Seismology Can’t address Global Clustering of M9 Earthquakes

Chris Goldfinger1, Yasutaka Ikeda2

 1Oregon State University, College of Oceanic and Atmospheric Sciences 104 Ocean Admin. Bldg., Corvallis OR 97331, USA.

gold@coas.oregonstate.edu

2 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 ?

http://www.gccapitalideas.com

Wharton Basin, 2012

http://www.gccapitalideas.com

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.

“There is no evidence of global large-earthquake clustering beyond localized aftershock sequences.“

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.

Oliviera, 2012 arXiv.org

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.

This is an estimate of the power of test 1 of Michael, 2011.

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…

Probabilities of p-values less than 5% by testing inter-event timedistribution for a Poisson distribution with a Kolmogorov-Smirnov test.

Oliviera, 2012 arXiv.org Cornell University

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 samplesrespectively.

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.

K. Feltzer, AGU 2006

Some tests of global clustering are based on assumed adherence to the GR relation at high magnitudes. True?

With small time-sampling, b-value is reasonably well estimated from smaller earthquakes, but not for the large ones.

Also, not true for Cascadia at present.

Back to the global question…

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.

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.

Let’s look at just three examples of very long term earthquake cycling that may bear on the problem of examining global clusters

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

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.

Event number Rupture segment

Agea BP

Rupture lengthkm

Horizontal Displacementm

14 3-segment 1920AD 237 7.0

13 Middle segment 912±149 82 2.0

12 Middle segment 2084±208 73  

11 Middle segment 2793±143 82 1.5

10 Western segment

2895±395 124 2.0

9 Middle segment 3382±589 73 1.5

8 Western segment

3970±170 124  

7 Middle segment 4413±613 82 1.5

6 3-segment 6137±9 237 5.6

5 Middle segment 6689±169 82  

4 Western segment

7546±330 124  

3 Western segment

8848±523 124  

2 3-segment 10770±1125 237  

1Western segment

13615±1105 124  

Table 2 Displacement, rupture length of paleoearthquakes and historical earthquake along the Haiyuan fault[1, 2]

Kindly provided by Junjie Ren,

6. Actual seismic performance of a fault over time.

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.

Cascadia

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.

Are Superquakes Random?

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. ????

Peng et al., 2012 BSSA, this meeting.

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.

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.

GEM Outreach Meeting, June 7-9 2011

Questions?

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.

Questionable prior assumptions…