ΤΑ ΝΕΑ ΤΗΣ ΕΕΕΕΓΜ – Αρ. 48 – ΑΥΓΟΥΣΤΟΣ 2012
Στις 8 Αυγούστου 2012 δημοσιεύθηκε στις ελληνικές εφη-
μερίδες η παρακάτω ανταπόκριση του Αθηναϊκού και Μακε-
δονικού Πρακτορείου Ειδήσεων για την πιθανή σχέση, βάσει
της θεωρίας «ντόμινο», μεταξύ των μεγάλων καταστροφι-
κών σεισμών που συνέβησαν στη γη τα τελευταία χρόνια.
Δεν ισχύει η σεισμική θεωρία του ντόμινο
Οι μεγάλοι σεισμοί του πλανήτη δεν συνδέονται
μεταξύ τους με τη θεωρία του «ντόμινο»
Κατά τα τελευταία χρόνια έχει καταγραφεί στη Γη μία σειρά
πολύ μεγάλων και καταστροφικών σεισμών (Σουμάτρα
2004, Αϊτή 2010, Χιλή 2010, Ιαπωνία 2011), που αποδόθη-
καν από μερικούς επιστήμονες σε πιθανή «επικοινωνία» με-
ταξύ τους, παρά τις μεγάλες αποστάσεις, με βάση τη «θεω-
ρία του ντόμινο». Όμως μία νέα αμερικανική επιστημονική
έρευνα έρχεται να καταρρίψει αυτή τη θεωρία περί πυροδό-
τησης διαδοχικών απομακρυσμένων μεγάλων σεισμών, κα-
ταλήγοντας -όπως και άλλες σχετικές μελέτες στο παρελ-
θόν- στο συμπέρασμα ότι τα καταστροφικά γεωλογικά συμ-
βάντα είναι τυχαία και δεν είναι δυνατό να αλληλοεπηρεα-
στούν σε τόσο μεγάλες αποστάσεις.
Οι σεισμολόγοι Τομ Πάρσονς και Έρικ Γκάιστ της Αμερικανι-
κής Γεωλογικής Υπηρεσίας, που έκαναν τη σχετική δημοσί-
ευση στο περιοδικό της Αμερικανικής Σεισμολογικής Εταιρί-
ας, μελέτησαν δύο ομάδες μεγάλων σεισμών: την πιο προσ-
φατη που έλαβε χώρα μετά το 2004 και άλλη μία στη δεκαε-
τία του ΄60, όταν πάλι είχαν τύχει να συμβούν πολλοί ισχυ-
ροί διαδοχικοί σεισμοί σε διάφορα σημεία του πλανήτη.
Για να δουν αν ήταν τυχαία ή όχι η συσσώρευση τόσων σει-
σμών στη δεκαετία του ΄60, καθώς και κατά τα τελευταία
χρόνια, οι δύο γεωλόγοι κατέγραψαν τη χρονική απόσταση
που έχει μεσολαβήσει ανάμεσα στους μεγαλύτερους σει-
σμούς (ισχύος άνω των 8,3 Ρίχτερ) κατά τα τελευταία 100
χρόνια και τη συνέκριναν με μία προσομοιωμένη χρονική
σειρά τυχαίων σεισμών. Τελικά κατέληξαν στο συμπέρασμα
ότι οι μεγάλοι σεισμοί λαμβάνουν χώρα με τυχαίο χρονισμό
και δεν φαίνεται καθόλου να αλληλοσυσχετίζονται.
Και πώς γίνεται τόσοι πολλοί ισχυροί σεισμοί να είναι τυχαί-
οι, αφού κατά καιρούς συμπίπτουν χρονικά; «Ναι, φαίνεται
παράξενο, όμως δεν είναι κάτι που δεν θα περίμενε κανείς
από μία τυχαία διαδικασία, στην οποία το φαινόμενο της
ομαδοποίησης (συγκέντρωσης) είναι απολύτως τυπικό. Αν
π.χ. κανείς παίξει κορώνα-γράμματα πολλές φορές, το από-
τέλεσμα δεν είναι μία ομαλή εναλλαγή ανάμεσα στις κορώ-
νες και τα γράμματα, αλλά μπορούν να εμφανιστούν στη
σειρά πολλές κορώνες ή πολλά γράμματα», δήλωσε ο Πάρ-
σονς. Αυτό, όπως αναφέρουν, έχει και μία επικίνδυνη όψη:
ότι ο κίνδυνος που απειλεί την ανθρωπότητα από μέγα-
σεισμούς είναι στατιστικά ίδιος οποιαδήποτε στιγμή, αφού η
πιθανότητα να συμβεί ένας επόμενος καταστροφικός σεισμός
δεν εξαρτάται από το αν πρόσφατα συνέβη ένας εξίσου ι-
σχυρός σεισμός σε κάποιο άλλο μέρος της Γης.
