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Good morning, everyone.

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Welcome to today’s
Earthquake Science Seminar.

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Before we begin, I have a couple
of quick announcements.

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First, tomorrow is the Great
ShakeOut at 10:18 in the morning.

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So remember to kind of
participate in this event.

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And then, as well, we have a couple
of seminars – one on Friday.

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Warren Wood from the
U.S. Naval Research Laboratory

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will be talking about a
machine learning approach

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to characterization of sediment
via reflection seismic profiles.

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And then, next week, for our
regularly scheduled seminar,

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we have Jens Lund Snee coming
down from Stanford University.

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Andy’s going to
introduce our speaker.

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- Okay, so I thought I would
give Andrea a bit of an introduction

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for people who might not
know everything she’s up to.

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I first met Andrea in Erice
at a statistical seismology meeting

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while she was a grad student at MIT/
Woods Hole and in their joint program.

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And that, I understand now, is not
surprising because actually she’s

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an intrepid traveler and has a goal of
one new country every year, at least?

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Something like that.
No, she’s going – when she’s not –

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and she’s actually spent two stints
at the Institute of Statistical

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Mathematics in Japan over the years.
So she’s – really is an intrepid traveler.

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When she’s home, she also –
besides being a seismologist,

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actually teaches elementary school
music and sings in three chorales.

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For the last several years, I’ve had the
real pleasure of writing a whole series –

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or actually, Andrea writing a whole
series of Llenos and Michael papers.

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And she’s covered a really wide
range of somewhat related topics.

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One started with the earthquake
behavior in Arkansas and Oklahoma

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and also the Salton Sea looking at
both natural and induced swarms.

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She’s been a major contributor
to the series of one-year hazard maps

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for the central and
eastern United States

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And after the Napa earthquake,
she took on the forecasting

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of the aftershocks, and her work
on that earthquake led to

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two major and important changes in
how we estimate parameters during

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aftershock forecasting that made things
much more robust and meaningful.

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And finally, we’ve been working
lately on improving – both improving

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declustering for PSHA and also trying
to get rid of declustering and do

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full-catalog – use the full catalog
for seismic hazard assessment.

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But I think really the work
she’s going to talk about today

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is some that I’m actually
most excited about.

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For many years, the idea of forecasting
swarms, it was treated in statistical

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seismology as, oh, yeah, that’s the
thing we don’t know how to do.

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But I think, at the end of this talk, we
might conclude that actually Andrea is

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the one who knows how to do it now.
So I’ll let you talk.

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- Maybe.

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All right,
well, let’s see.

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Can everyone –
can everyone hear me okay?

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Yes? All right. Well, thank you
for the lovely introduction, Andy.

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I’m not sure if I’ve completely solved
the problem of swarm forecasting yet,

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but I think this is – what I’m going to
show today is pretty much the building

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blocks we need that put us,
you know, in the right direction.

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And, fun fact, this is actually the work
that I proposed to do as a Mendenhall

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in my proposal that I wrote
pretty much nine years ago today.

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[laughter]
So stick around long enough,

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and you’ll eventually do what
you said you were going to do.

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[laughter]

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So before I begin, I just want to
acknowledge the people that

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I’ve collaborated with on various
aspects of the work that I’m going to

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be talking about today,
especially Andy, of course,

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as well as Nicholas van der Elst,
Morgan Page and [loud static] – sorry.

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I’m going to try not to
move around very much.

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Morgan Page
and Sara McBride.

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And then, of course, sincere apologies
to Bob Dylan for – because I’m

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shamelessly using his song titles
and lyrics throughout this talk.

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So I’m going to start off by
talking a little bit about the

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2016 Bombay Beach swarm, which I
think is a good, motivating example.

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So, as Andy sort of mentioned,
working on swarm forecasting has been

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a problem that, you know,
we’ve been trying to – we’ve been

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thinking about for a long time now,
even before this 2016 swarm.

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But I think this swarm
really demonstrates why

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having such a forecasting
system is so important.

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And so, from there, I’m going to
describe some of the building blocks

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that we’ve put together
for a swarm operational earthquake

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forecasting system.
And these are going to include

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having a original swarm model,
developing a swarm duration model,

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incorporating time-varying background
rates during a swarm, and then finally –

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well, not finally, but constructing
ensemble forecasts to

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combine these different
aspects together.

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And then finally, communicating
these forecasts to the general public.

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All right, so the 2016 Bombay Beach
swarm began on September 26th.

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This figure here just shows
the cumulative number of earthquakes

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of magnitude, I guess,
1.8 and higher over time.

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The swarm lasted
a little less than a week.

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There were about 100 earthquakes
with magnitudes ranging from 2 to 4.3.

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And three of those earthquakes
had magnitudes greater than 4.

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So this map here shows that the swarm
was located in the Salton Sea offshore

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of Bombay Beach here in southern
California in the Salton Trough.

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And, of course, the San Andreas Fault,
the southern terminus of it,

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comes down right about here.
So the swarm’s proximity within

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a few kilometers to the San Andreas
drew responses from the USGS,

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the California Earthquake Prediction
Evaluation Council – or CEPEC –

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and the California Office
Emergency Services, or Cal OES.

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And so the big question that everybody
wanted to know the answer to was,

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how does this swarm affect the
likelihood of a larger earthquake,

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so a magnitude 7 or higher
earthquake happening,

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on the southern
San Andreas?

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So this is a basic timeline
of some of the events

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that happened in
response to the swarm.

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So you’ll see here that the swarm
began on September 26th.

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Later that afternoon,
forecast calculations were begun

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to try and answer that question
of what – how the likelihood

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had been affected on
the southern San Andreas.

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Those – some of those calculations
ran overnight, and then the

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following morning, CEPEC –
so the California Earthquake Prediction

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Evaluation Council – convened
to review those forecast results.

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And ultimately, they passed on an
advisory to the director of Cal OES.

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And this led to the release of earthquake
advisories later in the afternoon –

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that afternoon. So this is the afternoon
of the second day of the swarm.

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So I’m going to return to this timeline
towards the end of my talk when I talk

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a little bit more about how these
forecasts are being communicated.

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For now, I just want to focus on
what the main scientific question that

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we were trying to address here was.
And that’s, what’s the likelihood

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of triggering this large earthquake
on the southern San Andreas

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over some
time interval?

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And, in this case, we happened to be
interested in the one-week time interval.

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It turns out that, for swarms –
this isn’t actually a very trivial –

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well, maybe for
other earthquakes too,

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but particularly for swarms,
this is not a trivial thing to compute.

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So currently, the USGS is,
of course, producing aftershock

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forecasts following
magnitude 5-and-higher earthquakes

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in California and throughout
the rest of the U.S. now.

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And these forecasts have been based
on the Reasenberg and Jones

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earthquake model. So this –
the basic equation is shown here.

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And this is basically the
earthquake rate following –

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at some time following a main shock.
And this model combines a number of

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empirical aftershock laws, including
Omori’s law describing the time decay

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and the number of aftershocks,
a Gutenberg-Richter magnitude

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frequency distribution, and then
an Utsu aftershock productivity.

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So you – in this equation, though, there
isn’t really a background rate term.

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And it also doesn’t
include secondary triggering.

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So this basically
just describes the aftershock rate

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following a
single main shock.

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So this is a problem for earthquake
swarms because generally,

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swarms are thought to be driven
by some transient external process,

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such as slow slip or shallow creep,
fluid flow, dike intrusions, volcanism,

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human-induced processes like
wastewater injection, and so on.

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So one example
is shown here.

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This is the 2005
Obsidian Buttes swarm.

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This also happened in the Salton
Trough, but further south, so on the

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southern shore of the Salton Sea as –
from the Bombay Beach swarm.

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And Lohman and McGuire found
that this swarm was primarily driven

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by shallow aseismic slip that
was detected through InSAR.

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If you look at – whoops.

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If you look at the magnitude –
where – okay.

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If you look at the magnitude
time history of the swarm,

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which is shown here, you can see
that the magnitude time history

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differs a lot from your typical
main shock/aftershock sequence.

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There’s really not
an obvious main shock.

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I mean, this is the largest earthquake,
but you can see that there are

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other earthquakes that
are rather similar in size to it.

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And you can see that there’s no simple,
straightforward Omori-type decay.

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So that means that, generally,
earthquake swarms are modeled as

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transient changes in background rate,
or changes in the rate of spontaneous

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or independent earthquakes,
rather than changes in rate

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that are triggered by other –
by other earthquakes.

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So that means that the Reasenberg
and Jones model isn’t really

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well-suited to answer this
question for earthquake swarms.

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An alternative earthquake
forecast model is the

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Epidemic-Type Aftershock Sequence
model, or the ETAS model.

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Like the Reasenberg
and Jones model,

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it’s also based on
empirical aftershock laws.

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But this model actually includes
a background rate term.

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So the main equation of the
model is shown down here.

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In this model, the observed
seismicity rate at some time, t,

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is going to be the sum of a
background seismicity rate, mu,

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plus the aftershocks that are –
the aftershock rates that are triggered

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by all of the earthquakes in that region
that have occurred prior to time, t.

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And so this aftershock rate
is parameterized by an

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aftershock productivity,
a magnitude scaling parameter, alpha,

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and then the two Omori
decay parameters, c and p.

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So this – so the ETAS model includes –
lets us characterize both

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a background rate as well as –
not just one triggered aftershock rate,

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but basically it says that every
earthquake is capable of triggering

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its own aftershock sequence. So it
includes secondary triggering as well.

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The other model that was
run in response to the

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2016 swarm was the
UCERF3-ETAS model.

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So this also – this model also
included an ETAS component.

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So it had secondary triggering,
and it also includes information about

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the fault and spatial – in particular,
spatial information, as well as

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implementing a characteristic magnitude
frequency distribution on the

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San Andreas Fault, which you couldn’t
really do with a standard ETAS model.

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But this model did not really include
the high background rate that you

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would expect during a swarm.
And so, for the rest of this talk,

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I’m really going to focus
just on the – sort of the

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standard temporal-only
ETAS model shown here.

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So how do we use this model
to make earthquake forecasts?

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Well, typically, what’s done is
you fit this model to a long time –

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long-term catalog, and you get
these parameters, mu, K, alpha, p,

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and c to fit the seismicity in
that particular catalog or region.

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And then you can use that in
simulations to generate a bunch of

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stochastic event sets or synthetic
earthquake catalogs and use the

00:11:42.760 --> 00:11:47.720
distribution of those events to
forecast the – to estimate the

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expected number of earthquakes in
some given time interval in the future.

00:11:52.920 --> 00:11:57.640
So, in the case for the Bombay Beach
swarm, in order to capture the

00:11:57.650 --> 00:12:00.790
high background rate that we
would expect during the swarm,

00:12:00.790 --> 00:12:02.950
what we ended up doing was,
rather than fitting the ETAS model

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to the entire time period – to all the
seismicity that occurred prior to

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the swarm, we just decided to
fit it to the previous swarms

00:12:10.389 --> 00:12:12.830
that had occurred in the region.
So there were a couple of swarms

00:12:12.830 --> 00:12:16.770
that occurred here –
one in 2001, one in 2009.

