WEBVTT
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Language: en

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[ Silence ]

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[inaudible background conversations]

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Good morning.
Welcome to seminar.

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First a few announcements.
Next week, we will have

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David Blake from NASA Ames
who will present some results

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from our
science laboratory.

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This week we have Fred Pollitz –
our own Fred Pollitz here at USGS who

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probably needs no introduction for many
of you, but I will introduce him anyway.

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Fred received his bachelor’s degree
from MIT, Ph.D. from Princeton,

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and then did a number of postdocs
spread far across the U.S. as well as

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in Europe before ultimately
joining the USGS in 2000.

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Today Fred will present some
results about crustal seismicity

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and connection to stress changes
in southern California.

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- Thank you, Belle.
Can you hear me?

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Okay, my collaborator on this work is
Camilla Cattania, who is presently

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at Stanford but is about to return to
Potsdam where she did her Ph.D. work.

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So about 10 years ago, there was
forecasting experiments that were

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supported by the Southern California
Earthquake Center and the USGS.

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It had the acronym RELM.
And I remember, 10 years ago,

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we were hearing all about it,
but I haven’t heard a lot about it lately.

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It kind of turned into CCEP.

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So that stands Regional
Earthquake Likelihood Models.

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And the forecasting experiment was
five years long and it was to forecast

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basically magnitude 5 and greater
seismicity from 2006 to 2011.

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And there were 17
time-invariant forecasts.

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And they were judged by
several different measures,

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which I’m not
going to go into.

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And the best one of those was
by Helmstetter and others,

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published in 2007, and you can
just see the earthquake rates

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correlate pretty well with the few
magnitude 5s which actually occurred.

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So this model had
some predictive power.

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But it was one of several
time-invariant forecasts,

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and all but one of the forecasts was
essentially statistical or empirical.

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Only one of the forecasts, which was
Steve Wood’s earthquake simulator,

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was based on physics.
So I’ve had a longstanding interest

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in trying to understand
time-dependent motions,

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especially in the Mojave Desert,
where I’ve studied the

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viscoelastic relaxation process
from large earthquakes.

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And also to make time-dependent 
forecasts based on these processes.

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So the Coulomb rate-state model,
which I’ll describe in a little more

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detail later, is one means of
providing a time-dependent forecast.

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So here I’m just looking at the
seismicity in the years 2015 and 2016

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and comparing that with the
rate of earthquakes – with the

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earthquakes that actually occurred.
And I’m looking at not only

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magnitude 5 and higher,
but the magnitude 4s and 3s

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so we have a larger data set,
and things look pretty good.

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Things are happening where
the colors are the brightest.

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And so, in some measure,
it would be a successful forecast.

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And I actually wonder if
this type of forecast would have

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done well or not
during the RELM period.

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A thing I’m particularly interested in
is what the different components

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of this forecast are doing.
So two of the components that

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go into this are the static stress change
and the postseismic stress change

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driven by viscoelastic relaxation
of the lower crust and the mantle.

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And I was interested in ways of
isolating these different effects.

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So in the right-hand plot, which I will
again describe in greater detail later,

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we can isolate the
postseismic effects and

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quantify the postseismic
seismicity rate gain.

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And this, once again, plotting up
the same bunch of earthquakes,

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and there is some kind of a
correlation here which –

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just qualitatively is suggestive that
maybe the postseismic relaxation

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process is shaping or influencing
the locations of earthquakes.

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So when I embarked on this work,
I looked at this type of a plot,

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and I was, like, wow,
this model is predictive.

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And I started to feel like this person
in the movie San Andreas.

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[laughter]

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Okay, but to take a step back,
people have been pondering

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for a really long time what mechanisms
govern aftershock triggering.

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And the first earthquake that was
really studied in great detail

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was the Loma Prieta
earthquake of 1989.

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And that was looked at by
Tom Parsons and others in 1999.

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And they found that strike-slip faults,
such as the San Gregorio Fault,

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tended to have a high
correlation of post-earthquake

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seismicity with a
positive shear stress change.

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Whereas, thrust faults, such as the
Sargent Fault, tended to have a positive

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correlation of aftershock activity
with the normal stress change.

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So that basically suggested a
low effective coefficient of friction

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on the strike-slip faults
and a much higher

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effective coefficient of
friction on thrust faults.

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Now, Camilla, in her thesis work,
looked in detail at aftershock

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triggering following the Parkfield
and Tohoku earthquakes.

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So this is an example from the
2004 Parkfield earthquake.

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And she’s made the point that
coseismic stress changes driven by

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the coseismic slip distribution
can directly lead to changes

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in the seismicity rate, but they will
also lead to aseismic processes,

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such as afterslip, viscoelastic relaxation,
poroelastic response, and those things,

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in turn, will produce
their own stresses,

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which will again feed
into seismicity rates.

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And so one process that she studied in
detail was the effective afterslip and

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how that modifies the stress field with
time and leads to generated seismicity.

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In this case, she’s looking at
a time period of 250 days

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after the
Parkfield earthquake.

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And she also looked at secondary
triggering, which is basically

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aftershocks triggering themselves,
and she found that both of these

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processes are important,
and I’ll be closing the presentation

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with a couple of slides
demonstrating that from her work.

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So another postseismic mechanism
is the viscoelastic stress transfer.

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That’s the one that
I’m particularly interested in.

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So this is just a little example showing
how this works for a strike-slip fault.

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So we have uniform slip on a fault,
shown by the white line.

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And at the time of an earthquake,
the coseismic stress change

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produces a large shadow around that.
However, we produce a lot of positive

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strain into the viscoelastic substrate –
let’s say the lower crust – and that

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has to relax with time, and that will
couple to continued deformation

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in the upper elastic plate, and that
will continue to develop with time.

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So the viscoelastic substrate is flowing,
so its strain is increasing.

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The stresses in the elastic plate, in the
sense to reload the original fault zone,

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and the – to start out with, the shadow –
stress shadow moves out with time,

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but eventually, a wide zone around
the original fault zone reloads,

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and the shadow
diminishes with time,

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and that’s pretty much the story
as you keep going out in time.

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So this is what the viscoelastic
stress transfer process looks like

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in cross-section.
And in map view, Phoebe DeVries

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has recently published a paper
where she looked at this process.

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So the coseismic stress change for
uniform slip on a planar fault

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will again lead to a stress shadow
around that fault, and it will lead to

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this pattern of positive and negative
stress changes so that the positive stress

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changes are going to be off the
ends of the fault and off to the side.

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The postseismic stress changes
due to the viscoelastic relaxation,

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as I mentioned, they tend to
reload the fault, and they also

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tend to increase stress
off to the sides of the fault.

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And that’s a pretty ubiquitous feature of
the viscoelastic relaxation process.

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And it definitely adds time-dependent
stresses to the system, and it’s something

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to take into consideration
when predicting seismicity rates.

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So these are means of producing
time-dependent stresses, but to

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convert that into seismicity rates, there’s
the so-called Coulomb rate-state model,

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and it’s based on the
Dieterich rate-state theory.

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And so we imagine, before an event
happens on this gray fault surface,

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we have a population of potentially
failing faults that are at all stages of

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their earthquake cycles, ranging
from just failed to ready to fail.

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And we imagine a slip event
on the gray fault, and that turns

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a lot of these patches bluer, so they’re
going to be more ready to fail.

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We’re assuming a
positive stress step here.

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And a lot of them are
going to fail very quickly.

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And eventually, we’re going to
reach a situation where we

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return to the equilibrium that
existed before the event –

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sort of an equal distribution of patches
that are ready to fail or just failed.

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And so we gradually come
down to the background rates.

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And this can be quantified here.

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This is a slide that I borrowed
from one of Camilla’s presentations.

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So imagine we have a receiver fault,
and that receives a shear stress change

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and a normal stress change
from a nearby main shock.