Από την άλλη, κατά τους Αμερικανούς γεωλόγους, η πιο
αισιόδοξη όψη της μελέτης τους είναι ότι αφού οι μέγα-
σεισμοί είναι τυχαίοι και ήδη έχουν γίνει αρκετοί από αυτούς
κατά τα τελευταία χρόνια σε κοντινά χρονικά διαστήματα,
είναι σχετικά μικρότερη η πιθανότητα να επαναληφθεί κά-
ποια τέτοια παρόμοια συσσώρευση καταστροφών στο άμεσο
μέλλον. Πάντως, προηγούμενες έρευνες έχουν δείξει ότι οι
μεγάλοι σεισμοί όντως φαίνεται να έχουν κάποια επίπτωση
σε μεγαλύτερες αποστάσεις, αλλά χωρίς να αποκτούν μεγά-
λη ισχύ. «Μετά από μεγάλους σεισμούς, βλέπουμε πολλούς
μικρο-σεισμούς σε όλο τον πλανήτη, οι οποίοι όμως για κά-
ποιο λόγο δεν φαίνεται να εξελίσσονται σε μέγα-σεισμούς»,
όπως είπε ο Πάρσονς.
Η διαπίστωση περί τυχαίου χαρακτήρα των σεισμών, εξάλ-
λου, δυσκολεύει την πρόβλεψή τους, αφού μερικοί ερευνη-
τές έλπιζαν ότι η τυχόν παγκόσμια «επικοινωνία» των μέγα-
σεισμών θα διευκόλυνε την πρόβλεψη ενός επόμενου ανά-
λογου συμβάντος. Πάντως οι επιστήμονες διαφωνούν ακό-
μα, σε ποιό βαθμό είναι δυνατή η πρόβλεψη των μελλοντι-
κών σεισμών. Μερικοί επιμένουν ότι το εν λόγω γεωλογικό
φαινόμενο, τελικά, είναι χαοτικό και η πρόβλεψή του είναι
αδύνατη, ενώ άλλοι δεν έχουν σταματήσει να ερευνούν νέ-
ους τρόπους, πιο αποτελεσματικής πρόβλεψης των σεισμών.
Η ΚΑΘΗΜΕΡΙΝΗ, Τετάρτη 8 Αυγούστου 2012,
Επικοινωνήσαμε με τον εκ των συγγραφέων Tom Parsons, ο
οποίος είχε την καλωσύνη να μας στείλη το άρθρο τους, που
δημοσιεύθηκε στο Bulletin of the Seismological Society of
America, Vol. 102, No. 4, pp. 1583–1592, August 2012,
doi: 10.1785/0120110282, και να επιτρέψη την επανδημο-
σίευσή του στα ΝΕΑ ΤΗΣ ΕΕΕΕΓΜ.
Were Global M ≥8:3 Earthquake Time Intervals
Random between 1900 and 2011?