00:12:16.770 --> 00:12:20.240
And so we used the
seismicity in those swarms alone

00:12:20.240 --> 00:12:23.320
to try and capture this
high background rate.

00:12:23.320 --> 00:12:28.399
And so, with those ETAS model
parameters now, we used those as a –

00:12:28.399 --> 00:12:33.570
as our initial guess, and used those to
generate 10,000 earthquake catalogs.

00:12:33.570 --> 00:12:37.980
And, again, we used the distribution
of those sequences to compute the

00:12:37.980 --> 00:12:42.520
expected number of earthquakes
over the next one-week time period.

00:12:43.180 --> 00:12:48.920
Now, the thing that we had to –
that was – the thing that we had to

00:12:48.920 --> 00:12:52.199
do here was make an assumption as to
how long the swarm was going to last.

00:12:52.199 --> 00:12:55.610
Because we didn’t have
a good swarm duration model.

00:12:55.610 --> 00:12:58.149
And what we ended up doing was
computing two end member models.

00:12:58.149 --> 00:13:02.670
So one end member was assuming
that the high background rate –

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so the swarm – was going to
continue at the same rate for the

00:13:05.860 --> 00:13:09.660
next week – the next forecast interval.
And that’s what’s shown up here.

00:13:09.660 --> 00:13:12.500
So this figure here is showing
the cumulative number of aftershocks

00:13:12.500 --> 00:13:17.700
over time, with blue being observed,
and then the black being the forecast,

00:13:17.700 --> 00:13:19.400
assuming that the
high background rate

00:13:19.400 --> 00:13:22.290
would continue
unabated for the next week.

00:13:22.290 --> 00:13:25.420
The other end member model that
we considered was one where the high

00:13:25.420 --> 00:13:28.730
background rate stopped immediately,
as soon as we made the forecast.

00:13:28.730 --> 00:13:31.400
And so that’s what’s
being shown down here.

00:13:32.040 --> 00:13:37.400
And so you can see that these
two end member models cover

00:13:37.410 --> 00:13:41.459
quite a range of probabilities.
And these two models ended up

00:13:41.459 --> 00:13:46.840
leading to a range going from
about 0.01 to about 0.1%.

00:13:46.840 --> 00:13:50.339
And this is the probability of a
magnitude 7 – at least one magnitude 7

00:13:50.340 --> 00:13:55.060
or higher happening on the southern
San Andreas Fault over the next week.

00:13:56.100 --> 00:13:59.560
So this is just to summarize
the forecast calculations

00:13:59.569 --> 00:14:04.970
that were made back in 2016.
And this is – eventually, it got reported

00:14:04.970 --> 00:14:09.440
in the earthquake advisories that were
released by the USGS and Cal OES.

00:14:10.400 --> 00:14:14.940
So, again, as of the morning
of the second day of the swarm,

00:14:14.940 --> 00:14:19.800
the probability of at least one
magnitude 7-or-higher earthquake on

00:14:19.800 --> 00:14:25.420
the southern San Andreas was about
0.03 to 1% over the next week.

00:14:26.280 --> 00:14:32.579
These probabilities were revised a few
days later to reflect the decreasing –

00:14:32.580 --> 00:14:35.800
the decrease in swarm
activity that happened.

00:14:36.400 --> 00:14:39.970
And so this figure down here just
kind of illustrates how the probabilities

00:14:39.970 --> 00:14:43.790
evolve over time given
a retrospective ETAS model.

00:14:43.790 --> 00:14:47.090
And you can see that the
probabilities are highest shortly after

00:14:47.090 --> 00:14:49.970
the magnitude 4 earthquakes
occur in the swarm, but then they

00:14:49.970 --> 00:14:53.380
decrease fairly rapidly
over the next few days.

00:14:54.320 --> 00:14:59.160
All right, so this is
what happened back in 2016.

00:14:59.780 --> 00:15:02.380
And now I’m going to spend the
rest of the talk describing ways

00:15:02.389 --> 00:15:04.579
that we can improve on
how we computed –

00:15:04.580 --> 00:15:08.500
how we went about trying to
compute that likelihood.

00:15:08.990 --> 00:15:13.820
So I’ve already talked
about this first – this first –

00:15:13.839 --> 00:15:16.740
this building block here, and that’s
having a regional swarm model.

00:15:16.740 --> 00:15:19.770
As I mentioned before,
what we did was we were able to

00:15:19.770 --> 00:15:23.610
fit the ETAS model to previous swarms
that had occurred in that region.

00:15:23.610 --> 00:15:27.160
And having those parameters
on hand was really helpful to have

00:15:27.160 --> 00:15:29.819
as a sort of initial model, so that
we were able to capture the

00:15:29.819 --> 00:15:35.980
high background rate that typically
occurs during earthquake swarms.

00:15:35.980 --> 00:15:39.230
So next I’m going to talk about
developing a swarm duration model.

00:15:39.230 --> 00:15:41.269
This is work I’ve been doing
with Nicholas van der Elst,

00:15:41.269 --> 00:15:45.640
and it’s shortly to
be submitted to BSSA.

00:15:46.180 --> 00:15:50.000
But, as I mentioned a couple slides ago,
we had these two end member models

00:15:50.000 --> 00:15:53.839
that we ended up having to use,
assuming – one assuming that

00:15:53.839 --> 00:15:57.620
the swarm ended immediately,
and one assuming that it continued on

00:15:57.620 --> 00:16:00.639
at a constant rate
for the next week.

00:16:00.639 --> 00:16:07.259
And, as I showed, this leads to a
pretty wide range in the probabilities,

00:16:07.259 --> 00:16:13.600
going from either 0.01% in the case
where the high background rate ends,

00:16:13.600 --> 00:16:15.720
all the way to 0.1%
where the high background rate

00:16:15.720 --> 00:16:18.230
continues at the same –
at the same rate.

00:16:18.230 --> 00:16:20.350
And this assumption also
leads to about 8 times more

00:16:20.350 --> 00:16:25.600
earthquakes being forecast.
So obviously, if you are applying

00:16:25.600 --> 00:16:29.040
a constant background rate in your
forecast, how long you assume that

00:16:29.040 --> 00:16:33.150
background rate is going to last has
a huge effect on the forecast itself.

00:16:33.560 --> 00:16:37.019
Now, the problem with earthquake
swarms is that there’s actually a large

00:16:37.019 --> 00:16:42.279
amount of variability in how long
swarms last, even in a specific location.

00:16:42.279 --> 00:16:48.779
So this table shows the swarms that
have actually – have occurred in the

00:16:48.780 --> 00:16:52.880
San Ramon area, so here in
northern California, since 1970.

00:16:52.880 --> 00:16:55.580
And the second – the middle column
shows the number of earthquakes

00:16:55.580 --> 00:17:00.080
that the swarm contains,
and then the right column

00:17:00.089 --> 00:17:02.730
shows the duration of the swarms.
And you can see that the

00:17:02.730 --> 00:17:05.060
durations range all the way
from things as short as two days

00:17:05.060 --> 00:17:08.120
to things as long as
about a month and a half.

00:17:10.480 --> 00:17:13.559
We can see similar sort of –
similar variability for swarms in the

00:17:13.559 --> 00:17:17.169
Salton Trough. So this is where the
Bombay Beach swarm occurred.

00:17:17.169 --> 00:17:20.140
This is a table of about
20 swarms that were identified by

00:17:20.140 --> 00:17:23.040
Chen and Shearer
in their 2011 paper.

00:17:25.560 --> 00:17:28.900
And they used a slightly different
definition of swarm – not swarm –

00:17:28.909 --> 00:17:33.240
of duration here.
This is actually the time delay

00:17:33.240 --> 00:17:37.750
from the start of the swarm to the –
well, the time delay

00:17:37.750 --> 00:17:40.990
from the first event
that occurred in the swarm.

00:17:40.990 --> 00:17:45.419
And – but you can still see
that there’s a – there’s a

00:17:45.420 --> 00:17:48.760
great amount of variability
in these – in these durations.

00:17:48.760 --> 00:17:50.980
And this is, you know,
not entirely unexpected.

00:17:50.980 --> 00:17:53.350
Because, if we assume that
swarms are being driven by

00:17:53.350 --> 00:17:57.390
some transient process,
you’d expect that, even in the

00:17:57.390 --> 00:18:01.240
same location, that process
is going to vary over time.

00:18:01.240 --> 00:18:03.929
And so variations in that
process are naturally going to

00:18:03.929 --> 00:18:07.500
lead to variations in the
seismicity that it triggers.

00:18:07.500 --> 00:18:10.820
So how can we use this
information to try and

00:18:10.820 --> 00:18:13.620
develop a swarm
duration model?

00:18:14.600 --> 00:18:17.820
To do that, we’re going to
turn to actuarial statistics.

00:18:17.820 --> 00:18:20.650
So this is a type of approach
that’s used by, for example,

00:18:20.650 --> 00:18:25.049
the Social Security Administration
to compute actuarial life tables,

00:18:25.049 --> 00:18:27.559
or life expectancy tables
like the one shown here.

00:18:27.559 --> 00:18:33.440
So this is basically a table showing,
for – well, using survival or

00:18:33.440 --> 00:18:36.961
mortality data in a given population,
you can summarize the probability

00:18:36.961 --> 00:18:41.799
of a person in that population
at a certain age of –

00:18:41.799 --> 00:18:44.890
what the probability is that they’ll
die before their next birthday.

00:18:44.890 --> 00:18:46.880
And then you can also
compute their life expectancy,

00:18:46.880 --> 00:18:50.620
so the average number of years
remaining before death.

00:18:50.620 --> 00:18:54.820
So this table shows, for example,
you know, a person having survived

00:18:54.820 --> 00:19:01.820
to age 6 has about a 0.000145
probability of dying before they turn 7.

00:19:02.420 --> 00:19:06.120
And so this is all – this is all
computed from population statistics.

00:19:07.320 --> 00:19:08.950
We can put together
a similar sort of table

00:19:08.950 --> 00:19:12.760
for earthquake swarms,
given enough data.

00:19:12.760 --> 00:19:17.220
And so this table now shows the
Salton Trough swarm life expectancy.

00:19:17.220 --> 00:19:21.289
So we’re computing these statistics
using the set of 20 Salton Trough

00:19:21.289 --> 00:19:25.370
swarms from Chen and Shearer.
And so this table shows,

00:19:25.370 --> 00:19:28.490
for a given swarm age,
or swarm duration,

00:19:28.490 --> 00:19:32.660
the number of swarms that have
lasted to that age, or duration.

00:19:32.720 --> 00:19:36.040
And then, from those numbers,
we can compute the probability

00:19:36.040 --> 00:19:39.690
that a swarm that has
lasted to that age –

00:19:39.690 --> 00:19:43.190
the probability that it is
going to end in the next 24 hours.

