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  • 1
    Electronic Resource
    Electronic Resource
    Dimension Estimates of Earthquake Epicentres and Hypocentres (1998)
    Springer
    Journal of nonlinear science 8 (1998), S. 581-618 
    Details
    ISSN: 1432-1467
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary. We use the Hill estimator to estimate the correlation dimension of epicentres and hypocentres from four earthquake catalogues: Wellington micro earthquakes, New Zealand catalogue, Kanto micro earthquakes, and the Japanese (JMA) catalogue. We wanted to determine if the fracturing process is fractal, and whether it is different in the four selected regions. We found that the spatial pattern of tabulated shallow events in Japan is more tightly clustered than in New Zealand, while for deeper events the spatial pattern is similar. In both regions, tabulated shallow events are more clustered than tabulated deeper events. It may appear that if one had a sufficiently large amount of data (enabling one to look at sufficiently small interpoint distances), the dimension of the epicentres and hypocentres would appear to be two or three, respectively; however, this may not be a true reflection of the fracturing process. Estimates that indicate that the fracturing tends ultimately to fill the entire space are probably caused by measurement errors in hypocentre locations. Similarly, for large values of interpoint distances, the power law exponent tends to be underestimated because of the boundary effect. When these two effects are sufficiently severe, they tend to merge, and it is difficult to determine power law exponents. These biases are not peculiar to the estimation procedure we have used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003329900060
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    Paper (German National Licenses)
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  • 2
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    An ETAS model with varying productivity rates (2014)
    Oxford University Press
    Details
    Publication Date: 2014-06-21
    Description: We present an epidemic type aftershock sequenc (ETAS) model where the offspring rates vary both spatially and temporally. This is achieved by distinguishing between those space–time volumes where the interpoint space and time distances are small, and those where they are considerably larger. We also question the nature of the background component in the ETAS model. Is it simply a temporal boundary correction ( t  = 0) or does it represent an additional tectonic process not described by the aftershock component? The form of these stochastic models should not be considered to be fixed. As we accumulate larger and better earthquake catalogues, GPS data, strain rates, etc., we have the ability to ask more complex questions about the nature of the process. By fitting modified models consistent with such questions, we should gain a better insight into the earthquake process. Hence, we consider a sequence of incrementally modified ETAS type models rather than ‘the’ ETAS model.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 3
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    Log-likelihood of earthquake models: evaluation of models and forecasts (2015)
    Oxford University Press
    Details
    Publication Date: 2015-03-13
    Description: There has been debate in the Collaboratory for the Study of Earthquake Predictability project about the most appropriate form of the likelihood function to use to evaluate earthquake forecasts in specified discrete space–time intervals, and also to evaluate the validity of the model itself. The debate includes whether the likelihood function should be discrete in nature, given that the forecasts are in discrete space–time bins, or continuous. If discrete, can different bins be assumed to be statistically independent, and is it satisfactory to assume that the forecasted count in each bin will have a Poisson distribution? In order to discuss these questions, we start with the most simple models (homogeneous Poisson), and progressively develop the model complexity to include self exciting point process models. For each, we compare the discrete and continuous time likelihoods. Examples are given where it is proven that the counts in discrete space–time bins are not Poisson. We argue that the form of the likelihood function is intrinsic to the given model, and the required forecast for some specified space–time region simply determines where the likelihood function should be evaluated. We show that continuous time point process models where the likelihood function is also defined in continuous space and time can easily produce forecasts over discrete space–time intervals.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 4