Tom Parsons and Eric L. Geist
The pattern of great earthquakes during the past ∼100 yr
raises questions whether large earthquake occur-rence is
linked across global distances, or whether temporal cluster-
ing can be attributed to random chance. Great-earthquake
frequency during the past decade in particular has engen-
dered media speculation of heightened global hazard. We
therefore examine interevent distributions of Earth’s largest
earthquakes at one-year resolution, and calculate how
compatible they are with a random-in-time Poisson proc-
ess.We show, using synthetic catalogs, that the probability
of any specific global interevent distribution hap-pening is
low, and that short-term clusters are the least repeatable
features of a Poisson process. We examine the real catalog
and find, just as expected from synthetic cata-logs, that the
least probable M ≥8:3 earthquake intervals during the past
111 yr were the shortest (t < 1 yr) if a Poisson process is
active (mean rate of 3.2%). When we study an M ≥8:3
catalog with locally triggered events re-moved, we find a
higher mean rate of 9.5% for 0–1 yr in-tervals, comparable
to the value (11.1%) obtained for simulated catalogs drawn
from random-in-time exponential distributions. We empha-
size short interevent times here because they are the most
obvious and have led to specu-lation about physical links
among global earthquakes. We also find that comparison of
the whole 111-yr observed M ≥8:3 interevent distribution
(including long quiescent peri-ods) to a Poisson process is
not significantly different than the same comparison made
with synthetic catalogs. We therefore find no evidence that
global great-earthquake occurrence is not a random-in-time
We are curious whether clusters of great earthquakes in the
1960s and 2000s that bounded an intervening period of
quiescence (Fig. 1) point to a physical process (Bufe and
Perkins, 2005; Pollitz et al., 1998), or whether these inter-
event times are consistent with a random-in-time Poisson
process. A Poisson process is one in which events occur
independently and with an exponential distribution of times
between events. We therefore calculate the frequency that
ΤΑ ΝΕΑ ΤΗΣ ΕΕΕΕΓΜ – Αρ. 48 – ΑΥΓΟΥΣΤΟΣ 2012
observed earthquake intervals came from an exponential
distribution of the form p(T) = (1/μ) exp(-T/μ) (where T is
time, and μ is mean interevent time) because this function
yields uniform probability (P) versus time for a given period
(ΔT) as P(T≤ΔT) = 1 − exp(-ΔT/μ). Consistency with a
Poisson process means that the global large-earthquake
hazard is constant in time and, outside of local aftershock
zones (Parsons and Velasco, 2011), not related to past
events. Inconsistency at high confidence could be inter-
preted to imply a global seismic cycle, as Bufe and Perkins
The possibility that earthquakes communicate across global
distances could revolutionize our concept of timedependent
worldwide hazard, but past study has yielded differing an-
swers (Bufe and Perkins, 2005; Geist and Parsons, 2011;
Michael, 2011; Shearer and Stark, 2012). In this paper, we
focus on finding out how often the observed frequency of
interevent times, discretized into one-year bins, could have
occurred randomly. We examine these features closely be-
cause short-term clusters of high global activity get noticed
by seismologists, the public, and the press (e.g., Barcott,
2011; Winchester, 2011), with all parties concerned about
the possible heightened worldwide earthquake hazard.
M ≥8:3 Earthquakes between 1900 and 2011
We extract M ≥8:3 events from the 1900–1999 Centennial
catalog (Engdahl and Villaseñor, 2002; Fig. 2), augmented
for the period 2000–2011 with the Advanced National
Seismic System (ANSS) and Global Seismograph Network
(GSN) catalog (Table 1). The M ≥8:3 level is well above the
completeness threshold, and moment magnitudes have
been calculated and compiled by Engdahl and Villaseñor
(2002). Our lower magnitude of interest is arbitrarily cho-
sen to some extent, but there are reasons why M ≥8:3
turns out to be a good number both for catalog complete-
ness and for identifying triggered events. Magnitude com-
pleteness is a very serious issue when assessing interevent
time distributions, as we do in this paper. Even one missing
event could completely alter the conclusions, particularly
when it comes to studying long periods of quiescence (as
can be seen in Fig. 1).
Figure 1. Graphical representation of the M ≥8:3 earthquake
catalog we use in this study (Engdahl and Villaseñor, 2002)
augmented for the period 2000–2011 with the ANSS catalog.
All event sizes are given as moment magnitudes. Clusters of
events interspersed with quiescent periods are evident. (a) All
catalog events are shown. (b) A catalog with likely after-
shocks/triggered earthquakes removed is shown.
