhang, Qingqing Li
Journal: Geophysics
Published: 10 January 2018
Geophysics (2018) 83 (2): T69–T86.
DOI: https://doi.org/10.1190/geo2016-0414.1
... and Srolovitz, 1989 ; Ladd and Kinney, 1997 ; Ladd et al., 1997 ). To model the materials with different Poisson’s ratios, angular springs were added into the original linear spring system ( Wang, 1989 ). Ladd and Kinney (1997) introduce the idea of an elastic element to improve the simulation precision...
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View PDF for article title, A rectangular-grid lattice spring <span class="search-highlight">model</span> for <span class="search-highlight">modeling</span> elastic waves in <span class="search-highlight">Poisson’s</span> solids
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Rate of exceedance (Rp(n)(GMr=1≥x)) for the M ≥ 5 caldera collapse earthquakes at Kīlauea, during a 50 yr period, for the preferred non‐Poisson model shown in Figure 6 and a Poisson distribution with the same mean rate and using the ground‐motion exceedance model from Figure 5b. The rates for the non‐Poisson model are computed using 10 million Monte Carlo simulations, and the Poisson calculations use equation (2). The color version of this figure is available only in the electronic edition.

Rate of exceedance ( R p ( n ) ( GM r = 1 ≥ x ) ) f...

Published: 02 March 2022
Figure 8. Rate of exceedance ( R p ( n ) ( GM r = 1 ≥ x ) ) for the M ≥ 5 caldera collapse earthquakes at Kīlauea, during a 50 yr period, for the preferred non‐Poisson model shown in Figure  6 and a Poisson distribution with the same mean rate and using the ground
Image
Deaggregated seismic hazard from BPT (α=0.5) and Poisson models for the city of Rome (indicated with the yellow disk) for 10% in 50 yr probability of exceedance on crystalline rock with no site amplifications: PGA (a, b, left) and SA1 (c, d, right). PGA and SA1 are 0.14–0.13 g and 0.080–0.075 g in Rome, respectively.

Deaggregated seismic hazard from BPT ( α =0.5) and Poisson models for the...

Published: 01 April 2009
Figure 12. Deaggregated seismic hazard from BPT ( α =0.5) and Poisson models for the city of Rome (indicated with the yellow disk) for 10% in 50 yr probability of exceedance on crystalline rock with no site amplifications: PGA (a, b, left) and SA 1 (c, d, right). PGA and SA 1 are 0.14
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Deaggregated seismic hazard from BPT (α=0.5) and Poisson models for the city of L’Aquila (indicated with the yellow disk) for 10% in 50 yr probability of exceedance on crystalline rock with no site amplifications: PGA (a, b, left) and SA1 (c, d, right). PGA and SA1 are 0.39–0.42 g (PGA) and 0.36–0.41 g (SA1) in L’Aquila, respectively. Here and figure 12, 13, 14, 15, 16, 17, and 18, the color of the bar over each location indicates the average magnitude of all potential seismic sources at that location. The height of the bar is proportional to the hazards from all sources at the location. Red lines represent surface traces of the faults. Major faults are numbered and correspond to one as given in Tables 1 and 2. F09: Fault number 9, Fucino, as in Tables 1 and 2; Smoothed seismicity (SS).

Deaggregated seismic hazard from BPT ( α =0.5) and Poisson models for the...

Published: 01 April 2009
Figure 11. Deaggregated seismic hazard from BPT ( α =0.5) and Poisson models for the city of L’Aquila (indicated with the yellow disk) for 10% in 50 yr probability of exceedance on crystalline rock with no site amplifications: PGA (a, b, left) and SA 1 (c, d, right). PGA and SA 1 are 0.39
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The frequency of concretions observed on the outcrops is matched adequately by a Poisson model with λ = 0.014 m-2. In the vertical and horizontal directions, the Poisson models cannot be rejected at the 90% confidence level using x2 tests.

The frequency of concretions observed on the outcrops is matched adequately...