00:19:43.190 --> 00:19:46.800
And then also the expected
time remaining in that swarm.

00:19:47.280 --> 00:19:51.220
So, for example, you can see that,
for Salton Trough swarms, if it has

00:19:51.220 --> 00:19:59.600
lasted a week, it has about, you know, a
12-1/2% chance of ending the next day.

00:19:59.600 --> 00:20:03.309
And then the expected time remaining
in a swarm is going to be about 6 days.

00:20:03.309 --> 00:20:05.600
So an additional week.

00:20:06.490 --> 00:20:10.640
So this figure here just summarizes
the numbers from that table.

00:20:10.650 --> 00:20:16.760
So the top plot here is showing the –
well, for a given swarm duration,

00:20:16.760 --> 00:20:20.720
or a given swarm age,
the black line – solid black line

00:20:20.720 --> 00:20:24.440
shows the probability
that that swarm has ended.

00:20:24.440 --> 00:20:26.480
And then the blue line
shows the probability

00:20:26.480 --> 00:20:31.120
that that swarm is going to
end within the next 24 hours.

00:20:31.750 --> 00:20:35.760
The plot down here shows, again,
for a given swarm duration,

00:20:35.760 --> 00:20:39.100
what the average time
remaining in that swarm is.

00:20:39.880 --> 00:20:43.299
So you can see that, within the
first couple of weeks of a swarm,

00:20:43.299 --> 00:20:45.610
the probability of ending
on any given day is actually

00:20:45.610 --> 00:20:48.400
pretty constant
at about 15%.

00:20:48.400 --> 00:20:58.280
And the swarm – the swarms have an
average duration of about 6-1/2 days.

00:20:58.290 --> 00:21:02.510
It turns out that, from that data set
of 20 swarms, the durations are

00:21:02.510 --> 00:21:06.309
pretty well-explained by
an exponential distribution.

00:21:06.309 --> 00:21:10.820
And so this constant probability
of ending on any given day,

00:21:10.820 --> 00:21:14.659
plus the exponential
distribution of durations,

00:21:14.659 --> 00:21:19.820
suggests that we can use a Poisson
model of swarm termination.

00:21:19.820 --> 00:21:24.100
So basically, the daily probability of
termination in the swarm is going to be,

00:21:24.100 --> 00:21:30.000
on average, the – is the inverse of
the average duration of a swarm.

00:21:31.490 --> 00:21:35.860
So the dashed lines here are
showing the fits using this –

00:21:35.870 --> 00:21:38.000
using this Poisson
model termination,

00:21:38.000 --> 00:21:42.460
or you can also think about it as
an exponential model of duration.

00:21:42.460 --> 00:21:45.779
So the dashed lines are showing the
model, and you can see that actually,

00:21:45.779 --> 00:21:49.670
for the most part, it fits the
swarm observations really well.

00:21:49.670 --> 00:21:54.090
Except down here, you can see
that it deviates – the average

00:21:54.090 --> 00:21:56.900
life expectancy deviates from
the ideal Poisson or

00:21:56.900 --> 00:22:00.400
exponential model
after the first week or so.

00:22:00.400 --> 00:22:05.000
But it turns out that this deviation
can be explained by sample size effects.

00:22:05.000 --> 00:22:10.480
Because the – our sample size
here is actually pretty small.

00:22:10.480 --> 00:22:12.820
We’re only looking at – you know,
we’re only using about 20 swarms

00:22:12.820 --> 00:22:15.820
to generate these statistics.
And for small samples,

00:22:15.820 --> 00:22:18.549
the sample mean is a –
is going to be a –

00:22:18.549 --> 00:22:20.740
end up being a biased estimate
of distribution mean.

00:22:20.740 --> 00:22:25.279
So, if we correct for that, then we
end up with this dotted line here.

00:22:25.279 --> 00:22:26.850
Now you can see that,
with that correction –

00:22:26.850 --> 00:22:30.680
that sample size correction, we’re
actually able to fit the data really well.

00:22:31.650 --> 00:22:35.180
We can – so we also applied
this approach to a set of swarms

00:22:35.190 --> 00:22:38.640
that happened around
the San Jacinto Fault Zone.

00:22:38.640 --> 00:22:42.380
And this is a data set of 89 swarms that
were identified by Zhang and Shearer.

00:22:42.380 --> 00:22:45.860
And they used a different method of
identification from Chen and Shearer.

00:22:45.870 --> 00:22:48.679
But, again, looking at
these similar plots, you can see

00:22:48.679 --> 00:22:51.210
that the probability of the
swarm ending on any given day

00:22:51.210 --> 00:22:54.560
within the first couple
of weeks is about 17%.

00:22:55.300 --> 00:22:57.640
And it’s pretty –
and it’s pretty constant.

00:22:57.640 --> 00:23:00.549
And then the average
duration here is about 6 days.

00:23:00.549 --> 00:23:06.240
So this suggests that this actuarial
approach can be widely applicable

00:23:06.240 --> 00:23:09.640
to swarms elsewhere. So that’s
something to explore in the future.

00:23:10.220 --> 00:23:14.360
All right, so now that we have this
exponential model for swarm duration,

00:23:14.360 --> 00:23:16.669
we can apply it to our
forecasts and see how it would have

00:23:16.669 --> 00:23:20.360
changed the forecast that we made
for the Bombay Beach swarm.

00:23:20.740 --> 00:23:25.800
So we’re still going to be making –
and these are – we’re still going to

00:23:25.800 --> 00:23:29.150
be making forecasts using
simulated earthquake catalogs.

00:23:29.150 --> 00:23:31.880
But now we’re going to –
well, each simulation is going to

00:23:31.880 --> 00:23:36.000
sample a random duration from this –
from our swarm duration model,

00:23:36.000 --> 00:23:39.660
over which we’re going to project this
high background rate into the future.

00:23:41.060 --> 00:23:49.840
So, um – um [laughs] – I don’t
know how to fix that. [laughs]

00:23:51.600 --> 00:23:54.960
All right, well, okay,
now we’re all very blue.

00:23:54.960 --> 00:23:56.400
[laughter]

00:23:59.040 --> 00:24:07.660
All right, well, the number of –
so the – so these – if we focus here

00:24:07.670 --> 00:24:10.610
on the column on the left,
this is the one-week forecast.

00:24:10.610 --> 00:24:12.611
And the Y axis on each of these
plots is going to be the number

00:24:12.611 --> 00:24:17.179
of earthquakes that are
forecast over the next seven days.

00:24:17.179 --> 00:24:20.760
And so the black line – oh, dear.
[laughs]

00:24:20.760 --> 00:24:24.700
The black line –
let’s see.

00:24:29.540 --> 00:24:33.540
- [inaudible]
- All right. Well, okay. [laughs]

00:24:33.540 --> 00:24:38.039
All right, so the black line, which is
this line, is going to be the forecast.

00:24:38.039 --> 00:24:39.950
And then the red line
is the number of earthquakes

00:24:39.950 --> 00:24:41.440
that were
actually observed.

00:24:41.440 --> 00:24:44.060
And the top panel here
is the forecast that’s made

00:24:44.070 --> 00:24:47.110
using an exponential
swarm duration model.

00:24:47.110 --> 00:24:49.880
And then the bottom two panels
are the forecasts that were made using

00:24:49.880 --> 00:24:54.950
our end member models from before.
So the middle panel is the one where

00:24:54.950 --> 00:24:58.460
we assume that the swarm is going
to continue at the same high rate.

00:24:58.460 --> 00:25:00.350
And then the bottom panel is the
forecast where we assumed that

00:25:00.350 --> 00:25:03.500
the swarm was just going
to end instantaneously.

00:25:04.620 --> 00:25:10.840
So if you – so you can – you can
see that incorporating this swarm

00:25:10.840 --> 00:25:16.420
duration model shows marginal
improvement over the forecast,

00:25:16.430 --> 00:25:19.279
assuming that the swarm
continues over the next week.

00:25:19.279 --> 00:25:22.290
And the reason why this –
the improvement isn’t so drastic

00:25:22.290 --> 00:25:28.750
is likely because the length of the
forecast interval is on the same order

00:25:28.750 --> 00:25:34.250
as the length of the – well, the average –
the likely duration of the swarm itself.

00:25:34.250 --> 00:25:38.110
So the swarm was about – it was
expected to last about seven days.

00:25:38.110 --> 00:25:39.679
The forecast interval
was about seven days.

00:25:39.679 --> 00:25:43.380
So you wouldn’t really
expect a lot of difference

00:25:43.380 --> 00:25:45.940
by incorporating
this duration model.

00:25:45.940 --> 00:25:48.909
Where we actually start to see
a lot of improvement is if we

00:25:48.909 --> 00:25:52.110
consider longer-term forecasts.
So, for example, the column here

00:25:52.110 --> 00:25:55.179
on the right shows one-month forecasts
using those three different models.

00:25:55.179 --> 00:26:00.399
And now you can see that there’s
significant improvement in the forecast

00:26:00.399 --> 00:26:04.299
when we include a swarm duration
model over the case where we assume

00:26:04.300 --> 00:26:08.380
that the swarm is going to continue
at the same rate for the next month.

00:26:10.150 --> 00:26:16.760
So this – so our results show that really
including a model for swarm durations,

00:26:16.770 --> 00:26:21.200
when you have the statistics to
put the number of – when you have

00:26:21.200 --> 00:26:25.710
a good number of earthquake swarms
to draw the statistics from can

00:26:25.710 --> 00:26:29.080
really improve your earthquake
forecast during swarms.

00:26:29.820 --> 00:26:33.820
All right, so to summarize this
first part of the talk, actuarial statistics

00:26:33.820 --> 00:26:38.140
can be used to characterize typical
swarm durations in a region.

00:26:38.140 --> 00:26:40.860
Forecasts that incorporate
a duration model show

00:26:40.870 --> 00:26:44.409
some improvement, particularly
when the forecast interval

00:26:44.409 --> 00:26:46.649
exceeds the likely
duration of the swarm.

00:26:46.649 --> 00:26:50.450
There are a number of caveats using
this approach, primarily because,

00:26:50.450 --> 00:26:55.840
again, this is derived from
population statistics,

00:26:55.840 --> 00:26:58.169
and so it’s best suited for
regions with a good number

00:26:58.169 --> 00:27:01.720
of previous swarms from which
you can derive those statistics.

00:27:01.720 --> 00:27:04.779
It’s possible because, you know, we’re
working with fairly small sample sizes

00:27:04.779 --> 00:27:09.600
here, that we haven’t really resolved the
tail of the distributions very well yet.

00:27:09.600 --> 00:27:13.600
It’s almost certain that the maximum
duration that we’ve seen so far is

00:27:13.600 --> 00:27:16.520
shorter than what the maximum
possible duration actually is.