An important component to this study is identifying likely
triggered earthquakes that have occurred through identified
physical processes. This becomes increasingly difficult to do
with lower magnitude thresholds and requires the use of
declustering algorithms, which bring their own sources of
significant uncertainty. With the M ≥8:3 cutoff, we have the
ability to assess each earthquake individually and can cite
past studies where the interaction physics have been mod-
eled. We identify likely nonspontaneous M ≥8:3 events
(Fig. 2) as those that have been directly associated with
stress-change models (Chery et al., 2001; Nalbant et al.,
2005; Stein et al., 2010), or that fit empirical observations
of aftershock characteristics in time and space (Parsons,
2002; Ruppert et al., 2007). Where there is specific infor-
mation about a possible M ≥8:3 aftershock that is inconsis-
tent with a known physical process, we do not remove it
from the catalog, as in the case of the 2007 M ≥8:6 Sunda
earthquake (Wiseman and Bürgmann, 2011).
Figure 2. (a) The magnitude-frequency distribution of all cata-
log events (columns). (b) The magnitude-frequency distribution
of a catalog with likely aftershocks/triggered earthquakes re-
moved. The red lines are b-value = 1 slopes for reference.
Fit of the Raw Catalog to Time-Dependent and Time-
Simple statistical analyses can be performed on the catalog
to determine whether it is consistent with a timedependent
process, a Poisson process, and/or with a clustertype mo-
del. In particular, the distribution of interevent times can be
compared to a lognormal distribution, an exponential distri-
bution in the case of a Poisson process, or a gamma distri-
bution that better accounts for aftershocks and triggered
events (Corral, 2004; Hainzl et al., 2006). We compare the
empirical density function for M ≥8:3 interevent times with
the best-fit lognormal, exponential, and gamma distribu-
tions using maximum likelihood estimation (Fig. 3).
Figure 3. Density distribution of interevent times (years) for the
M ≥8:3 earthquake catalog. The dots show the empirical den-
sity function using exponential binning (Corral, 2004). The red
dashed line shows the best-fit (using maximum likelihood esti-
mation) exponential distribution, the black dashed line shows
the best-fit gamma distribution, and the green dashed line
shows the best-fit lognormal distribution.
ΤΑ ΝΕΑ ΤΗΣ ΕΕΕΕΓΜ – Αρ. 48 – ΑΥΓΟΥΣΤΟΣ 2012
Because the distributions are similar, and because the log-
normal and gamma distributions include an additional
shape parameter, the Akaike information criterion (AIC) is
lowest for the exponential distribution (138.6), increases to
140.2 for the gamma distribution, and is highest for the
lognormal (141.6). The significance of the AIC difference
between lognormal and the other distributions is difficult to
judge, because they are not from the same family. How-
ever, if the AIC is used as a goodness-of-fit measure (e.g.,
Ogata, 1998), then the exponential distribution is the pre-
ferred statistical model for the interevent distribution of M
A Kolmogoroff–Smirnoff (K–S) test on global large earth-
quake interevent times for different magnitude cutoffs was
performed on a declustered catalog by Michael (2011), who
found that the exponential distribution cannot be rejected
for large magnitude cutoffs (M ≥7:5, 8.5, 9) at 95% confi-
dence. We repeat these K–S calculations for the three dis-
tributions shown in Figure 3 and find that the null hypothe-
sis of the data being distributed according to each of the
three distributions cannot be rejected at the 5% signifi-
cance level. Therefore the raw data are not sufficient to
prove any of the common earthquake recurrence distribu-
tion families. This generalized approach shows that the
overall interevent distribution can be fit in a number of
ways but does not give us insight into how unusual specific
features of greatearthquake clusters and gaps are relative
to the possibility that they have happened by random
chance. Further, we have not yet accounted for magnitude
Assembling post-1900 earthquake catalogs requires us to
address uncertainties about earthquake size. Actual magni-
tudes might be higher or lower than the catalog values, and
because a magnitude cutoff has to be applied in any analy-
sis, interevent times will be affected. Magnitude is ex-
pressed on a logarithmic scale, meaning that a uniform plus
or minus error estimate in magnitude units would system-
atically bias the implied moment (energy) upward. We in-
stead convert reported catalog magnitudes to linear mo-
ment, apply Gaussian uncertainties centered on reported
values, and then convert those distributions back to magni-
tudes (Fig. 4).
Figure 4. Magnitude uncertainty is addressed by applying a
Gaussian distribution to the moment estimates (red columns) of
each catalog earthquake. In these examples, the mean moment
is derived from an M 8.3 earthquake. The resulting logarithmic
magnitude uncertainty distributions are shown as blue columns.
