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[Silence]

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Welcome to the
weekly seminar, everyone.

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We have Grace Parker,
our Mendenhall Fellow –

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one of our new Mendenhall
Fellows – here speaking today.

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Just quickly, next week’s
seminar person is a lawyer.

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His name is Mark White, and
he specializes in building law.

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I think it’s going to be a really
different seminar for us,

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but really interesting, so I encourage
you all to come to that one.

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And Annemarie is going to
give the introduction.

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- Thanks, Sara.
All right. So today it’s my pleasure

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to introduce Grace Parker, who is
a Mendenhall here with us.

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She did her undergrad at UCLA in the
Earth and Planetary Science Department

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and – as well as her Ph.D. in civil
and environmental engineering,

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working on NGA subduction,
that she’ll talk about today,

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and also the Vs30 relations for
central and eastern U.S. that are –

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were presented as recommendations,
that were adopted, I think,

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into the hazard map.
So Grace originally hails from

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the East Bay, so maybe she prefers
northern California, but unfortunately,

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got messed up by the
shutdown when she started.

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So we’re really excited that she’s here.
Take it away.

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- Thanks, Annemarie.

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Today I’m going to be talking about
NGA subduction ground motion models

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for interface and interslab events,
with some additional focus on

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how we regionalize
the models for Cascadia.

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And this work was done as part of
my Ph.D. at UCLA in collaboration

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with my adviser, Jonathan Stewart,
as well as Behzad Hassani and

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Gail Atkinson at the
University of Western Ontario

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and Dave Boore.

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So I’m first going to give a brief
introduction to engineering

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seismic demand parameters,
ground motion models,

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and the NGA subduction project.
Then I’m going to go through an

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overview of our model developer
team’s approach to model development.

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Then I’m going to talk about
the fitting of individual model terms

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and what the
data looks like.

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Then I’m going to have a few slides on
regionalization of the Cascadia model,

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in particular focusing on
the site term component.

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And lastly, I’ll have a handful of
slides on my current work at the

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USGS related to earthquake
early warning.

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So engineers needs some quantification
of seismic demand for the design

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ground motion of buildings,
liquefaction triggering analysis,

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or seismic slope stability, as examples.
And sometimes they use the entire

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ground motion time history,
shown here, as an example,

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from the 1994 Northridge earthquake as
recorded at Santa Monica City Hall –

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acceleration, velocity, and
displacement as a function of time.

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But oftentimes, engineers want
a more concise representation

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of the information contained
in an entire time series.

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And that’s done through what are
called intensity measures, or IMs,

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that are partial representations of
either shaking intensity of frequency

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content contained in the time series.
And examples of that include PGA

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and PGV, which are pretty intuitive.
Just the peak acceleration and

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velocity of the time series.
But also include things like

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Arias intensity, shaking duration,
and pseudo-spectral acceleration,

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or PSA, which is very commonly
used when designing buildings.

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And that’s slightly less
intuitive to understand.

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It is meant to represent how
shaking affects structures.

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And what is done is the time –
acceleration time series

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of an earthquake is used
to excite a single degree of freedom

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damped harmonic oscillator.

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And the displacement of
that oscillator is computed.

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The maximum displacement
is then found – S-d –

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and multiplied by the natural
frequency of the oscillator, omega.

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So this oscillator has some
natural frequency, and that’s

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used to compute PSA.
You can do that for a variety

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of oscillator frequencies,
and when those are plotted

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as a function of oscillator frequency,
that’s a response spectra.

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And so ground motion models are then
used to compute response spectra and

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PGA and PGV, for example, for a given
scenario earthquake for a building.

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And those are developed
mostly empirically,

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but sometimes
using simulations.

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And this is a generalized form of
a ground motion model equation.

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So you have mu-i-j, which is
the median intensity measure.

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So it can be PGA, PGV, PSA,
duration – any of the above

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from earthquake i
recorded at station j.

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And that is taken as the
sum of three terms, usually.

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One that is a
function of the source.

