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Good morning, everyone.

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And welcome to the Earthquake
Science Center seminar series.

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This is our first
presentation of August.

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And next week, we’ll have a
presentation by our own Erol Kalkan

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talking about software that’s been
developed to process the data

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from the National Strong
Motion Project automatically.

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Richard has some time available –
our speaker has time available

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this afternoon if anyone
wants to meet with him.

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And he’ll be staying
on campus for the next month.

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So if today is not convenient for you,
there’s plenty of time to talk to Richard.

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Richard – we’re delighted
to have Richard today.

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He has both his master’s and his
bachelor of sciences in geology

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from the University of Arkansas.
He did his Ph.D. in geology from the

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University of Kansas and a postdoc
at the University of Michigan.

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And he’s been a consultant for the
Instituto Colombiano del Petroleo,

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and he’s a principal
at Earth Analysis.

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Currently, he’s working as an active
fault specialist at GEM in Pavia, Italy,

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where he’s helping to compile
the world’s active faults.

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He’s worked in Tibet, China,
Nevada, the Andes, Mexico,

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Himalaya, and other places,
so we’re looking forward to

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his presentation this morning
on faults in the Puget Lowland.

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Richard?

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- Okay. Is the mic on?
Okay.

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Well, I’d like to
thank you all for coming.

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And please feel free to
interrupt me and ask questions

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or offer any other points of clarification
or anything during the talk.

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So this is work that I started doing
when I was in Seattle a few years ago

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with Brian Sherrod, just doing some
statistical analysis of paleoseismic data,

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which is something I do for fun
when I don’t have funding to go map.

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And so it’s been kind of an evenings
and weekends project for a while.

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And then, now that I’m at GEM,
we’re trying to use some of

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what we’ve been observing here to
kind of advance the state of

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probabilistic seismic
hazard and risk analysis.

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And so I’m kind of bringing it
full circle back to my new work.

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So I would like to thank
my collaborators on this.

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Mostly Brian Sherrod at this point,
although Kate Scharer has also joined in

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very recently working on some time-
dependent stuff on the San Andreas

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Fault as a kind of contrast to
the Puget Lowlands earthquakes.

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And then my collaborators at GEM –
Anirudh Rao, Robin Gee, and Marco

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Pagani, who are helping me incorporate
seismic hazard modeling into all of this.

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So the title of the talk is Survival
in Seattle – Magnitude estimation,

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survival analysis, and hazard and loss
from Puget Lowland paleoearthquakes.

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And so all of this data that I’m
going to be talking about has been

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gathered by people at – mostly from
the U.S. Geological Survey and

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also collaborators in
Washington and elsewhere.

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And I’m not responsible for any of that,
so I have to thank everyone

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who has contributed.
I know people in this room have.

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So to start things out,
so work by the USGS and others

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gives evidence for
about 30 paleoearthquakes –

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surface-breaking
earthquakes in the

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Puget Sound region of Washington
over the past about 16,000 years.

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Brian thinks this is a
reasonably complete catalog.

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The area has a glacial –
or, post-glacial unit of

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vash and till that
covers a lot of the surface.

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With the Lidar data, it’s very easy
to find out where there have been

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earthquakes in the past.
The surface is very well exposed.

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In the topography data,
it’s not always well-exposed

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when you’re standing on
the ground due to vegetation.

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But there are a lot of scarps that are pretty
visible in the Lidar, and things are mapped

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pretty thoroughly. And when you
dig down into the Holocene units

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on top of the vash and till,
you can use the till as a marker

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for how much, you know, faulting
there has been since 16,000 years.

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And so this gives us a reasonably
good catalog for what’s happened

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in the area since then.
And since we think that,

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as far as surface-breaking
earthquakes go, this is a somewhat

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complete catalog, using this data is
probably the best way to characterize

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shallow crustal seismicity
of reasonably large magnitudes

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as well as hazard
and loss in the region.

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So what we want to know is,
how big were these earthquakes?

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You know, we don’t have
instrumental records. We just have

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observations of displacement and –
you know, and some scarp mapping.

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We also want to know what the temporal
patterns of earthquake occurrence are.

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Are these things, you know,
spread out with faulting basically

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random or Poissonian in the region?
Were things clustered?

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Or, you know, are they characteristic
on different fault zones?

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And finally, we want to know,
you know, if these earthquakes

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occurred today, what kind of
damage would they do in an area

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that’s rapidly urbanizing and is
economically vital for the U.S.?

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How do we prepare
for earthquakes like this?

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So as an overview in
answering these questions,

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I’ve got kind of
three approaches.

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And they decrease as we go down
the list in order of completeness.

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The top part is,
for the most part, done.

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And things get more and
more in progress as we go.

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So the first part of the talk is
going to be on estimating the

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magnitude of the paleoearthquakes.
It’s pretty simple, for the most part.

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We’re basically trying to
incorporate both the estimates

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of displacement that are found through
scarp mapping and measurement

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as well as measurement
in paleoseismic trenches.

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And also using
estimates of rupture length

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jointly to invert
for the magnitudes.

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When we do this, this results in
the reduction in both the estimated

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magnitude of the earthquakes and
the uncertainty of the magnitude.

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This is a good thing for the region –
basically to summarize quickly, the

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lengths of these faults are pretty short
relative to the amounts of displacement.

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So if you just use displacement
scaling relationships,

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it over-predicts the
magnitude of the earthquakes.

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A big part of the talk is on earthquake
recurrence in time and survival analysis.

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And so we’re going to estimate
empirically the recurrence probability

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distributions in the area
and on selected fault zones.

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And this allows us to calculate
time-dependent earthquake hazard

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that’s conditional on the
time since the last earthquakes.

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And we’re also going to do some
analysis of clustering in this data set.

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And then finally, we’re going to
incorporate all of this into

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probabilistic seismic
hazard and risk.

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Hazard being the occurrence
of the earthquakes themselves, and

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risk being the damage to infrastructure
and the likelihood of observing this.

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The bottom part is especially
kind of in development,

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and a lot of what I’m going to talk about
is kind of my vision for how to proceed.

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And I would love to get
people’s feedback on that.

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But in particular,
we’re going to be simulating

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some of these earthquakes that we’ve
observed in the paleoseismic data –

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looking at clustering,
looking at aftershocks.

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And then incorporating kind of
cutting edge seismic engineering work

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on looking at cumulative damage
due to repeated earthquakes

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on individual structures
as well as structural and

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community-level rebuilding
of infrastructure.

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Okay, so first, just a
little bit overview of Cascadia.

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So this is the Cascadia Megathrust here –
Washington, Oregon, California.

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Subduction of the Juan de Fuca Plate
underneath Cascadia is kind of

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moderate speeds for subduction.
It’s about 36 millimeters a year.

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And it’s oblique.
There’s both a right lateral component

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and a reverse component
to the subduction.

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Strain release is probably
fairly partitioned,

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so we have purely reverse events
at the trench, based on what we see

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of big subduction zone
earthquakes worldwide.

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And then this leaves us with a right
lateral component to the displacement

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that is – results in translation
of the forearc to the northwest.

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And the translation of that
kind of stops in northern

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Washington/southern British Columbia.
And this leads to 3 to 7 millimeters

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per year of shortening –
mostly north-south shortening –

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in the Puget Lowland region of
Washington, which is right here.

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So we’re going to
zoom into this box.

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And so we have reverse faults and
strike-slip faults through the forearc.

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And these, for the most part,
coincide with population centers.

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So up here, we have Bellingham,
which I have not noted.

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Then we have the Darrington-
Devils Mountain Fault Zone here.

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The South Whidbey Island Fault Zone, 
which crosses very close

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to the city of Everett.
And you all will politely forgive me

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for putting the barbs on
the wrong side of this fault.

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Then we have the Seattle Fault Zone,
which runs through Seattle.

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And to the south, Tacoma and
Olympia Fault Zones

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running through their
namesake cities as well.

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The Saddle Mountains Fault Zone
here and the Lake Creek-

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Boundary Creek Fault Zone
on the north side of the Olympics.

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There’s about 3 million people
in the area. It’s rapidly growing.

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It’s economically very
important to the region.

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And from a lot of paleoseismic
observation sites that are shown here

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in these circles, we’ve inferred about
30 earthquakes in the past 16,000 years.

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So the first thing we’re going to
talk about is estimating the

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magnitude of these.

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So observed fault offsets in trenches,
in scarp profiles, and in

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uplifted shorelines are between
about half a meter and 8 meters.

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Most of these
are vertical offsets.

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So displacement on the
faults can be a little bit higher.

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The ruptures that are clearly observable
in mapping on the ground or in Lidar

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are about 1 to 30 kilometers long.
But the ruptures may be much longer.

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They may be, you know, up to the
full length of the mapped fault zones.

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Most of these faults cross
underneath the Puget Sound area.

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The area is heavily vegetated.

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You know, in areas, there’s
rapid erosion, urbanization.

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So the extent of the –
of the ruptures initially

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isn’t necessarily
observable today.

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Both the displacement observations
and the rupture length observations

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can help us constrain
the earthquake magnitude.

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And to do this, we’re going to
extend the methods of Biasi and

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Weldon 2006 that incorporate –
or, that estimate magnitude

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given displacement observations
to estimate magnitude given

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both displacement and
length observations.

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So this is – this paper is sitting on Brian’s
desk ready to go out for internal review.

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If anyone’s interested in reading it,
I would suggest calling him.

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Because I would – I would love to
see it come back from vacation.

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So the maximum rupture lengths
that we observe are, you know,

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between maybe 10 to 20 and
70 kilometers based on, you know,

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just the maximum length of the –
of the mapped faults.

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These faults are,
for the most part,

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confined to the forearc low here –
the Puget Lowland.

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They – some of the fault zones
possibly extend, like, you know,

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through the Cascades and onto the
east side, but I think it’s unlikely that

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individual earthquakes are going to
propagate across that mountain range.

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So I think, for the maximum
estimates of rupture length,

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we can – we can use
what we see here.

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The minimum rupture
lengths are much lower.

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They’re basically just the
extents of the mapping on the Lidar,

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which can be up to
about 30 kilometers.

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The Darrington-Devils Mountain Fault
has a pretty well-exposed scarp.

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But in most cases, it’s just a few
kilometers surrounding the trench.

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So, again, we’re going to extend the
methods of Biasi and Weldon.

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What they do – they have a very
clever and important methodology

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that they’ve developed where they
use a Bayesian scheme that

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estimates magnitude given
displacement observations.

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But the important thing about it is, they
are able to use the fact that, you know,

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an observation of displacement at a
point on an earthquake rupture may –

00:14:19.579 --> 00:14:23.829
is probably not going to be representative
of the average displacement that we

00:14:23.829 --> 00:14:30.259
use in scaling relationships to
infer what the magnitude may be.