We apply in (a) a 0.5 COV to moment of pre 1950 events and
in (b) a 0.2 COV to post 1950 earthquakes.
We use moment uncertainty distributions with coefficient of
variation (COV, standard deviation divided by the mean) of
0.5 for earthquakes before 1950 and a COV of 0.2 for those
after, which matches given magnitude uncertainty limits
(Engdahl and Villaseñor, 2002) with logarithmic weighting.
We draw 100 catalogs at random from possible magnitudes
(Fig. 4) for cutoff thresholds between M ≥8:3 and M ≥8:7
and calculate interevent times for each draw, yielding a
range of possible observed intervals for each one-year bin
(the mean values from this exercise are shown in Fig. 5).
Figure 5. (a) The probability of the same number of intervals
occurring in a 111 yr period if earthquakes occur randomly
through a Poisson process as determined from 1000 synthetic
catalogs drawn at random from exponential distributions. The
blue curve shows values for allM ≥8:3 events (31 in 111 yr),
and the red curve shows the same information but intended to
simulate the catalog with likely triggered earthquakes removed
(25 events in 111 yr). The 0–1-yr interevent bin has the lowest
probability of repeating at
11%. (b) A histogram showing the
distribution of the number of events (ranges from 1 to 15) hap-
pening at 0–1-yr intervals for 31 events in 111 yr from syn-
thetic catalogs. (c) The same information as in (b) except for a
simulation of the catalog with aftershocks removed.
Probability of a Given Number of Interevent Intervals
in One-Year Bins Determined from Synthetic Catalogs
The global pattern of large earthquakes has long periods of
quiescence interspersed with short-term clusters of events
that are calculated to be unlikely outcomes from a Poisson
process by Bufe and Perkins (2005). This is true, though
any specific outcome is unlikely if earthquake occurrence is
random. We show this by conducting a simple experiment;
we create 1000 synthetic earthquake catalogs by drawing
sets of 31 events at random from an exponential distribu-
tion of intervals (mean rate parameter found by dividing 31
events by 111 yr). We see no two interevent distributions
out of 1000 that are exactly alike when the synthetic cata-
logs are discretized in one-year bins.
ΤΑ ΝΕΑ ΤΗΣ ΕΕΕΕΓΜ – Αρ. 48 – ΑΥΓΟΥΣΤΟΣ 2012
To get to the issue of specific observed features, we can
narrow the focus to a particular attribute of the synthetic
catalogs, for example the 0–1 yr interevent period, and
count how many times a given number of intervals is seen
in that bin (values from synthetic catalogs span a range
from 1 to 15) (Fig. 5b, c). This just amounts to comparing
each synthetic catalog of intervals to all the others. The
average frequency that any number of intervals falls into
the 0–1 yr bin is 11.1% of the 1000 synthetic catalogs,
where any number refers to repeats of values from the en-
tire 1-to-15 range. The percentage of synthetic catalogs
that repeat the number of intervals in a given one-year bin
can be thought of as the probability of a particular cluster-
ing behavior that might arise if 31 earthquakes occurred at
random over a 111-yr period (or 25 in 111 yr if a catalog
with aftershocks removed is considered). Generally, the
probability of seeing a particular number of intervals in-
creases with longer interevent times because most of them
are zero in the synthetic catalogs (Fig. 5a). Further, the
exponential distribution has the most weight at small val-
ues, therefore its histogram has more possible integer val-
ues in the short time bins, making them less likely to be
The results of this numerical experiment are useful because
they provide a context to consider when we compare the
observed record of M ≥8:3 earthquakes over the past 111
yr to synthetic catalogs. For example, if we think the num-
ber of great earthquakes that has happened closely spaced
in time (say, less than one year apart) is anomalous, we
might take note that any number of events that have hap-
pened less than one year apart is unusual under a Poisson
process. If great earthquakes are independent of one an-
other, we would expect any given 111-yr period to display
shortterm (t ≤ 1 yr) earthquake clustering that has only
about an 11% chance of occurring.