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So it represents behavior in the
ground motion due to

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earthquake properties, like magnitude,
depth, focal mechanism.

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The second is the path term.
So that represents the attenuation

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of the ground motion as it
travels from the source to site,

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and it’s usually conditioned
on a source-to-site distance metric.

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And lastly, the site term.
And that’s a function that represents the

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change in ground motion due to the soil
conditions in the upper-most crust.

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That’s typically – contains both a linear
or site amplification component,

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also sometimes called Vs30 scaling,
and a nonlinear component.

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And that linear component is due to
impedance contrasts in the

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upper-most crust. So here you see shear
wave velocity as a function of depth.

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And as a vertically propagating shear
wave, travels up towards the surface.

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The shear wave velocity
often decreases.

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And due to conservation of energy,
the amplitude of the ground shaking

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increases. So that’s site
amplification captured by this term.

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So now getting to NGA subduction,
NGA, or next-generation attenuation

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subduction, is a multi-year,
multi-disciplinary project organized

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by the Pacific Earthquake
Engineering Research Center – PEER.

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And it had two goals.
To assemble a global database of

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ground motions from subduction zones,
including time series, intensity

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measures, and the associated metadata
with the event and the sites.

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And the second goal was to develop
a suite of ground motion models

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using that database, for both global
events and considering regionalization.

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And this is a figure from Stern,
2002, showing global convergent plate

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boundaries. And NGA
subduction considered data

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from seven regions here –
Cascadia, Alaska, Japan,

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Taiwan, Central America and Mexico,
South America, and New Zealand.

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And I’ve tried to keep the color coding
consistent throughout this presentation,

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so when I show data from Cascadia,
it will always be pink.

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Japan will always
be red, et cetera.

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This is a breakdown of the NGA
subduction database by region for the

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number of records here on the left.
So you can see that Japan

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really dominates the recordings.
We have about – over 50%

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of our recordings from Japan.
Another quarter are from Taiwan,

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and the rest of the five regions
make up the remaining quarter.

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This is the regional variation –
or, the regional breakdown of events.

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So South America has
the most events and stations.

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Japan just has a very
dense seismic network.

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So we get a lot of
recordings from Japan.

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And, before I get into
model development,

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I just want to briefly show this slide.
I think that this is very familiar

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to everyone in this room.
But this is a schematic cross-section

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of a subduction zone, and typically
there are two types of events –

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interface events that occur at the
interface between the two plates –

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the subducting slab and
the overriding lithosphere.

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And, in-slab, or interslab, events that
occur within the subducting slab,

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and they tend to be sub-horizontal
to sub-vertical normal faults.

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And, due to the different source
properties of these two events,

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and the different paths that the seismic
waves sample from the two events,

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we observe pretty significant differences
in the ground motion properties between

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the two. So we developed the two
models – one for interface,

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and one for slab, separately.
They have very similar

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functional forms, but most of
the model coefficients are

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different between the
two event types.

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So now I’m going to give an overview
of our model development approach.

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This is the same GMPE generalized
equation that I showed earlier.

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And it can sometimes be difficult to
separate the ground motion into three

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components representing the source,
path, and site in a way that’s physically

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realistic. There are lots of
tradeoffs between these.

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And this is the way that
we’ve approached doing that.

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We first started with the site term.
And we corrected all of the data in our –

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that we were considering for model
development to a single reference site

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condition of 760 meters per second
Vs30 using an NGA-West2 Seyhan

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and Stewart 2014 site amplification
model that was developed primarily

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using data from California
and some data from Japan.

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This is a schematic of what it looks
like in shear wave velocity space.

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We know that this is probably not
capturing the true site amplification

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in our data, but it’s our best first guess.
Once the data is all at a single site

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condition, it’s kind of on even footing.
We can then look at the event and path

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components of the model and go back
for site amplification at the end.

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So, in the end, we do develop an
NGA subduction-specific site

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amplification model, but we start by
assuming Seyhan and Stewart 2014.

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We then look at the path
component of the model.