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So what they’ve done is taken a
whole host of observed earthquake

00:14:35.449 --> 00:14:39.699
displacement profiles and
normalized those to the mean

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and come up with probabilities for
how the mean displacement might scale

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given an observed displacement
somewhere at a point on those faults.

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So it’s a Bayesian scheme, so we also
need to incorporate the prior magnitudes.

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And so this is just what we
consider the probability of

00:15:04.310 --> 00:15:07.100
earthquake occurrence before
considering – or, of earthquake

00:15:07.100 --> 00:15:10.600
magnitude, excuse me, before
considering any observations.

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There are kind of a choice
of priors that we can use.

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The simplest is some
uniform distribution.

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We can also use a
Gutenberg-Richter distribution.

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Those are both pretty
obvious choices.

00:15:25.459 --> 00:15:29.050
And we can incorporate those
with surface breaks or without.

00:15:29.050 --> 00:15:33.279
And so smaller earthquakes are
less likely to break the surface.

00:15:33.279 --> 00:15:35.320
So if we’re looking at
surface-breaking earthquakes,

00:15:35.320 --> 00:15:37.900
then we may come up
with different priors.

00:15:37.900 --> 00:15:45.079
For simplicity, I’ve just chosen a
uniform prior, but that’s not

00:15:45.079 --> 00:15:51.110
a modeling choice that I feel is,
you know, the only way to proceed.

00:15:51.110 --> 00:15:55.149
So in order to calculate the magnitude
given both displacement and length,

00:15:55.149 --> 00:16:00.179
again, we’re using a Bayesian
scheme here where here, on the left,

00:16:00.179 --> 00:16:05.540
we have the posterior distribution
of earthquake magnitude given M –

00:16:05.540 --> 00:16:07.899
given both
displacement and length.

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And so this is the product of the
prior distribution – I’ve used

00:16:12.619 --> 00:16:21.589
magnitude 6 through 8.5 –
times the likelihood – or, excuse me –

00:16:21.589 --> 00:16:26.089
a likelihood function that is the –
what we would expect of

00:16:26.089 --> 00:16:29.600
earthquake magnitudes
given the length observations.

00:16:29.600 --> 00:16:33.679
And to get the length observations,
basically, I just took a uniform

00:16:33.679 --> 00:16:38.119
distribution between the minimum and
maximum lengths that I showed earlier

00:16:38.120 --> 00:16:42.569
and then used scaling relationships
from Wells and Coppersmith.

00:16:43.540 --> 00:16:49.139
And then we multiply this by the
likelihood function that results

00:16:49.139 --> 00:16:55.649
from the magnitude estimated based
on the observed displacement.

00:16:55.649 --> 00:17:01.889
And this incorporates both scaling
between displacement and magnitude

00:17:01.889 --> 00:17:07.230
and the probability for displacement –
you know, mean displacement given

00:17:07.230 --> 00:17:11.000
displacement observed at a point
that we talked about briefly earlier.

00:17:11.000 --> 00:17:12.939
And this work is
from Biasi and Weldon.

00:17:12.939 --> 00:17:17.610
So we can multiply all of these
and rescale it so that the

00:17:17.610 --> 00:17:21.120
probability integrates to 1,
and we end up with fairly

00:17:21.120 --> 00:17:27.309
well-constrained probabilities
for earthquake magnitude.

00:17:27.309 --> 00:17:33.480
So if we compare the earthquake
magnitudes given just displacement

00:17:33.480 --> 00:17:38.880
at the top with earthquake magnitudes
given both displacement and length,

00:17:38.880 --> 00:17:43.450
for the Puget Lowland earthquakes,
which again, are pretty high magnitude

00:17:43.450 --> 00:17:48.620
of displacements, but pretty
low rupture length earthquakes.

00:17:49.920 --> 00:17:55.140
The first thing that we notice,
that the magnitudes drop a lot.

00:17:55.140 --> 00:17:59.649
And a lot of these very, you know,
wide probabilities collapse a lot.

00:17:59.649 --> 00:18:06.320
And so we reduce both the magnitude
that’s estimated and the uncertainty.

00:18:08.020 --> 00:18:12.340
And so we can see that here.
This line is basically 1-to-1.

00:18:12.340 --> 00:18:16.981
We have magnitude given displacement
and length on the Y axis, and magnitude

00:18:16.981 --> 00:18:20.551
given just displacement on the X axis.
So anything that’s dropped below this

00:18:20.551 --> 00:18:26.669
line has seen a reduction in the – in the
magnitude by incorporating length.

00:18:26.669 --> 00:18:28.960
And we can also see that
the error bars are a lot wider

00:18:28.960 --> 00:18:32.120
on the X axis
than on the Y axis.

00:18:34.740 --> 00:18:38.660
So to summarize this, these new
methods incorporate rupture length

00:18:38.661 --> 00:18:43.640
into the magnitude estimation.
All of these earthquakes have maximum

00:18:43.640 --> 00:18:49.549
likelihood posteriors between about
6.4 and 7.5. And this is a big reduction

00:18:49.549 --> 00:18:56.600
from having earthquakes above 8
for some of these paleoearthquakes.

00:18:56.600 --> 00:19:00.320
So that’s really good news
for the people of Washington.

00:19:02.640 --> 00:19:04.940
Okay, so now we’re going to
switch gears a little bit

00:19:04.950 --> 00:19:07.679
and talk about earthquake
timing and recurrence.

00:19:07.679 --> 00:19:14.559
What we’ve done for this is
taken all of the data from

00:19:14.559 --> 00:19:20.130
published work about the – you know,
the stratigraphy and carbon dating

00:19:20.130 --> 00:19:25.370
results and stuff like that for all of
these paleoearthquakes and remodeled

00:19:25.370 --> 00:19:28.770
everything in OxCal just to be
completely consistent about it.

00:19:28.770 --> 00:19:34.140
Then we’ve estimated
the recurrence distributions,

00:19:34.140 --> 00:19:38.019
which is the distribution of inter-event
times through Monte Carlo simulations

00:19:38.019 --> 00:19:43.899
of the earthquake ages from OxCal
and calculated empirical distributions

00:19:43.899 --> 00:19:49.169
instead of fitting different models,
like Weibull or Brownian passage-time

00:19:49.169 --> 00:19:53.260
or whatever to it.
From these empirical distributions,

00:19:53.260 --> 00:19:58.299
we can look at time-dependent
recurrence using methods called survival

00:19:58.299 --> 00:20:02.630
analysis that are common in biology
and engineering and some other fields.

00:20:02.630 --> 00:20:04.851
And from this,
we can also start to

00:20:04.851 --> 00:20:09.210
characterize earthquake
clustering and evaluate this.

00:20:09.210 --> 00:20:13.809
So this is work that I’m doing both
in the Puget Lowlands and then also

00:20:13.809 --> 00:20:17.840
from the Wrightwood and Pallett Creek
data sets from Kate Scharer.

00:20:17.840 --> 00:20:24.809
And so I’ll talk a little bit about the San 
Andreas as kind of a contrasting point,

00:20:24.809 --> 00:20:30.230
but not presenting, like, a lot of
conclusions from the San Andreas.

00:20:30.230 --> 00:20:33.880
So here are the
paleoearthquake ages.

00:20:35.740 --> 00:20:37.840
You’ve got
about 30 events here.

00:20:37.840 --> 00:20:41.110
And we’ve remeasured everything
in OxCal from published data.

00:20:41.110 --> 00:20:45.820
What we can see is that these
earthquakes may be clustered.

00:20:45.820 --> 00:20:51.549
There’s some debatable clusters of –
kind of clumps of older events.

00:20:51.549 --> 00:20:57.630
And then there’s a major group
from about 1,200 to 900 years

00:20:57.630 --> 00:21:03.220
before present where there’s
ruptures in a few hundred years

00:21:03.220 --> 00:21:07.060
on eight to nine
separate fault zones,

00:21:07.060 --> 00:21:10.340
depending on which ones you want to,
you know, include in the box.

00:21:10.340 --> 00:21:15.390
And given the sort of mean recurrence
intervals on these different fault zones,

00:21:15.390 --> 00:21:18.880
the likelihood – some of which
have only ruptured once

00:21:18.880 --> 00:21:22.309
during this time period –
you know, in the Holocene.

00:21:22.309 --> 00:21:27.309
So the likelihood of this all occurring
given a Poissonian probability and,

00:21:27.309 --> 00:21:34.440
you know, assumptions of earthquake
independence is, like, 7 in 1 billion.

00:21:34.440 --> 00:21:37.900
So this is pretty good evidence that
we’re seeing non-Poissionian behavior.

00:21:37.900 --> 00:21:43.640
We’re seeing clustering, earthquake
triggering, perhaps, somewhere in here.

00:21:43.640 --> 00:21:50.960
So to analyze this a little bit more, I’m
taking all of the fault zones that we have

00:21:50.960 --> 00:21:55.610
and calculating empirical earthquake
recurrence distributions from that.

00:21:55.610 --> 00:21:59.090
And then – so I’m doing this for each of
the fault zones that have multiple events.

00:21:59.090 --> 00:22:02.360
And then from all of the
Puget Lowlands as a whole.

00:22:02.360 --> 00:22:06.659
So what I’m doing is basically
taking the probabilities of

00:22:06.659 --> 00:22:09.730
each individual earthquake
coming from OxCal here

00:22:09.730 --> 00:22:13.779
and doing a Monte Carlo
sampling system where I basically

00:22:13.780 --> 00:22:17.240
just calculate the time difference
between successive events.

00:22:17.240 --> 00:22:22.900
And so for example,
one sample in between this red

00:22:22.900 --> 00:22:28.200
and this yellow event produces
kind of an orange event down here.

00:22:28.200 --> 00:22:33.450
Do this, you know, 10,000 times,
and we get histograms

00:22:33.450 --> 00:22:36.580
for each of the inter-event times
between all of these earthquakes.

00:22:36.580 --> 00:22:40.019
There’s a couple different ways
to actually do this depending on

00:22:40.019 --> 00:22:45.450
the kind of data that you have
and the constraints.

00:22:45.450 --> 00:22:48.440
For earthquakes that, you know,
may have occurred on independent

00:22:48.440 --> 00:22:52.360
fault lines, you just calculate the time,
you know, in between.

00:22:52.360 --> 00:22:54.909
But if you have a situation
like you do in the San Andreas,

00:22:54.909 --> 00:22:58.520
where you know the earthquakes
happen in succession, even though the

00:22:58.520 --> 00:23:04.200
probabilities may overlap, we –
when we generate all these samples,

00:23:04.210 --> 00:23:10.179
we have to reject samples where the –
an older earthquake happened,

00:23:10.180 --> 00:23:15.240
you know, later than an earlier
earthquake in the – in the data sets.