Matching Observed Features in the Global Interevent
Distribution to Exponential (Random-in-Time) Distri-
The exercise shown in Figure 3, and those conducted by
Michael (2011), imply that the observed record of great
earthquakes is insufficiently persuasive to rule out repre-
sentative functions of the interevent distribution families
thought to underlie earthquake occurrence. However, we
remain curious about how unusual specific features of the
past 111 yr of M ≥8:3 earthquakes are, particularly short-
term clusters like the period from 2000 to 2011. So, to ad-
dress public concerns about apparent large earthquake
clustering (e.g., Barcott, 2011; Winchester, 2011), we at-
tempt to replicate these features—observation and nonob-
servation of interevent times at one-year resolution—of the
global interevent distribution with synthetic catalogs gener-
ated through a Poisson process, while assessing the impact
of magnitude uncertainty.
We focus on the exponential distribution because it can
represent a null hypothesis of independent earthquake tim-
ing when event intervals are drawn from it at random (we
test the observed catalog for independence in a later sec-
tion).We calculate the rates that observed intervals within
one-year bins match a Poisson process by comparing with
1000 interevent distributions from synthetic catalogs made
randomly from exponential distributions (Fig. 6). The idea is
that, because a 111-yr period is relatively short compared
with recurrence intervals of great earthquakes, we can ex-
amine many synthetic catalogs to look for patterns that
replicate observations and gain some insight as to how
common observed features are, such as temporal earth-
quake clustering. This is similar to the general experiment
described previously, but now we compare directly to ob-
served values. Multiple synthetic catalogs give us a way to
assess the impact of the small sampling.
Construction of Synthetic Catalogs and Method of
Comparison with Observations
A group of 1000 synthetic catalogs is made for each of the
100 potentially observed catalogs. Each of the 100 catalogs
is a potential observation because of magnitude uncer-
tainty. This means that some events can drop under a
given lower magnitude threshold because, in some of the
100 realizations, they can end up with too small of a mag-
nitude to be included. Therefore each of the 100 catalogs is
possibly the correct observed data, and each has an indi-
vidual interevent distribution. For every lower magnitude
threshold between M ≥8:3 and M ≥8:7, there are thus 100
realizations of the observed catalogs, and for each of those,
we tally up how many of 1000 synthetic catalogs have the
same number of intervals in one-year bins.We give the
means of these results and the ranges across 95% of the
calculated number of matches in Figure 6.
Figure 6. (a) The blue curves show calculated rates (in % of
1000 synthetic catalogs) that the number of time intervals ob-
served between M ≥8:3 earthquakes is matched by a Poisson
process (left vertical axis). The red columns show mean ob-
served interevent distributions (right vertical axis). (b–e) The
same calculations as in (a) but for higher magnitude cutoffs.
The error bars give the effects of the small observed sample
(found from 1000 simulations) and magnitude uncertainty (100
draws from distributions like those shown in Fig. 4). (f) The
same analysis is performed assuming that reported magnitudes
are exactly correct. As expected (Fig. 5), the lowest rates are
found for the shortest intervals (<1 yr) in all cases (values are
shown by the horizontal dashed lines).
Generation of synthetic catalogs using Monte Carlo sam-
pling of exponential distributions accounts for the expected
variability because of the small number (31) of global M
≥8:3 earthquakes (Fig. 2). We treat the period between
1900 and the first event of a given magnitude cutoff after
1900 as an additional interval, which is likely shorter than
the actual duration. However, we want to include this inter-
val because information can be conveyed by a long ob-
served gap between 1900 and the first event above a given
magnitude cutoff. There is no corresponding interval at the
end of the catalog because of the 2011 M 9.0 Tohoku
earthquake. Each distribution mean used to make synthetic
catalogs is adjusted to equal the number of intervals for
each of the 100 potentially observed catalogs (as described
ΤΑ ΝΕΑ ΤΗΣ ΕΕΕΕΓΜ – Αρ. 48 – ΑΥΓΟΥΣΤΟΣ 2012
previously) and can have different numbers of events be-
cause of magnitude variation. This process yields a total of
100,000 simulations for each cutoff magnitude studied (M
≥8:3 to M ≥8:7 in 0.1 magnitude units).
