dc.contributor.advisor | Main, Ian | en |
dc.contributor.advisor | Naylor, Mark | en |
dc.contributor.author | Touati, Sarah | en |
dc.date.accessioned | 2012-08-07T14:45:20Z | |
dc.date.available | 2012-08-07T14:45:20Z | |
dc.date.issued | 2012-06-25 | |
dc.identifier.uri | http://hdl.handle.net/1842/6224 | |
dc.description.abstract | Earthquake statistics is a growing field of research with direct application to probabilistic
seismic hazard evaluation. The earthquake process is a complex spatio-temporal phenomenon,
and has been thought to be an example of the self-organised criticality (SOC) paradigm, in
which events occur as cascades on a wide range of sizes, each determined by fine details of the
rupture process. As a consequence, deterministic prediction of specific event sizes, locations,
and times may well continue to remain elusive. However, probabilistic forecasting, based on
statistical patterns of occurrence, is a much more realistic goal at present, and is being actively
explored and tested in global initiatives.
This thesis focuses on the temporal statistics of earthquake populations, exploring the uncertainties
in various commonly-used procedures for characterising seismicity and explaining
the origins of these uncertainties. Unlike many other SOC systems, earthquakes cluster in
time and space through aftershock triggering. A key point in the thesis is to show that the
earthquake inter-event time distribution is fundamentally bimodal: it is a superposition of a
gamma component from correlated (co-triggered) events and an exponential component from
independent events. Volcano-tectonic earthquakes at Italian and Hawaiian volcanoes exhibit a
similar bimodality, which in this case, may arise as the sum of contributions from accelerating
and decelerating rates of events preceding and succeeding volcanic activity. Many authors, motivated
by universality in the scaling laws of critical point systems, have sought to demonstrate
a universal data collapse in the form of a gamma distribution, but I show how this gamma form
is instead an emergent property of the crossover between the two components. The relative size
of these two components depends on how the data is selected, so there is no universal form.
The mean earthquake rate—or, equivalently, inter-event time—for a given region takes time
to converge to an accurate value, and it is important to characterise this sampling uncertainty.
As a result of temporal clustering and non-independence of events, the convergence is found to
be much slower than the Gaussian rate of the central limit theorem. The rate of this convergence
varies systematically with the spatial extent of the region under consideration: the larger the
region, the closer to Gaussian convergence. This can be understood in terms of the increasing
independence of the inter-event times with increasing region size as aftershock sequences overlap
in time to a greater extent. On the other hand, within this high-overlap regime, a maximum
likelihood inversion of parameters for an epidemic-type statistical model suffers from lower
accuracy and a systematic bias; specifically, the background rate is overestimated. This is
because the effect of temporal overlapping is to mask the correlations and make the time
series look more like a Poisson process of independent events. This is an important result
with practical relevance to studies using inversions, for example, to infer temporal variations
in background rate for time-dependent hazard estimation. | en |
dc.contributor.sponsor | Engineering and Physical Sciences Research Council (EPSRC) | en |
dc.language.iso | en | |
dc.publisher | The University of Edinburgh | en |
dc.relation.hasversion | M. Naylor, I. G. Main, and S. Touati. Quantifying uncertainty in mean earthquake interevent times for a finite sample. Journal of Geophysical Research-Solid Earth, 114(B01316), 2009. | en |
dc.relation.hasversion | S. Touati, M. Naylor, and I. G. Main. Origin and Nonuniversality of the Earthquake Interevent Time Distribution. Physical Review Letters, 102(16), 2009. | en |
dc.relation.hasversion | S. Touati, M. Naylor, I. G. Main, and M. Christie. Masking of earthquake triggering behavior by a high background rate and implications for epidemic-type aftershock sequence inversions. Journal of Geophysical Research-Solid Earth, 116, 2011. | en |
dc.subject | complexity | en |
dc.subject | aftershocks | en |
dc.subject | earthquake statistics | en |
dc.subject | point processes | en |
dc.title | Complexity, aftershock sequences, and uncertainty in earthquake statistics | en |
dc.type | Thesis or Dissertation | en |
dc.type.qualificationlevel | Doctoral | en |
dc.type.qualificationname | PhD Doctor of Philosophy | en |