Seismology Can’t address Global Clustering of M9 Earthquakes
Chris Goldfinger1, Yasutaka Ikeda2
1Oregon
2
State University, College of Oceanic and Atmospheric Sciences 104 Ocean Admin. Bldg., Corvallis OR 97331, USA.
gold@coas.oregonstate.edu
Department of Earth and Planetary Science, University of Tokyo (Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan,
ikeda@eps.s.u-tokyo.ac.jp
This picture alone should serve as
a reminder that we shouldn’t toss
out an observation because we
can’t explain it.
That’s the whole talk, any
questions?
Alfred Wegener, 1910
Ok, one more….
J. Harlen Bretz, 1926.
 Clustered or not clustered?
 Statistically meaningful or not?
 If not statistically meaningful, does the Earth care?
 How can opposing models exist?
 Is there a mechanism ?
Wharton
Basin,
2012
http://www.gccapitalideas.com
http://www.gccapitalideas.com
“There is no evidence of global large-earthquake clustering beyond
localized aftershock sequences.“
 Temporal clustering of M> 8.5 earthquakes is clear.
 Arguments both in favor and against statistical significance of this
clustering are not strong.
 There is just not enough statistical power in such a short time series
to convincing prove or disprove the clustering hypothesis.
 Frequency based statistical approaches require large sample size,
which we do not have.
I’m a geologist, so
can’t assess the
efficacy and power of
each of he multiple
tests that have been
applied to the 110
year catalog. But
here are a few tests
from others that are
out there…
Distribution of p-values obtained by testing the fit of an
exponential distribution with the Kolmogorov-Smirnov test for
inter-event times in a clustered-by construction process. The bins
of this histogram have width of 5%, thus the first bin corresponds
to the probability of hypothesis rejection under the 5%
significance level.
This is an
estimate of the
power of test 1
of Michael, 2011.
Type II error or false negative rate of 60%: failing to detect a known structure in
the data (3 clusters of 4-5 members per century, similar to the catalog.
Oliviera, 2012 arXiv.org
Probabilities of p-values less than 5% by testing inter-event time
distribution for a Poisson distribution with a Kolmogorov-Smirnov test.
Oliviera, 2012 arXiv.org Cornell University
This test (Shearer and Stark, 2011) is
more powerful , and correctly rejects
the null hypothesis most of the time.
But, it works well only if the sample
rate is the same as the long term
rate of clusters, otherwise it loses
power rapidly. The best case is a
false negative rate of ~ 20%, not
trivial.
Distributions of p-values using Pearson -square for a
Poisson hypothesis testing multiple-events inter event
times. The stochastic process has parameters of 3
clusters per century and 4 events per decades within
each cluster. The samples were tested for hypothesized
Poisson distribution of different annual frequency
parameters . The average over all 2000/110 years
samples is = 0:12. The values = 0:15 and = 0:20
correspond approximately to the 70% and 90% quantiles
of the distribution of average frequency for all samples
respectively.
Oliviera, 2012 arXiv.org Cornell University
Back to the global question…
Some tests of global clustering
are based on assumed
adherence to the GR relation at
high magnitudes. True?
With small time-sampling, bvalue is reasonably well
estimated from smaller
earthquakes, but not for the large
ones.
Also, not true for Cascadia at
present.
K. Feltzer, AGU 2006
Pointed out by Phillip Stark in his talk, statistical tests applied
to this problem generally do not consider the order of the data,
(time). They also do not consider any spatial relationships.
Moreover, other things that are not considered:
1) M9 earthquakes are fundamentally different in total energy
release, so mechanisms linking them could well be unique
to very energetic events. Triggering of many smaller
events may not follow.
2) M9+ events may sometimes rupture into the mantle,
(Sumatra, Wharton Basin) or have deep slow events
associated (Chile 1960??) another potentially distinguishing
characteristic setting them apart from smaller earthquakes
 “Failed to eliminate the null hypothesis”
 This statement of failure to disprove a pre-defined
alternative says little about whether something actually
happened or not, and whether it has significance or not in
the case of very small sample size. The Earth may not have
read statistical textbooks….
 “Absence of evidence is not evidence of absence”
 This is a more conservative statement that acknowledges
our chronically data poor situation in the earth sciences.
Absence of evidence also proves nothing.
 In the case of potential global clustering, we do not have
absence of evidence, we have evidence. The argument
against is instead, a much weaker twofold argument that we
have:
1) Failed to eliminate the null hypothesis
2) No Mechanism is apparent.
Let’s look at just three examples of very long term
earthquake cycling that may bear on the problem
of examining global clusters
NE Japan
Evidence that the 869
AD Jogan tsunami
and two predecessors
penetrated ~ 5 km
inland in the Sendai
plain, compared to < 1
km for recent events
was published in 2001
by Minoura et al.
Additional work by
Sawai et al., 2007 and
2008 confirmed this
result.
869 Jogan
tsunami
inundation
(From
Shishikura et
al., 2007).
We trenched at
the 5 red dots,
and confirmed
and added to
this analysis.
We also found
that the Jogan
tsunami was at
least locally
much larger
than 2011!!
Figure from Goldfinger, Ikeda, and Yeats, in review.