The error bars on Figure 6 combine the effects of sampling
interevent times and magnitudes because each of 1000
draws is compared with one of 100 realizations of the pos-
sible event magnitudes. For all magnitude cutoffs we exam-
ine betweenM ≥8:3 andM ≥8:7, we note that the lowest
match rate between observations and synthetic catalogs is
for interevent times of <1 yr (Fig. 6), with mean values
ranging from 3.2% for M ≥8:3 to 25.9% for M ≥8:7. There-
fore, the feature that appears least likely when compared
with a Poisson process is the occurrence of so many earth-
quakes (∼9 on average) with short (t < 1 yr) interevent
periods that are present in the global M ≥8:3 catalog (Fig.
6). However, as can be seen in Figure 5, the 0–1 yr intere-
vent time bin has the smallest chance (∼11%) of being re-
peated generally if a Poisson process is active.
We note the thresholds where 95% of the random draws
from exponential distributions are found (error bars and r
values given in Figure 6). We therefore take the high end of
these ranges to be the points of maximum compatibility of
a random-in-time model with the observations and the low
end to be the minimum. Under these criteria, we interpret
the shortest interevent times of M ≥8:3 earthquakes as
having up to an 11.9% rate of matching a random process.
This interpretation changes as a function of interevent time.
Long quiescent periods in the global catalog (up to 36 yr for
M ≥8:3) do not preclude a Poisson process in any of our
calculations. For example, in the M ≥8:3 catalog, we note a
broad range of match rates between 0% and 100% of the
1000 synthetic catalogs with the longest observed intere-
vent time being 36 yr, with a mean over the calculations of
86.0% (Fig. 6). One could turn this argument around and
point out that the low thresholds on probability that specific
intervals came from an exponential distribution can be 0%
(Fig. 6), meaning that the null hypothesis could be false.
Test of the Independence of Interevent Times
A Poisson process is defined as one in which independent
events are separated by exponentially distributed timing.
We are unable to rule out an exponential distribution under-
lying global M ≥8:3 earthquake interevent times, but that
alone does not establish whether there is (or is not) tempo-
ral dependence among them. In a Poisson process, the
amount of time since the last event contains no information
about the amount of time until the next event. One test to
determine if such dependence is present is an autocorrela-
tion on sequential earthquake intervals. This process tests
for functional dependence by identifying repeating or peri-
odic patterns within the interevent distribution.
We conducted autocorrelations on the observed M ≥8:3
catalogs to see if there is any significant dependence but
were unable to find any values that exceeded the 95% con-
fidence bounds (Fig. 7). Confidence bounds were calculated
using the formula derived by Bartlett (1946) for variance,
n is the number of intervals, and ρ(i) is autocorrelation val-
ues for given lags (v) (e.g., Brockwell and Davis, 2002). For
comparison purposes, we sorted the observed interevent
times from shortest to longest to create the appearance of
a functional dependence between them and ran an autocor-
relation test (Fig. 7d). In that case, we do note significant
correlations over the first two lags, as would be expected.
Figure 7. Autocorrelation test of observedM ≥8:3 interevent
times. (a) Events in sequence are shown as a function of the
number of days separating them. (b) Interevent times are
autocorrelated; that is, the trace of (a) is compared with itself
to see if there is any periodicity or dependence between intere-
vent times. The lag gives the interevent time in sequence that
is being compared. When (b) all events are studied, or (c)
spontaneous events are studied, there is no significant (at 95%
confidence) dependence among the observed intervals. When
(d) intervals are artificially sorted from least to greatest, then
dependence is evident in the autocorrelations. This is done to
show the efficacy of the test.