00:27:16.520 --> 00:27:19.530
And this also means that long-lived
swarms, such as the ongoing Cahuilla

00:27:19.530 --> 00:27:23.419
swarm, which has been going on for
well over a year now in southern

00:27:23.419 --> 00:27:30.570
California, they might be difficult
to deal with with this approach.

00:27:30.570 --> 00:27:33.789
But the work I’m going to
describe next might give us

00:27:33.789 --> 00:27:39.120
a way to get a – sort of tackle
those long-lived swarms.

00:27:39.680 --> 00:27:44.940
So the next part of this talk –
well, in this next part of the talk,

00:27:44.950 --> 00:27:48.860
we’re going to be looking at
slightly more sophisticated

00:27:48.860 --> 00:27:52.510
swarm forecasting models.
Because previously,

00:27:52.510 --> 00:27:54.230
even though we incorporated
the swarm duration model,

00:27:54.230 --> 00:27:55.930
we were still assuming
a constant background rate.

00:27:55.930 --> 00:27:59.880
So either it’s, you know,
it’s high or it’s not, but it’s –

00:27:59.880 --> 00:28:01.800
either way,
it’s constant rate.

00:28:01.800 --> 00:28:05.559
So now we’re going to be looking at
models where we vary the –

00:28:05.559 --> 00:28:08.370
allow the background rate to
vary over time during this swarm.

00:28:08.370 --> 00:28:10.260
And this is work I’ve
been doing with Andy.

00:28:10.260 --> 00:28:15.300
And, again, this paper is also going to
be submitted hopefully fairly shortly.

00:28:16.100 --> 00:28:17.460
So now we’re going to
shift gears and take a look

00:28:17.470 --> 00:28:20.980
at the 2015
San Ramon swarm.

00:28:20.980 --> 00:28:24.580
So this happened up
here in the East Bay.

00:28:24.580 --> 00:28:27.630
It began on October 13th,
and it lasted about a month.

00:28:27.630 --> 00:28:32.080
So this is a longer swarm than
the Bombay Beach swarm was.

00:28:32.080 --> 00:28:33.660
You can see the
cumulative number

00:28:33.660 --> 00:28:36.480
of earthquakes here with
the magnitudes over time.

00:28:36.490 --> 00:28:41.460
And it had about 100 earthquakes
with magnitudes between 2 and 3.6.

00:28:41.460 --> 00:28:44.059
And this region has had a number
of swarms in the past, which you

00:28:44.060 --> 00:28:48.520
can see in this color-coded map here,
going all the way back to 1970.

00:28:49.780 --> 00:28:52.560
So we started off with
some basic ETAS modeling.

00:28:52.570 --> 00:28:54.820
The figure here is showing the
cumulative number of earthquakes

00:28:54.820 --> 00:28:59.740
during the first 20 days of the swarm,
with the observed in the black.

00:28:59.740 --> 00:29:02.179
If we fit the ETAS model
just with the swarm by itself,

00:29:02.179 --> 00:29:06.510
that’s what’s being
shown by the blue line here.

00:29:06.510 --> 00:29:09.240
And the parameters from that model
are being shown up here in this table.

00:29:09.240 --> 00:29:11.790
So, again, we’re mostly
concerned with the background rate,

00:29:11.790 --> 00:29:14.440
so that’s going to be
this parameter, mu.

00:29:15.100 --> 00:29:17.580
If we compare that with an
ETAS model that’s fit to all of the

00:29:17.590 --> 00:29:21.290
prior seismicity that occurred in this
region, that’s what’s shown here.

00:29:21.290 --> 00:29:24.190
I’m going to refer to this
model as the Fixed-All model,

00:29:24.190 --> 00:29:30.890
which – for reasons that will become
apparent in the next slide or two.

00:29:30.890 --> 00:29:35.500
But – so you can see that the
background rate during the swarm

00:29:35.500 --> 00:29:38.000
increases by about
two orders of magnitude.

00:29:38.700 --> 00:29:43.360
And if you take a look at how those
Fixed-All model parameters fit

00:29:43.360 --> 00:29:51.340
the swarm, by looking at this yellow-ish
line here, you can see that that model

00:29:51.340 --> 00:29:54.570
greatly underestimates the
earthquakes rates during the swarm.

00:29:55.080 --> 00:29:59.340
Now, if we do what we ended up –
what we ended up doing for the

00:29:59.340 --> 00:30:04.100
2016 Bombay Beach swarm and develop
a swarm model conditioned on – well,

00:30:04.100 --> 00:30:08.419
tuned to the – all the previous
swarms that occurred in the region,

00:30:08.419 --> 00:30:11.820
you can see that that does
a better job of fitting this swarm

00:30:11.820 --> 00:30:14.710
than the Fixed-All model.
So that’s shown –

00:30:14.710 --> 00:30:18.250
the Fixed-Swarm model is
now shown in the gray line here.

00:30:18.250 --> 00:30:21.110
And you can see that the
background rate is slightly higher,

00:30:21.110 --> 00:30:24.710
but not as high as the rate
was during the 2015 swarm.

00:30:24.710 --> 00:30:29.539
And that’s likely because, if –
what we also ended up doing was

00:30:29.539 --> 00:30:33.070
looking at how the background rate by
itself changed from swarm to swarm.

00:30:33.070 --> 00:30:35.159
And it turns out that the
background rate during the

00:30:35.159 --> 00:30:38.630
2015 swarm was higher
than the background rate than –

00:30:38.630 --> 00:30:42.140
of much of the previous
swarms that have occurred.

00:30:43.400 --> 00:30:46.960
Okay. [laughs] So the main
question we were trying to

00:30:46.970 --> 00:30:49.059
address here was how well
can we forecast the rate

00:30:49.059 --> 00:30:51.630
of magnitude 2 and higher
earthquakes during the swarm?

00:30:51.630 --> 00:30:53.500
And we’re going to compare
five different models.

00:30:53.500 --> 00:30:56.361
So two of the models are
what I call fixed models.

00:30:56.361 --> 00:30:58.610
So these are models where the
parameters are going to be constant

00:30:58.610 --> 00:31:01.950
throughout the entire swarm.
And so these are the two models

00:31:01.950 --> 00:31:04.230
I talked about in the previous slide –
the Fixed-All model,

00:31:04.230 --> 00:31:07.140
where the parameters are
fit to all the previous seismicity.

00:31:07.140 --> 00:31:08.780
And then the
Fixed-Swarm model,

00:31:08.780 --> 00:31:12.840
where the model is fit only to
the previous swarm seismicity.

00:31:13.360 --> 00:31:15.720
And then the other set of models
we’re going to be considering

00:31:15.720 --> 00:31:17.720
are updated models.
So these are models where

00:31:17.720 --> 00:31:20.840
the background rate is updated
every three days or so –

00:31:20.840 --> 00:31:25.299
every three days in the swarm using
data over different lengths of

00:31:25.299 --> 00:31:28.520
look-back time windows
to estimate the background rate.

00:31:28.520 --> 00:31:32.970
And so the different look-back time
windows we considered were 10 days,

00:31:32.970 --> 00:31:35.570
five days, and two days.
And so I’m going to refer to

00:31:35.570 --> 00:31:40.000
these models as the LB10,
LB5, and LB2 models.

00:31:40.000 --> 00:31:45.970
So this figure shows the
ETAS background rate estimates

00:31:45.970 --> 00:31:51.570
for all of those different models
over the course of the swarm.

00:31:51.570 --> 00:31:54.220
So you can see the two fixed models.
Again, the background rate

00:31:54.220 --> 00:31:56.700
is going to be constant.
They’re down here.

00:31:56.700 --> 00:31:59.740
And then you can see the –
how the background rate changes

00:31:59.740 --> 00:32:02.640
for each of these
updated models.

00:32:02.640 --> 00:32:04.620
As you might expect,
for the shorter look-back

00:32:04.620 --> 00:32:07.250
time window models,
so the LB2 and LB5 models,

00:32:07.250 --> 00:32:13.040
those background rates
are able to vary more quickly.

00:32:13.040 --> 00:32:18.970
But for the longer look-back time
window, so the LB10 window,

00:32:18.970 --> 00:32:21.230
while that might not be able to react
more quickly with the changes in the

00:32:21.230 --> 00:32:24.980
swarm, it might provide us a more
stable estimate of the background rate.

00:32:24.980 --> 00:32:26.440
So we can compare
how these different

00:32:26.440 --> 00:32:30.600
look-back windows
perform during the swarm.

00:32:30.600 --> 00:32:32.029
And so we’re going to
go about the same exercise

00:32:32.029 --> 00:32:34.790
at the start of each these
three-day forecast windows.

00:32:34.790 --> 00:32:37.139
And I should mention that the reason
we’re using three-day forecasts as

00:32:37.140 --> 00:32:41.760
opposed to one-day forecasts is
because they provide stabler estimates.

00:32:43.140 --> 00:32:46.080
So, at the start of each forecast window,
we update the seismicity catalog

00:32:46.080 --> 00:32:50.450
to include all the earthquakes
that had occurred in the

00:32:50.450 --> 00:32:54.210
previous forecast window. And then
we update our background rate.

00:32:54.210 --> 00:32:56.299
And then we used the new
parameters to generate

00:32:56.299 --> 00:32:59.160
100,000 earthquake catalogs
with the different models

00:32:59.160 --> 00:33:04.300
to forecast the number of
earthquakes over the next three days.

00:33:05.940 --> 00:33:08.380
So here are
the results.

00:33:08.389 --> 00:33:12.179
So on the left, I’m showing the
three-day forecasts of the

00:33:12.179 --> 00:33:14.330
number of magnitude 2 earthquakes
and higher during the swarm.

00:33:14.330 --> 00:33:18.820
Each of these –
in each of these time bins.

00:33:19.600 --> 00:33:22.799
The error bars are – the different
symbols are the different models,

00:33:22.799 --> 00:33:25.970
and the error bars are the
95% confidence limits.

00:33:25.970 --> 00:33:28.220
And then the white squares
the number of earthquakes

00:33:28.220 --> 00:33:31.360
that were actually observed
in each of those time bins.

00:33:33.540 --> 00:33:36.370
We can quantitatively assess the
performance of each of these models

00:33:36.370 --> 00:33:40.480
by computing the model’s log likelihood.
So that’s – which is computed

00:33:40.480 --> 00:33:42.190
by comparing the
observed number of events

00:33:42.190 --> 00:33:44.680
and the predicted
number of events.

00:33:46.520 --> 00:33:50.140
And, if we sum up the log
likelihoods in each of these

00:33:50.150 --> 00:33:53.039
time bins for a particular model,
that gives us the joint log likelihood.

00:33:53.039 --> 00:33:55.380
And those are the
numbers that are shown here.

00:33:55.380 --> 00:33:58.919
And the models with the highest
likelihoods are the ones that are,

00:33:58.919 --> 00:34:01.630
in some sense, best.
So they’re the ones whose

00:34:01.630 --> 00:34:05.720
predictions are more – most consistent
with what was actually observed.