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Because of that complex subduction
zone geometry, we expect it to be one of

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the more complex terms of the model,
so we wanted to start with that.

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This is a schematic of log of
PSA and log of rupture distance.

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This is our
model functional form.

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It has three components, the first of
which is the near-source saturation.

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So this is where the model
bends over at close distances.

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And this is a geometrical effect.
So, as the source-to-site distance

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between your recording and your
fault plane decreases, only the

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portions of the fault nearest to the
site dominate the ground motion.

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So the fault looks smaller or farther
away, and you get this saturation.

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The second component of the path
model is the geometrical spreading.

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This is linear in log of distance space,
and it is also a geometrical effect.

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It’s the attenuation due to a seismic
wave as it’s generated along a fault

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plane, propagating from a point along a
larger and larger spherical wave front.

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Conservation of energy means
the amplitude will decrease.

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In an elastic homogeneous half-space,
this should decay as 1 over R.

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But of course, Earth is
not homogeneous.

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And we do see some
variation from that value.

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The last term in the path model is
the anelastic attenuation, and this is –

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this causes the curvature
in log of distance space.

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And that’s the per-cycle
damping of seismic waves

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as they propagate
through the crust.

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So it’s strongest for a shorter period and
weaker for longer period seismic waves.

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And, because it’s a crustal property,
we expect it to vary regionally.

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And we’ve tried to capture
that in our model.

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Lastly, we look at the
event or source term.

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And, to do this, we use a
two-step regression approach.

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The term was coined by
Joyner and Boore in 1981.

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And when we fit our path model,
we allow each event to have

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a unique constant. And that is a way
to account for magnitude scaling

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as well as event-to-event variability
when we’re fitting the path model.

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Once we fit the path model,
we can the look at those constants

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as a function of magnitude
and fit our magnitude scaling.

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And this is what it looks like in log
of ground motion magnitude space,

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where we have a parabolic function
at small to moderate magnitudes

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up to a breakpoint, M-b, and then the
magnitude scaling is linear beyond that.

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And we do observe
some saturation there.

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Let’s see. And, like I said,
after we fit these two terms,

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we then go back for this.

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And I wanted to show a slide
in a little more detail about how we

00:14:19.420 --> 00:14:25.380
fit those individual event constants
during our path model fitting.

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We use a mixed effects analysis,
which allows you to have both

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fixed effects and random effects.
That’s why it’s called mixed effects.

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And regression procedures often
assume that each data point that

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you’re considering is independent, but
when you’re dealing with earthquake

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data, this is not the case. Recordings
from one event will be correlated.

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And mixed effects is
a way to account for that.

00:14:56.510 --> 00:15:02.260
So it allows you to fit a model
with coefficients that are the same

00:15:02.260 --> 00:15:06.020
for all data points. So this is a
schematic from Al Atik et al., 2010.

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So, in this example, this is
ground motion and distance.

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The path model is the same for all of
these data points, but each event has a

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separate constant. So it’s shifted up or
shifted down relative to the path model.

00:15:25.760 --> 00:15:30.080
So those are the random effects.
And those can be combined and nested.

00:15:30.080 --> 00:15:34.040
We can consider regional variation
in a very similar way to this.

00:15:34.040 --> 00:15:37.400
So when we fit our path model,
we don’t have a magnitude scaling term,

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and that magnitude scaling is
captured in these event terms.

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Now I’m going to go through each
model term and show you the data

00:15:51.110 --> 00:15:57.670
and how we fit the model, the first of
which is the near-source saturation term,

00:15:57.670 --> 00:16:00.610
which is one component
of the path model.

00:16:00.610 --> 00:16:05.740
And this ended up being really
hard to constrain using data

00:16:05.740 --> 00:16:10.440
that we had from subduction zones.
Because there’s just not a lot of data

00:16:10.440 --> 00:16:14.860
recorded at these close distances.
Slab events are too deep.

00:16:14.860 --> 00:16:18.800
And interface events
occur offshore usually.