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And the Coulomb failure stress change
is going to be a linear combination

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of the shear stress change
the normal stress change

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weighted by a
coefficient of friction.

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There’s a pore pressure change
term here, but that can be kind of

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funneled into the coefficient of friction
if you assume that it’s proportional to

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the normal stress change, which is a
common practice in this type of study.

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Now, Dieterich, in 1994, he showed
that the time-dependent friction

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takes into account velocity –
velocity dependence and

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state dependence can be turned
into a seismicity rate,

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which is given by this formula.
So capital R is generally going to

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denote here a seismicity rate –
an instantaneous rate.

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Whereas, small r is going to
be a background rate.

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So the instantaneous rate is equal to
the background rate divided by the

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background stressing rates times a state
parameter, or right evolution parameter.

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And that evolves with time
according to the lower equation,

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and we can look at the different
components of the lower equation.

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So for example, if we have a
positive Coulomb failure stress,

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then it’s going to lower the value of the
state variable, and then the first equation

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says we’re going to get a jump in the
seismicity rate, as we saw on the last slide.

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Whereas, immediately after such
a stress step, all we’re dealing with

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is the first term, and then we’re going to
have a monotonic increase of the state

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variable, and then the seismicity rate
is going to monotonically go down.

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And how quickly it goes down
is governed by the so-called

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aftershock decay time,
which is given by this expression.

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So the other thing I wanted to
emphasize here is to construct

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a Coulomb rate-state model,
we have to have a set of main shocks,

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obviously, to transfer stress
to all the receiver faults.

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We need to have an idea
of the background seismicity rates

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at all points in the
volume of interest.

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We need to know the
background stressing rate.

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And the aftershock decay time,
we’ll use as a proxy

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for the A and
sigma parameters.

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So this type of
study was previously

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done in southern California by
Shinji Toda and others in 2005.

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And this is a plot of the
magnitude 5-1/2 and greater earthquakes

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in their study period,
which was from 1981 to 2003.

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And they used magnitude 6
and greater earthquakes

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as their sources of deformation.
And the first one of those would have

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been the magnitude 6.0 North
Palm Springs event in 1986.

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So essentially, they’re using the period
1981 to 1986 background period,

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and then a test period
from 1986 onward.

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And so they can track
the predicted seismicity rate.

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In this case, it’s a rate gain normalized
by the average background rates.

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And after each of the major source
earthquakes that happened during this

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time, you get the same pattern that
we saw in the previous illustration.

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Seismicity rates over the
area are generally high.

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And then they diminish with time
and eventually tend to approach

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the background rate.

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And they found that, not only
in the area overall, but even

00:14:49.209 --> 00:14:56.019
within specific smaller areas in this
study area, that the predicted

00:14:56.019 --> 00:15:01.730
seismicity rate was often
well-correlated with the model –

00:15:01.730 --> 00:15:06.699
with the observed seismicity rate.
And that’s based on a lot of data.

00:15:06.699 --> 00:15:11.620
They were looking at magnitude 1.4
and greater magnitude events,

00:15:11.620 --> 00:15:14.149
so they had a quite large catalog
they were looking at.

00:15:14.149 --> 00:15:16.880
This is another example
from their study.

00:15:16.880 --> 00:15:20.709
So here they’re looking –
very early on aftershocks

00:15:20.709 --> 00:15:22.529
after the Hector Mine earthquake.

00:15:22.529 --> 00:15:27.429
So 68-hour time span beginning 33
hours after the Hector Mine quake.

00:15:27.429 --> 00:15:33.480
And they note a jet of
aftershocks kind of shooting off

00:15:33.480 --> 00:15:36.900
from the Hector Mine earthquake.

00:15:38.480 --> 00:15:43.840
And they note that that is due
primarily to residual stresses

00:15:43.850 --> 00:15:47.690
left over from the Landers earthquake,
which occurred seven years previously,

00:15:47.690 --> 00:15:55.240
and the North Palm Springs event,
which happened even earlier than that.

00:15:55.240 --> 00:15:58.130
Another thing they note is that their
model could predict the location of

00:15:58.130 --> 00:16:04.139
stress shadows – so these regions
labeled A, B, C, and D were active

00:16:04.139 --> 00:16:10.499
during the background period, but during
a 231-day period starting four years after

00:16:10.499 --> 00:16:14.279
the Hector Mine quake, those areas were
shut off compared with other areas.

00:16:14.279 --> 00:16:16.889
So that is basically scored
as another success

00:16:16.889 --> 00:16:20.360
for the predictability
of their model.

00:16:20.360 --> 00:16:26.000
Now, as successful as that model was,
it still raises the question,

00:16:26.000 --> 00:16:32.720
what will the time-dependent
postseismic stressing do to the picture.

00:16:32.720 --> 00:16:38.850
So a number of people, beginning
with Yuehua Zeng, started looking at

00:16:38.850 --> 00:16:44.670
the possibility that time-dependent
stresses from the Landers earthquake

00:16:44.670 --> 00:16:46.460
could have triggered the
Hector Mine earthquake.

00:16:46.460 --> 00:16:50.060
I mean, it was a seven-year time
difference between the two earthquakes,

00:16:50.069 --> 00:16:54.279
and so the static stresses from the
Landers earthquake, which we see

00:16:54.279 --> 00:17:00.639
on this first figure, they obviously
didn’t produce the Hector Mine

00:17:00.639 --> 00:17:03.329
earthquake instantaneously,
but as you allow the lower crust

00:17:03.329 --> 00:17:09.630
and the mantle to relax, as we see in
some of Yuehua’s further figures –

00:17:09.630 --> 00:17:13.199
two years after the earthquake,
four years after Landers, six years,

00:17:13.199 --> 00:17:20.670
and eight years, the total stress resolved
on the future Hector Mine rupture zone

00:17:20.670 --> 00:17:25.350
has increased, and the argument can be
made that these very slowly developing

00:17:25.350 --> 00:17:29.370
time-dependent stresses helped to
trigger the Hector Mine earthquake.

00:17:29.370 --> 00:17:33.800
And I wanted to mention that there
was no color scale in this paper,

00:17:33.809 --> 00:17:37.380
which is why [chuckles]
I don’t have it on here.

00:17:37.380 --> 00:17:40.180
But I’m guessing these stresses
are on the order of one bar.

00:17:40.960 --> 00:17:45.260
Okay, I did a similar study, published it
in 2002, with Selwyn Sacks.

00:17:45.270 --> 00:17:48.221
So on the left are the –
is the coseismic stress change

00:17:48.221 --> 00:17:52.760
pattern from the Landers earthquake.
And as we saw in Yuehua’s study,

00:17:52.760 --> 00:17:57.960
it positively stressed the northern part of
the future Hector Mine rupture zone.

00:17:57.960 --> 00:18:02.520
And we can add postseismic stresses
to that over the intervening seven-year

00:18:02.529 --> 00:18:07.809
period, and if you compare the two,
the stresses have increased.

00:18:07.809 --> 00:18:11.911
And in the next plot, I’m just showing
you what that stress increase is.

00:18:11.911 --> 00:18:15.031
So this is seven years’ worth
of postseismic stress increase.

00:18:15.040 --> 00:18:20.040
And it’s somewhere between 0.3
and 1 bar developing on the

00:18:20.040 --> 00:18:21.770
future Hector Mine
rupture zone.

00:18:21.770 --> 00:18:25.840
So the argument is that the
viscoelastic stresses do matter.

00:18:25.840 --> 00:18:30.960
They add to the budget of stress
very slowly, but they do matter.

00:18:32.420 --> 00:18:35.260
Okay, so for the rest
of this presentation,

00:18:35.260 --> 00:18:39.549
we’ll build on what Shinji Toda
and others did in 2005.