00:34:05.720 --> 00:34:08.791
But even more instructive is to
plot up how that log likelihood

00:34:08.791 --> 00:34:11.930
for each model changes over
time in each of these forecast bins.

00:34:11.930 --> 00:34:15.790
So this is now just showing
the log likelihood of each model

00:34:15.790 --> 00:34:19.930
in each of the forecast intervals.
And so this allows us to track

00:34:19.930 --> 00:34:24.120
which of the models is
actually doing better over time.

00:34:24.120 --> 00:34:27.820
So here are the main results
of the two fixed models.

00:34:27.820 --> 00:34:32.790
The Fixed-All model, which is
shown by the green, or yellow,

00:34:32.790 --> 00:34:36.060
almost always underestimates the
earthquake rates during the swarm.

00:34:36.060 --> 00:34:39.120
And then you can – and you
can see how it typically has

00:34:39.120 --> 00:34:43.260
the lowest likelihood of
all the models here over time.

00:34:43.260 --> 00:34:47.340
The Fixed-Swarm model, which is
shown by the gray, performs the best,

00:34:47.340 --> 00:34:49.540
for the most part, especially
during the first half of the swarm.

00:34:49.540 --> 00:34:54.630
But you can see that,
somewhere towards the end –

00:34:54.630 --> 00:34:58.160
the second half of the swarm, it ends up
over-predicting the number of events.

00:34:58.160 --> 00:35:00.830
And this is because, again,
the swarm model is assuming

00:35:00.830 --> 00:35:04.040
that the same high background rate is
going to continue at the same rate.

00:35:04.040 --> 00:35:06.490
It’s not varying the
background rate at all.

00:35:06.490 --> 00:35:09.630
And so, by this time, around,
you know, day 21 or so,

00:35:09.630 --> 00:35:11.870
the swarm has already begun
to die down, for the most part.

00:35:11.870 --> 00:35:15.800
And so that’s why it ends up
over-predicting the number of events.

00:35:15.800 --> 00:35:19.850
In general, the updated models,
which are these symbols here,

00:35:19.850 --> 00:35:21.710
tend to perform better
than the fixed models.

00:35:21.710 --> 00:35:24.410
And you can see that because their,
you know, likelihoods are consistently,

00:35:24.410 --> 00:35:27.700
for the most part,
higher than the two fixed models.

00:35:27.700 --> 00:35:32.880
But which of the two look-back
models perform best varies over time.

00:35:32.880 --> 00:35:37.380
So you can see sometimes it’s the LB2
model. Sometimes it’s the LB5 model.

00:35:37.380 --> 00:35:42.670
And this makes it hard to decide
which one to use for the swarm.

00:35:42.670 --> 00:35:45.840
You can see that no single
model of the five always provides

00:35:45.840 --> 00:35:47.660
the best forecast
throughout the entire swarm.

00:35:47.660 --> 00:35:52.760
So my question is, which –
how do we – how do we decide –

00:35:52.760 --> 00:35:57.540
how do we choose which of
these models to use objectively?

00:35:57.960 --> 00:36:01.860
And to answer that question, we turned
to ensemble forecasts, which basically

00:36:01.860 --> 00:36:06.940
gives us the opportunity to essentially
choose not to choose, in some sense.

00:36:06.940 --> 00:36:09.980
So, to avoid making arbitrary
choices about, you know,

00:36:09.980 --> 00:36:13.140
what single model is going to perform
the best at the outset of the swarm,

00:36:13.140 --> 00:36:15.640
what we can do is construct an
ensemble forecast using

00:36:15.640 --> 00:36:19.130
a weighted combination of all the
five models that we’ve investigated.

00:36:19.130 --> 00:36:24.840
And we’re going to be using
the methods that were –

00:36:24.840 --> 00:36:29.200
that were – the methods
of Marzocchi et al.

00:36:29.210 --> 00:36:32.280
And so, in their approach,
the model weights are going to

00:36:32.280 --> 00:36:38.190
count for both model correlation –
so that is to say the models that

00:36:38.190 --> 00:36:42.140
provide – that are more independent,
that can provide more different

00:36:42.140 --> 00:36:44.560
information, are going to receive
higher weight in the ensemble.

00:36:44.560 --> 00:36:47.670
And then, most importantly,
they account for the

00:36:47.670 --> 00:36:49.410
past performance
of each of the models.

00:36:49.410 --> 00:36:52.760
So how this works is that,
at the end of each forecast interval,

00:36:52.760 --> 00:36:55.850
the weight of the i-th model is
going to be updated based on

00:36:55.850 --> 00:36:59.610
how well it performed in
that previous forecast interval.

00:36:59.610 --> 00:37:02.350
And we’re going to be
using two weighting schemes.

00:37:02.350 --> 00:37:05.230
One is a Bayesian Model
Averaging scheme, or BMA,

00:37:05.230 --> 00:37:07.950
shown here, where the
weight of the model is going to

00:37:07.950 --> 00:37:11.920
be proportional to the
exponential of its likelihood.

00:37:11.920 --> 00:37:15.590
And then we’re going to be also using
a Score Model Averaging scheme, or

00:37:15.590 --> 00:37:20.840
SMA, where the weight of the model is
inversely proportional to its likelihood.

00:37:22.040 --> 00:37:25.720
So this figure just shows how –
for the San Ramon swarm,

00:37:25.720 --> 00:37:28.370
how the ensemble
weights evolve over time.

00:37:28.370 --> 00:37:31.960
So, on the X axis, we’re showing each
of the different – each of the different

00:37:31.960 --> 00:37:35.700
bars are each of the different forecast
intervals during the swarm.

00:37:35.700 --> 00:37:38.560
The different colors
represent the different models,

00:37:38.560 --> 00:37:41.570
and so the bars are representing the
relative weights that each of the models

00:37:41.570 --> 00:37:45.660
are receiving within the ensemble
during each of these forecasts.

00:37:45.660 --> 00:37:51.200
On the left are the BMA weights.
On the right are the SMA weights.

00:37:51.210 --> 00:37:55.310
So you can see that,
for the BMA weights,

00:37:55.310 --> 00:37:58.110
the BMA ensemble ends up being
dominated by the single best model.

00:37:58.110 --> 00:38:00.570
And this is because,
if you go back, again,

00:38:00.570 --> 00:38:04.330
the BMA weights are basically
the exponential of the log.

00:38:04.330 --> 00:38:07.790
This is very strong – this is a
very strong weighting scheme.

00:38:07.790 --> 00:38:11.040
And so that ends up having
the ensemble pretty much

00:38:11.040 --> 00:38:15.500
just being dominated
by the best one or two models.

00:38:16.240 --> 00:38:20.300
So this means it behaves more
like a model selection algorithm

00:38:20.300 --> 00:38:22.980
than anything, but that’s not
really what we’re going for.

00:38:22.980 --> 00:38:24.640
[static]

00:38:25.720 --> 00:38:27.720
[static]

00:38:29.000 --> 00:38:34.480
Okay. Here on the right,
you can see that the SMA weights

00:38:34.480 --> 00:38:38.300
end up being distributed more
broadly among the different models.

00:38:38.300 --> 00:38:42.780
And so, it displays
a more stable behavior.

00:38:42.780 --> 00:38:46.540
You can still – and you can still
see some interesting things here.

00:38:46.540 --> 00:38:50.110
So, for example, you can see
the decrease in the performance

00:38:50.110 --> 00:38:53.721
of the Fixed-Swarm model
by how – the relative weight

00:38:53.721 --> 00:38:57.090
it receives within the
ensemble decreases over time.

00:38:57.090 --> 00:38:59.030
And then you can also see that
overall better performance

00:38:59.030 --> 00:39:02.320
of the updated versus the
fixed models because the –

00:39:02.320 --> 00:39:06.500
if you consider the updated models
as a group, you can see that, in general,

00:39:06.500 --> 00:39:12.800
they’re receiving more weight than the –
than the fixed models are.

00:39:14.080 --> 00:39:17.100
Okay, so now that we
have these ensemble weights,

00:39:17.110 --> 00:39:20.280
we can look at the forecasts
that result from them.

00:39:20.280 --> 00:39:24.500
And so these are the same plots that
I showed before – again, the forecast

00:39:24.500 --> 00:39:28.630
number of events on the left, and then
the log likelihood over time on the right.

00:39:28.630 --> 00:39:32.500
And now, plotted on top of the
individual model forecasts are the

00:39:32.500 --> 00:39:37.020
ensemble forecasts, in the left-
and the right-pointing triangles.

00:39:39.000 --> 00:39:44.030
So now you can see that the –
particularly if you look at the

00:39:44.030 --> 00:39:46.530
likelihood comparison over time,
you can see that the ensemble models –

00:39:46.530 --> 00:39:51.180
both of them consistently have
the highest likelihood over time.

00:39:51.180 --> 00:39:55.030
And they consistently out-perform all
of the individual component models.

00:39:55.030 --> 00:39:57.430
And this is consistent with what
other researchers have found

00:39:57.430 --> 00:40:00.860
when they’ve applied these
ensemble approaches to things like

00:40:00.860 --> 00:40:07.860
time-dependent seismic hazard
and [static] global seismic [static] –

00:40:07.860 --> 00:40:10.560
I’m not even moving.
[laughter]

00:40:10.560 --> 00:40:16.020
[static]

00:40:18.100 --> 00:40:19.440
Global seismic –
all right, so …

00:40:19.460 --> 00:40:21.120
[static]

00:40:22.760 --> 00:40:27.680
[static]

00:40:30.880 --> 00:40:32.560
[laughter]

00:40:32.560 --> 00:40:34.280
All right.

00:40:35.110 --> 00:40:39.980
So – okay, so ensembles are the best.
[laughs]

00:40:39.990 --> 00:40:43.931
You’ll also note that the likelihoods
of the BMA and SMA forecasts

00:40:43.931 --> 00:40:46.790
aren’t really significantly different here.
You can see that both of the left

00:40:46.790 --> 00:40:49.040
and right triangles
are tracking pretty closely.

00:40:49.040 --> 00:40:53.410
But, as we saw in the previous slide,
the more stable behavior of the

00:40:53.410 --> 00:40:57.180
SMA ensemble really makes it our
preferred – our preferred model.

00:40:58.180 --> 00:41:01.470
We can also – we also applied
this approach to a few of the other

00:41:01.470 --> 00:41:05.580
San Ramon area swarms,
including the 1976 Danville swarm,

00:41:05.580 --> 00:41:09.200
the 1990 Alamo swarm,
and the 2018 Danville swarm.

00:41:10.390 --> 00:41:13.200
And so, for each of these
other swarms, we, you know,

00:41:13.210 --> 00:41:15.850
re-estimated the fixed model so that,
you know, they include

00:41:15.850 --> 00:41:18.820
all the seismicity that occurs
prior to that particular swarm.

00:41:18.820 --> 00:41:26.700
And you can’t really see very much
in these plots, but basically,

00:41:26.700 --> 00:41:28.420
one thing to note is that the
fixed swarm models tend to

00:41:28.420 --> 00:41:32.440
perform more poorly for the earlier
swarms than for the later swarms.

