Space-Time Point-Process Models for Earthquake Occurrences

Ogata, Yosihiko

doi:10.1023/a:1003403601725

Cited by 1,079 publications

(1,037 citation statements)

References 27 publications

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“…For instance [Oga98] suggests anisotropic kernel smoothing of larger events in order to estimate the spatial background intensity for all earthquakes. In this application, we investigate various spatial background seismicity rate estimates involving kernel smoothings of only the 2030 earthquakes of magnitude 3.5 and higher, by using K W (h) to assess their fit to the earthquake data set.…”

Section: Resultsmentioning

confidence: 99%

“…This suggests that spatial background rate estimates in commonly used models for seismic hazard, such as the epidemic-type aftershock sequence (ETAS) model of [Oga98], might possibly be improved in this way as well. Seismologically, the results are consistent with the notion that Southern California earthquakes, though certainly far more likely to occur on known faults, can potentially occur on unknown faults as well, and these faults may be quite uniformly dispersed.…”

Section: Resultsmentioning

confidence: 99%

“…Likelihood statistics, such as Akaike's Information Criterion (AIC, [Aka74]) and the Bayesian Information Criterion (BIC, [Sch79]) are often used to assess more general classes of models; see e.g. [Oga98] for an application to earthquake occurrence models.…”

Section: Introductionmentioning

confidence: 99%

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Assessing Spatial Point Process Models Using Weighted K-functions: Analysis of California Earthquakes

Veen

Schoenberg

Lecture Notes in Statistics

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We investigate the properties of a weighted analogue of Ripley's K-function which was first introduced by Baddeley, Møller, and Waagepetersen. This statistic, called the weighted or inhomogeneous K-function, is useful for assessing the fit of point process models. The advantage of this measure of goodnessof-fit is that it can be used in situations where the null hypothesis is not a stationary Poisson model. We note a correspondence between the weighted Kfunction and thinned residuals, and derive the asymptotic distribution of the weighted K-function for a spatial inhomogeneous Poisson process. We then present an application of the use of the weighted K-function to assess the goodness-of-fit of a class of point process models for the spatial distribution of earthquakes in Southern California.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Assessing Spatial Point Process Models Using Weighted K-functions: Analysis of California Earthquakes

Veen

Schoenberg

Lecture Notes in Statistics

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“…For applications such as those in seismology [23], extensions of our results and algorithms to the heavy-tailed cases are important. The epidemic-type aftershock sequences (ETAS model) [22], used for modelling times and magnitudes of earthquakes, is a heavy-tailed marked Hawkes process.…”

Section: Extensions and Open Problemsmentioning

confidence: 99%

“…[8]), and they have applications in seismology [13], [22], [23], [27] and neurophysiology [7]. There are many ways to define a marked Hawkes process, but for our purposes it is most convenient to define it as a marked Poisson cluster process X = {(t i , Z i )} with events (or times) t i ∈ R and marks Z i defined on an arbitrary (mark) space M equipped with a probability distribution Q.…”

Section: Introductionmentioning

confidence: 99%

Perfect simulation of Hawkes processes

Møller

Rasmussen

2005

Adv. Appl. Probab.

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Our objective is to construct a perfect simulation algorithm for unmarked and marked Hawkes processes. The usual straightforward simulation algorithm suffers from edge effects, whereas our perfect simulation algorithm does not. By viewing Hawkes processes as Poisson cluster processes and using their branching and conditional independence structures, useful approximations of the distribution function for the length of a cluster are derived. This is used to construct upper and lower processes for the perfect simulation algorithm. A tail-lightness condition turns out to be of importance for the applicability of the perfect simulation algorithm. Examples of applications and empirical results are presented.

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The stress shadow problem in physics-based aftershock forecasting: Does incorporation of secondary stress changes help?

Segou

Parsons

2014

Geophys. Res. Lett.

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Main shocks are calculated to cast stress shadows across broad areas where aftershocks occur.Thus, a key problem with stress-based operational forecasts is that they can badly underestimate aftershock occurrence in the shadows. We examine the performance of two physics-based earthquake forecast models (Coulomb rate/state (CRS)) based on Coulomb stress changes and a rate-and-state friction law for their predictive power on the 1989 M w = 6.9 Loma Prieta aftershock sequence. The CRS-1 model considers the stress perturbations associated with the main shock rupture only, whereas CRS-2 uses an updated stress field with stresses imparted by M ≥ 3.5 aftershocks. Including secondary triggering effects slightly improves predictability, but physics-based models still underestimate aftershock rates in locations of initial negative stress changes. Furthermore, CRS-2 does not explain aftershock occurrence where secondary stress changes enhance the initial stress shadow. Predicting earthquake occurrence in calculated stress shadow zones remains a challenge for stress-based forecasts, and additional triggering mechanisms must be invoked.

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Space-Time Point-Process Models for Earthquake Occurrences

Cited by 1,079 publications

References 27 publications

Assessing Spatial Point Process Models Using Weighted K-functions: Analysis of California Earthquakes

Assessing Spatial Point Process Models Using Weighted K-functions: Analysis of California Earthquakes

Perfect simulation of Hawkes processes

The stress shadow problem in physics-based aftershock forecasting: Does incorporation of secondary stress changes help?

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