00:23:17.090 --> 00:23:20.580
So then finally, you know,
we can end up with some situation here

00:23:20.580 --> 00:23:27.000
where we have inter-event distributions
from a bunch of different – you know,

00:23:27.000 --> 00:23:29.600
between each of the different
earthquakes that incorporates

00:23:29.600 --> 00:23:32.399
the uncertainties seen in the –
in the actual age data.

00:23:32.399 --> 00:23:36.059
We can combine all that and
get a final probability distribution

00:23:36.059 --> 00:23:41.840
for the – for that fault zone.
And that’s shown here in orange.

00:23:41.840 --> 00:23:44.350
So when I actually do this,
I don’t use histograms.

00:23:44.350 --> 00:23:47.300
I use a kernel density estimate
so it’s a little more smooth.

00:23:47.300 --> 00:23:50.180
So here’s what we see
for the Seattle Fault Zone.

00:23:50.190 --> 00:23:54.169
There are eight earthquakes in this data
set that are – that are well-dated.

00:23:54.169 --> 00:23:58.799
There’s a couple of them that
don’t really have age constraints

00:23:58.800 --> 00:24:02.540
from the Crane Lake sites,
and so those aren’t included in here.

00:24:02.540 --> 00:24:10.700
And what we see is these sort of,
you know, occur possibly in clusters.

00:24:10.710 --> 00:24:13.010
They’re not
particularly widely spaced.

00:24:13.010 --> 00:24:15.700
And so in the recurrence
distribution here, we see

00:24:15.700 --> 00:24:22.059
high probabilities very soon
after the previous earthquake.

00:24:22.059 --> 00:24:25.519
And these kind of drop
down to pretty low levels

00:24:25.519 --> 00:24:29.370
and then pick up a little bit
at many thousands of years.

00:24:29.370 --> 00:24:34.409
If we zoom in here
in the first 400 years,

00:24:34.409 --> 00:24:41.360
we can see that the highest estimates are
here in the first 100 years to 200 years.

00:24:41.360 --> 00:24:46.570
And this is the cumulative probability
distribution that’s shown here in blue.

00:24:46.570 --> 00:24:50.009
And so what it says is that almost
half of the earthquakes that happen

00:24:50.009 --> 00:24:54.330
are going to occur a few hundred years
following the previous event,

00:24:54.330 --> 00:24:56.659
even though the mean
earthquake occurrence

00:24:56.659 --> 00:25:00.639
is about 800 – or, is almost
2,000 years. It’s 1,700 years.

00:25:00.639 --> 00:25:07.490
And the median earthquake
recurrence is 750 years.

00:25:07.490 --> 00:25:09.519
And the exact form of this
depends on this – you know,

00:25:09.519 --> 00:25:11.880
the kind of bandwidth size that you
use with the kernel density estimate,

00:25:11.880 --> 00:25:14.289
and so there are other
kind of technical issues.

00:25:14.289 --> 00:25:19.309
But what we can see is this – based on
just this data doesn’t exactly resemble,

00:25:19.309 --> 00:25:23.300
like, a Weibull distribution, Brownian
passage-time, log-normal, et cetera.

00:25:23.300 --> 00:25:26.900
And one of the important things
is that it’s possible, given these –

00:25:26.909 --> 00:25:33.230
the overlap in the data – and the
Seattle Fault Zone is multi-stranded,

00:25:33.230 --> 00:25:35.620
and so this may
be important here.

00:25:35.620 --> 00:25:38.509
But the probabilities for
earthquake recurrence

00:25:38.509 --> 00:25:43.029
at basically time zero following
an earthquake are not zero.

00:25:43.029 --> 00:25:45.690
So we don’t completely reset
and then have to build up.

00:25:45.690 --> 00:25:49.110
We can have earthquakes in close
succession in this fault system.

00:25:49.110 --> 00:25:51.330
Some of this is probably
from uncertainty in the data,

00:25:51.330 --> 00:25:57.220
but not necessarily.
We don’t know that independently.

00:25:57.220 --> 00:26:00.159
So if we look at all of
the Puget earthquakes –

00:26:00.160 --> 00:26:03.780
I think there are 31 earthquakes
in this data set here.

00:26:04.740 --> 00:26:07.420
And we have a distribution
that looks a little bit more like

00:26:07.420 --> 00:26:12.880
an exponential distribution that you
would expect from a Poisson model.

00:26:13.980 --> 00:26:17.900
But again, it doesn’t start from zero.
It starts from a little bit higher.

00:26:17.900 --> 00:26:23.740
It peaks at 19 years and then
drops monotonically from there.

00:26:23.740 --> 00:26:27.460
The median is 166 years,
and the mean is 400 years.

00:26:27.460 --> 00:26:30.409
So we can say, in general,
there’s an average recurrence interval

00:26:30.409 --> 00:26:34.730
of 400 years in the Puget Sound,
but that’s not exactly what

00:26:34.730 --> 00:26:38.240
we would expect the next
earthquake to be following

00:26:38.240 --> 00:26:44.130
a previous earthquake.
The most likely time is 19 years.

00:26:44.130 --> 00:26:48.520
To contrast this on the San Andreas,
we’ve looked independently at

00:26:48.520 --> 00:26:51.680
both the Wrightwood and
the Pallett Creek data sets here.

00:26:51.690 --> 00:26:55.179
Wrightwood is shown in cyan.
Pallett Creek is in magenta.

00:26:55.179 --> 00:27:01.870
And these, for the most part,
look pretty similar, which is nice.

00:27:01.870 --> 00:27:04.160
Even though, you know,
a lot of the earthquakes

00:27:04.160 --> 00:27:08.170
don’t match this, so, like, a relatively
similar statistical behavior.

00:27:10.740 --> 00:27:13.500
Here, you know, we have the mean –
I didn’t put the exact figures on here,

00:27:13.500 --> 00:27:16.080
but we have a
mean about 150 years.

00:27:16.080 --> 00:27:21.370
And we don’t have this really long tail
extending out to, you know,

00:27:21.370 --> 00:27:28.270
a factor of 10 higher than the mean and
a factor of 100 higher than the mode.

00:27:28.270 --> 00:27:31.610
So we see kind of a more typical
behavior that we would expect for,

00:27:31.610 --> 00:27:37.960
you know, possibly something
characteristic like on the San Andreas.

00:27:39.570 --> 00:27:44.980
So to summarize this, the regional
fault recurrence PDFs show a very

00:27:44.990 --> 00:27:50.720
short mode – earthquake clusters,
possibly, and, you know, long tails.

00:27:50.720 --> 00:27:55.340
The short modal recurrence may
result from earthquake triggering.

00:27:55.340 --> 00:27:58.610
We can’t exactly evaluate the
physical mechanisms behind this.

00:27:58.610 --> 00:28:00.550
It’s something I’m
interested and think about,

00:28:00.550 --> 00:28:05.539
but I’m not going to make
any firm judgments quite yet.

00:28:05.540 --> 00:28:10.020
And so we can use this to
answer another question.

00:28:11.570 --> 00:28:15.040
So the longer it has been since
the last earthquake, the longer

00:28:15.059 --> 00:28:19.289
the expected time until the next?
And so this is from a paper in BSSA

00:28:19.289 --> 00:28:22.710
in 1989, and it’s something
that’s still debated somewhat.

00:28:22.710 --> 00:28:29.830
And the answer you get depends on
the recurrence model that you get.

00:28:29.830 --> 00:28:34.139
So lots of people – or, a few people,
at least, have done work on this

00:28:34.140 --> 00:28:37.520
using different assumptions for
what recurrence distributions can be.

00:28:37.520 --> 00:28:41.600
And – but we can also
answer these questions

00:28:41.600 --> 00:28:45.490
using the empirical
recurrence models as well.

00:28:45.490 --> 00:28:47.149
And so to do this,
we’re going to use some tools

00:28:47.149 --> 00:28:51.460
that are called survival analysis.
And these deal with the statistics

00:28:51.460 --> 00:28:54.700
of the timing of events,
or the timing between event.

00:28:54.700 --> 00:28:59.380
It’s pretty common in sociology,
epidemiology, and engineering.

00:28:59.380 --> 00:29:04.080
In engineering, it’s usually
called failure or liability analysis.

00:29:04.080 --> 00:29:07.240
The main aspect of this
that we’re going to look at today

00:29:07.240 --> 00:29:10.679
is what’s called the hazard –
or the hazard rate.

00:29:10.679 --> 00:29:13.559
And this is the
instantaneous probability

00:29:13.560 --> 00:29:18.360
of occurrence of an event
given the time since the last event.

00:29:19.520 --> 00:29:26.300
And this comes up pretty frequently,
and a lot of authors will show equations

00:29:26.309 --> 00:29:33.990
for this, but these equations are often
derivations of – from different statistical

00:29:33.990 --> 00:29:39.320
models for recurrence – you know,
from a – you know, a log-normal

00:29:39.320 --> 00:29:43.090
or a Weibull or exponential
distribution or whatever.

00:29:43.090 --> 00:29:46.240
And they rarely just show
the basic equations here.

00:29:46.240 --> 00:29:48.760
Instead, you know, they’ll show
the analytical derivations for

00:29:48.760 --> 00:29:53.509
more complicated recurrence models –
more complicated PDFs.

00:29:53.509 --> 00:29:58.200
But the basic methods are pretty simple,
and so I like – I like looking at them

00:29:58.200 --> 00:30:03.740
with these empirical distributions
because the kind of logic

00:30:03.740 --> 00:30:06.190
and the reasoning behind it
are a little bit more clear.

00:30:06.190 --> 00:30:09.220
So basically, the hazard rate
at any time, t, given that there

00:30:09.220 --> 00:30:13.629
hasn’t been an earthquake up
until that time, is the probability

00:30:13.629 --> 00:30:20.799
of that time divided by the total
probability that’s elapsed since then,

00:30:20.799 --> 00:30:25.840
which is 1 minus the cumulative
distribution function at that time.

00:30:25.840 --> 00:30:31.519
So the math is pretty simple
when you look at it generically.

00:30:31.519 --> 00:30:37.450
And so we can use this to calculate
the expected time until the next event,

00:30:37.450 --> 00:30:40.650
which, in demographic studies,
is called the mean lifetime remaining.

00:30:40.650 --> 00:30:44.919
We can calculate the probability in
different time intervals, et cetera.

00:30:44.919 --> 00:30:52.490
Survival analysis also has a lot that –
on incorporation of open intervals.

00:30:52.490 --> 00:30:59.700
So in our paleoseismic data sets,
you know, we start the clock,

00:30:59.700 --> 00:31:06.280
basically, at the retreat of the –
of the Puget Ice Sheet.