00:41:32.440 --> 00:41:35.030
And this is because, again,
they’re being tuned to the swarms

00:41:35.030 --> 00:41:36.550
that occurred
prior to that swarm.

00:41:36.550 --> 00:41:40.151
So, in the case of the 1976
Danville swarm, this was – the swarm

00:41:40.160 --> 00:41:43.240
parameters were pretty much tuned
only to the 1970 Danville swarm.

00:41:43.240 --> 00:41:46.960
For the 1990 Alamo swarm,
these parameters were tuned primarily

00:41:46.960 --> 00:41:52.230
by the 1970 and 1976 Danville swarms.
So these regional swarm models

00:41:52.230 --> 00:41:55.820
are going to become more
useful as more swarms occur.

00:41:57.900 --> 00:42:01.640
But the key thing to note is that, for all
of these swarms, the ensemble models,

00:42:01.640 --> 00:42:04.260
both of them, still performed
the best overall.

00:42:04.260 --> 00:42:10.060
So this – so this suggests that this
approach works even if there aren’t

00:42:10.060 --> 00:42:14.870
very many past swarms in a region on
which you can tune a swarm model.

00:42:16.380 --> 00:42:19.820
All right, so to summarize
this part of the talk, we used

00:42:19.820 --> 00:42:22.160
the 2015 San Ramon swarm to
explore different ways to

00:42:22.160 --> 00:42:24.680
improve earthquake
forecasts during the swarms.

00:42:24.680 --> 00:42:27.240
These include having a regional
swarm model based on prior swarms

00:42:27.240 --> 00:42:29.720
to capture high background rates.
And, again, we saw how this

00:42:29.720 --> 00:42:33.800
helped things in the 2016
Bombay Beach swarm as well.

00:42:33.800 --> 00:42:35.800
Updating background rates
mid-swarm can improve

00:42:35.810 --> 00:42:38.640
the forecast significantly
when it’s possible to do so.

00:42:38.640 --> 00:42:43.350
But, again, it’s difficult to determine
what the optimal look-back window

00:42:43.350 --> 00:42:45.940
over which to estimate
the background rate is.

00:42:45.940 --> 00:42:49.410
But ensemble forecasts really
provide us a way to combine

00:42:49.410 --> 00:42:54.050
both fixed and updated models using
all these different look-back windows,

00:42:54.050 --> 00:42:57.880
which allow us to avoid having to
make this arbitrary decision.

00:42:57.880 --> 00:43:02.150
So ensemble models really ultimately
provide the optimal earthquake

00:43:02.150 --> 00:43:05.450
forecasts during earthquake swarms.
And I think this is really going to

00:43:05.450 --> 00:43:10.220
be a valuable tool as we further
develop these methods in the future.

00:43:10.840 --> 00:43:14.340
All right, so really quickly,
in this last part of the talk,

00:43:14.340 --> 00:43:17.690
I just want to touch really briefly
on the issue of communication.

00:43:17.690 --> 00:43:19.900
Because communication is,
of course, a fundamental aspect

00:43:19.900 --> 00:43:22.030
of any successful
forecast system.

00:43:22.030 --> 00:43:25.300
Our forecasts are no good if we don’t
have a good plan to communicate them

00:43:25.300 --> 00:43:29.410
to the stakeholders who really
could use them to make decisions.

00:43:29.410 --> 00:43:33.600
And so this is actually work that’s
being headed up by Sara McBride.

00:43:35.340 --> 00:43:40.390
And what we’re doing is
taking a look at what happened

00:43:40.390 --> 00:43:43.120
during the 2016
Bombay Beach swarm.

00:43:43.800 --> 00:43:48.790
So because this was a relatively
short and self-contained event,

00:43:48.790 --> 00:43:52.320
this really gives us an opportunity
to examine what exactly happened

00:43:52.320 --> 00:43:55.590
to our forecasts after we made them.
And you can kind of see that now,

00:43:55.590 --> 00:43:59.170
you know, if you go back to this
timeline of events during the swarm.

00:43:59.170 --> 00:44:02.450
You know, we made the
forecasts on the first day or so.

00:44:02.450 --> 00:44:06.230
Probabilities were passed on
to CEPEC to review them.

00:44:06.230 --> 00:44:09.320
CEPEC them passed those
probabilities on to Cal OES.

00:44:09.320 --> 00:44:12.900
And Cal OES and USGS released
earthquake advisories to the

00:44:12.900 --> 00:44:17.180
general public in public statements
incorporating these probabilities.

00:44:18.360 --> 00:44:23.260
And so – what was
I going to say about this?

00:44:23.260 --> 00:44:27.460
So this really – this really
gives us the opportunity

00:44:27.460 --> 00:44:34.720
to examine what happens to
these forecasts after they’re made.

00:44:36.380 --> 00:44:40.360
So I’m just going to highlight
a couple of main points here.

00:44:40.370 --> 00:44:43.140
And first is the
issue of timeliness.

00:44:43.140 --> 00:44:45.930
So we take – this is
another way of looking at –

00:44:45.930 --> 00:44:47.760
well, this plot
I showed earlier.

00:44:47.760 --> 00:44:52.570
So this is, again, giving you a sense of
how the probability of a magnitude 7 or

00:44:52.570 --> 00:44:56.650
higher earthquake on the San Andreas
Fault evolved during this swarm.

00:44:56.650 --> 00:44:59.910
You can see that that probability
was highest shortly after the –

00:44:59.910 --> 00:45:01.680
when the magnitude 4
earthquakes occurred.

00:45:01.680 --> 00:45:08.020
Plotted on top of this now are
some of the main response events.

00:45:08.020 --> 00:45:10.550
So, for example,
this gray shaded area here

00:45:10.550 --> 00:45:14.220
shows when the forecasts
were being modeled.

00:45:16.190 --> 00:45:18.960
You can see where CEPEC
convened here on the 27th.

00:45:18.960 --> 00:45:25.500
Here’s when the various advisories
were released later that day. And so on.

00:45:25.500 --> 00:45:28.380
Now, some actions were actually
taken in response to the

00:45:28.380 --> 00:45:30.400
earthquake advisories
that were released.

00:45:30.400 --> 00:45:34.610
So, for example, on October 3rd,
San Bernardino city officials

00:45:34.610 --> 00:45:37.910
made a decision to close their
City Hall building because it had been

00:45:37.910 --> 00:45:40.711
identified as likely to fail
in the event of a large

00:45:40.711 --> 00:45:45.270
magnitude 6 or higher earthquake.
And so, after the officials had learned

00:45:45.270 --> 00:45:47.470
about the earthquake advisories
the weekend before –

00:45:47.470 --> 00:45:51.130
so October 3rd was a Monday.
So the officials had learned about

00:45:51.130 --> 00:45:54.760
the advisories the weekend
before from media reports.

00:45:54.760 --> 00:45:58.980
And so they decided to close the
building for a couple of days

00:45:58.980 --> 00:46:03.530
out of an abundance of caution.
But you can see that, by the time

00:46:03.530 --> 00:46:06.180
they had received the media reports,
by the time they made a decision

00:46:06.180 --> 00:46:10.230
to close City Hall, the likelihood
of a large earthquake

00:46:10.230 --> 00:46:13.380
had pretty much passed,
for the most part.

00:46:13.380 --> 00:46:16.870
And so this really suggests that there’s
a need to improve the timeliness –

00:46:16.870 --> 00:46:20.380
how quickly we can make these
forecasts and get the information

00:46:20.380 --> 00:46:24.860
out to the people who are
using them to make decisions.

00:46:24.860 --> 00:46:26.950
Because forecasts aren’t really
much good when you’re

00:46:26.950 --> 00:46:32.140
making decisions after
the hazard has passed, right?

00:46:32.680 --> 00:46:42.020
The other point I want to make is that
it’s also – it’s also good to consider

00:46:42.020 --> 00:46:47.460
what was being communicated to the
general public from these forecasts.

00:46:49.380 --> 00:46:54.200
So, again, this is – this is work
that’s still very much in prep.

00:46:54.210 --> 00:46:59.560
And I just want to highlight a couple
points that we’ve found so far.

00:46:59.560 --> 00:47:04.670
So this figure from Sara is showing –
this is basically a different way of

00:47:04.670 --> 00:47:07.720
looking at events during the swarm.
So the circles here are showing

00:47:07.720 --> 00:47:10.930
some of the main swarm events.
So this is when the swarm happened.

00:47:10.930 --> 00:47:12.960
This is when USGS
released its advisory.

00:47:12.960 --> 00:47:16.290
This is when Cal OES
released its own advisory.

00:47:16.290 --> 00:47:19.110
And then the little circles in between
are showing the number of

00:47:19.110 --> 00:47:24.340
media stories that were published
in between these different events.

00:47:24.340 --> 00:47:27.990
And so, you can see that the
number of stories – so the media

00:47:27.990 --> 00:47:32.570
interest peaked basically after the
earthquake advisories were released.

00:47:32.570 --> 00:47:36.450
And around the same time – this is
also when #EarthquakeAdvisory

00:47:36.450 --> 00:47:40.670
started trending on Twitter,
both regionally and nationally.

00:47:40.670 --> 00:47:43.850
So two things that we found –
that have been found so far.

00:47:43.850 --> 00:47:46.510
One is that the social media
discourse was largely informed

00:47:46.510 --> 00:47:50.150
by media statements rather than
the official statements that were

00:47:50.150 --> 00:47:54.480
put out by USGS or Cal OES.
So this means that the media was

00:47:54.480 --> 00:47:58.060
pretty much – was, for the most part,
driving the narrative, rather than

00:47:58.060 --> 00:48:02.380
the agencies that were responsible
for generating the forecasts.

00:48:03.250 --> 00:48:09.540
The second point is that this – there
was really a lack of sort of online

00:48:09.550 --> 00:48:17.500
discourse on the part of the [static] –
there was a lack of online discourse.

00:48:17.500 --> 00:48:21.490
And this lack of sort of engagement
in online discourse left social media

00:48:21.490 --> 00:48:24.830
commentators without the resources
that they could use to either

00:48:24.830 --> 00:48:28.090
extract meaning from or, you know,
answer scientific questions

00:48:28.090 --> 00:48:30.460
about the forecast or further
inform decision-making.

00:48:30.460 --> 00:48:38.070
[static] So this is giving us –
this is giving us a sense of what –

00:48:38.070 --> 00:48:42.500
what is actually being communicated
out to the general public?

00:48:42.500 --> 00:48:44.850
What’s the information from our
forecasts that are being discussed,

00:48:44.850 --> 00:48:46.420
and how are
they being discussed?

00:48:46.420 --> 00:48:50.360
How are probabilities being discussed
in both media and social media?

00:48:50.360 --> 00:48:53.660
So stay tuned for
further updates on this front.