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    Statistical estimation of the duration of aftershock sequences (2016)
    Oxford University Press
    Details
    Publication Date: 2016-04-07
    Description: It is well known that large earthquakes generally trigger aftershock sequences. However, the duration of those sequences is unclear due to the gradual power-law decay with time. The triggering time is assumed to be infinite in the epidemic type aftershock sequence (ETAS) model, a widely used statistical model to describe clustering phenomena in observed earthquake catalogues. This assumption leads to the constraint that the power-law exponent p of the Omori-Utsu decay has to be larger than one to avoid supercritical conditions with accelerating seismic activity on long timescales. In contrast, seismicity models based on rate- and state-dependent friction observed in laboratory experiments predict p ≤ 1 and a finite triggering time scaling inversely to the tectonic stressing rate. To investigate this conflict, we analyse an ETAS model with finite triggering times, which allow smaller values of p . We use synthetic earthquake sequences to show that the assumption of infinite triggering times can lead to a significant bias in the maximum likelihood estimates of the ETAS parameters. Furthermore, it is shown that the triggering time can be reasonably estimated using real earthquake catalogue data, although the uncertainties are large. The analysis of real earthquake catalogues indicates mainly finite triggering times in the order of 100 days to 10 years with a weak negative correlation to the background rate, in agreement with expectations of the rate- and state-friction model. The triggering time is not the same as the apparent duration, which is the time period in which aftershocks dominate the seismicity. The apparent duration is shown to be strongly dependent on the mainshock magnitude and the level of background activity. It can be much shorter than the triggering time. Finally, we perform forward simulations to estimate the effective forecasting period, which is the time period following a mainshock, in which ETAS simulations can improve rate estimates after the occurrence of a mainshock. We find that this effective forecasting period is only in the order of 100 days for moderate mainshocks and in the order of a few years for large events, even if the underlying triggering process lasts much longer.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 5
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    A Revised Local Magnitude (ML) Scale for New Zealand Earthquakes (2016)
    Seismological Society of America (SSA)
    Details
    Publication Date: 2016-04-07
    Description: In this study, a new local magnitude ( M L ) scale is developed for New Zealand and adjacent offshore regions. SeisComP3 (SC3) has been in use for earthquake analysis in New Zealand since September 2012 with the original Richter (1935) log A 0 attenuation relationship for calculating M L . The attenuation characteristics of New Zealand differ significantly from southern California, where M L was originally defined, and therefore result in M L that is consistently high when compared with moment magnitude ( M w ). Using M w from 528 regional moment tensor solutions along with peak observed amplitudes, a new log A 0 curve is derived, along with station correction factors that define a revised M L scale for New Zealand earthquakes that is more consistent with M w . The new log A 0 curve is similar to the original Richter (1935) definition at hypocentral distances of ~100–200 km but differs significantly at closer and farther distances. The new M L is more consistent with M w across New Zealand, including crustal earthquakes and earthquakes below the crust. The California Institute of Technology (Caltech)–U.S. Geological Survey seismic processer (CUSP) system was used for earthquake analysis prior to SC3, and previous studies have derived regression relationships relating CUSP M L with M w . After applying the regression relationships to CUSP M L , we found very good agreement between CUSP M L and the new SC3 M L , which is important for developing a consistent M L between different catalogs. Online Material: Table of station corrections for the New Zealand seismograph network.