00:16:18.810 --> 00:16:23.850
And this is shown – this is an example
of that, where this is data from one

00:16:23.850 --> 00:16:33.150
event in – sorry – one event in
Japan, where two models are fit.

00:16:33.150 --> 00:16:38.030
They have the same form except for
the near-source saturation distance.

00:16:38.030 --> 00:16:40.790
One is 10,
and one is 30.

00:16:40.790 --> 00:16:48.210
And they fit the data with
the same level of goodness of fit.

00:16:48.210 --> 00:16:51.770
So we really just weren’t able
to constrain that empirically.

00:16:51.770 --> 00:16:54.780
And what we did instead was
look to existing models

00:16:54.780 --> 00:16:58.450
developed for other regions.
For example, Gail Atkinson has

00:16:58.450 --> 00:17:01.800
done a lot of work on this
near-source saturation term using

00:17:01.800 --> 00:17:07.560
events from active
crustal regions like California.

00:17:07.560 --> 00:17:13.020
And we also ran finite fault EXSIM
simulations to try to constrain this.

00:17:14.480 --> 00:17:19.500
So when we ran those simulations,
we got data that looked a lot like this,

00:17:19.509 --> 00:17:23.110
but we were able to control the station
locations that we could populate

00:17:23.110 --> 00:17:30.999
this portion of the distance space.
And we fit h values, or values at which

00:17:30.999 --> 00:17:34.950
the saturation begins, and looked
at those as a function of magnitude.

00:17:34.950 --> 00:17:38.980
And that’s what this looks like,
where you have h, or the distance at

00:17:38.980 --> 00:17:47.149
which saturation occurs, which ranges
from 5 kilometers up to about 35 here

00:17:47.149 --> 00:17:52.700
at the max, as a function of magnitude.
This black line and the black points are

00:17:52.700 --> 00:17:56.580
from work that Gail Atkinson has done,
where each of these points are an

00:17:56.580 --> 00:18:00.990
estimate from an earthquake that
occurred in a active crustal region.

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And these colorful points are values
from our EXSIM simulations.

00:18:05.700 --> 00:18:10.820
So what we did was constrain the
model based on empirical data

00:18:10.820 --> 00:18:14.450
at very small magnitudes and then
used EXSIM simulations to

00:18:14.450 --> 00:18:20.780
constrain it at larger magnitudes,
shown in this pink line.

00:18:24.070 --> 00:18:26.840
The next term in the path model
is the geometrical spreading.

00:18:26.840 --> 00:18:32.029
It has this functional form.
It’s a multiplier on the log of R.

00:18:32.029 --> 00:18:36.340
C-1 represents the value in
Fourier amplitude space, where it’s

00:18:36.340 --> 00:18:40.820
magnitude- and period-independent.
So there’s just one value.

00:18:40.820 --> 00:18:44.330
When you’re in response spectra space,
that introduces an oscillator period

00:18:44.330 --> 00:18:50.660
and magnitude dependence, so b-3
and b-4 are meant to capture that.

00:18:52.480 --> 00:18:58.340
And we had some trouble constraining
this magnitude dependence empirically.

00:18:58.350 --> 00:19:01.340
There are multiple components
in the model that depend on magnitude,

00:19:01.340 --> 00:19:05.259
and they all trade off.
So what we did was constrain b-3 and

00:19:05.260 --> 00:19:11.280
b-4 from some simulations by Hassani
and Atkinson, and we fit c-1 to the data.

00:19:12.780 --> 00:19:16.580
We also wanted to avoid any tradeoffs
with the anelastic attenuation, so we fit

00:19:16.580 --> 00:19:21.330
c-1 to data at less than 100 kilometers.
This is before that curvature really

00:19:21.330 --> 00:19:25.860
starts to occur that is meant to be
captured by the anelastic attenuation.

00:19:26.920 --> 00:19:30.060
And, as you can see, we have different
values for the two event types.

00:19:30.070 --> 00:19:35.230
So slab data is shown in blue.
Interface data is shown in red.