00:31:06.289 --> 00:31:07.630
We don’t know
how long it had been

00:31:07.630 --> 00:31:11.629
previous to that since earthquakes
on different fault zones.

00:31:11.629 --> 00:31:14.529
We only know, you know,
the first occurrence that we can see.

00:31:14.529 --> 00:31:17.909
Furthermore, we don’t know
the time from the last earthquakes

00:31:17.909 --> 00:31:21.690
until the next one.
And so both of these are kind of

00:31:21.690 --> 00:31:24.920
considered open intervals in the data set.
We only have part of it.

00:31:24.920 --> 00:31:28.320
And survival analysis has a
lot of tools for dealing with that.

00:31:28.330 --> 00:31:33.700
I’m starting to get into that,
but I’m not a, you know, long-time

00:31:33.700 --> 00:31:38.100
expert in this stuff, and so I’m just
kind of teaching myself as I go along.

00:31:38.100 --> 00:31:42.759
So I haven’t incorporated any of that
into it, but it’s – these techniques are

00:31:42.759 --> 00:31:46.139
called censoring in general,
but I’m looking forward to doing that.

00:31:46.139 --> 00:31:49.269
So that’s
work-in-progress.

00:31:49.269 --> 00:31:53.520
So the name “survival analysis”
comes from mortality studies,

00:31:53.520 --> 00:31:56.499
particularly conditional
mortality and survival.

00:31:56.499 --> 00:32:01.080
So a very common example given,
and usage for this,

00:32:01.080 --> 00:32:04.360
that many of us are
familiar with is life expectancy.

00:32:04.360 --> 00:32:07.019
So if a child, you know,
is born somewhere that has

00:32:07.019 --> 00:32:09.720
reasonably high infant
mortality rates, at birth,

00:32:09.720 --> 00:32:14.880
they may have a life expectancy,
or an average lifetime, of 60 years.

00:32:14.880 --> 00:32:21.010
If they’ve made it past
all of the diseases that kill infants,

00:32:21.010 --> 00:32:23.850
they may live, on average,
to be 75 years old.

00:32:23.850 --> 00:32:27.940
So then we have a conditional
life expectancy based on

00:32:27.940 --> 00:32:32.659
surviving up to a certain point.
And those are the tools –

00:32:32.659 --> 00:32:35.249
that’s the kind of – like,
the main part of survival analysis.

00:32:35.249 --> 00:32:38.019
And we can extend that to
earthquake recurrence as well.

00:32:38.019 --> 00:32:41.519
So this gives us an ability to
answer the question posed by

00:32:41.519 --> 00:32:45.210
Davis et al. of how long we
should keep waiting for an earthquake

00:32:45.210 --> 00:32:48.820
based on how long
we’ve already been waiting.

00:32:50.450 --> 00:32:54.760
So when we look at hazard curves –
so the rate – the failure rate,

00:32:54.779 --> 00:33:02.210
or the rate of earthquake occurrence
with time, there’s a very common thing

00:33:02.210 --> 00:33:08.850
that we see empirically that’s not
always incorporated into the hazard rate

00:33:08.850 --> 00:33:13.529
from particular statistical models.
It’s what’s called a bathtub curve.

00:33:13.529 --> 00:33:16.259
And so this is this curve
that we see here in blue.

00:33:16.259 --> 00:33:21.840
So this is the observed failure rate.
And this failure rate that we see,

00:33:21.840 --> 00:33:25.980
it starts out high early on,
and then it decreases for a while,

00:33:25.980 --> 00:33:30.090
kind of at a – at a baseline level,
and then it ramps back up at the end.

00:33:30.090 --> 00:33:35.919
And this is commonly inferred,
or known, to be the result of

00:33:35.919 --> 00:33:41.470
several superposed processes. So one
of them is a very early failure rate.

00:33:41.470 --> 00:33:44.740
And this – you know,
in, like, demographics,

00:33:44.740 --> 00:33:49.790
this can be due to infant mortality.
With lots of engineering products,

00:33:49.790 --> 00:33:54.139
like electronics or, you know,
bike components or whatever,

00:33:54.139 --> 00:33:58.019
there’s a lot of very
early failure of these products

00:33:58.019 --> 00:34:00.300
that happen because of
manufacturing defects.

00:34:00.300 --> 00:34:03.460
So you get something from the factory.
It’s a lemon. It doesn’t work.

00:34:03.460 --> 00:34:07.669
Those get weeded out pretty quickly.
And then we drop down to a

00:34:07.669 --> 00:34:15.429
much lower rate of failure due to
engineering defects or whatever.

00:34:15.429 --> 00:34:18.440
Then there can also just be a constant –
random failures that may have

00:34:18.440 --> 00:34:23.159
something that are independent of
anything to do with the device itself.

00:34:23.159 --> 00:34:26.609
You know, the person alive, this is,
you know, car accidents,

00:34:26.609 --> 00:34:28.300
getting hit by
meteors or whatever.

00:34:28.300 --> 00:34:33.020
You know, it’s not – it’s nothing
to do with the internal processes.

00:34:33.020 --> 00:34:35.659
And then finally, at the end,
there’s wear-out failures.

00:34:35.659 --> 00:34:38.119
This is old age.
This is – you know,

00:34:38.119 --> 00:34:43.200
you have 400,000 miles
on your car, et cetera.

00:34:43.200 --> 00:34:47.690
So these individual processes
all have very different rates.

00:34:47.690 --> 00:34:53.159
But when we sum then all and look at
aggregate behavior, we can get

00:34:53.159 --> 00:34:56.220
something that doesn’t look like
any of the individual processes.

00:34:56.220 --> 00:34:59.470
But if we do get something that looks
like the individual processes, this can

00:34:59.470 --> 00:35:05.120
give us some insight into what is
causing most of the failures that we see.

00:35:06.850 --> 00:35:09.460
This is a figure from
Matthews et al. 2002 –

00:35:09.460 --> 00:35:12.510
the paper that really introduces
the Brownian passage-time model

00:35:12.510 --> 00:35:20.069
for failure and kind of quasi-periodic
failure on individual faults.

00:35:20.069 --> 00:35:28.220
And so we have hazard curves here
from some common statistical models.

00:35:28.220 --> 00:35:32.190
So the Weibull distribution
has this pretty linear increase

00:35:32.190 --> 00:35:33.829
in hazard rate with time.

00:35:33.829 --> 00:35:40.240
The gamma distribution also increases
with time, although less linearly.

00:35:40.240 --> 00:35:43.600
The Brownian passage-time model
increases pretty rapidly and then –

00:35:43.619 --> 00:35:48.940
and then basically levels off and
becomes asymptotic with time.

00:35:48.940 --> 00:35:51.990
The log-normal model
decreases with time.

00:35:51.990 --> 00:35:56.310
The power law model, which he doesn’t
show here, also decreases with time.

00:35:56.310 --> 00:35:59.920
And so to answer this earlier
question about how long we

00:35:59.920 --> 00:36:05.240
keep waiting for earthquakes based on
how long we’ve already been waiting,

00:36:05.240 --> 00:36:07.840
if the hazard rate
increases with time,

00:36:07.840 --> 00:36:11.320
the time until the next
event continues to decrease.

00:36:11.320 --> 00:36:15.360
So, you know,
the hazard rate always goes up.

00:36:15.360 --> 00:36:18.780
If the hazard rate drops off,
the longer we’ve been waiting,

00:36:18.780 --> 00:36:21.860
the longer we’ll
continue to wait, on average.

00:36:21.860 --> 00:36:27.530
Now, a lot of this behavior
really only happens far out

00:36:27.530 --> 00:36:31.440
after the mean – kind of at the
tails of the recurrence distribution.

00:36:31.440 --> 00:36:34.760
And early on, they all give
relatively similar behaviors.

00:36:34.760 --> 00:36:37.130
Except for the Poisson,
or exponential, model,

00:36:37.130 --> 00:36:39.190
which is completely
independent of time.

00:36:39.190 --> 00:36:43.820
So, again, this is a
memory-less process

00:36:43.820 --> 00:36:46.859
and is sort of just like the
baseline scenario for we

00:36:46.859 --> 00:36:51.250
don’t know what it’s going to do,
so we’re not going to predict anything.

00:36:51.250 --> 00:36:54.539
One thing all these models have in
common, other than the Poisson model,

00:36:54.539 --> 00:36:59.280
is that the hazard rate
is zero at time zero.

00:36:59.280 --> 00:37:02.319
Immediately following
an earthquake, there’s – you know,

00:37:02.319 --> 00:37:04.369
we don’t expect there
to be another earthquake.

00:37:04.369 --> 00:37:08.400
And this is – this is something
that’s embedded in a lot of –

00:37:08.400 --> 00:37:11.800
both the models we use and the
way we think about earthquakes,

00:37:11.800 --> 00:37:17.000
particularly in the framework
of elastic rebound theory.

00:37:18.000 --> 00:37:21.540
Using the empirical models
that we’ve made, we don’t make

00:37:21.550 --> 00:37:24.790
these assumptions
about the recurrence model.

00:37:24.790 --> 00:37:29.200
And many of these recurrence models
are based on – or related to different

00:37:29.200 --> 00:37:34.650
kind of physical ideas for strain
accumulation and release on faults.

00:37:34.650 --> 00:37:38.460
And so we’re not making
any of those assumptions.

00:37:38.460 --> 00:37:44.610
We are able to easily accommodate
multiple faults, multiple rupture modes.

00:37:44.610 --> 00:37:47.570
Maybe something like, you know,
long-term strain accumulation

00:37:47.570 --> 00:37:55.060
and release and also triggering
due to various different processes.

00:37:55.060 --> 00:37:57.300
It’s kind of
agnostic of all of that.

00:37:57.300 --> 00:38:02.920
However, we’re subject to
sampling problems, you know.

00:38:02.920 --> 00:38:05.670
Some of these recurrence
distributions – you know, we may –

00:38:05.670 --> 00:38:09.290
like the Seattle Fault Zone,
it only has eight events.

00:38:09.290 --> 00:38:12.320
How well you think that
characterizes the whole behavior

00:38:12.320 --> 00:38:19.079
is some other question. And there’s
certainly issues associated with it.

00:38:19.079 --> 00:38:22.000
So I’m not saying that the way
we’re doing things is the best way.

00:38:22.000 --> 00:38:26.480
It’s an alternative way of doing it
that involves less assumptions

00:38:26.480 --> 00:38:32.480
but probably has accuracy and
precision issues related to sampling bias.

00:38:34.720 --> 00:38:38.120
Okay, so if we – if we calculate
the hazard rate – and so this is

00:38:38.130 --> 00:38:41.210
the probability function –
so these recurrence functions

00:38:41.210 --> 00:38:46.520
that I showed earlier divided by
the complement of the CDF.

