All the recent hoopla regarding “The Really Big One” (2015 New Yorker article describing the terrifying possibility and risks associated with a magnitude 9 earthquake in the Pacific Northwest) motivated me to do two things: take some reasonable actions to be more prepared; calm my relatives down a bit by elucidating the risks of living with the Cascadia Subduction Zone based on my reading the relevant primary scientific literature. The key to the latter task is clarifying two key parts of Schultz’s story:

“…the odds of the big Cascadia earthquake happening in the next fifty years are roughly one in three. The odds of the very big one are roughly one in ten.”

and (adding bold emphasis and changing written out numbers to actual numbers)

“Thanks to that *[Goldfinger’s]* work, we now know that the Pacific Northwest has experienced 41 subduction-zone earthquakes in the past 10,000 years. If you divide 10,000 by 41, you get 243, which is Cascadia’s recurrence interval: the average amount of time that elapses between earthquakes. That timespan is dangerous both because it is too long—long enough for us to unwittingly build an entire civilization on top of our continent’s worst fault line—and because it is not long enough. Counting from the earthquake of 1700, we are now 315 years into a 243 year cycle.

**It is possible to quibble with that number.** Recurrence intervals are averages, and averages are tricky…”

Ok, so let’s quibble by looking at Goldfinger’s work, specifically his analysis of layers of submarine mud that avalanche deeper into the sea during big earthquakes (a.k.a. turbidites). In “Turbidite Event History—Methods and Implications for Holocene Paleoseismicity of the Cascadia Subduction Zone” (Goldfinger et al., 2012), you can find in the abstract the results that underlie Schultz’s prose:

The combined stratigraphic correlations, hemipelagic analysis, and ^{14}C framework suggest that the Cascadia margin has three rupture modes: (1) 19–20 full-length or nearly full length ruptures; (2) 3 or 4 ruptures comprising the southern 50–70 percent of the margin; and (3) 18–20 smaller southern-margin ruptures during the past 10 k.y., with the possibility of additional southern-margin events that are presently uncorrelated. The shorter rupture extents and thinner turbidites of the southern margin correspond well with spatial extents interpreted from the limited onshore paleoseismic record, supporting margin segmentation of southern Cascadia. The sequence of 41 events defines an average recurrence period for the southern Cascadia margin of ~240 years during the past 10 k.y.

19+3+18=40 events, and 20+4+20=44 events

so it seems Schultz tries to be sort-of conservative and chooses to divide by 41:

**10,000 years / 41 events = 243.9 years between events**

**= 244 year average recurrence time**

We could get a range of recurrence times instead by using the range of number of events — 40-44:

10,000/40 = 250 years

10,000/44 = 227 years

And if we average those estimates, we’d get (250+227)/2 = 238 years

So, rounded down (for whatever reason) the bold math above yields (approximately) Schultz’s 243 year average recurrence time for a “big Cascadia earthquake” by which she means either a full-rupture earthquake (involving the whole boundary between the North American and Juan de Fuca tectonic plates, from British Columbia down to northern California) or a shorter/smaller ruptures at the southern half or 2/3 of the margin (CA and OR). But we could break these averages down for big full plate ruptures (let’s assume 20 rather than 19), 50-70% southern ruptures, and smaller partial southern ruptures. In the grey literature (not peer-reviewed) document “CHARACTERIZING THE CASCADIA SUBDUCTION ZONE FOR SEISMIC HAZARD ASSESSMENTS” Wong et al. (2014) make a similarly motivated division of earthquakes, assuming they would fall into groups of magnitude 9, 8-8.8, and <8. Adopting a similar terminology (and implicit assumptions), we can go back to the Goldfinger abstract and calculate

**10,000 years / 20 full-length events = 500 years between magnitude 9 events**

**10,000 years / 50-70% length events = 2,500 years between 8-8.8 events**

**10,000 years / 20 full-length events = 500 years between magnitude <8 events**

In the spirit of quibbling, what magnitude earthquakes are we talking about in the New Yorker article? Schultz implies we are talking about the really big (~9.0) and big ones (>8), but not the <8 events:

If, on that occasion, only the southern part of the Cascadia subduction zone gives way—your first two fingers, say—the magnitude of the resulting quake will be somewhere between 8.0 and 8.6. *That*’*s* the big one. If the entire zone gives way at once, an event that seismologists call a full-margin rupture, the magnitude will be somewhere between 8.7 and 9.2. That’s the very big one.