00:48:54.580 --> 00:48:59.780
All right. So to summarize this
entire talk, earthquake swarms

00:48:59.790 --> 00:49:02.110
have presented challenges –
well, they present challenges

00:49:02.110 --> 00:49:05.250
to our current forecast models,
which are really pretty much

00:49:05.250 --> 00:49:09.480
designed to work best for typical
main shock/aftershock sequences.

00:49:09.480 --> 00:49:12.710
What I’ve presented here
are the basic building blocks

00:49:12.710 --> 00:49:16.090
of a swarm operational
earthquake forecasting system.

00:49:16.090 --> 00:49:19.300
And these include a regional swarm
model that’s been tuned to previous

00:49:19.300 --> 00:49:22.840
swarms if previous swarms have
occurred, a swarm duration model

00:49:22.850 --> 00:49:26.130
that’s based on actuarial statistics
of those previous swarms,

00:49:26.130 --> 00:49:28.860
incorporating time-varying
background rates in our forecasts,

00:49:28.860 --> 00:49:31.860
and then taking advantage of
ensemble models to sort of

00:49:31.860 --> 00:49:35.040
combine the skills of all
these different approaches.

00:49:35.050 --> 00:49:37.130
But, again, these are –
these are still building blocks.

00:49:37.130 --> 00:49:40.130
There’s still a lot of work
that could be done.

00:49:40.130 --> 00:49:43.550
Sort of the next step you could
consider was to – is to combine

00:49:43.550 --> 00:49:46.710
sort of the swarm duration models
that were presented first with this

00:49:46.710 --> 00:49:50.060
ensemble approach to develop
a sort of more comprehensive

00:49:50.060 --> 00:49:55.980
swarm OEF model, or a grand
unified theory of swarm forecasting.

00:49:57.580 --> 00:50:00.800
The – when it comes to the
swarm duration models, we can –

00:50:00.810 --> 00:50:04.110
we can investigate how widely
applicable the exponential

00:50:04.110 --> 00:50:08.110
swarm duration model that we found
fit pretty well for Salton Trough

00:50:08.110 --> 00:50:11.920
than for the San Jacinto Fault Zone –
how widely applicable is it?

00:50:11.920 --> 00:50:14.540
Can the exponential distribution
fit swarm durations observed

00:50:14.540 --> 00:50:20.070
in other regions?
So, for example, Nevada or in Utah?

00:50:20.070 --> 00:50:22.330
And how might the probability
of shutting down each day

00:50:22.330 --> 00:50:25.560
vary from place to place?
Is it really going to be constant

00:50:25.560 --> 00:50:28.920
at about, you know,
15% no matter where you go?

00:50:28.920 --> 00:50:31.500
Who knows?
We can find out.

00:50:33.770 --> 00:50:36.480
In other, you know, further –
another avenue of investigation

00:50:36.490 --> 00:50:40.720
is the question of swarm detection.
So all of what I presented so far

00:50:40.720 --> 00:50:44.810
has pretty much been done assuming
that the swarm had already started.

00:50:44.810 --> 00:50:48.420
So somewhere, somebody – someone
along the line said, here’s a swarm.

00:50:48.420 --> 00:50:50.730
What can we
do to forecast?

00:50:50.730 --> 00:50:56.040
How can we objectively determine when
a swarm forecast model is necessary?

00:50:57.500 --> 00:51:01.600
Actually, if we consider sort of
the ensemble approach,

00:51:01.600 --> 00:51:05.920
this might give us a way to make
that sort of objective decision.

00:51:05.920 --> 00:51:08.040
So I’m showing, again,
the SMA weights from

00:51:08.040 --> 00:51:10.320
the 2015 San Ramon swarm.

00:51:10.320 --> 00:51:13.460
You’ll note – if you pay attention
to how the Fixed-Swarm model

00:51:13.460 --> 00:51:16.560
changed over time, you can see that
the model weight was higher after the

00:51:16.560 --> 00:51:20.390
swarm began, and it decreased after the
swarm, for the most part, had ended.

00:51:20.390 --> 00:51:23.740
You can imagine that, if you had these
ensemble models running continuously

00:51:23.740 --> 00:51:28.300
through time, even before the swarm
started, at some point, you know,

00:51:28.300 --> 00:51:31.300
perhaps in a non-swarm situation,
the swarm models would receive

00:51:31.300 --> 00:51:34.160
much lower weight.
At some point in these ensembles,

00:51:34.160 --> 00:51:36.450
they’d start receiving much
higher weight, and that would

00:51:36.450 --> 00:51:41.980
provide a way to objectively
determine that a swarm is going on.

00:51:42.570 --> 00:51:44.660
And then, at that point,
you wouldn’t even really need to

00:51:44.670 --> 00:51:47.820
make that determination, necessarily.
It would just continue on its merry way

00:51:47.820 --> 00:51:53.750
and start using these swarm models
to make forecasts that were based on

00:51:53.750 --> 00:51:58.300
higher – based on – be based on
ensembles that have higher weights

00:51:58.300 --> 00:52:02.140
on the swarm components as opposed
to the non-swarm components.

00:52:04.240 --> 00:52:07.000
So a couple of other things that we
can work on – swarm characterization.

00:52:07.000 --> 00:52:11.400
I didn’t touch on this at all, but some of
the work – other work I’ve been doing,

00:52:11.400 --> 00:52:14.080
particularly in the case for
induced seismicity, is,

00:52:14.080 --> 00:52:16.360
how might we be able
to use external information?

00:52:16.360 --> 00:52:21.200
So, for example, things like fluid
injection to better inform our forecasts?

00:52:21.200 --> 00:52:25.900
And then finally, of course,
how can we improve how we

00:52:25.910 --> 00:52:28.700
communicate these
swarm-specific forecasts?

00:52:28.700 --> 00:52:31.560
So I think I’m going to end there.
Thank you very much.

00:52:31.560 --> 00:52:38.480
[Applause]

00:52:39.900 --> 00:52:49.820
[Silence]

00:52:50.920 --> 00:52:53.100
- Thanks. That was
a very interesting talk.

00:52:53.100 --> 00:52:56.480
And I was interested in the
second bullet from the bottom.

00:52:56.960 --> 00:53:00.140
Obviously, if you’re in an area
without a lot of prior swarm history,

00:53:00.140 --> 00:53:02.910
you don’t have much to go on
in terms of looking back

00:53:02.910 --> 00:53:05.930
and establishing
backgrounds for swarms.

00:53:05.930 --> 00:53:08.210
How would you do –
how would you use fluid injection

00:53:08.210 --> 00:53:10.400
history to improve
this kind of modeling?

00:53:10.400 --> 00:53:13.721
In other words, bringing
the physics into the problem?

00:53:13.721 --> 00:53:17.870
- Yeah, so for that, I was actually
thinking more of – so, for example,

00:53:17.870 --> 00:53:26.610
the work that Jack Norbeck and
Justin were working on with their

00:53:26.610 --> 00:53:30.290
hydromechanical model, you know,
predicting – forecasting earthquake

00:53:30.290 --> 00:53:33.600
rates based on fluid injection history
in Oklahoma and Kansas.

00:53:34.460 --> 00:53:37.500
Some of the work I’ve been doing
has been to take their model and

00:53:37.510 --> 00:53:41.910
implement it into an ETAS framework.
So combining both – it predicted

00:53:41.910 --> 00:53:44.520
background rate change,
so you can use the history of

00:53:44.520 --> 00:53:49.060
fluid injection to predict what the
background rate is going to be doing.

00:53:49.060 --> 00:53:55.340
And then combine that with sort of the –
with the aftershocks that are,

00:53:55.340 --> 00:53:59.100
you know,
using the ETAS model.

00:53:59.100 --> 00:54:03.520
So that would be – that would be
one way of potentially going about it.

00:54:05.080 --> 00:54:08.000
- Could you – if you –
say, Bombay Beach.

00:54:08.000 --> 00:54:11.990
You mentioned earlier that a lot of these
swarms may be related to fluids or not.

00:54:11.990 --> 00:54:15.500
Even not knowing that, could you
establish sort of an equivalent hydraulic

00:54:15.500 --> 00:54:20.040
diffusivity and come up with a model
that would add a little bit – you know,

00:54:20.040 --> 00:54:22.860
there’s a presumption of physics,
but it might add a little bit more

00:54:22.860 --> 00:54:27.160
predictive capability than
relying on statistics alone.

00:54:28.640 --> 00:54:31.140
- You might be able to.

00:54:32.960 --> 00:54:35.660
Yeah, I’d have to …

00:54:37.240 --> 00:54:38.840
Yeah.
You might be able to do it.

00:54:38.850 --> 00:54:44.000
There’s a lot of – you know,
as I showed in that table,

00:54:44.000 --> 00:54:48.440
there’s a lot of variability in how –
you know, in how the swarms behave.

00:54:48.440 --> 00:54:50.540
I mean, even just by
looking at how long they last.

00:54:50.540 --> 00:54:52.200
So presumably,
there’s a lot of variability

00:54:52.210 --> 00:54:55.160
in the process
that’s driving them.

00:54:55.160 --> 00:54:58.260
Especially in a part – you know,
an area like the Salton Sea, where you

00:54:58.260 --> 00:55:02.150
have swarms that are being triggered
by all manner of things, potentially.

00:55:02.150 --> 00:55:06.930
You know, some might be related to –
you know, some might be induced.

00:55:06.930 --> 00:55:09.220
Some might be just
related to natural fluid flow.

00:55:09.220 --> 00:55:12.380
Some might be
driven by magmatism.

00:55:13.270 --> 00:55:18.740
I think it’s – you might be able to
untangle that in a less-complicated area.

00:55:18.740 --> 00:55:20.520
- Okay. Okay. Thanks.

00:55:22.340 --> 00:55:24.860
- [inaudible]
- [inaudible]

00:55:24.860 --> 00:55:28.190
- I was just going to comment that, if
you want to have physical parameters,

00:55:28.190 --> 00:55:30.780
I think you’re limited in
exactly the same way, which is,

00:55:30.780 --> 00:55:33.180
if you’re in a region with
very few prior swarms,

00:55:33.180 --> 00:55:37.900
you have no idea what the
variability in the natural process is.

00:55:37.900 --> 00:55:40.640
But the other thing that could come in –
I was thinking back to your

00:55:40.640 --> 00:55:47.090
thesis work. If the – if the process
is enough to provide deformation,

00:55:47.090 --> 00:55:49.580
then the deformation processes
could give us some window into

00:55:49.580 --> 00:55:53.490
what’s going on
in the transient processes.

00:55:53.490 --> 00:55:56.130
And then you have some – you know,
use, you know, various models

00:55:56.130 --> 00:56:02.390
to tie deformation or aseismic slip to
rate-and-state and into ETAS that way.

00:56:02.390 --> 00:56:04.780
So there may be some roots.
But, again, the question is, in how

00:56:04.780 --> 00:56:09.420
many of these swarms do we actually
have an observable deformation signal?