00:38:47.600 --> 00:38:48.900
We get something
that looks like this.

00:38:48.900 --> 00:38:52.540
So Seattle Fault Zone is on top.
Puget Lowland is on the bottom.

00:38:52.540 --> 00:38:56.010
On the X axis, we just have the
years since the last earthquake.

00:38:56.010 --> 00:39:00.280
And these are linear scales.
These two figures are just

00:39:00.280 --> 00:39:06.480
details of the short-term behavior
following an earthquake.

00:39:06.480 --> 00:39:09.880
So we – for both of those,
we see kind of, like, you know,

00:39:09.880 --> 00:39:14.520
modified bathtub-like behavior.
We have relatively high recurrence

00:39:14.520 --> 00:39:18.720
intervals following an earthquake
in the years to decades to centuries.

00:39:18.720 --> 00:39:24.000
Then this drops off to a low level
for a couple thousand years.

00:39:24.000 --> 00:39:27.540
And then it starts to
ramp back up.

00:39:27.540 --> 00:39:30.599
In the Puget Lowland, we have
a lot of weird oscillations and stuff.

00:39:30.599 --> 00:39:35.260
What happens is we’re dividing
very low numbers by very low numbers

00:39:35.260 --> 00:39:38.300
once we get to the
tail of these distributions.

00:39:38.300 --> 00:39:41.151
So this is numerical noise.
I don’t think that there’s any

00:39:41.160 --> 00:39:46.300
meaningful rapid fluctuation
between 4,000 and 4,500 years.

00:39:46.980 --> 00:39:51.200
You know, there’s only one
or two earthquakes –

00:39:51.200 --> 00:39:54.600
or recurrence intervals down out here,
so there are numerical issues.

00:39:55.820 --> 00:39:59.280
Nonetheless, we’re not too worried
about what happens here, either.

00:39:59.280 --> 00:40:07.730
Because we are right here.
So at 2017, or 2016 when I made

00:40:07.730 --> 00:40:14.660
these figures, we’re not, you know,
at the highest likelihood.

00:40:14.660 --> 00:40:18.590
So, you know, we’re not a year to –
or 20 to 200 years after an earthquake.

00:40:18.590 --> 00:40:23.320
But we’re still in the kind of
high initial failure regime before

00:40:23.320 --> 00:40:26.869
dropping down
into a low-level thing.

00:40:26.869 --> 00:40:30.880
So once it’s the year 3000, we can
all breathe a little bit more easy.

00:40:32.630 --> 00:40:35.900
So – oh, and so one thing
going back here, again,

00:40:35.910 --> 00:40:39.230
we have a finite, you know,
non-zero possibility of

00:40:39.230 --> 00:40:43.140
earthquake rupture immediately
following the last earthquake.

00:40:43.140 --> 00:40:47.760
And again, both of these are fault zones.
The Seattle Fault is multi-stranded.

00:40:47.760 --> 00:40:51.990
At the surface, you know,
it probably folds into

00:40:51.990 --> 00:40:57.320
a big single reverse fault
at depth, but who knows?

00:40:58.980 --> 00:41:04.799
And – you know, and the Puget
Lowland is obviously not a single fault.

00:41:04.799 --> 00:41:10.619
But whether this behavior right here is
something that people are okay with –

00:41:10.619 --> 00:41:15.290
I got some grief at AGU about it,
and people were thinking

00:41:15.290 --> 00:41:17.550
I’m double-counting earthquakes
and stuff like that.

00:41:17.550 --> 00:41:23.400
But, you know, it can happen.
So in the central –

00:41:23.400 --> 00:41:29.460
most recent part of the central Italy
sequence, the Vettore Fault –

00:41:29.460 --> 00:41:32.980
the same single point on a fault –
not a fault zone, collection of faults,

00:41:32.980 --> 00:41:37.109
et cetera – slipped 20 centimeters
during the Amatrice earthquake.

00:41:37.109 --> 00:41:42.640
And then over a meter at the
same location two months later.

00:41:42.640 --> 00:41:48.540
So this here – this white band, if you
can see it, is the Amatrice earthquake.

00:41:48.540 --> 00:41:52.299
So previously, this was the
exposed part of this fault plane.

00:41:52.299 --> 00:41:55.800
Just beautiful,
beautiful fault plane.

00:41:55.800 --> 00:41:59.760
This was Amatrice slip.
This Is Norcia slip.

00:41:59.760 --> 00:42:03.120
And the paleoseismic data – you know,
so if you were to trench this in a

00:42:03.120 --> 00:42:07.809
thousand years, how many events would
you say that happened? Probably one.

00:42:07.809 --> 00:42:11.010
Maybe – [laughs] maybe one for
this whole thing, you know?

00:42:11.010 --> 00:42:13.170
But we don’t trench across
bedrock quite as – you know,

00:42:13.170 --> 00:42:16.359
it’s kind of hard to
dig on the footwall there.

00:42:16.359 --> 00:42:19.069
But, so – you know,
so this can happen.

00:42:19.069 --> 00:42:22.680
It’s observed.
I’m not going to say it’s common.

00:42:22.680 --> 00:42:26.849
You know, and this is a couple months.
Could this happen at a couple seconds?

00:42:26.849 --> 00:42:34.500
I think that, if we dig through
some of the – I’m forgetting the name,

00:42:34.500 --> 00:42:39.210
but source-time functions – you know,
the – what slip looks like through time

00:42:39.210 --> 00:42:43.299
on single earthquakes, there’s probably
some that are kind of pulsed.

00:42:43.299 --> 00:42:46.599
We may see a couple different waves
passing through if we really

00:42:46.599 --> 00:42:52.660
did a lot of detail and had
inversions methods to resolve this.

00:42:52.660 --> 00:42:57.440
Again, it’s probably not common,
but I don’t think that it’s impossible.

00:42:58.500 --> 00:43:03.420
And so we might not want to
completely discount it out of hand.

00:43:03.420 --> 00:43:05.210
It’s not going to make that much
of a difference, you know,

00:43:05.210 --> 00:43:08.570
two seconds later in how
we view earthquake hazard.

00:43:08.570 --> 00:43:10.660
But a couple months later,
a couple days later,

00:43:10.660 --> 00:43:13.010
a couple years later –
this is absolutely something

00:43:13.010 --> 00:43:19.319
that’s really important for
time-dependent earthquake hazard.

00:43:19.319 --> 00:43:22.030
So if we go and
compare this to the San Andreas,

00:43:22.030 --> 00:43:24.730
we see some pretty
different behavior.

00:43:24.730 --> 00:43:27.970
This is Wrightwood in cyan
and Pallett Creek in magenta.

00:43:27.970 --> 00:43:34.590
This is linear scaling on the top
and log scaling on the bottom.

00:43:34.590 --> 00:43:42.010
These start more or less at zero
and increase linearly – well,

00:43:42.010 --> 00:43:45.660
kind of linearly, you know,
at least for the first 100 years.

00:43:45.660 --> 00:43:48.260
Then there’s some divergence between
Wrightwood and Pallett Creek.

00:43:48.260 --> 00:43:51.610
I think there may be – you know,
if we’re missing an earthquake or two

00:43:51.610 --> 00:43:53.830
in the Pallett Creek data set,
that could explain it.

00:43:53.830 --> 00:43:56.020
I don’t know a whole lot
about this data set.

00:43:56.020 --> 00:43:59.240
Probably people in this room
know a lot more than me.

00:43:59.240 --> 00:44:02.340
And then, out here past 400 years,
you know, this is where we’re getting

00:44:02.340 --> 00:44:08.530
into just the very tails of the distribution.
There’s a lot of noise.

00:44:08.530 --> 00:44:13.119
But nonetheless, I don’t think we have
any evidence that the San Andreas Fault

00:44:13.119 --> 00:44:17.530
will just be quiescent for, you know,
500, 1,000 years, something like that.

00:44:17.530 --> 00:44:23.540
So the hazard rate probably bumps up
pretty rapidly, consistent with this idea

00:44:23.540 --> 00:44:27.630
that we’ve accumulated a huge
amount of shear stress on the fault.

00:44:27.630 --> 00:44:30.260
It’s got to rupture
at some point.

00:44:30.260 --> 00:44:35.720
Here’s where we are,
kind of at a midpoint in 2017.

00:44:35.720 --> 00:44:40.549
Okay, so I’ll go a little bit
more briefly through this

00:44:40.549 --> 00:44:44.490
so I can get through
the rest of the talk here.

00:44:44.490 --> 00:44:47.760
So one of the things I talked
about was using survival analysis

00:44:47.760 --> 00:44:51.260
to estimate what the earthquake
likelihoods are, you know,

00:44:51.260 --> 00:44:55.460
at some point, given how long
it’s been since the last event.

00:44:55.460 --> 00:44:58.579
And so here’s
some graphs.

00:44:58.579 --> 00:45:02.590
This is the Seattle Fault on top.
Puget Lowlands on the bottom.

00:45:02.590 --> 00:45:05.920
This is the number of years –
sorry there’s no axis label –

00:45:05.920 --> 00:45:09.520
since now – you know,
from now and into the future.

00:45:09.520 --> 00:45:12.520
And this is the kind of
cumulative hazard for

00:45:12.520 --> 00:45:16.350
this many years,
from 2016 going forward.

00:45:16.350 --> 00:45:19.470
So up to 50 years on the
Seattle Fault Zone itself,

00:45:19.470 --> 00:45:25.580
there’s about a 2.5 chance of a 6.5-plus –
a surface-breaking earthquake on this

00:45:25.580 --> 00:45:31.490
fault given that it’s been 750 years
since the last known earthquake.

00:45:31.490 --> 00:45:36.109
If it’s been less time, these numbers
would be higher, remember.

00:45:36.109 --> 00:45:41.600
So if we’re missing an earthquake, the
danger is bigger than we think, unlike

00:45:41.600 --> 00:45:45.940
what would happen on the San Andreas
if we’re missing a recent earthquake.

00:45:45.940 --> 00:45:50.560
For the Puget Lowland as a whole,
there’s a 12% chance of a surface-

00:45:50.560 --> 00:45:55.920
breaking earthquake in the next 50 years,
given 312 years since the last event.

00:45:55.920 --> 00:45:59.690
So these are non-negligible probabilities.
Fortunately, in Washington

00:45:59.690 --> 00:46:03.910
people are coming around to the
fact that there is not only

00:46:03.910 --> 00:46:09.100
Cascadia seismicity to worry about,
but crustal seismicity as well.

00:46:09.100 --> 00:46:12.220
There’s a couple people at the
Seattle Times – Daniel Gilbert is

00:46:12.230 --> 00:46:15.619
a name that is in my head –
I may be wrong – who’s been

00:46:15.619 --> 00:46:21.490
very good about keeping abreast
of the research coming out and –

00:46:21.490 --> 00:46:23.190
you know, and writing
about this in the paper.