Published: 01 December 2002
Figure 8 The frequency of concretions observed on the outcrops is matched adequately by a Poisson model with λ = 0.014 m -2 . In the vertical and horizontal directions, the Poisson models cannot be rejected at the 90% confidence level using x 2 tests.
Journal Article

Effect of Time Dependence on Probabilistic Seismic-Hazard Maps and Deaggregation for the Central Apennines, Italy

A. Akinci, F. Galadini, D. Pantosti, M. Petersen, L. Malagnini, D. Perkins
Published: 01 April 2009
Bulletin of the Seismological Society of America (2009) 99 (2A): 585–610.
DOI: https://doi.org/10.1785/0120080053
...Figure 12. Deaggregated seismic hazard from BPT ( α =0.5) and Poisson models for the city of Rome (indicated with the yellow disk) for 10% in 50 yr probability of exceedance on crystalline rock with no site amplifications: PGA (a, b, left) and SA 1 (c, d, right). PGA and SA 1 are 0.14...
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View PDF for article title, Effect of Time Dependence on Probabilistic Seismic-Hazard Maps and Deaggregation for the Central Apennines, Italy
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Mean hazard curve as computed in Figure 1(red), along with mean curves where the Empirical Poisson model and BPT models (blue and green, respectively) are given exclusive weight on all faults. Curves for the BPT-step and Poisson models being given exclusive weight are very close to that of the BPT model (not shown for clarity).

Mean hazard curve as computed in Figure 1 (red), along with mean curves wh...

Published: 01 March 2005
Figure 5. Mean hazard curve as computed in Figure 1 (red), along with mean curves where the Empirical Poisson model and BPT models (blue and green, respectively) are given exclusive weight on all faults. Curves for the BPT-step and Poisson models being given exclusive weight are very close
Journal Article

Stochastic time-predictable model for earthquake occurrences

T. Anagnos, A. S. Kiremidjian
Published: 01 December 1984
Bulletin of the Seismological Society of America (1984) 74 (6): 2593–2611.
DOI: https://doi.org/10.1785/BSSA0740062593
... fault near Parkfield, where data has suggested time-predictable behavior, are obtained for illustrative purposes. Comparisons are made with the Poisson model. Results indicate that currently used Poisson models may give lower estimates of the seismic hazard when there has been a seismic gap...
View PDF for article title, Stochastic time-predictable <span class="search-highlight">model</span> for earthquake occurrences
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Journal Article

Stochastic slip-predictable model for earthquake occurrences

Anne S. Kiremidjian, Thalia Anagnos
Published: 01 April 1984
Bulletin of the Seismological Society of America (1984) 74 (2): 739–755.
DOI: https://doi.org/10.1785/BSSA0740020739
... on the time of occurrence of the last event. The hazard along the Middle America Trench, Mexico, where data has suggested slip-predictable behavior, is obtained for illustrative purposes. Comparisons of this model with the Poisson model show that probability forecasts are underestimated with the Poisson model...
View PDF for article title, Stochastic slip-predictable <span class="search-highlight">model</span> for earthquake occurrences
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Maps of ratios of PGA (A, B, C, left) and SA1 (D, E, F, right) hazard between time-dependent and Poisson models. Maps show ratios, BPT over Poisson model for 10% exceedance in 50-tear hazard, using different α values: (a, d) 0.3, (b, e) 0.5, and (c, f) 0.7.

Maps of ratios of PGA (A, B, C, left) and SA 1 (D, E, F, right) hazard b...

Published: 01 April 2009
Figure 10. Maps of ratios of PGA (A, B, C, left) and SA 1 (D, E, F, right) hazard between time-dependent and Poisson models. Maps show ratios, BPT over Poisson model for 10% exceedance in 50-tear hazard, using different α values: (a, d) 0.3, (b, e) 0.5, and (c, f) 0.7.
Journal Article

Accounting for the Variability of Earthquake Rates within Low‐Seismicity Regions: Application to the 2022 Aotearoa New Zealand National Seismic Hazard Model

Pablo Iturrieta, Matthew C. Gerstenberger, Chris Rollins, Russ Van Dissen, Ting Wang, Danijel Schorlemmer
Published: 12 January 2024
Bulletin of the Seismological Society of America (2024) 114 (1): 217–243.
DOI: https://doi.org/10.1785/0120230164
.... This work investigates the performance of stationary Poisson and spatially precise forecasts, such as smoothed seismicity models (SSMs), in terms of the available training data. Catalog bootstrap experiments are conducted to: (1) identify the number of training data necessary for SSMs to perform spatially...
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View PDF for article title, Accounting for the Variability of Earthquake Rates within Low‐Seismicity Regions: Application to the 2022 Aotearoa New Zealand National Seismic Hazard <span class="search-highlight">Model</span>
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Frequency distribution functions of intensity difference for shallow events. (a) Data and the Poisson and geometric models. (b) Data and the bimodal Poisson model.

Frequency distribution functions of intensity difference for shallow events...

Published: 01 April 2011
Figure 12. Frequency distribution functions of intensity difference for shallow events. (a) Data and the Poisson and geometric models. (b) Data and the bimodal Poisson model.