00:19:35.230 --> 00:19:38.540
And there is a pretty significant
difference in the slope there.

00:19:39.830 --> 00:19:43.100
The last term in the path model
is the anelastic attenuation.

00:19:43.110 --> 00:19:47.389
This is a multiplier on
the linear or arithmetic R.

00:19:47.389 --> 00:19:49.990
It looks curved in
log distance space.

00:19:49.990 --> 00:19:55.380
And, like I mentioned, this is
regionally dependent in our model.

00:19:58.450 --> 00:20:01.620
The next term we considered
is magnitude scaling.

00:20:01.639 --> 00:20:05.340
So here’s a plot of all those
event terms determined relative

00:20:05.340 --> 00:20:08.490
to the path model as
a function of magnitude.

00:20:08.490 --> 00:20:11.070
And you can see, as you might
expect, they’re increasing.

00:20:11.070 --> 00:20:13.519
So the ground motion is
getting bigger with magnitude.

00:20:13.519 --> 00:20:15.049
The different colors
represent different regions.

00:20:15.049 --> 00:20:20.420
So you can see we have some
Cascadia slab events shown in pink.

00:20:20.420 --> 00:20:24.460
A cluster of events from
South America in green here.

00:20:25.560 --> 00:20:34.049
And so on. The function that we fit
is piece-wise, where the term at

00:20:34.049 --> 00:20:38.179
small to intermediate magnitudes
is parabolic up to a breakpoint.

00:20:40.280 --> 00:20:42.700
And then it’s
linear beyond that.

00:20:42.710 --> 00:20:46.750
This breakpoint is constrained using
work that Ralph Archuleta and

00:20:46.750 --> 00:20:52.210
Chen Ji have done based on
geometry of the subduction zone.

00:20:52.210 --> 00:20:57.800
So they’ve estimated
the magnitude of saturation

00:20:57.800 --> 00:21:01.000
based on the
geometry of the slab.

00:21:01.010 --> 00:21:04.460
And that’s therefore different
for different subduction zones.

00:21:04.460 --> 00:21:07.640
So that’s another regionalized
component of the model.

00:21:10.400 --> 00:21:13.720
Okay, the last portion
is the site amplification.

00:21:13.730 --> 00:21:16.950
Like I mentioned,
the site amplification term

00:21:16.950 --> 00:21:20.889
has a linear and
nonlinear component.

00:21:20.889 --> 00:21:24.619
And because we don’t really expect this
to depend on source properties, we’ve

00:21:24.619 --> 00:21:30.210
combined the data from the interface
interslab events to set this term.

00:21:30.210 --> 00:21:33.289
This is what the linear component
looks like. It’s a function of Vs30,

00:21:33.289 --> 00:21:37.499
or the time-averaged shear wave
velocity in the upper 30 meters.

00:21:37.499 --> 00:21:43.200
So, if the Vs30 is lower,
the site is softer, and we expect

00:21:43.200 --> 00:21:47.790
more site amplification.
If the Vs30 is higher, we expect

00:21:47.790 --> 00:21:50.980
the site to be stiffer and
have less site amplification.

00:21:52.169 --> 00:21:56.320
And that’s what this looks like
in Vs30 space for two different

00:21:56.330 --> 00:22:00.480
oscillator periods.
There’s pretty big variability here,

00:22:00.480 --> 00:22:05.649
but there is a pretty
significant trend with Vs30.

00:22:05.649 --> 00:22:08.659
And you can see that
a little more clearly here.

00:22:08.659 --> 00:22:13.190
This is a plot of the slope of that
line with Vs30 as a function of PSA

00:22:13.190 --> 00:22:19.320
oscillator period for different regions.
So the SS14 NGA-West2 model that

00:22:19.320 --> 00:22:23.320
I was referencing earlier,
the slope is shown here.

00:22:23.320 --> 00:22:27.460
Our NGA subduction slope
is shown in the solid dots.