00:46:23.190 --> 00:46:27.420
So hopefully this isn’t,
you know,

00:46:27.420 --> 00:46:30.569
completely new information
to a lot of people.

00:46:30.569 --> 00:46:33.839
But nonetheless, it’s nice to
look at it like this versus

00:46:33.839 --> 00:46:36.460
the kind of
time-independent models

00:46:36.460 --> 00:46:39.380
that Art Frankel has been
putting out to contrast those.

00:46:39.380 --> 00:46:43.260
You know, those also involve
a lot more faults, off-fault seismicity,

00:46:43.260 --> 00:46:47.069
and things like that that
I’m not accounting for here.

00:46:47.069 --> 00:46:51.440
So to summarize all the survival analysis
stuff, there’s significant time-dependent

00:46:51.440 --> 00:46:55.040
earthquake hazards on both the Seattle
Fault Zone and Puget Lowland faults.

00:46:55.040 --> 00:47:00.290
The earthquake hazard is highest in the
decades following an earthquake.

00:47:00.290 --> 00:47:04.670
So previously damaged
infrastructure may be very risky.

00:47:04.670 --> 00:47:09.730
We can’t just assume that –
you know, that the storm has passed.

00:47:09.730 --> 00:47:13.470
And so we need to
think about this in plans for how we

00:47:13.470 --> 00:47:18.089
deal with earthquakes –
how we rebuild, you know,

00:47:18.089 --> 00:47:23.340
whether we want to evacuate and
keep people out for a while, et cetera.

00:47:23.340 --> 00:47:25.890
So this is – this is something
that’s really important

00:47:25.890 --> 00:47:28.839
from an engineering perspective,
from emergency planning perspective,

00:47:28.839 --> 00:47:34.060
as well as interesting
from the scientific perspective.

00:47:34.060 --> 00:47:37.130
And so, for the rest of the talk,
I’m going to be kind of getting more into

00:47:37.130 --> 00:47:41.920
the engineering part of things because
that’s what I’m doing at GEM.

00:47:42.820 --> 00:47:48.589
And, you know, it’s cool.
It’s cool to be able to

00:47:48.589 --> 00:47:51.230
bring the science that I’m doing
back to the – kind of the

00:47:51.230 --> 00:47:55.730
public consciousness, which is –
when you’re studying Miocene

00:47:55.730 --> 00:47:59.470
low-angle normal faults in Tibet,
it’s a little bit harder to do.

00:47:59.470 --> 00:48:02.980
So if we go back to this question,
for the earthquakes in the fault systems

00:48:02.980 --> 00:48:05.760
that we’re looking at,
I think we can come up with a no.

00:48:05.760 --> 00:48:09.280
You know, in both of these things,
the hazard rate tends to ramp up.

00:48:10.020 --> 00:48:14.609
It’s a conditional no. If it’s been a few
thousand years, we can wait longer.

00:48:14.609 --> 00:48:18.460
But I think the idea of
simply just discounting

00:48:18.460 --> 00:48:22.720
future earthquakes is
not supported by the data.

00:48:23.840 --> 00:48:27.500
Okay, so now we’re going to
talk a little bit about

00:48:27.510 --> 00:48:31.260
time dependence before
we get into the risk stuff.

00:48:31.260 --> 00:48:36.200
So clustering and periodicity
are common things that we see

00:48:36.200 --> 00:48:40.270
or that we, you know,
infer or that we invoke.

00:48:40.270 --> 00:48:43.410
And a lot of this is linked to
the physics of the Earth.

00:48:43.410 --> 00:48:47.410
So we have triggering that
may lead to earthquake clusters.

00:48:47.410 --> 00:48:50.900
We may have broad
changes in crustal state.

00:48:50.900 --> 00:48:54.650
Pore fluid pressures from earthquake –
or, from fluid injection, for example,

00:48:54.650 --> 00:49:00.640
may lead to crustal states that are easier
to fail than they were previously.

00:49:00.640 --> 00:49:05.600
Elastic rebound and, you know,
periodic strain accumulation

00:49:05.610 --> 00:49:09.470
and release that we see on faults like
the San Andreas – you know,

00:49:09.470 --> 00:49:15.450
that’s another physics, and that’s
another type of earthquake behavior

00:49:15.450 --> 00:49:23.540
that is, in many cases, supported by the
observations, at least – at least by some.

00:49:24.300 --> 00:49:26.480
So the distribution of
inter-event times matters.

00:49:26.490 --> 00:49:29.260
That’s what’s going to
determine the recurrence interval.

00:49:29.270 --> 00:49:33.150
That’s what’s going to determine
the time-dependent hazard.

00:49:33.150 --> 00:49:34.950
Something else that I’ve
been exploring a little bit,

00:49:34.950 --> 00:49:39.790
but don’t have a lot of physical insight
yet, is the ordering of inter-event times.

00:49:39.790 --> 00:49:45.920
If the last period was short, is the next
one going to be shorter or longer?

00:49:47.020 --> 00:49:48.800
So I’m going to talk
a little bit about this.

00:49:48.810 --> 00:49:51.100
So this is stuff I was
just doing last week.

00:49:51.100 --> 00:49:53.430
There’s a good paper
by Goh and Barabasi.

00:49:53.430 --> 00:49:58.310
Barabasi is kind of the lord of
network science and – you know,

00:49:58.310 --> 00:50:05.170
in this nonlinear dynamics
and graph theory community.

00:50:05.170 --> 00:50:09.900
And so the work that they’ve
been doing on a lot of

00:50:09.900 --> 00:50:13.180
different phenomena kind of
breaks what we would consider

00:50:13.180 --> 00:50:19.950
clustering or periodicity into two
different aspects, or two different axes.

00:50:19.950 --> 00:50:21.830
One of them
is the burstiness.

00:50:21.830 --> 00:50:26.440
So this is more or less the scaled
coefficient of variation, which is

00:50:26.440 --> 00:50:32.320
the standard deviation of recurrence
or inter-event times over the mean.

00:50:32.320 --> 00:50:38.020
And it’s scaled to go between
minus 1 and 1 instead of zero to infinity,

00:50:38.020 --> 00:50:41.440
which is nice for analysis.
And so this is the probability

00:50:41.440 --> 00:50:44.980
distribution of inter-event times
compared to the mean.

00:50:46.060 --> 00:50:50.080
On top here – and then there’s
another thing that’s called the memory,

00:50:50.080 --> 00:50:52.600
and this is more or less
scaled autocorrelation.

00:50:52.600 --> 00:50:56.020
And so this is the ordering
of inter-event times.

00:50:56.020 --> 00:51:02.320
And so we have five different sequences
of events with time, t, on the bottom.

00:51:02.329 --> 00:51:04.090
The events are
these thin lines.

00:51:04.090 --> 00:51:08.549
Where the lines look thick,
that’s a lot of closely spaced events.

00:51:08.549 --> 00:51:12.500
On top here,
we have a Poissonian model.

00:51:12.500 --> 00:51:22.000
And so this model has a burstiness of
zero, a coefficient of variation of 1.

00:51:22.000 --> 00:51:28.309
And it also has a memory of zero.
So it has no autocorrelation.

00:51:28.309 --> 00:51:31.000
There’s no memory
in the system.

00:51:32.750 --> 00:51:37.600
For b and c here, we have –
for b, we have a high burstiness.

00:51:37.609 --> 00:51:40.530
So we have a lot of events
that are very closely spaced

00:51:40.530 --> 00:51:46.220
and then kind of wide
separations in between them.

00:51:46.220 --> 00:51:49.630
And so this is a positive
value of burstiness.

00:51:49.630 --> 00:51:51.589
The burstier it is,
the closer to 1.

00:51:51.589 --> 00:51:54.940
For c, we have
very, very, very periodic events.

00:51:54.940 --> 00:51:59.390
This is a very low burstiness.
Perfectly periodic,

00:51:59.390 --> 00:52:04.410
perfectly recurring metronome
events have a value of minus 1.

00:52:04.410 --> 00:52:09.589
Over here, we have –
so both of these data sets shown

00:52:09.589 --> 00:52:14.599
actually have a memory of zero.
These both have a burstiness of zero.

00:52:14.599 --> 00:52:21.530
So there’s no statistical clustering
like we normally think of it.

00:52:21.530 --> 00:52:24.580
But these events have
varying degrees of autocorrelation.

00:52:24.580 --> 00:52:29.800
So the top has positive autocorrelation.
It has a memory of 1.

00:52:29.800 --> 00:52:33.240
And so a high event is followed –
you know, or widely spaced events

00:52:33.240 --> 00:52:35.410
are followed by
more widely spaced events.

00:52:35.410 --> 00:52:38.609
Shortly spaced events are
followed by shortly spaced events.

00:52:38.609 --> 00:52:43.470
On the bottom, we have the opposite.
So a wider interval than average

00:52:43.470 --> 00:52:47.260
is followed by a shorter interval
than average, and vice versa.

00:52:48.460 --> 00:52:51.890
This isn’t something that’s
discussed a lot in the literature.

00:52:51.890 --> 00:52:57.980
The autocorrelation does come up a little
bit in kind of my literature reviews.

00:52:59.000 --> 00:53:01.339
But there’s not a lot
of discussion about it.

00:53:01.339 --> 00:53:04.220
There’s not a lot of kind of,
you know, physics that we

00:53:04.220 --> 00:53:06.900
know about it behind it yet,
at least that I’m aware of.

00:53:06.900 --> 00:53:08.820
You know, you guys have been
doing this stuff a lot longer than me

00:53:08.820 --> 00:53:11.940
and maybe have some insight,
and I’d love to hear it.

00:53:12.800 --> 00:53:19.140
So if you look at all of the events that
we have, and plot samples from, you

00:53:19.150 --> 00:53:23.200
know, all the inter-event times that we
calculated earlier, this is where they plot.

00:53:23.200 --> 00:53:29.060
So down here – okay, the axes, first off.
So this is burstiness –

00:53:29.060 --> 00:53:33.620
clumpiness, if you want –
on the X – or, the Y axis.

00:53:33.620 --> 00:53:38.800
Clustered behavior –
very clumped behavior is on top.

00:53:38.800 --> 00:53:42.740
And perfectly periodic
behavior is on the bottom.

00:53:42.740 --> 00:53:47.720
On the X axis, we have the memory.
So positive autocorrelation – long events

00:53:47.720 --> 00:53:54.859
followed by – or, long intervals
followed by long intervals is on the right.

00:53:54.859 --> 00:53:58.040
And long intervals followed by
short intervals is on the left.