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
    Published by Seismological Society of America (SSA)
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  • 6
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    Model parameter estimation bias induced by earthquake magnitude cut-off (2016)
    Oxford University Press
    Details
    Publication Date: 2016-01-01
    Description: We evaluate the bias in parameter estimates of the ETAS model. We show that when a simulated catalogue is magnitude-truncated there is considerable bias, whereas when it is not truncated there is no discernible bias. We also discuss two further implied assumptions in the ETAS and other self-exciting models. First, that the triggering boundary magnitude is equivalent to the catalogue completeness magnitude. Secondly, the assumption in the Gutenberg–Richter relationship that numbers of events increase exponentially as magnitude decreases. These two assumptions are confounded with the magnitude truncation effect. We discuss the effect of these problems on analyses of real earthquake catalogues.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 7
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    Bias in fitting the ETAS model: a case study based on New Zealand seismicity (2012)
    Oxford University Press
    Details
    Publication Date: 2012-12-19
    Description: We fit various forms of the ETAS model to a large region that includes all of the most seismically active areas of New Zealand. The ETAS model contains two components: a component describing background or immigrant events, and a part describing aftershocks of the background events and aftershocks of the aftershocks. We refer to the first part as the background part and the second as the ETAS part. Generally all of the sophistication, and the bulk of the model parameters, lies in the ETAS part of the model. The background component is generally treated as a nuisance component and is often very simplistic. While the main interest lies in the ETAS part of the model, the poor model description of the background part imposes considerable bias on the ETAS part of the model. For example, a poorly specified spatial density of the background events causes many of the background events to be seen as ETAS events. It can also cause the estimated Omori power-law decay p to be too small, and hence the aftershock sequences appear to continue for too long. On the other hand, the boundary of the observation region can impose a reverse bias which causes aftershocks that are close but within the boundary to be seen as background events. In almost all of the large NZ event sequences since 1965, the model consistently under-fits these sequences. Consequently, it over-fits those space-time regions where there is ‘normal’ seismicity with no major events present. This may indicate that the space-time region of a major event sequence is much closer to criticality, in that aftershock events appear to be much more easily initiated. The standard ETAS model does not reflect this observation.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 8
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    A Revised Local Magnitude (ML) Scale for New Zealand Earthquakes [Article] (2016)
    Seismological Society of America (SSA)
    Details
    Publication Date: 2016-04-15
    Description: In this study, a new local magnitude ( M L ) scale is developed for New Zealand and adjacent offshore regions. SeisComP3 (SC3) has been in use for earthquake analysis in New Zealand since September 2012 with the original Richter (1935) log A 0 attenuation relationship for calculating M L . The attenuation characteristics of New Zealand differ significantly from southern California, where M L was originally defined, and therefore result in M L that is consistently high when compared with moment magnitude ( M w ). Using M w from 528 regional moment tensor solutions along with peak observed amplitudes, a new log A 0 curve is derived, along with station correction factors that define a revised M L scale for New Zealand earthquakes that is more consistent with M w . The new log A 0 curve is similar to the original Richter (1935) definition at hypocentral distances of ~100–200 km but differs significantly at closer and farther distances. The new M L is more consistent with M w across New Zealand, including crustal earthquakes and earthquakes below the crust. The California Institute of Technology (Caltech)–U.S. Geological Survey seismic processer (CUSP) system was used for earthquake analysis prior to SC3, and previous studies have derived regression relationships relating CUSP M L with M w . After applying the regression relationships to CUSP M L , we found very good agreement between CUSP M L and the new SC3 M L , which is important for developing a consistent M L between different catalogs. Online Material: Table of station corrections for the New Zealand seismograph network.
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
    Published by Seismological Society of America (SSA)
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  • 9
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    SSLIB: A Programming Environment for the Fitting and Analysis of Point Process and Hidden Markov Models (2007)
    Details
    Publication Date: 2017-04-04
    Description: SSLIB: A Programming Environment for the Fitting and Analysis of Point Process and Hidden Markov Models
    Description: Istituto Nazionale di Geofisica e Vulcanologia (INGV), Rome, Italy Institute of Statistical Mathematics (ISM), Tokyo, Japan Swiss Seismological Service, Institute of Geophysics (ETH), Zürich, Switzerland
    Description: Unpublished
    Description: Erice, Italy
    Description: open
    Keywords: statistical seismology ; software ; 04. Solid Earth::04.06. Seismology::04.06.99. General or miscellaneous
    Repository Name: Istituto Nazionale di Geofisica e Vulcanologia (INGV)
    Type: Oral presentation
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  • 10
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    Statistical estimation of the duration of aftershock sequences (2016)
    In:  Geophysical Journal International
    Details
    Publication Date: 2020-02-12
    Type: info:eu-repo/semantics/article
    Format: application/pdf
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