00:18:39.549 --> 00:18:42.760
So we’re going to use
three decades of southern California

00:18:42.760 --> 00:18:46.240
seismicity going
up to 2014.

00:18:46.240 --> 00:18:50.720
I’ll go through the mechanical model
and the stress evolution.

00:18:50.730 --> 00:18:55.370
Then we’ll look at predicted
time-dependent model seismicity rates

00:18:55.370 --> 00:18:58.049
and get into a quantitative
comparison of that model

00:18:58.049 --> 00:19:00.289
with the observed
seismicity rates.

00:19:01.220 --> 00:19:04.880
So I’m using a catalog
that was first described

00:19:04.890 --> 00:19:08.310
in a publication by Yang
and others in 2012.

00:19:08.310 --> 00:19:12.950
And Egill Hauksson makes
this catalog available online.

00:19:12.950 --> 00:19:18.330
There are about 176,000 magnitude 1
and greater earthquakes in this

00:19:18.330 --> 00:19:23.670
catalog from 1981 to 2014,
so it’s a very valuable resource.

00:19:23.670 --> 00:19:26.040
And they all come with
focal mechanisms as well.

00:19:26.040 --> 00:19:29.460
So it’s really an
amazing resource.

00:19:29.460 --> 00:19:37.800
And the magnitude of
completeness would be around 2.

00:19:37.800 --> 00:19:44.740
I’m choosing to look at magnitude 3-1/2
and greater earthquakes.

00:19:45.560 --> 00:19:51.200
That’s much lower magnitude that was
used, say, in the RELM studies, but it’s a

00:19:51.200 --> 00:19:56.380
higher magnitude that was used in the
Toda et al., which was magnitude 1.4.

00:19:56.390 --> 00:20:02.340
So I want to have a fairly large data set,
but it’s my personal preference

00:20:02.340 --> 00:20:09.980
that I don’t want to be swamped by
all the magnitude 1s in the study.

00:20:10.820 --> 00:20:20.460
So at the magnitude 3-1/2 level and
greater, we have 2,288 earthquakes.

00:20:20.460 --> 00:20:25.520
And I’ve subdivided that into the period
before the Landers earthquake

00:20:25.520 --> 00:20:30.280
and the seven-year period between the
Landers and Hector Mine earthquake,

00:20:30.280 --> 00:20:35.380
and 11-year period between the time of
the Hector Mine and El Mayor-Cucapah

00:20:35.380 --> 00:20:41.120
earthquakes, and then the few years
since the El Mayor-Cucapah earthquake.

00:20:41.120 --> 00:20:45.000
And all the earthquakes that I’ve
labeled here are going to be sources

00:20:45.000 --> 00:20:49.260
of deformation in my study.
So these are all magnitude 7

00:20:49.270 --> 00:20:52.601
or greater except for the
Big Bear quake, which is a 6-1/2

00:20:52.601 --> 00:20:56.661
and the Northridge quake –
actually it was a 6.7.

00:20:56.661 --> 00:21:00.851
And there is – there are a couple
things that we could notice here,

00:21:00.851 --> 00:21:04.840
which is, in the background period,
we have very few earthquakes in the

00:21:04.840 --> 00:21:08.610
eastern California shear zone
north of the Landers rupture zone.

00:21:08.610 --> 00:21:11.730
But we get quite a few of them
during the seven years between

00:21:11.730 --> 00:21:15.049
the Landers and
Hector Mine earthquakes.

00:21:15.049 --> 00:21:18.740
And similarly, the southern part
of the San Jacinto Fault was

00:21:18.740 --> 00:21:22.309
very productive during the
background period, but,

00:21:22.309 --> 00:21:26.460
to a large extent, it gets shut off
after the Landers earthquake.

00:21:26.460 --> 00:21:31.140
It was much less active.
So those are a couple of things

00:21:31.149 --> 00:21:35.400
that we might hope a quantitative
model could replicate.

00:21:36.780 --> 00:21:38.940
Now, to do this analysis,
we have to have the

00:21:38.950 --> 00:21:42.750
focal mechanisms of the
earthquakes that actually happened.

00:21:42.750 --> 00:21:45.770
And here I’m just plotting the
magnitude 4-1/2s and greater

00:21:45.770 --> 00:21:48.640
to avoid cluttering up the plot,
but we’re really using all the

00:21:48.640 --> 00:21:52.900
magnitude 3-1/2 and
greater in this study.

00:21:53.680 --> 00:21:56.860
And we don’t use
optimally oriented planes.

00:21:56.870 --> 00:22:02.149
We use the focal mechanism
solutions to basically define

00:22:02.149 --> 00:22:04.949
the receiver fault geometry.

00:22:04.949 --> 00:22:09.960
And we don’t know which focal plane –
which of the two focal planes,

00:22:09.960 --> 00:22:14.080
for any event, is appropriate,
so we basically do Monte Carlo

00:22:14.080 --> 00:22:19.789
simulations over all possible choices
of the two focal planes in the analysis.

00:22:19.789 --> 00:22:24.110
So that generates some
randomness in the results.

00:22:25.420 --> 00:22:29.400
Now, there were complications
involved with including all of the

00:22:29.400 --> 00:22:34.680
aftershocks in the near field or
early after each of the main shocks.

00:22:34.680 --> 00:22:37.500
And the principal culprit
is dynamic triggering.

00:22:37.500 --> 00:22:40.660
So Tom Parsons
studied this in 2002.

00:22:40.660 --> 00:22:45.800
He found that about 61% of
earthquakes following magnitude –

00:22:45.809 --> 00:22:51.789
a set of magnitude 7 earthquakes
distributed globally were located

00:22:51.789 --> 00:22:55.529
in a region of predicted positive
Coulomb failure stress.

00:22:55.529 --> 00:22:59.450
But the other 39% didn’t fit that
and were arguably due to

00:22:59.450 --> 00:23:01.630
dynamic triggering.

00:23:01.630 --> 00:23:06.660
And in a different kind of analysis,
van der Elst and Brodsky were

00:23:06.669 --> 00:23:12.290
finding that peak dynamic strain is
what controls the scaling of far field

00:23:12.290 --> 00:23:15.809
triggering, and they could extrapolate
that to the near field and conclude

00:23:15.809 --> 00:23:22.720
that 15 to 60% of earthquakes that
are close to magnitude 3 to

00:23:22.720 --> 00:23:28.860
magnitude 5.5 main shocks are
probably subject to dynamic stressing.

00:23:28.860 --> 00:23:35.520
So dynamic triggering is a –
is a problem if you’re trying to

00:23:35.530 --> 00:23:39.649
isolate the effects of static and
viscoelastic stress changes.

00:23:39.649 --> 00:23:45.860
And then there’s the thing which
Camilla studied, which is secondary

00:23:45.860 --> 00:23:48.510
triggering – aftershocks
triggering themselves.

00:23:48.510 --> 00:23:56.220
So Meier and others found that 27% of aftershocks,
they receive a greater positive stress from

00:23:56.220 --> 00:23:58.560
aftershocks
than the main shocks.

00:23:58.560 --> 00:24:02.560
And Camilla also concluded that
stress redistribution by aftershocks

00:24:02.570 --> 00:24:06.299
plays a first-order role
in aftershock triggering.

00:24:06.299 --> 00:24:10.850
So because of all these complications,
I’m declustering the catalog,

00:24:10.850 --> 00:24:12.970
which is going to bring it down
even further from the –

00:24:12.970 --> 00:24:17.310
from the 2,200 that
I started out with.

00:24:20.660 --> 00:24:23.059
Okay, so one of the things that
I mentioned we need is the

00:24:23.059 --> 00:24:28.340
background seismicity rates,
and we need to be able to query

00:24:28.340 --> 00:24:33.760
the background seismicity rate
at both the catalog epicenters

00:24:33.760 --> 00:24:37.440
as well as a set of
random hypocenters.