00:53:58.040 --> 00:54:01.010
Short intervals followed by
short intervals is also on the right.

00:54:01.010 --> 00:54:04.020
So this is contrasting.
This is the same.

00:54:04.020 --> 00:54:09.849
The San Andreas shows both
periodic behavior in the paleoseismic

00:54:09.849 --> 00:54:15.849
data sets and negative memory –
negative autocorrelation.

00:54:15.849 --> 00:54:19.420
So a longer interval is going to
be followed by a shorter interval.

00:54:22.480 --> 00:54:26.560
And again, Poisson behavior
is right here in the origin.

00:54:26.560 --> 00:54:29.960
And so this is pretty far
from Poissonian behavior.

00:54:29.960 --> 00:54:34.380
If you look at the number of events
that we have, and – you know,

00:54:34.380 --> 00:54:37.710
and just draw samples from these
distributions of the same –

00:54:37.710 --> 00:54:42.670
of, you know, like, the – however many
tens of earthquakes, like, you’re not

00:54:42.670 --> 00:54:45.609
going – from a Poissonian distribution,
you’re not going to get this.

00:54:45.609 --> 00:54:49.900
So we can – based on this data set,
we can reject Poissonian behavior

00:54:49.900 --> 00:54:52.420
for surface-breaking
earthquakes on the San Andreas.

00:54:52.420 --> 00:54:55.069
On the Pacific Northwest
data sets,

00:54:55.069 --> 00:54:57.900
they’re a little bit
closer to Poissonian,

00:54:57.900 --> 00:55:01.420
particularly in terms of
the clustering.

00:55:02.180 --> 00:55:06.920
But they’re not quite there.
They’re not straddling either axis, really.

00:55:06.920 --> 00:55:13.420
The Seattle Fault Zone right here
shows more positive autocorrelation,

00:55:13.420 --> 00:55:17.770
more positive memory,
but less clustering.

00:55:17.770 --> 00:55:23.360
So there seems to be kind of periods –
not periodic periods, but, you know,

00:55:23.360 --> 00:55:29.500
episodes, maybe, where we have high –
you know, lots of space in between

00:55:29.500 --> 00:55:33.880
events and then – you know, and then a
lot of events happening in succession.

00:55:35.100 --> 00:55:38.500
That’s less so for the
Puget Sound as a whole.

00:55:38.500 --> 00:55:40.890
We see a little bit more
variation in behavior.

00:55:40.890 --> 00:55:44.980
But the clustering
is a little bit higher.

00:55:44.980 --> 00:55:48.040
So, Jack, you’re raising your fingers.
- [inaudible]

00:55:48.040 --> 00:55:49.900
- Oh, okay, thanks.

00:55:52.160 --> 00:55:55.340
Okay, so what
do these mean?

00:55:55.340 --> 00:56:01.000
Periodic versus bursty – you know,
if we think about stress accumulation

00:56:01.000 --> 00:56:04.680
and release or strain accumulation and
release in the crust, triggering, et cetera,

00:56:04.680 --> 00:56:08.079
we can kind of come up with some
hypotheses for how this would work.

00:56:08.079 --> 00:56:11.299
So with periodic behavior,
we have elastic rebound.

00:56:11.299 --> 00:56:12.550
We have a
pretty stable system.

00:56:12.550 --> 00:56:18.839
It’s not easily perturbed
by the external world.

00:56:18.840 --> 00:56:21.980
And so we kind of
have fault independence.

00:56:21.980 --> 00:56:27.410
Each fault is rupturing by itself.
Stress builds up and then releases.

00:56:27.410 --> 00:56:30.940
With bursty behavior, we may
have long-term stress storage,

00:56:30.940 --> 00:56:34.079
but the system isn’t very stable.
If something – there’s a perturbation

00:56:34.079 --> 00:56:37.240
to it, you know, we kind of
have cascades of earthquakes.

00:56:37.240 --> 00:56:40.240
So faults are interdependent,
assuming that, you know, one fault

00:56:40.240 --> 00:56:44.720
is triggering the next, and they’re not
all responding to an external stimulus.

00:56:46.140 --> 00:56:48.260
With the memory,
it’s less clear to me.

00:56:48.260 --> 00:56:51.270
Granted, I’ve been thinking
about it for, like, six days.

00:56:51.270 --> 00:56:56.040
But – you know, but there’s
not a lot of work that I’m aware of.

00:56:56.040 --> 00:56:59.460
Maybe some of you
have some insight into this.

00:57:00.280 --> 00:57:04.060
Maybe it has to do with the crustal
stress budget and, you know,

00:57:04.070 --> 00:57:09.000
how stress is accumulated and released.
Maybe it has to do with failure states.

00:57:09.000 --> 00:57:13.859
So fluid pressure or something else,
you know, causes kind of shifts

00:57:13.859 --> 00:57:17.380
in state or mode of the crust.
They’re kind of – the crust will

00:57:17.380 --> 00:57:21.710
get into some state where it’s very
easy for earthquakes to happen.

00:57:21.710 --> 00:57:25.279
And so they do frequently.
And then maybe the budget is spent.

00:57:25.280 --> 00:57:28.540
Or, you know,
the external conditions change,

00:57:28.540 --> 00:57:32.560
and we go a really long time
without earthquakes.

00:57:32.560 --> 00:57:36.800
I think an intra-plate seismicity,
particularly, you know,

00:57:36.800 --> 00:57:41.540
where strain rates are very low,
I hypothesize that we’re going to

00:57:41.540 --> 00:57:47.411
see behavior that has
a high memory and, you know,

00:57:47.411 --> 00:57:49.880
maybe some failure
state type of behavior.

00:57:49.880 --> 00:57:53.000
And so particularly
throughout Australia,

00:57:53.000 --> 00:57:58.130
throughout mainland China,
there seem to be kind of fault zones that

00:57:58.130 --> 00:58:02.000
are active for a while and then subside,
and then activity shifts somewhere else.

00:58:02.000 --> 00:58:04.760
And there’s not a lot
of rhyme or reason to it.

00:58:04.760 --> 00:58:08.240
It doesn’t necessarily correlate with
what we can see in terms of

00:58:08.240 --> 00:58:13.960
decadal strain accumulation
from geodesy or other things.

00:58:16.100 --> 00:58:19.660
Okay, so maybe I don’t have
any time to get into the hazard stuff.

00:58:19.660 --> 00:58:23.559
Or should I just go over?
- Maybe just a …

00:58:23.560 --> 00:58:25.280
- An overview?
- Summarize and then

00:58:25.280 --> 00:58:27.740
we could ask some questions.
- Okay. Okay, yeah, yeah.

00:58:27.740 --> 00:58:32.020
Okay, to summarize – well,
I summarized it ad infinitum.

00:58:32.030 --> 00:58:39.640
So time-dependent PSHARA – so time-
dependent probabilistic seismic hazard

00:58:39.640 --> 00:58:46.390
and risk analysis is something that –
this is where I think we want to go.

00:58:46.390 --> 00:58:48.680
So we want to be able to
simulate earthquakes that match the

00:58:48.680 --> 00:58:54.930
paleoseismic behavior – that match other,
you know, instrumental behavior

00:58:54.930 --> 00:58:59.119
and be able to get away from
the kind of Poissonian assumptions

00:58:59.120 --> 00:59:02.380
where they’re not
supported by the data.

00:59:02.380 --> 00:59:06.480
You know, incorporating aftershocks
is the most obvious way to do this,

00:59:06.480 --> 00:59:10.869
but, you know, clustering and
stuff like that is important too.

00:59:10.869 --> 00:59:15.329
Model – we need to be able to model
damage and rebuilding of infrastructure,

00:59:15.329 --> 00:59:19.440
have cumulative fragility
functions for different structures.

00:59:19.440 --> 00:59:22.119
Probabilistic rebuilding.
These are both things that

00:59:22.119 --> 00:59:25.380
we’re working on in GEM
in the infrastructure engineering

00:59:25.380 --> 00:59:28.340
side of things and
social vulnerability.

00:59:28.340 --> 00:59:30.779
We need to identify areas
that are major concerns –

00:59:30.779 --> 00:59:38.589
areas that are slowly rebuilt, have
a lot of infrastructure that may expose

00:59:38.589 --> 00:59:42.039
a lot of the population to damage,
particularly repeated damage.

00:59:42.039 --> 00:59:44.320
Cumulative building damage is
something that’s just kind of

00:59:44.320 --> 00:59:48.579
getting on the forefront of the
seismic engineering community.

00:59:48.579 --> 00:59:50.790
This is sort of what it looks like.
We have a – you know,

00:59:50.790 --> 00:59:56.599
if this is the structural capacity –
it starts out at 1, after the first sequence

00:59:56.599 --> 01:00:00.140
of earthquakes, it decreases.
And it continues to decrease because

01:00:00.140 --> 01:00:05.339
the buildings age, and they may age
more rapidly with increasing damage.

01:00:05.339 --> 01:00:10.529
And then we’re subjected to the
sequence before failure occurs.

01:00:10.529 --> 01:00:13.350
So there’s a lot of, you know,
analog modeling, numerical modeling

01:00:13.350 --> 01:00:18.470
that happens in the engineering
community now modeling this stuff and

01:00:18.470 --> 01:00:22.040
being able to incorporate into ground
shaking models that we can produce.

01:00:22.040 --> 01:00:27.160
Capacity rebuilding is something
that’s kind of even newer.

01:00:27.170 --> 01:00:31.000
But the likelihood of some building –
you know, different components of it

01:00:31.000 --> 01:00:38.450
getting fixed or communities
having infrastructure that gets fixed,

01:00:38.450 --> 01:00:41.329
is dependent on, you know,
the resources that the community has

01:00:41.329 --> 01:00:43.059
and the damage
that it sustained.

01:00:43.059 --> 01:00:46.859
So with increasing damage,
communities are less able to respond.

01:00:46.859 --> 01:00:51.170
So there are a lot of nonlinearities
that are in this system.

01:00:51.170 --> 01:00:54.369
And obviously places like Haiti just,
you know, don’t even get off the ground

01:00:54.369 --> 01:00:59.220
with rebuilding in a lot of instances.
So when societal capital is really low,

01:00:59.220 --> 01:01:03.809
that’s very different than,
you know, a situation like Napa.

01:01:03.809 --> 01:01:07.080
And so there are both building-level
and community-level models

01:01:07.080 --> 01:01:09.960
that people are building.
GEM is working on this.

01:01:09.960 --> 01:01:16.720
USGS is probably working on this
with Hazus and FEMA as well.

01:01:16.720 --> 01:01:23.060
And – okay, so a work-in-progress is –
at GEM is calculating ground motions

01:01:23.060 --> 01:01:25.310
from all these
paleoearthquakes.

