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Is the coast toast? Exploring Cascadia earthquake probabilities

Seth Stein, Dept. of Earth and Planetary Sciences, Northwestern University, and Institute for Policy Research, Northwestern
University, Evanston, Illinois 60208, USA; Leah Salditch, Dept. of Earth and Planetary Sciences, Northwestern University, Evanston,
Illinois 60208, USA; Edward Brooks, Dept. of Earth and Planetary Sciences, Northwestern University and Institute for Policy
Research, Northwestern University, Evanston, Illinois 60208, USA; Bruce Spencer, Dept. of Statistics, Northwestern University and
Institute for Policy Research, Northwestern University, Evanston, Illinois 60208, USA; and Michael Campbell, Dept. of Earth and
Planetary Sciences, Northwestern University, Evanston, Illinois 60208, USA

The earthquake hazard in the Pacific earthquake occurred in 1700 CE. This cannot be “overdue.” Using the entire
Northwest due to subduction of the Juan record (Fig. 1B) spans 10,000 years, among paleoearthquake record, the chance of an
de Fuca plate beneath North America the world’s longest (Goldfinger et al., 2012, earthquake in the next 50 years is 50/530 =
(Fig. 1A) is drawing much media attention. 2013). 0.094 or 9.4%. Alternatively, assuming that
A The New Yorker article (Schulz, 2015) we are still in the recent cluster gives a
begins, “An earthquake will destroy a The recurrence intervals, differences probability about twice as large: 50/326 =
sizable portion of the coastal Northwest. between the dates of successive paleo 0.15 or 15%.
The question is when.” The article quotes earthquakes, are key to estimating when
a FEMA official saying “everything west the next may occur. The 18 intervals have Time-independent models are used in
of Interstate 5 will be toast.” CBS stated, a mean of 530 years and a standard devia- forecasting floods or hurricanes and in
“Northwest in fear of massive earthquake, tion of 271 years. However, earthquakes many earthquake hazard studies. However,
tsunami.” NPR reported “Sleeping giant seem to have happened in clusters of seismological instincts favor earthquake
overdue.” Stories include statements like, events, separated by 700–1000-year gaps. cycle models, in which strain builds up
“In the next 50 years, there is a 1-in-10 The recent cluster covering 1500 years has slowly after an earthquake to produce the
chance a ‘really big one’ will erupt,” or, a mean of 326 years and standard deviation next one. In this case, the probability of a
“the odds of the big Cascadia earthquake of 88 years. Earthquakes within a cluster large earthquake is small immediately
in the next fifty years are roughly one in occur more frequently and regularly than after one occurs and grows with time. In
three.” in the full record. Hence, when to expect such time-dependent models, the recur-
the next earthquake depends on whether rence interval is described by a probability
These stories lead students to ask where we assume that we are in the recent cluster, density function. The simplest uses the
these probabilities come from and what they or that the cluster is over. familiar Gaussian distribution. The “bell
mean, which offers an educational oppor- curves” in Figure 1C show probabilities of
tunity. Although earthquake probabilities EARTHQUAKE PROBABILITY an earthquake in the next year, which peak
are typically addressed in upper-level MODELS at dates corresponding to the assumed
classes (Stein and Wysession, 2003; Stein mean recurrence. Assuming we are in the
and Stein, 2014), they can be discussed at Most students have learned about prob- recent cluster, the probability is high,
an introductory level. ability models from games of chance—the because the 317 years since 1700 CE is
chance of a flipped coin coming up heads about the mean recurrence of 326 years.
Earthquake probability estimates is 50%. However, earthquake probabilities The probability is lower assuming that we
involve two primary choices: which data are more complicated. Despite years of are not in the cluster, because the mean
are used to describe when past earth- effort, seismologists have not found a recurrence for the entire record is 530
quakes happened and which models are good way to describe them. Although years, so we are not as far into the cycle.
used to forecast when future earthquakes many methods are used, all fall into two
will happen. These choices’ effects can be basic classes. To find the probability of an earthquake
illustrated with simple examples. in 50 years, we integrate under a bell curve
In one, large earthquakes’ recurrence is from a start time to 50 years in the future,
PAST EARTHQUAKE DATA described by a time-independent (Poisson) and include the fact that the earthquake
process. This has no “memory,” so a future hasn’t happened by the start time. The
Although no large earthquakes occurred earthquake is equally likely immediately resulting curves (Fig. 1D), called condi-
along the plate interface for hundreds of after the past one and much later. The tional probabilities, are small shortly after
years, a record of large paleoearthquakes probability of an earthquake in the next 1700 CE and increase with time. Using the
has been compiled from subsidence data t years is approximately t/τ, where τ is the entire record, the chance of an earthquake
on land and turbidites, offshore deposits assumed mean recurrence time. Because in 50 years after 2017 is 0.074 or 7.4%.
recording slope failure. The most recent this probability is constant, an earthquake

6 GSA Today | November 2017

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