00:22:27.470 --> 00:22:33.179
And the Parker et al. 2019 model
for central and eastern North America

00:22:33.179 --> 00:22:38.549
is shown in the diamonds.
So you can see that, in our database,

00:22:38.549 --> 00:22:43.409
Vs30 has more predictive power than
in the central and eastern U.S.,

00:22:43.409 --> 00:22:46.549
but less predictive power than
in a place like California,

00:22:46.549 --> 00:22:51.580
and that’s due to correlations with
deeper crustal velocity structure.

00:22:51.580 --> 00:22:56.679
California tends to have a pretty –
a gradient with depth – sorry –

00:22:56.679 --> 00:23:04.220
a gradient with depth, such that Vs30 is
highly correlated with deeper structure.

00:23:04.220 --> 00:23:06.160
And places like central and
eastern North America tend to

00:23:06.160 --> 00:23:08.720
have pretty strong
impedance contrasts,

00:23:08.720 --> 00:23:14.020
therefore Vs30 is not very correlated
with deep velocity structure.

00:23:17.809 --> 00:23:21.940
And this model – the model that
we developed is pretty dominated

00:23:21.940 --> 00:23:24.960
by Japan, so Japan is somewhere
in between those two.

00:23:25.640 --> 00:23:30.580
I don’t have too many details on the
nonlinear site amplification component,

00:23:30.590 --> 00:23:36.500
but I did want to show this figure.
So this is the linear condition.

00:23:36.500 --> 00:23:43.879
So if the shaking at a site is weak,
you get amplification all the way

00:23:43.879 --> 00:23:48.269
through low Vs30 values.
But the stronger the shaking at your site,

00:23:48.269 --> 00:23:52.309
the soft soil causes
more and more damping.

00:23:52.309 --> 00:23:54.490
And that’s captured by a
nonlinear term shown here

00:23:54.490 --> 00:23:58.129
for different input shaking values.
So the stronger the shaking –

00:23:58.129 --> 00:24:02.220
for example, this is for 1 g,
the more damping you get.

00:24:05.850 --> 00:24:10.080
And we – unlike some of
the models in NGA-West2,

00:24:10.080 --> 00:24:12.690
we developed this
term empirically.

00:24:12.690 --> 00:24:19.180
So there are no simulations used to
develop this portion of the model.

00:24:22.369 --> 00:24:27.499
And lastly, I haven’t mentioned yet,
we’ve considered basin effects

00:24:27.500 --> 00:24:31.120
or sediment depth
correction to our model.

00:24:32.020 --> 00:24:36.420
And when we develop our Vs30 scaling,
we aren’t considering sediment depth.

00:24:36.429 --> 00:24:40.419
But there is some correlation
between those two values.

00:24:40.419 --> 00:24:46.850
And that means that, for an average
Vs30, our model implies some implicit

00:24:46.850 --> 00:24:53.489
average Z-2.5, or sediment depth,
which we parameterize using Z-2.5,

00:24:53.489 --> 00:25:00.759
which is the depth to the 2,500 meter
per second shear wave velocity horizon.

00:25:00.760 --> 00:25:04.680
So it represents the
depth to hard bedrock.

00:25:06.680 --> 00:25:11.140
And in order to account for that
implicit value and that correlation,

00:25:11.149 --> 00:25:13.999
we condition the model
on something called delta Z-2.5.

00:25:13.999 --> 00:25:15.950
So we first examine
that correlation.

00:25:15.950 --> 00:25:19.580
And, as you can see,
it’s a weak correlation.

00:25:21.200 --> 00:25:25.120
But it does exist. So this is data
from Japan where we’ve plotted the

00:25:25.129 --> 00:25:34.760
sediment depth on the Y axis and the
Vs30 on the X axis and fit a curve here.

00:25:34.760 --> 00:25:37.210
This really isn’t supposed
to represent physical reality.

00:25:37.210 --> 00:25:40.960
I wouldn’t recommend using
this to estimate values of Z-2.5.