Analysis with Local Aftershocks Removed
We want to assess whether global M ≥8:3 earthquake oc-
curence is independent and random in time. A clear tempo-
ral dependence between mainshock earthquakes and after-
shocks has been demonstrated (e.g., Omori, 1894; Ogata,
1998), and a number of physical models for this depend-
ence have been identified. For example, there are stress-
change explanations of short-term links among earth-
quakes, particularly those that are near in space (Yama-
shina, 1978; Das and Scholz, 1981; Stein and Lisowski,
1983; King et al., 1994; Freed, 2005) and possibly at global
distances as well (Hill et al., 1993; Gomberg et al., 2004;
Hill, 2008), though this has been difficult to establish for
larger earthquakes (Parsons and Velasco, 2011). Therefore,
if we want to make comparisons between observed catalogs
and synthetic ones created assuming a Poisson process,
then events with close temporal and spatial associations
that are explicable by vetted physical models should be
We repeat the calculations made on the M ≥8:3 catalog
shown in Figure 6 with a new catalog comprised of sponta-
neous earthquakes (a list of removed events is given in
Table 2). The removal of likely aftershocks reduces the
number of short intervals in the catalog. As a result, we
calculate the shortest interevent times of M ≥8:3 earth-
quakes as having a mean matching rate of 9.5% to syn-
thetic catalogs and a maximum rate of 21.8% (Fig. 8). This
result implies that if global earthquakes are randomly dis-
tributed, short-term clustering in the 111-yr M ≥8:3 catalog
of spontaneous earthquakes is comparable to the expected
11% repeat rate from synthetic catalogs (Fig. 5). This
again points out that any specific outcome is unlikely, and
that the past decade of apparently increased rates of great
earthquakes is not necessarily anomalous. Matching rates
from the Poisson model for short interevent times are
higher for all tested magnitude thresholds when using the
spontaneous catalog (Fig. 8) than when all events are in-
cluded (Fig. 6).
We find, as did Michael (2011), that the interevent distribu-
tion of great earthquakes over the past 111 yr, when exam-
ined as a whole, cannot be excluded as having emerged
ΤΑ ΝΕΑ ΤΗΣ ΕΕΕΕΓΜ – Αρ. 48 – ΑΥΓΟΥΣΤΟΣ 2012
from a random-in-time Poisson process at 95% confidence.
Neither can they be excluded as having come from distribu-
tions representing time dependence or cluster-type models
Figure 8. (a–f) The same information is presented as in Figure 6
except the input catalog has the likely triggered events identi-
fied in Figure 2 removed.
We study the specifics of the apparent clustering behaviour
of the catalog that has captured scientific and public atten-
tion by breaking up the interevent distribution into one-year
bins. This enables us to assess features like short-term
clusters of events and intervening periods of quiescence.We
find that the number of shortestM ≥8:3 earthquake inter-
vals (<1 yr) over the past 111 yr is matched by a small
number of synthetic catalogs, with mean values ranging
from 3.2% for M ≥8:3 to 25.9% for M ≥8:7 (Fig. 6). When
we study a catalog with likely triggered events removed, we
find mean values ranging from 9.5% for M ≥8:3 to 53.4%
for M ≥8:7 (Fig. 8).
Observed earthquake intervals seem increasingly compati-
ble with a random-in-time distribution when higher magni-
tude cutoffs are imposed, or when longer interevent times
are considered. However, the results of examining specific
features of the interevent distribution should be interpreted
in the context that if global great earthquakes are occurring
at random then any specific number of events that happen
in a short time is unlikely to be repeated in a similar way in
an ∼100-yr span. We conduct an experiment with the pa-
rameters of the observed catalog of M ≥8:3 events to find
the probability of repeating a given number of intervals that
fall into one-year bins and find that the lowest value is for
0–1-yr interevent times at 11.1% (Fig. 5). This is a natural
feature of the exponential distribution, which has more
weight at small times. There is thus a larger range of possi-
ble integer values in the small-time bins, and the rate of
repeating any given value decreases. Thus, features in the
observed catalog seem unusual at first glance but are in
fact quite expected from a random-in-time Poisson process.
So, were global M ≥ 8.3 earthquake time intervals random
between 1900 and 2011? Our results do not disprove a
physical link that causes global earthquake clusters, but
they show that the past 111-yr pattern of M ≥ 8.3 earth-
quakes does not require one. We find no evidence that the
features of great-earthquake occurrence are inconsistent
with a random-in-time, Poisson process.
Data and Resources
Earthquake catalogs used in this study to were drawn from
the Centenial Catalog of Engdahl and Villaseñor, (2002) for
the period 1900–1999 and augmented for the period 2000–
2011 through the ANSS catalog search linked through the
Northern California Earthquake Data Center (NCEDC) web
site at http://www.ncedc.org/anss/catalogsearch.html (last
accessed November 2011).
We very much appreciate reviews by two anonymous re-
viewers and Associate Editor Zhigang Peng, all of whose
constructive suggestions made this a much better paper.
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