01:01:25.310 --> 01:01:28.930
Simulating aftershocks, calculating
ground motions from them.

01:01:28.930 --> 01:01:32.630
Placing them in time based on
what we’ve seen so far

01:01:32.630 --> 01:01:37.890
and calculating damage – you know,
including cumulative damage, loss,

01:01:37.890 --> 01:01:42.440
rebuilding through time for all
of the Puget Lowland region.

01:01:42.440 --> 01:01:45.180
We’re doing this
census tract by census tract.

01:01:45.180 --> 01:01:49.250
And this is – this is work in progress.
X means that it’s done,

01:01:49.250 --> 01:01:53.549
or at least I have the code for it.
A slash is half an X. It’s in progress.

01:01:53.549 --> 01:01:56.569
And this is,
you know, yet to start.

01:01:56.569 --> 01:01:59.730
But we want to be able to see
how much higher are losses – lives,

01:01:59.730 --> 01:02:05.920
dollars, et cetera – in these earthquake
clusters versus Poissonian assumptions.

01:02:05.920 --> 01:02:07.910
How much is this going to
bankrupt insurance companies

01:02:07.910 --> 01:02:13.010
and re-insurance companies?
How much – you know, how long

01:02:13.010 --> 01:02:18.500
do we need to stay away and
evacuate after – after evacuation?

01:02:18.500 --> 01:02:20.980
Where is infrastructure most vulnerable?
You know?

01:02:20.980 --> 01:02:23.559
So the dams in the region
are going to be a lot harder

01:02:23.559 --> 01:02:25.900
to rebuild than
single-frame houses.

01:02:25.900 --> 01:02:29.839
And so we need to have some
idea of how this is going to work.

01:02:30.660 --> 01:02:32.820
Okay, this is just
main shock and

01:02:32.820 --> 01:02:37.940
aftershock epicenters
from some simulations.

01:02:38.940 --> 01:02:45.860
Peak ground acceleration from a scenario
earthquake on the Seattle Fault Zone.

01:02:45.869 --> 01:02:47.260
All these dots
are census tracts.

01:02:47.260 --> 01:02:49.400
We’ve got very
high values of PGA,

01:02:49.400 --> 01:02:52.210
which maybe – they’re lower than I
expected, but I’m not an expert in this.

01:02:52.210 --> 01:02:56.850
You know, running right through
major metro areas, et cetera.

01:02:56.850 --> 01:03:00.220
So the conclusions
from all of this.

01:03:00.220 --> 01:03:03.010
So the magnitudes that we’ve
seen of Puget Sound paleoearthquakes

01:03:03.010 --> 01:03:07.950
are large – 6.5 to 7.5, but they’re
a little bit lower than what we

01:03:07.950 --> 01:03:12.860
would have expected just based on,
you know, the up to 8 meters of fault

01:03:12.860 --> 01:03:16.700
offset – up to 10 meters of, you know,
displacement on the fault.

01:03:18.660 --> 01:03:22.240
With time dependence, we kind of
have bathtub curves for hazard.

01:03:22.240 --> 01:03:24.640
So it starts out high,
and then they drop down,

01:03:24.640 --> 01:03:27.819
and then they ramp up again
after several thousand years.

01:03:27.819 --> 01:03:31.900
Puget Sound seismicity is more
clustered than a Poisson assumption,

01:03:31.900 --> 01:03:36.780
so we need to think about
how this affects hazard and risk.

01:03:36.780 --> 01:03:41.170
The first step is simulating
what has happened and then,

01:03:41.170 --> 01:03:44.040
you know, be able to predict
in the future based on that.

01:03:44.040 --> 01:03:48.140
To do all this, we need innovations
in how we model earthquake occurrence

01:03:48.140 --> 01:03:52.130
and how we model building damage,
rebuilding, community rebuilding,

01:03:52.130 --> 01:03:57.559
societal resilience, et cetera. So this is –
a lot of people are interested in this.

01:03:57.559 --> 01:04:01.289
The closer you get to kind of
societal loss and resilience,

01:04:01.289 --> 01:04:06.150
the more interest there are from
governments, re-insurance companies,

01:04:06.150 --> 01:04:10.180
et cetera – the World Bank –
you know, big NGOs like that.

01:04:10.180 --> 01:04:14.600
And so it’s really nice to be able to,
you know, have the pipeline

01:04:14.609 --> 01:04:18.319
where we can take these observations,
these trenches, you know,

01:04:18.319 --> 01:04:23.099
mapping eventually physical models for
earthquake triggering and that sort of

01:04:23.099 --> 01:04:28.309
thing and bring it all the way through,
how does this affect people’s lives?

01:04:28.309 --> 01:04:30.600
You know, how does
this affect communities?

01:04:30.600 --> 01:04:33.460
And so this is where we’re –
where we’re going.

01:04:33.460 --> 01:04:35.600
So I’d be happy to
take any questions.

01:04:35.600 --> 01:04:40.680
[ Applause ]

01:04:40.680 --> 01:04:43.690
- Thank you, Richard, for a
really interesting presentation.

01:04:43.690 --> 01:04:46.650
A bit broader than
we might have anticipated.

01:04:46.650 --> 01:04:49.900
Are there some
questions for Richard?

01:04:53.100 --> 01:04:57.130
Andy, Michael has one for you.
- Okay.

01:04:57.130 --> 01:04:59.190
I’ve never seen you before,
but I’ve seen your work.

01:04:59.190 --> 01:05:01.140
I didn’t know if you
were going to be here. Great.

01:05:01.140 --> 01:05:03.180
- Thanks. Yeah, and it was
really interesting to see a lot of this

01:05:03.180 --> 01:05:05.280
put together
in these ways.

01:05:05.289 --> 01:05:08.100
I think it’s actually pretty hard to
create burstiness physically

01:05:08.100 --> 01:05:11.230
without creating memory.
- Okay.

01:05:11.230 --> 01:05:15.040
- The reason is, okay, you can
create burstiness, say, empirically

01:05:15.040 --> 01:05:16.950
in a statistical model by, say,
sampling the inter-event times

01:05:16.950 --> 01:05:20.569
out of a gamma distribution
with no memory.

01:05:20.569 --> 01:05:25.369
But what that requires is that an
earthquake has an aftershock – only one.

01:05:25.369 --> 01:05:28.140
And the aftershock can’t
trigger something itself.

01:05:28.140 --> 01:05:31.559
So as soon as you have triggering
in a system that’s – like, you know,

01:05:31.560 --> 01:05:33.840
in aftershock sequences,
you see autocorrelation.

01:05:33.840 --> 01:05:36.260
So it becomes a little hard –
that’s one form of memory.

01:05:36.270 --> 01:05:38.410
- Okay.
- The other form of memory is, I think,

01:05:38.410 --> 01:05:41.150
sort of what you referenced in terms of
changing the failure criteria.

01:05:41.150 --> 01:05:43.490
And anything that
changes the underlying rate

01:05:43.490 --> 01:05:45.990
will create
memory in the system.

01:05:45.990 --> 01:05:50.440
And it may not actually be memory
between the events, but it’s apparent

01:05:50.440 --> 01:05:53.420
memory because the system changed.
- Yeah.

01:05:53.420 --> 01:05:55.680
- And if it goes back.
And of course, geodetically,

01:05:55.680 --> 01:05:57.980
we don’t see a lot of,
necessarily, variability in the

01:05:57.980 --> 01:06:00.680
strain coming in,
but maybe fluids moving around.

01:06:00.680 --> 01:06:04.579
But I think one thing to be
careful of is just that burstiness.

01:06:04.579 --> 01:06:07.789
If it’s not – if it’s not – if burstiness –
if you find burstiness without memory,

01:06:07.789 --> 01:06:11.510
than that actually suggests that you’re
missing a lot of the events that are in

01:06:11.510 --> 01:06:15.040
the system because there’s got to be
something connecting the burstiness.

01:06:15.040 --> 01:06:18.109
- Yeah, okay.
And I think that makes sense.

01:06:18.109 --> 01:06:20.770
I mean, this – you know,
we’re not getting scatter.

01:06:20.770 --> 01:06:22.880
And there’s not a lot
in these two quadrants.

01:06:22.880 --> 01:06:25.580
And so it makes sense
that these are correlated variables.

01:06:25.580 --> 01:06:27.280
- Yeah.
- Okay, thank you.

01:06:27.280 --> 01:06:28.680
- Sure.

01:06:31.620 --> 01:06:35.540
- Anyone else have a quick question?
- I’ve got one.

01:06:35.540 --> 01:06:39.010
There’s been a lot of discussion
on the crustal faulting in the

01:06:39.010 --> 01:06:43.599
Puget Lowland and whether
they might be related to Cascadia

01:06:43.599 --> 01:06:47.541
megathrust earthquakes in some way.
But I didn’t see – you know,

01:06:47.541 --> 01:06:51.200
the periodicity of the
megathrust is 500 to 600 years.

01:06:51.200 --> 01:06:57.660
I didn’t see that in your
periodicity in the crustal earthquakes.

01:06:57.660 --> 01:07:01.460
- Yeah. And, you know, I –
so one of the things that I

01:07:01.460 --> 01:07:03.950
haven’t done that I would
like to is look into that.

01:07:03.950 --> 01:07:07.500
And also just look at, you know,
if an earthquake happens on one fault,

01:07:07.500 --> 01:07:09.020
where is the next one?

01:07:09.020 --> 01:07:12.500
And do we see kind of patterns
in that at a more fine-grain level?

01:07:12.500 --> 01:07:17.750
I think that if you see a
series of events following Cascadia,

01:07:17.750 --> 01:07:21.690
it may disguise that, you know,
spectral component of the signal –

01:07:21.690 --> 01:07:26.750
that 500- or 600-year signal
in the fault data themselves.

01:07:26.750 --> 01:07:28.859
So it may be there.
It may not.

01:07:28.859 --> 01:07:34.029
I think Brian and Joan looked at it,
and they saw some evidence,

01:07:34.029 --> 01:07:38.940
and they saw more evidence
worldwide than in this data set itself.

01:07:39.760 --> 01:07:43.340
But, yeah, it’d be interesting to look at
and also, you know, model the stresses

01:07:43.340 --> 01:07:49.200
to see how this – yeah, how this works.
Because these faults are orthogonal.

01:07:54.000 --> 01:07:56.340
- Any more
questions for Richard?

01:07:57.080 --> 01:08:03.600
Well, let’s meet at the Tectonic
Grill in 10 to – about 10 to noon.

01:08:03.600 --> 01:08:06.220
- Okay.
- We’ll have lunch there. Thanks.

01:08:06.220 --> 01:08:07.600
- Thank you all.

01:08:07.600 --> 01:08:11.180
[ Applause ]

01:08:12.700 --> 01:08:16.380
[ Silence ]