Ikeda and Okada, JGR in revision
6. Actual seismic performance of a fault over time.
Event number
Rupture
segment
Age
a BP
Rupture length
km
14
3-segment
1920AD
237
Horizontal
Displacemen
t
m
7.0
Middle segment
912±149
82
2.0
Middle segment
2084±208
73
Middle segment
2793±143
82
1.5
Western segment
2895±395
124
2.0
Middle segment
3382±589
73
1.5
Western segment
3970±170
124
Middle segment
4413±613
82
1.5
3-segment
6137±9
237
5.6
Middle segment
6689±169
82
Western segment
7546±330
124
Western segment
8848±523
124
2
3-segment
10770±1125
237
1
Western
segment
13615±1105
124
13
12
11
10
9
8
7
6
5
4
3
Kindly provided by Junjie Ren,
Table 2 Displacement, rupture length of paleoearthquakes and historical earthquake
along the Haiyuan fault[1, 2]
The Haiyuan fault (as well as Nankai and many others), has single and multisegment ruptures in its
long term history. The three segment 1920 event was rare, its predecessor was ~ 6000 years prior.
Does slip scale with rupture length? This can be shown from field data such as the 3-D trenching of the
Haiyuan fault, and is consistent with modern data.
Cascadia
So what was the largest Holocene earthquake in Cascadia?
The well known AD 1700 earthquake is thought to be Mw=9.0, yet it is only
“average” in the turbidite record. There are about a dozen others like it in the 41
event record over 10,000 years. The largest events are T11 and T16, which we
estimate to have been about three times the mass, and possibly ~1.4 times the
energy (Mw=9.1) as the 1700 event.
Are Superquakes Random?
They may well be. But there is evidence from Chile and from Cascadia that subduction
zones may cycle energy over longer time scales than one or a few seismic cycles.
In this plot we arbitrarily scale Cascadia turbidite mass (energy loss) against recurrence
time (energy gain), setting the slope of the trend = 0 to maintain a long term constant
state. The resulting plot suggests long term energy cycling that are neither time nor slip
predictable, but does appear to have some periodicity.
Chile supercycles. Cisternas et al., 2005
Sumatra supercycles. Sieh et al., 2008.
Mechanisms? The arguments against global clustering fall back on
lack of a mechanism if it can’t be demonstrated statistically. Let’s
suppose that clustering does exist. What could be the mechanism?
 Dynamic triggering seems unlikely as it can’t explain global
clusters with years of separation between events.
 Static stress triggering deemed unlikely at large distances and
small perturbations.
Yet there are many thing that are poorly understood in global dynamics….
Daub et al (2012 GRL) also fail to falsify the null hypothesis of Poisson
behavior, but point out that here are many poorly understood processes,
such as VLF, tremor, ETS, and silent earthquakes that highlight the gaps in
understanding of global dynamics.
Deep slow precursors (1960)? Or large slow afterslip?
Perhaps dynamic triggering of tremor on deep plate interface serves to
additionally load the locked interface of subduction zones, bring them closer
to failure? Seems a minor effect, but could transfer stress at great distance.
????
Movie S6 [Tohoku-Oki_Shelly_PKD.mov; 6.7 MB].
Example of triggered tremor during the 2011 Mw 9.0
Tohoku-Oki earthquake. The top panel shows a
cross-section view along and parallel to the
Parkfield-Cholame section of the San Andreas
Fault. The blue dots mark the hypocenters of
regular earthquakes, and the small black plus
symbols show tremor family source locations.
When activity is detected in each family, the source
location lights up as a solid red circle.
Peng et al.,
2012 BSSA,
this meeting.
Lower panels show velocity seismograms recorded
near Parkfield, filtered 4-9 Hz showing mostly local
energy (upper) and unfiltered broadband station
PAGB vertical (black) and transverse (blue) in the
lowermost panel, showing mostly energy from the
distant earthquake.
Conclusions
• Global earthquake clustering is clearly apparent in recent records, and
the recent Wharton Basin earthquake continues the trend. But it could
well be random.
• Statistical tests of global clustering on both sides are relatively weak
with 110 years of record, which can be an order of magnitude shorter
(maybe two) than some seismic supercycles.
• Very long paleoseismic records can illuminate long term strain
patterns i.e. “Supercycles”. The origins of such patterns (if real) are
unknown, but local or global connections to other plate boundary
faults are a possibility.
• Global clustering is a basic observation of our time, and cannot be
rejected or validated with any current method statistical or otherwise.
Paleoseismology may be able to address this question as more long
records are developed, though radiocarbon is a limiting factor at
present.
Questions?
GEM Outreach Meeting, June 7-9 2011
Questionable prior assumptions…
The Poison distribution is sometimes falsely considered a neutral null hypothesis
to test against. However there are an infinite number of processes not satisfying
the two main attributes of Poissonian, that of no memory and equal probability at
any given time.
“This becomes relevant when the available data is limited and a consensus view
cannot be established since short data series could be explained adequately by
more than one stochastic process.”
A Poisson distribution can be postulated on arguments of simplicity and
plausibility, which, while appealing, does not constitute objectivity in the
explanation for a phenomenon.
Otherwise, a Poisson process should be regarded as only one among many
possible explanations.
In other words testing against a Poisson process has no particular appeal in this
case.