So maybe it would have been most appropriate for her to sum the number of these larger events from the turbidite record, but leave out what Goldfinger termed the “smaller southern-margin ruptures” —

**10,000/(20+4) = 10,000/24 **

**= 417 years between earthquakes greater than magnitude 8.0**

If so, then we can transform one of her scariest sentences into something substantially less terrifying: “Counting from the earthquake of 1700, we are now 315 years into a ~~243~~ 417 year cycle.” So, on average we shouldn’t expect a big or really big earthquake for another 100 years or so.

If you want to get more geographically explicit, consider this nice figure from “Tsunami impact to Washington and northern Oregon from segment ruptures on the southern Cascadia subduction zone” (Priest et al., 2014), modified from Goldfinger et al. (2012) —

Yellow text show (simple average) recurrence times for different inferred segments of the full-rupture patch of the Cascadia Subduction Zone.

Of course, all this averaging assumes that earthquakes are random (time-independent) rather than cyclical or periodic (time-dependent), but Goldfinger et al. (2012) point out that — conveniently — it doesn’t matter if you use simple averages or complicated earthquake modes, you get about the same computed likelihoods:

**Time-independent** probabilities for segmented ruptures range from 7–12 percent in 50 years for full or nearly full margin ruptures to ~21 percent in 50 years for a southern-margin rupture. **Time-dependent** probabilities are similar for northern margin events at ~7–12 percent and 37–42 percent in 50 years for the southern margin. Failure analysis suggests that by the year 2060, Cascadia will have exceeded ~27 percent of Holocene recurrence intervals for the northern margin and 85 percent of recurrence intervals for the southern margin.

These statistics are what underlie Schultz’s memorable 50-year odds: 1 in 3 (~30%) for a big one; 1 in 10 (~10%) for a really big one. To the extent that either probability is worrisome, it’s got to be the 30% chance of a big one down south in the next 50 years. Interestingly, in her follow-up article “How to Stay Safe When the Big One Comes” Schultz clarifies that the 30% probablity is indeed for a magnitude 8-8.6 event:

The odds I cite in the *[original]* story are correct: there is a thirty-per-cent chance of the M8.0**–**8.6 Cascadia earthquake and a ten-per-cent chance of the M8.7**–**9.2 earthquake in the next fifty years.

But from Seattle’s perspective, what will be our experience of a magnitude 8-8.6 earthquake, particularly one with an epicenter in Oregon? It’s not clear to me if the shake maps Schultz provides in her follow-up are for a full- or partial- rupture. The symmetry of the contours suggests they are for a full-margin rupture. We need clarification, or another model run (for the full Northwest region) of this most likely (30%) type of earthquake!

The most helpful things I’ve found as I continue to “feel” the risk and decide whether and how to proceed are this timeline from this PDF —

Seem likely the next one will be big, not really, big, and maybe pretty soon?

— and this figure depicting the height of a worst case tsunami as it moves up the OR/WA coast (from a magnitude 8.7 earthquake, aka simulation C588 centered in southern Oregon) —

As the tsunami propagates northward, the maximum wave height deceases from ~10 meters near the epicenter to ~2 meters in northern coastal Washington. There is no tsunami risk in Seattle from a big or even a really big subduction earthquake.

Despite all this scientific quibbling, I applaud Schultz on getting us all to be more prepared. Here in northeast Seattle, I plan to refresh our emergency plans and kits, and look into a seismic retrofit for our 1926 house.