00:24:37.450 --> 00:24:43.120
So that would be 3,000 randomly
distributed hypocenters in a volume

00:24:43.120 --> 00:24:45.240
that covers
southern California.

00:24:45.240 --> 00:24:50.060
So it covers this area, and the volume
goes down to 20 kilometers’ depth.

00:24:50.580 --> 00:24:56.340
And it looks about
as you would expect.

00:24:56.340 --> 00:25:00.120
Another thing that we require is
the background stressing rate,

00:25:00.120 --> 00:25:06.419
and this is based on my analysis
of the horizontal GPS velocity field

00:25:06.419 --> 00:25:09.450
that can be converted into
a smooth strain rate field

00:25:09.450 --> 00:25:14.010
and then converted into a
background stressing rate.

00:25:14.010 --> 00:25:20.659
And that was also one of the objectives
of the SCEC Community Stress Model,

00:25:20.659 --> 00:25:27.150
and this is one of the
models in that effort.

00:25:27.150 --> 00:25:29.830
And essentially,
it’s actually strain rate,

00:25:29.830 --> 00:25:32.570
but you can imagine
that it’s stressing rate.

00:25:32.570 --> 00:25:39.529
It agrees fairly well with the stressing
rate that I’ve derived with GPS data.

00:25:40.620 --> 00:25:43.500
Okay, so the mechanical model,
it’s going to be driven by

00:25:43.500 --> 00:25:48.240
coseismic stress steps and
viscoelastic relaxation following this

00:25:48.240 --> 00:25:53.500
set of large southern California
earthquakes beginning in 1992.

00:25:53.500 --> 00:25:57.820
And we’re computing 3D
time-dependent crustal stress

00:25:57.830 --> 00:26:03.980
using a 2-1/2-D model
of viscoelastic deformation.

00:26:03.980 --> 00:26:07.190
So that basically means the viscoelastic
structure is two-dimensional, but we’re

00:26:07.190 --> 00:26:11.820
still computing everything in 3D.
We’re solving the 3D equations.

00:26:11.820 --> 00:26:18.039
And that structure is shown here.
It’s based on an analysis of postseismic

00:26:18.039 --> 00:26:22.519
GPS data following the Landers
and Hector Mine earthquakes.

00:26:22.520 --> 00:26:27.980
And the structure that I derived
consists of a low-viscosity mantle

00:26:27.980 --> 00:26:32.100
asthenosphere along the
San Andreas corridor adjacent to

00:26:32.100 --> 00:26:37.360
a high-viscosity mantle asthenosphere
on the Basin and Range side.

00:26:37.360 --> 00:26:42.260
And one of the perplexing things
about this is that the higher viscosities

00:26:42.269 --> 00:26:45.450
are on the side that
has the higher heat flow.

00:26:45.450 --> 00:26:50.680
So the hotter side actually has higher
viscosity, but I argue in that study

00:26:50.680 --> 00:26:54.779
that the higher strain rates in the
San Andreas corridor,

00:26:54.779 --> 00:27:02.080
and arguably higher water content
in the mantle on the San Andreas side,

00:27:02.080 --> 00:27:05.230
manages to wrench the
viscosity towards much lower values

00:27:05.230 --> 00:27:08.330
in the San Andreas corridor.

00:27:09.840 --> 00:27:13.440
And this is just another depiction
of the viscoelastic structure.

00:27:13.450 --> 00:27:18.020
So it emphasizes that the viscosities
on the southwest side are lower than

00:27:18.020 --> 00:27:20.419
the viscosities on
the northeast side.

00:27:20.419 --> 00:27:23.759
And we’re using a Burger’s
body rheology here.

00:27:25.020 --> 00:27:33.100
Okay, so I’m going to show
an animation of a stress component

00:27:33.110 --> 00:27:37.790
over the area evaluated at
these random hypocenters.

00:27:37.790 --> 00:27:42.519
And this stress component basically
is putting positive stress on –

00:27:42.519 --> 00:27:48.870
right-lateral stress on northwest-
southeast-striking vertical faults.

00:27:48.870 --> 00:27:51.530
So that’s roughly a proxy
for the receiver faults

00:27:51.530 --> 00:27:55.179
that we’d have
in southern California.

00:27:55.179 --> 00:27:58.030
And nothing is going to happen
until 1992 when we get the

00:27:58.030 --> 00:28:02.810
Landers earthquake, but then we’re
going to see the static stress change.

00:28:05.490 --> 00:28:07.200
So it has a familiar pattern.

00:28:07.200 --> 00:28:10.940
The Northridge earthquake
happened soon thereafter.

00:28:12.130 --> 00:28:15.409
These things are actually growing
with time even though it’s hard to see.

00:28:15.409 --> 00:28:17.860
The Hector Mine earthquake
just happened.

00:28:17.860 --> 00:28:21.950
So the red regions and the blue
regions are being modified by

00:28:21.950 --> 00:28:26.019
viscoelastic relaxation, but it’s
very hard to see because

00:28:26.019 --> 00:28:29.809
the scale is usually saturated
here by the static stresses.

00:28:29.809 --> 00:28:33.450
But the animation that I’m
going to show after this one

00:28:33.450 --> 00:28:38.250
will let you see the contribution
from the viscoelastic stressing.

00:28:39.140 --> 00:28:40.240
Okay.

00:28:41.880 --> 00:28:44.200
So this one we’re
just concentrating on the

00:28:44.200 --> 00:28:48.080
postseismic stresses due to
the viscoelastic relaxation.

00:28:49.900 --> 00:28:54.120
And so, again, nothing is going to
happen before the Landers earthquake.

00:28:54.130 --> 00:28:55.850
And then we’re not going to
see a sudden jump.

00:28:55.850 --> 00:28:57.981
We’re going to see a gradual
growth because we’re only

00:28:57.981 --> 00:29:00.000
looking at the
postseismic stresses.

00:29:00.000 --> 00:29:03.690
So we see a gradual growth
of these stresses with time.

00:29:03.690 --> 00:29:08.990
You’re basically reloading the original
fault zone and the surrounding area.

00:29:08.990 --> 00:29:11.050
Also producing
adjacent shadow zones.

00:29:11.050 --> 00:29:14.260
The Hector Mine earthquake
has contributed to this as well.

00:29:14.260 --> 00:29:19.000
We see a really, really tiny contribution
from the Northridge earthquake.

00:29:19.000 --> 00:29:25.720
And the next one will be the El Mayor-
Cucapah quake, which is doing its thing

00:29:25.720 --> 00:29:32.460
and adding stress to its own rupture
zone as well as adjacent areas.

00:29:33.899 --> 00:29:38.420
And so things are reaching
half a bar or greater here,

00:29:38.420 --> 00:29:43.440
which is fairly significant
in this type of study.

00:29:44.360 --> 00:29:49.950
So the Coulomb rate-state model,
just to summarize, is informed by

00:29:49.950 --> 00:29:53.740
the background seismicity rate
and the background stressing rate.

00:29:53.740 --> 00:29:58.740
The crustal stress evolution,
which we just saw in the animations.

00:29:58.740 --> 00:30:02.580
And the focal mechanisms of the –
of the quakes.

00:30:02.580 --> 00:30:05.010
And, again, we have to
draw random samples

00:30:05.010 --> 00:30:09.690
of the primary and
auxiliary plane solutions.

00:30:11.110 --> 00:30:13.940
So a few more details.

00:30:13.940 --> 00:30:18.780
So we’re looking at the
time-dependent model seismicity rate.

00:30:18.780 --> 00:30:23.149
That’s always capital R.
We’re applying spatial smoothing

00:30:23.149 --> 00:30:28.209
to the background seismicity rate
as well as the reciprocal state variable.

