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| Titel |
Clustering of seismic events in equivalent dimension hyperspaces - premonitory effects of M8.8 Chile earthquake of February 27, 2010 |
| VerfasserIn |
Stanislaw Lasocki |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250049866
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| Zusammenfassung |
| Seismic events are described by their parameterizations. Specific parameters values linked to
every particular event define a point in the parameter space that represents that event. Hence,
to assess clustering among seismic events one must be able to compare objectively
distances between these points. Metric of most of the seismic parameters is, however,
complex and non-Euclidean and neither the Euclidean distance can be used, nor any
other pre-defined metric can be readily applied in the multidimensional parameter
space.
An equivalent dimension concept has been worked out to investigate, in a non-speculative
way, clustering of events in the spaces built by any combinations of the seismic event
parameterizations. Let earthquake parameters X1,-¦,Xp be continues and have the cumulative
distributions FX1(X1),-¦, FXp(Xp), respectively. We accept that for every Xk,
Xl: k, l -{1,-¦,p},k- lork = l, two intervals of the parameter values, Δxk, Δxl
are equivalent if Prob(Xk -Δxk) = Prob(Xl -Δxl). Since the transformations
Xk- > Uk = FXk(Xk), k=1,..,p return Ukuniformly distributed in [0, 1] the defined
equivalency condition is fulfilled for the same length intervals of Uk, Ul, k,l =
1,..,p. We call U1,-¦, Up equivalent dimensions of seismic parameterizations. An
earthquake is represented by the vector U(U1,-¦, Up) in the Euclidean metric hypercube
[0,1].
In general the probabilistic models for earthquake parameters, FXk(Xk), are not known.
We therefore replace FXk(Xk), k=1,..,p with their model-free, data-driven estimators.
Suppose that we have a series of seismic events from a certain seismogeneic region and a
certain time period. As long as we do not have new data this series of events is the entire
information on the seismic process from the region and time under study, which means that it
is a population of seismic events. Such a population is used to estimate FXk(Xk) by
means of the non-parametric kernel estimation method (e.g. Silverman, 1986 and the
references therein). We apply adaptive kernel estimators with the Gaussian kernel
function.
The transformation to equivalent dimensions is applied to investigate clustering of smaller
seismic events before the giant M8.8 Chile earthquake of February 27, 2010. 5930 seismic
events of M -¥3.5 that occurred in the Flinn-Engdahl region #135 from the beginning of 1991
until the main rupture are regarded as the background population to estimate parameters’
distributions. Time-varying patterns of seismic events are observed in moving time-windows
of various combinations of equivalent dimension parameters. The most significant results
are obtained for the equivalent hyperspace of {dt, dr, M}, where dt and dr are
the time and epicentral distance between every two consecutive events and M is
magnitude of the second event. Systematic event clustering process began some 2.5
year before the main rupture. Formation of two distinct clusters is visible on {dt,
dr}-equivalent plane. Some events tend to group close to the point (0,0) – simultaneous
shortening the interevent time and distance, whereas the other organize themselves
around the point (1,1) – both dt and dr simultaneously elongated. In the last year
before the main rupture magnitude of events building both clusters is distinctly
increased.
This work has been done in the framework of the research project 3935/B/T02/2010/31,
financed by the Ministry of Science and Higher Education for the period 2010-2012 |
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