00:56:09.420 --> 00:56:11.440
- [inaudible]
- Yeah.

00:56:12.900 --> 00:56:17.120
- So, Andrea, thanks for that talk.
It was really interesting.

00:56:17.120 --> 00:56:19.520
I had a question about –
you showed a timeline

00:56:19.520 --> 00:56:23.740
of probabilities in the
various events that occurred.

00:56:24.960 --> 00:56:26.400
Yeah, right here.
- Uh-huh.

00:56:26.400 --> 00:56:30.100
- So forecast modeling took
an entire day. Is that correct?

00:56:30.100 --> 00:56:36.190
- [laughs] Yeah, well, not – maybe not
an entire day, but it ran overnight.

00:56:36.190 --> 00:56:40.240
And so this is – this is actually the –
I think – I hope I measured –

00:56:40.240 --> 00:56:44.170
so the two models that were
run for Bombay Beach were sort of

00:56:44.170 --> 00:56:48.210
the standard ETAS model.
That does not take very long at all.

00:56:48.210 --> 00:56:52.460
And then the UCERF3-ETAS model.
And the UCERF3-ETAS model

00:56:52.460 --> 00:56:55.650
is a very computationally
intensive model to run.

00:56:55.650 --> 00:56:58.230
And that had to run overnight.
- Okay.

00:56:58.230 --> 00:57:01.500
- So it didn’t take quite a full day.
I think it started sometime

00:57:01.500 --> 00:57:05.070
in the afternoon, and it
finished by the next morning.

00:57:05.070 --> 00:57:10.480
- Okay. So maybe in the –
in a couple years –

00:57:10.480 --> 00:57:14.080
or since then, that window might
have gotten shorter or something.

00:57:14.080 --> 00:57:17.340
But do you think that –
does it take too long?

00:57:17.340 --> 00:57:20.120
In terms of our response to a …

00:57:21.100 --> 00:57:23.220
- Yeah. I think that’s
definitely part of it.

00:57:23.220 --> 00:57:26.420
That’s definitely an area that
we can – we can improve.

00:57:31.600 --> 00:57:34.180
Certainly, when we think about –
you know, as we – as we start to think

00:57:34.180 --> 00:57:41.360
about operationalizing forecasts, this is
something we would like to shorten.

00:57:41.360 --> 00:57:47.660
I’m – given the computational
resources that are required by

00:57:47.660 --> 00:57:53.670
the UCERF3-ETAS model, I’m not
sure how much shorter that can get.

00:57:53.670 --> 00:58:00.540
But, I mean, if – you know, we’re –
if we stick to just sort of plain, standard

00:58:00.540 --> 00:58:07.300
ETAS models, that should be able to,
you know, shorten significantly.

00:58:07.680 --> 00:58:09.200
- Thanks.

00:58:13.460 --> 00:58:17.320
- Well, following up, how –
what is our obstacle to implementing

00:58:17.320 --> 00:58:21.130
and sort of continually
running your ensemble model?

00:58:21.130 --> 00:58:24.940
And to see what it does?
Like, statewide?

00:58:24.940 --> 00:58:27.380
- I don’t know. [laughs]

00:58:28.160 --> 00:58:32.420
That’s sort of the next – you know,
the next step would be to actually

00:58:32.420 --> 00:58:36.330
see what happens if – well, you know,
okay, so I started these ensemble

00:58:36.330 --> 00:58:40.880
models after the swarm had started.
It’s really easy to – you know, okay,

00:58:40.880 --> 00:58:44.330
well, start a month or maybe six
months before the swarm happens.

00:58:44.330 --> 00:58:47.980
And then see how the ensemble
weights change over time.

00:58:47.980 --> 00:58:51.210
So that’s sort of the
easy next thing to try.

00:58:51.210 --> 00:58:56.600
And then, you know, based on that,
I mean, I don’t – you know, I don’t –

00:58:56.600 --> 00:58:59.740
I don’t know how hard
it would be to [laughs] –

00:58:59.740 --> 00:59:05.220
to test this sort of
on a statewide level.

00:59:09.700 --> 00:59:11.840
- My question is about –
I guess it’s about the difference

00:59:11.840 --> 00:59:16.190
between UCERF-ETAS
and the version of ETAS –

00:59:16.190 --> 00:59:19.760
or, the kinds of modeling
that you’ve been doing.

00:59:19.760 --> 00:59:24.020
And it’s related to
the Bombay sequence.

00:59:24.030 --> 00:59:27.150
Because that sequence is
happening along the San Andreas,

00:59:27.150 --> 00:59:32.090
we’re all concerned about a
large earthquake being triggered.

00:59:32.090 --> 00:59:35.360
But it’s not clear to me how
the modeling you does takes account

00:59:35.360 --> 00:59:37.810
of the fact – of the proximity
to the San Andreas.

00:59:37.810 --> 00:59:43.580
If that swarm were occurring in
some other place, some other

00:59:43.580 --> 00:59:50.470
body of water in – wherever,
and there’s no river fault map nearby,

00:59:50.470 --> 00:59:55.140
would you get the same answer?
- Um …

00:59:55.140 --> 00:59:56.820
- About the probability
of a magnitude 7.

00:59:56.820 --> 00:59:57.820
- Yeah.

00:59:58.540 --> 01:00:04.040
Yeah, so the – yeah, that’s – you know,
that is one of the weaknesses of

01:00:04.040 --> 01:00:08.020
just running that standard ETAS
model for this particular problem.

01:00:08.020 --> 01:00:13.760
It doesn’t account for – [chuckles] it
doesn’t account for the fault, basically.

01:00:13.760 --> 01:00:17.350
Which is, you know, why the UCERF3-
ETAS model was so important.

01:00:17.350 --> 01:00:20.300
- Right.
- In trying to sort of, you know,

01:00:20.300 --> 01:00:22.490
get at that probability.
But neither of the models – neither

01:00:22.490 --> 01:00:26.100
of the two models were really perfect
in trying to answer that question.

01:00:26.100 --> 01:00:30.900
Which is why we ended up with this
range of probabilities that was reported.

01:00:32.140 --> 01:00:33.640
- Thanks.

01:00:35.260 --> 01:00:39.500
[Silence]

01:00:40.300 --> 01:00:42.140
- Final questions?

01:00:46.680 --> 01:00:50.220
- So, I mean, this is a big problem
also with the aftershock forecasts

01:00:50.220 --> 01:00:52.620
that I think we have to address,
which is, first of all,

01:00:52.620 --> 01:00:57.920
UCERF3-ETAS matters if
you believe, and you have faith,

01:00:57.920 --> 01:01:02.230
that the fault is characteristic and
that the largest earthquakes

01:01:02.230 --> 01:01:05.900
are over-representative
compared to an extrapolation

01:01:05.900 --> 01:01:07.530
from the
smallest magnitudes.

01:01:07.530 --> 01:01:12.210
And, of course, that’s – you know,
in UCERF3, we tried to kill that,

01:01:12.210 --> 01:01:15.480
and we failed.
So we have some belief that the

01:01:15.480 --> 01:01:19.820
data may actually require it, but there’s
a lot of controversy about that.

01:01:19.820 --> 01:01:25.050
Dave Jackson feels that he can
kill our inability to kill it. [laughs]

01:01:25.050 --> 01:01:26.580
I mean,
he’s working on that.

01:01:26.580 --> 01:01:29.190
So I think that’s a –
that’s a really open question.

01:01:29.190 --> 01:01:31.460
It’s fairly easy,
in any of these forecasts,

01:01:31.460 --> 01:01:34.920
to include a
maximum magnitude.

01:01:34.930 --> 01:01:37.630
So you would get different things
when you were – if you were sure

01:01:37.630 --> 01:01:42.350
you were away from any fault that
could produce large earthquakes.

01:01:42.350 --> 01:01:46.040
There may be ways to sort of
approximate some corrections to

01:01:46.040 --> 01:01:50.971
the probabilities after the fact
to account for, you know,

01:01:50.971 --> 01:01:53.820
the shape of the magnitude frequency
distribution if you think there’s

01:01:53.820 --> 01:01:57.450
a characteristic thing in there,
but there’s some limitations to that,

01:01:57.450 --> 01:02:01.130
which is that, you know,
you think that there’s a high likelihood,

01:02:01.130 --> 01:02:04.130
perhaps, of a magnitude 7
on the southern San Andreas.

01:02:04.130 --> 01:02:08.500
But you probably don’t think there’s
a high likelihood of two magnitude 7s

01:02:08.500 --> 01:02:12.170
on the southern San Andreas.
Because you believe in elastic rebound.

01:02:12.170 --> 01:02:14.520
And it’s incorporating the elastic
rebound, which is one of the things

01:02:14.520 --> 01:02:17.860
that really requires you then to
start running UCERF3-ETAS.

01:02:17.860 --> 01:02:22.420
Which then starts requiring the
Stampede cluster for 12 hours.

01:02:23.370 --> 01:02:26.940
So the question is, how exact
do we need these things?

01:02:26.940 --> 01:02:30.040
How much do we really believe
in each of these ingredients?

01:02:30.040 --> 01:02:32.910
And, as Andrea pointed out,
the UCERF3-ETAS model, we have

01:02:32.910 --> 01:02:37.160
no way in there currently to incorporate
a changing background rate.

01:02:37.160 --> 01:02:44.220
So, like, none of the models are perfect.
And which ones we want to focus on,

01:02:44.220 --> 01:02:46.960
you know, depends on sort of
what we really think goes on

01:02:46.970 --> 01:02:51.150
in the earthquake process.
And I think I actually – Ned sent out

01:02:51.150 --> 01:02:54.030
an email this morning about, you know,
progress in operationalizing

01:02:54.030 --> 01:02:57.690
UCERF3-ETAS so that
actually more people can run it.

01:02:57.690 --> 01:03:00.180
But it’s still a
supercomputing model,

01:03:00.180 --> 01:03:03.960
and there’s – you know, there’s
just limits to what we can do.

01:03:03.960 --> 01:03:06.080
So it’s – I think these are
interesting questions that

01:03:06.080 --> 01:03:09.800
come back to what we think
the earthquakes really do.

01:03:09.800 --> 01:03:11.920
But I think there’s a lot of
utility in these sort of

01:03:11.920 --> 01:03:14.130
standard models that
we can run quickly.

01:03:14.130 --> 01:03:17.320
Because they get rid of that gap. [chuckles]

01:03:18.320 --> 01:03:21.700
[Silence]

01:03:22.640 --> 01:03:24.640
- Okay. Thank you, Andrea.

01:03:24.640 --> 01:03:26.960
Thanks, everyone, for coming.
Remember to ShakeOut tomorrow.

01:03:26.960 --> 01:03:31.040
And then we have a seminar
Friday at 11:00 a.m.

01:03:31.040 --> 01:03:33.170
So hopefully we’ll see you there.
Thanks.

01:03:33.170 --> 01:03:37.720
[Applause]

01:03:38.400 --> 01:03:40.560
[Silence]