00:30:29.060 --> 00:30:32.140
And the controlling parameters
include the viscosity structure,

00:30:32.149 --> 00:30:36.950
the effective coefficient of friction,
and the aftershock time scale.

00:30:37.940 --> 00:30:41.139
We’re going to look at a range of
aftershock time scales, but we’re going

00:30:41.139 --> 00:30:47.339
to fix the effective coefficient of friction
at a value of 0.2 just for definiteness.

00:30:47.340 --> 00:30:51.480
Now, here’s an example of a
time series of the model

00:30:51.480 --> 00:30:55.960
seismicity rate gain
at a particular point.

00:30:55.960 --> 00:31:00.049
And this point is just off the southern
end of the Hector Mine rupture zone.

00:31:00.049 --> 00:31:06.220
And the snapshot on the left is sometime
between the Landers and Hector Mine –

00:31:06.220 --> 00:31:10.680
or, rather, Landers and
Northridge quakes.

00:31:10.680 --> 00:31:13.800
So we’re looking at the
ratio of the total predicted

00:31:13.809 --> 00:31:17.270
seismicity rate divided by
the background rate.

00:31:17.270 --> 00:31:20.400
So we’re – that’s what we call
the model seismicity rate gain.

00:31:20.400 --> 00:31:23.640
And before the Landers earthquake,
nothing has happened.

00:31:23.640 --> 00:31:27.220
That ratio is just 1. We’re in a shadow
zone of the Landers earthquake,

00:31:27.220 --> 00:31:31.320
so it goes down, and it doesn’t really
see the Northridge earthquake.

00:31:31.320 --> 00:31:36.520
You gradually recover from a stress
shadow, but it takes a very long time.

00:31:36.520 --> 00:31:38.840
At the time of the Hector Mine
earthquake, we’re off the southern end

00:31:38.850 --> 00:31:43.950
of the rupture, so we get a really big
boost in the predicted seismicity rate,

00:31:43.950 --> 00:31:48.889
and that diminishes very quickly.
And in fact, we even achieve a

00:31:48.889 --> 00:31:55.680
ratio less than 1 because the
positive kick has kind of died down,

00:31:55.680 --> 00:32:02.420
whereas the stress shadow effect
needs a much longer time to vanish.

00:32:02.420 --> 00:32:06.429
And in this and other sort of
forward models that I’m showing,

00:32:06.429 --> 00:32:12.450
I need to remind myself we’re
fixing the aftershock decay time

00:32:12.450 --> 00:32:15.690
at a value of 13 years.

00:32:18.040 --> 00:32:24.800
Okay, this and the next few slides
summarizes the average seismicity rate

00:32:24.800 --> 00:32:31.679
gain in 2-1/2-year-long periods starting
half a year after the major sources.

00:32:31.679 --> 00:32:36.700
So in addition to de-clustering,
I’m removing the first half a year

00:32:36.700 --> 00:32:43.230
of quakes in the entire area to really get
rid of this effect of near field activity and

00:32:43.230 --> 00:32:51.500
early activity that could be corrupted by
that dynamic stressing or afterslip.

00:32:51.509 --> 00:32:59.869
So the seismicity rate gain is
plotted on this logarithmic scale.

00:32:59.869 --> 00:33:04.920
Superimposed on this are the
epicenters of the quakes that actually

00:33:04.920 --> 00:33:09.720
occurred during this time period.
And visually, there’s a decent correlation

00:33:09.730 --> 00:33:14.910
between the two for this period after the
Landers and Big Bear earthquakes.

00:33:14.910 --> 00:33:19.250
And we can do the same thing for
the half-year – 2-1/2 years period

00:33:19.250 --> 00:33:25.400
after the Northridge earthquake
starting half a year after that quake.

00:33:25.400 --> 00:33:30.560
We’ve got – obviously we see still a
strong effect from the Northridge quake.

00:33:30.570 --> 00:33:34.370
We have leftover effects
from the Landers quakes.

00:33:34.370 --> 00:33:37.120
And visually, we’ve got
still some correlation

00:33:37.120 --> 00:33:40.159
with the seismicity
that occurred.

00:33:40.159 --> 00:33:44.159
The Hector Mine quake
changes the picture again.

00:33:46.120 --> 00:33:50.380
We don’t see much left from the
Landers or the Northridge quakes here.

00:33:50.380 --> 00:33:52.529
Everything is dominated by the
stress changes following the

00:33:52.529 --> 00:33:57.070
Hector Mine quake, and that, again,
is comparable with the seismicity

00:33:57.070 --> 00:33:59.380
which actually occurred
during that time period.

00:33:59.380 --> 00:34:06.059
And after the El Mayor-Cucapah quake,
we don’t have, on this scale,

00:34:06.059 --> 00:34:12.010
much left from the other source
earthquakes, but the El Mayor-Cucapah

00:34:12.010 --> 00:34:15.899
quake has taken over, and we
see activity shifting to the south.

00:34:15.899 --> 00:34:20.830
And again, more or less in
areas that the model predicts.

00:34:20.830 --> 00:34:24.350
So one way to quantify this is
just look at histograms

00:34:24.350 --> 00:34:31.440
of the rate gain at the – at the locations
of the hypocenters in that exercise.

00:34:31.440 --> 00:34:35.120
And if we carry out that exercise
using all of the post-Landers events –

00:34:35.120 --> 00:34:37.700
so I’m no longer excluding
those half-year periods.

00:34:37.700 --> 00:34:39.820
I’m looking at everything.

00:34:39.820 --> 00:34:43.319
We have quite a few things
with a rate gain less than 1,

00:34:43.319 --> 00:34:45.950
which means the model
is not doing well there.

00:34:45.950 --> 00:34:50.030
But most of the rate
gain is greater than 1.

00:34:50.030 --> 00:34:54.550
So in some sense,
the model is predicting partially

00:34:54.550 --> 00:34:57.100
where these quakes
are going to happen.

00:34:57.100 --> 00:34:59.160
The model is doing better
if we remove those half-year

00:34:59.170 --> 00:35:01.770
periods after the
major source quakes.

00:35:01.770 --> 00:35:05.850
Things are more skewed
towards the positive rate gains.

00:35:07.680 --> 00:35:09.450
So another thing we can
do is concentrate on the

00:35:09.450 --> 00:35:12.540
so-called postseismic
seismicity rate gain.

00:35:12.540 --> 00:35:16.360
And this would be the ratio
of the seismicity rate

00:35:16.360 --> 00:35:21.800
that includes coseismic and
postseismic stressing and

00:35:21.800 --> 00:35:24.200
the rate gain that includes
only coseismic stressing.

00:35:24.200 --> 00:35:29.540
So it’s an attempt to really
isolate the postseismic stresses.

00:35:29.540 --> 00:35:33.300
And it’s a subtle effect,
and that’s why it’s being plotted

00:35:33.300 --> 00:35:35.440
on a much
smaller scale.

00:35:35.440 --> 00:35:41.160
It’s more like a 5% effect
rather than a factor of 10.

00:35:41.160 --> 00:35:45.570
So we can look at the same time periods
that we looked at on the previous slides,

00:35:45.570 --> 00:35:49.790
and even plot up the seismicity,
and our eyes can tell us

00:35:49.790 --> 00:35:53.810
that we’ve got correlations.
Again, which is good.

00:35:53.810 --> 00:35:58.590
So after Landers and Big Bear,
or after Northridge, or after the

00:35:58.590 --> 00:36:04.869
Hector Mine quake – one thing
I wanted to point out is,

00:36:04.869 --> 00:36:09.000
unlike the coseismic stressing case,
where seismicity rates tend to diminish

00:36:09.000 --> 00:36:15.940
with time, the postseismic stresses are
continually adding stress to the system.

00:36:15.940 --> 00:36:20.700
And so seismicity rate is going up
when we’re considering just

00:36:20.700 --> 00:36:23.260
the postseismic stresses,
whereas they’d be going down

00:36:23.270 --> 00:36:27.130
if we’re considering
only the coseismic stresses.

00:36:27.130 --> 00:36:32.290
So things really get another kick
after the Hector Mine earthquake.

00:36:32.290 --> 00:36:35.650
And this is the time period after the
El Mayor-Cucapah quake.

00:36:35.650 --> 00:36:41.180
And a lot of the activity has shifted
to the south, but we still have sort of

00:36:41.180 --> 00:36:47.890
long-lived relaxation effects from the
Landers, Hector Mine earthquakes.

00:36:47.890 --> 00:36:51.400
And one interesting thing is that the
El Mayor-Cucapah earthquake

00:36:51.400 --> 00:36:56.280
kind of created a stress shadow zone
to its north, which wiped out

00:36:56.280 --> 00:36:59.750
a lot of the rate increases
that the Hector Mine earthquake

00:36:59.750 --> 00:37:02.130
otherwise would
have produced.

00:37:03.270 --> 00:37:10.520
And we can look at histograms
again of the seismicity rates at the –

00:37:10.520 --> 00:37:15.530
at the time and place that
these events actually occurred.

00:37:15.530 --> 00:37:19.560
And of course there are quite a few
of them which happened with

00:37:19.560 --> 00:37:23.180
a rate gain less than 1, which don’t
necessarily agree with the model,

00:37:23.180 --> 00:37:27.240
but most of them are associated
with a rate gain greater than 1.

00:37:27.240 --> 00:37:33.079
And that’s true whether you
look at all the post-Landers events

00:37:33.079 --> 00:37:38.020
or you exclude the first half year
after the major quakes.

00:37:38.020 --> 00:37:44.410
So we can quantify this even further
by using a log likelihood function.

00:37:44.410 --> 00:37:50.610
And this was first put forth,
that I’m aware of, by Ogata in 1983.

00:37:50.610 --> 00:37:54.940
And to evaluate this, we require
the model seismicity rate at

00:37:54.940 --> 00:37:58.980
catalog hypocenters and origin times.
And we also need the model

00:37:58.990 --> 00:38:02.370
seismicity rates at all points
within the volume of interest.

00:38:02.370 --> 00:38:08.280
And that’s basically why we’ve
been looking at results

00:38:08.290 --> 00:38:10.329
at a collection of
random hypocenters.

00:38:10.329 --> 00:38:13.560
I’ve used that to represent
the volume of interest.

00:38:13.560 --> 00:38:16.780
And this log likelihood function,
it’s basically the log of the

00:38:16.780 --> 00:38:20.369
probability that an observed
set of earthquakes will happen

00:38:20.369 --> 00:38:26.270
given an overall productivity
rate of earthquakes.

00:38:26.270 --> 00:38:30.400
So that’s why we have the
two terms and the definition

00:38:30.400 --> 00:38:35.880
of the log likelihood function.
And we can kind of process this further

00:38:35.880 --> 00:38:40.440
by evaluating the information gains –
so comparing two models.

00:38:40.440 --> 00:38:44.760
So we can look at the log likelihood
of a model that includes just

00:38:44.760 --> 00:38:49.490
coseismic stress steps from all of
the source earthquakes and compare that

00:38:49.490 --> 00:38:54.069
with the log likelihood of a null model
that doesn’t include any stress steps.

00:38:54.069 --> 00:38:57.040
It’s just a model of background
seismicity, essentially.

00:38:57.040 --> 00:39:03.099
And that information gain
gives us a measure, in that case,

00:39:03.099 --> 00:39:08.539
of how significant the
coseismic stress steps are.

00:39:10.650 --> 00:39:18.760
So if we look at all the post-Landers
seismicity, we can examine the

00:39:18.760 --> 00:39:24.300
coseismic rate gain as a function
of the aftershock decay time.

00:39:24.300 --> 00:39:30.810
And again, using the formula
on the previous slide,

00:39:30.810 --> 00:39:34.961
we’re comparing the coseismic –
a model with coseismic stress

00:39:34.961 --> 00:39:38.980
versus a model with basically
just background seismicity.

00:39:38.980 --> 00:39:43.020
And we’re getting very
positive information gains.

00:39:43.030 --> 00:39:50.470
This is pretty high for an information
gain due to a physical process.

00:39:50.470 --> 00:39:53.829
The postseismic rate gain –
there we’re comparing a log likelihood

00:39:53.829 --> 00:39:57.230
of a model that has coseismic
and postseismic stressing

00:39:57.230 --> 00:40:00.030
with a model that has
only coseismic stressing.

00:40:00.030 --> 00:40:03.640
And the information gain in
that case, it’s much smaller,

00:40:03.640 --> 00:40:11.320
but it’s still systemically high
at all values in the considered range

00:40:11.320 --> 00:40:14.560
of the aftershock decay time.

00:40:15.900 --> 00:40:18.080
And we can look at
these things further.

00:40:18.080 --> 00:40:22.260
If we exclude the first half year
after the major quakes,

00:40:22.260 --> 00:40:24.849
these log likelihood
values go up a little bit.

00:40:24.849 --> 00:40:26.940
This is with
all the seismicity.

00:40:26.940 --> 00:40:32.320
If you exclude half a year after the major
source quakes, they go up a little bit.

00:40:32.329 --> 00:40:37.470
Now, it may be okay to look at these
and say, well, these values are positive,

00:40:37.470 --> 00:40:41.260
so we’re doing okay.
But how significant is it?

00:40:41.260 --> 00:40:45.200
So one question that started to
trouble me was maybe the

00:40:45.200 --> 00:40:51.309
background seismicity itself would have
information gains that are just as high

00:40:51.309 --> 00:40:56.369
as what we see here because background
seismicity might lie in the lobes of

00:40:56.369 --> 00:41:00.650
stress that are predicted to be high
following the models because –

00:41:00.650 --> 00:41:07.480
following these earthquakes because the
predicted earthquake rate gains are high

00:41:07.480 --> 00:41:10.800
in the eastern California shear zone
and parts of the San Andreas and

00:41:10.800 --> 00:41:14.490
San Jacinto Faults, which have
a lot of earthquakes anyway.

00:41:14.490 --> 00:41:20.290
So I redid this exercise where
we’re essentially testing the

00:41:20.290 --> 00:41:26.720
spatial distribution of the quakes where –
going through this exercise again,

00:41:26.720 --> 00:41:30.070
we’re retaining the origin time of the
events, but we’re exchanging the

00:41:30.070 --> 00:41:35.900
location of actual quakes with randomly
chosen pre-Landers hypocenters.

00:41:35.900 --> 00:41:40.220
And we get this pattern for the coseismic
and postseismic rate gains,

00:41:40.220 --> 00:41:45.140
and you can just tell by comparing
that they’re systemically less.

00:41:45.140 --> 00:41:51.540
And we can now sort of identify
5% and 95% background levels

00:41:51.540 --> 00:41:55.900
for the coseismic rate gain
and the postseismic rate gain

00:41:55.900 --> 00:42:04.130
and superimpose that on the pattern
using the real catalog of events.

00:42:04.130 --> 00:42:09.280
So when you look at it from
this point of view,

00:42:09.280 --> 00:42:13.980
the coseismic stressing
appears highly significant.

00:42:13.980 --> 00:42:18.770
So we’re basically testing,
did the spatial pattern of seismicity

00:42:18.770 --> 00:42:24.450
shift away from background seismicity
to something that’s aligned with

00:42:24.450 --> 00:42:27.250
the stresses predicted
from our physical model?

00:42:27.250 --> 00:42:31.859
And that is very much the
case for coseismic stresses.

00:42:31.859 --> 00:42:36.100
It’s still the case for the
postseismic stresses, but now,

00:42:36.100 --> 00:42:41.200
you know, we’re not at 99.99%.
We’re more like 95%,

00:42:41.200 --> 00:42:47.620
especially for aftershock decay times
that are less than about 25 years.

00:42:47.620 --> 00:42:52.339
And we can actually turn to the
question of, what is the appropriate

00:42:52.339 --> 00:42:58.460
aftershock decay time for a
region like the Mojave Desert?

00:42:58.460 --> 00:43:02.359
So Toda and others
actually addressed this question.

00:43:02.359 --> 00:43:08.180
They looked at aftershock decay rates
after Landers and Big Bear, for example,

00:43:08.180 --> 00:43:12.900
and they could fit an [inaudible]
decay curve to that.

00:43:12.900 --> 00:43:16.059
And they defined the aftershock
decay time as the place where

00:43:16.059 --> 00:43:19.839
that decay curve would
intersect the background rate.

00:43:19.839 --> 00:43:26.170
And I need to look on the screen
for what that was – 51 years for

00:43:26.170 --> 00:43:32.470
the Landers quake, and I think it’s
seven years for the Big Bear quake.

00:43:33.160 --> 00:43:36.559
It’s a little troubling that you get
wildly different durations for the same

00:43:36.559 --> 00:43:41.650
geographic region, but that’s –
well, that’s the result that they found.

00:43:41.650 --> 00:43:46.400
This question of what’s the appropriate
aftershock decay time has been

00:43:46.400 --> 00:43:52.770
examined by Seth Stein and Mian Liu
in a paper published in 2009.

00:43:52.770 --> 00:43:57.560
And they give some examples.
So for example, for the Loma Prieta

00:43:57.560 --> 00:44:04.410
quake, the aftershock decay time
is on the order of seven years.

00:44:04.410 --> 00:44:08.119
For the Dixie Valley, Nevada, quake,
it’s on the order of 100 years.

00:44:08.119 --> 00:44:12.119
For the New Madrid Seismic Zone, they
come up with a value of 1,000 years.

00:44:12.740 --> 00:44:18.580
Although that’s questionable.
There’s a long debate over that.

00:44:18.580 --> 00:44:24.069
And especially Morgan Page and
Sue Hough have questioned that value.

00:44:24.069 --> 00:44:28.079
But at any rate, they’re noting
the different tectonic environments

00:44:28.079 --> 00:44:29.640
for these earthquakes.

00:44:29.640 --> 00:44:37.559
So the Loma Prieta quake is
in a plate – it’s a boundary fault.

00:44:37.559 --> 00:44:42.030
Whereas the Dixie Valley quake,
it’s in a plate boundary zone.

00:44:42.030 --> 00:44:46.160
And then New Madrid Seismic Zone
is in a plate interior.

00:44:46.160 --> 00:44:52.980
And they summarize the estimates
of aftershock decay time and find that

00:44:52.980 --> 00:44:58.040
there’s this whole gradation from an
intraplate zone, which has very low

00:44:58.040 --> 00:45:02.670
loading rates, to a plate boundary zone,
which has much higher loading rates.

00:45:02.670 --> 00:45:06.809
So in the Mojave Desert, where we’re
studying, we’re somewhere in this range.

00:45:06.809 --> 00:45:12.460
And they’re coming up with a value of
10 years for the Landers earthquake.

00:45:12.460 --> 00:45:19.780
So if we’re concerned – where are we
on this plot where we’re testing

00:45:19.780 --> 00:45:24.860
the spatial distribution of aftershocks
with respect to postseismic stressing?

00:45:24.860 --> 00:45:30.690
That would say that we’re somewhere
in this region, and so well above 95%.

00:45:30.690 --> 00:45:35.610
Which is reassuring, but again, it
depends on Stein and Liu’s analysis.

00:45:37.660 --> 00:45:45.160
Okay, so Joan Gomberg has thought
a lot about the different sources

00:45:45.160 --> 00:45:50.180
of stress perturbations that
can affect seismicity rates.

00:45:50.180 --> 00:45:54.670
And this is a slide from one of
her presentations looking at

00:45:54.670 --> 00:45:57.099
slowly developing
permanent load changes.

00:45:57.099 --> 00:45:59.660
And she notes, of course,
earthquake slip.

00:45:59.660 --> 00:46:03.940
There’s also afterslip
and slow slip.

00:46:03.940 --> 00:46:08.220
If she had put viscoelastic relaxation
on this slide, it would probably

00:46:08.220 --> 00:46:12.990
look essentially the same
as the slow slip curve.

00:46:12.990 --> 00:46:17.990
Things develop very slowly,
but they’re very long-lasting.

00:46:17.990 --> 00:46:21.770
But I wanted to return to the question
of the effective afterslip just to

00:46:21.770 --> 00:46:24.410
provide another example
of postseismic stresses

00:46:24.410 --> 00:46:27.380
that have a tangible
effect on seismicity rates.

00:46:27.380 --> 00:46:31.920
So we’re returning to
Camilla’s work on Parkfield afterslip

00:46:31.920 --> 00:46:43.340
in secondary triggering.
So she looked at the rate gains predicted

00:46:43.350 --> 00:46:50.430
by model coseismic stress only and also
a model of coseismic slip and afterslip.

00:46:50.430 --> 00:46:54.780
And I believe she was looking
at a time period of 250 days

00:46:54.780 --> 00:46:58.559
after the Parkfield main shock.
And just visually, you can see

00:46:58.559 --> 00:47:05.500
that there’s a better correlation
of the aftershock activity in the case

00:47:05.500 --> 00:47:11.380
that has the coseismic and
afterslip-generated stresses.

00:47:11.380 --> 00:47:15.569
And that has been quantitative
in this kind of summary slide

00:47:15.569 --> 00:47:22.329
where she isolated the information
gain due just to afterslip,

00:47:22.329 --> 00:47:25.469
and it’s on the order of 0.1.

00:47:26.440 --> 00:47:28.530
Due to secondary triggering,
it’s much higher.

00:47:28.530 --> 00:47:32.630
And if you combine the two,
it gets even higher.

00:47:32.630 --> 00:47:36.280
So that’s encouraging for being able
to come up with quantitative

00:47:36.280 --> 00:47:44.200
models of postseismic stressing.
And it was a good picture at Parkfield.

00:47:44.210 --> 00:47:49.000
Things are more complicated when you
look at the Tohoku earthquake,

00:47:49.000 --> 00:47:54.630
possibly because the models of the
afterslip may be not be so reliable.

00:47:54.630 --> 00:47:59.320
They may trade off with the
viscoelastic relaxation, in my opinion.

00:47:59.320 --> 00:48:04.740
But anyway, instead of a conclusion
slide, I wanted to finish with this.

00:48:04.741 --> 00:48:12.089
This is in the USGS fact sheet
summarizing the UCERF3 model.

00:48:12.089 --> 00:48:17.530
And although we usually see the
time-independent model from UCERF3,

00:48:17.530 --> 00:48:20.630
they also produce a
time-dependent forecast.

00:48:20.630 --> 00:48:25.450
And this summarizes the difference
between the time-dependent forecast

00:48:25.450 --> 00:48:32.020
and the time-independent forecast
in terms of which faults have higher

00:48:32.020 --> 00:48:36.280
or lower probability compared
with the time-independent forecast.

00:48:36.280 --> 00:48:42.430
So those that are colored
red have a higher probability.

00:48:42.430 --> 00:48:45.859
And those colored blue
have a lesser probability.

00:48:45.859 --> 00:48:51.200
And the main thing that went into this
map was elastic stress interaction,

00:48:51.200 --> 00:48:55.220
so taking into account, for example,
the 1906 stress shadow.

00:48:55.220 --> 00:48:59.520
So I think, in general,
incorporating physical models

00:48:59.520 --> 00:49:03.250
that have coseismic stressing
and postseismic stressing

00:49:03.250 --> 00:49:08.420
is useful for developing future
versions of this type of map.

00:49:08.420 --> 00:49:10.440
So I’ll finish there.
Thank you.

00:49:10.440 --> 00:49:16.060
[ Applause ]

00:49:17.020 --> 00:49:22.840
[ Silence ]

00:49:23.840 --> 00:49:26.160
- Questions for Fred?

00:49:27.420 --> 00:49:33.640
[ Silence ]

00:49:34.780 --> 00:49:38.940
- Your model had lower viscosity
in the San Andreas region.

00:49:38.950 --> 00:49:41.539
Did that make any
difference in your results?

00:49:41.539 --> 00:49:45.710
- It doesn’t make much difference,
but I wanted to use what I considered

00:49:45.710 --> 00:49:52.230
to be the best available model
for the viscoelastic stresses.

00:49:53.620 --> 00:50:06.880
[ Silence ]

00:50:07.900 --> 00:50:10.580
- Hi, thanks.

00:50:10.589 --> 00:50:17.650
So the aftershock decay period –
the TA – so in the rate-state model,

00:50:17.650 --> 00:50:23.550
that depends on the background
loading rate. Correct?

00:50:24.599 --> 00:50:26.939
The background stressing rate.
- Yes, it does.

00:50:26.940 --> 00:50:30.880
Oh, it depends on a number of –
well, a couple of things

00:50:30.880 --> 00:50:36.079
that are changing with time.
And so it’s a very gross simplification

00:50:36.079 --> 00:50:41.499
to just let it be constant while
everything else is changing.

00:50:41.500 --> 00:50:43.940
- Yeah. Well, yeah, that gets
to my question, actually.

00:50:43.950 --> 00:50:48.700
So I was wondering whether,
you know, your viscoelastic model

00:50:48.700 --> 00:50:54.309
could somehow just be represented as,
you know, a time-dependent loading –

00:50:54.309 --> 00:50:56.420
you know,
background loading rate.

00:50:56.420 --> 00:50:59.880
Because the – you know,
the initial jump in the seismicity rate

00:50:59.890 --> 00:51:06.760
is dominated by the static stress change.
And so couldn’t it – couldn’t the

00:51:06.760 --> 00:51:11.520
viscoelastic effects just kind of
be resulting from an apparent

00:51:11.520 --> 00:51:14.771
time-dependent loading –
background loading rate?

00:51:14.771 --> 00:51:17.811
- Well, that’s an interesting question.
Yeah, it’s – the way you’ve asked it,

00:51:17.829 --> 00:51:21.489
it seems to me it could be.
But I don’t know if theoretically

00:51:21.490 --> 00:51:27.130
it would be completely equivalent
to implementing it as a perturbation

00:51:27.130 --> 00:51:31.790
and kind of accounting for
with the rate – or with the

00:51:31.790 --> 00:51:35.490
state variable
evolution equation.

00:51:38.780 --> 00:51:42.019
Yeah, it’s really hard to tell.
- Okay.

00:51:42.019 --> 00:51:45.760
- But, yeah, there is one other thing
which sometimes the Coulomb

00:51:45.760 --> 00:51:54.420
rate-state model makes the assumption
that the background rate of seismicity

00:51:54.420 --> 00:51:58.070
jumps at the time that you
have a coseismic stress step.

00:51:58.070 --> 00:52:00.950
I have a little bit of problem with that
because I think the background rate

00:52:00.950 --> 00:52:03.760
is the background rate.
But the idea is that you’ve shortened

00:52:03.760 --> 00:52:08.869
the time to the next earthquake,
and so the background rate is going to

00:52:08.869 --> 00:52:14.549
adjust to reflect a clock advance.
So that’s – so that is one place

00:52:14.550 --> 00:52:17.510
where you could be changing
the background rate.

00:52:18.520 --> 00:52:20.380
- Okay, thank you.

00:52:21.440 --> 00:52:26.860
[ Silence ]

00:52:27.640 --> 00:52:31.780
- Yeah, nice talk, Fred.
Do you want to comment at all on –

00:52:31.790 --> 00:52:34.720
you know, is there any hope
for doing better in the future?

00:52:34.720 --> 00:52:37.630
What kinds of things are
we missing in particular?

00:52:37.630 --> 00:52:42.220
Is it mostly knowledge of the stress
state that’s on faults currently?

00:52:42.220 --> 00:52:44.600
Or are there sort of missing
pieces of the physics, you think?

00:52:44.600 --> 00:52:48.840
- Well, that’s certainly – yeah, yeah.
Initial conditions are very important.

00:52:48.840 --> 00:52:53.000
Probably the best thing we could do
would be to have a very accurate

00:52:53.000 --> 00:52:58.160
earthquake simulator, which means
not only accurate initial conditions,

00:52:58.160 --> 00:53:02.300
but enough of the physics in it.
And a lot of attention has been paid

00:53:02.309 --> 00:53:06.660
to the RSQSim earthquake
simulator by Keith Richards-Dinger

00:53:06.660 --> 00:53:11.340
and Jim Dieterich. And that does
have a lot of the physics in it.

00:53:11.340 --> 00:53:16.000
They’re missing the
viscoelastic relaxation.

00:53:16.000 --> 00:53:20.260
So maybe one day I’ll
convince them to include it.

00:53:20.260 --> 00:53:24.140
But, yeah, you know, the more that
we can add to the simulators, that’s –

00:53:24.140 --> 00:53:28.660
I think that’s a good path forward.
- Thanks.

00:53:29.780 --> 00:53:34.280
[ Silence ]

00:53:35.300 --> 00:53:38.000
- Hey, Fred.
I think Dave Sandwell,

00:53:38.010 --> 00:53:42.140
shortly after that – you know,
you put up the map of strain rates.

00:53:42.140 --> 00:53:47.440
Dave Sandwell did a comparison of,
I don’t know, 15 different people

00:53:47.440 --> 00:53:51.980
asked to do – to make a strain rate map,
and that you get 15 different results.

00:53:51.980 --> 00:53:54.420
- [laughs]
- So I’m wondering how sensitive

00:53:54.420 --> 00:54:00.040
is this to your –
our understanding of strain rate?

00:54:01.480 --> 00:54:07.980
- It’s not – yeah, I think the results
that I – that I pushed through the

00:54:07.980 --> 00:54:11.559
whole Coulomb rate-state analysis
aren’t going to be too sensitive

00:54:11.559 --> 00:54:15.130
to the background
stressing rates.

00:54:15.780 --> 00:54:21.500
I compared with the Hunter-Smith
and Sandwell plot because it agreed

00:54:21.520 --> 00:54:24.260
with mine, but there – of course,
there were a few that didn’t agree,

00:54:24.260 --> 00:54:26.530
but I’m not going to show you those.
[laughter]

00:54:26.530 --> 00:54:29.520
- Okay.
- But, you know, if you’re looking at

00:54:29.530 --> 00:54:35.441
seismicity rate gain, for example,
then the background stressing rate

00:54:35.441 --> 00:54:38.441
almost drops out. Not completely.
There’s still some coupling with it.

00:54:38.441 --> 00:54:43.681
But it almost drops out, so you can have
kind of a second-order error in that.

00:54:43.681 --> 00:54:45.301
- Okay.

00:54:47.280 --> 00:54:53.280
[ Silence ]

00:54:54.340 --> 00:54:58.460
- Okay. Thanks, everybody.
We will meet for lunch outside –

00:54:58.460 --> 00:55:03.950
or, well, inside the front doors of
building 3 in, let’s say, 10 minutes.

00:55:03.950 --> 00:55:05.910
And let’s thank
our speaker again.

00:55:05.910 --> 00:55:10.470
[ Applause ]

00:55:10.470 --> 00:55:31.930
[ Silence ]