00:25:40.960 --> 00:25:46.820
It’s purely a model-centering tool
to account for any correlations that

00:25:46.820 --> 00:25:52.799
might exist in the Vs30 scaling term.
So we developed this average

00:25:52.799 --> 00:25:58.389
Z-2.5 value, and then we can
compute the difference between the

00:25:58.389 --> 00:26:05.590
actual Z-2.5 for a site and the average.
And if that difference is positive,

00:26:05.590 --> 00:26:12.539
the site has a shallower sediment
depth than average, and we might

00:26:12.539 --> 00:26:18.070
expect some de-amplification
relative to Vs30 scaling.

00:26:18.070 --> 00:26:26.309
If that delta is in the other direction,
so the site is deeper than the average,

00:26:26.309 --> 00:26:29.580
we might expect some
additional amplification.

00:26:32.660 --> 00:26:36.450
So I mentioned that was for Japan.
This is the same correlation in Cascadia.

00:26:36.450 --> 00:26:41.400
There’s very little data here, but
this is just a model-centering tool.

00:26:42.549 --> 00:26:45.900
So that’s what this
basin amplification looks like.

00:26:45.909 --> 00:26:49.309
So this is the delta Z-2.5.
If it’s positive, you’re deeper than

00:26:49.309 --> 00:26:52.600
average, and you might
have some amplification.

00:26:52.600 --> 00:26:55.340
If it’s negative, you’re shallower
than average, and you might have

00:26:55.340 --> 00:26:58.869
some de-amplification
shown here for Japan.

00:26:58.869 --> 00:27:03.290
And because we expect these basin
structures to be unique, we developed

00:27:03.290 --> 00:27:07.040
these two models separately, one
for Cascadia, and one for Japan.

00:27:10.940 --> 00:27:15.299
Now I’m going to talk about model
regionalization, and in particular,

00:27:15.299 --> 00:27:18.179
with respect to Cascadia.
So there are multiple components of

00:27:18.179 --> 00:27:22.359
this model that are regionalized, and
I think I’ve touched on most of them.

00:27:22.359 --> 00:27:25.900
The anelastic attenuation, or
per-cycle damping, is regionalized.

00:27:25.900 --> 00:27:29.399
The magnitude scaling breakpoint.
The overall constant value,

00:27:29.399 --> 00:27:33.419
or model amplitude, that shifts the
model up and down over all magnitudes

00:27:33.420 --> 00:27:38.520
and distances is regionalized.
And the site amplification term.

00:27:40.240 --> 00:27:43.509
This is the data that we used to
develop the model, and it gives you

00:27:43.509 --> 00:27:47.399
a sense of the regional breakdown.
So what’s controlling the

00:27:47.399 --> 00:27:53.059
regionalization for interface and slab.
And you can see that, in Cascadia,

00:27:53.059 --> 00:27:57.399
we don’t have really any data
in the magnitude range of interest

00:27:57.400 --> 00:27:59.920
for interface events.

00:28:00.980 --> 00:28:05.960
And that’s a problem if you want to
develop a regionalized Cascadia model.

00:28:05.970 --> 00:28:09.869
So what we recommend doing here
is using a global constant that was

00:28:09.869 --> 00:28:13.590
developed using all of this data
as well as a global anelastic

00:28:13.590 --> 00:28:19.080
attenuation coefficient.
But because these two terms are

00:28:19.080 --> 00:28:23.720
developed – the breakpoint on
geometry and the site amplification

00:28:23.720 --> 00:28:26.309
on the combined interface
and slab data – we do have

00:28:26.309 --> 00:28:29.440
a regionalized value
for Cascadia here.

00:28:30.620 --> 00:28:35.700
On the other hand, we do have some
data in Cascadia for slab events,

00:28:35.700 --> 00:28:37.970
the most significant of which,
or the biggest of which,

00:28:37.970 --> 00:28:42.200
was Nisqually, 6.8,
shown right here.

00:28:42.200 --> 00:28:49.759
But we observe that this Cascadia data
has significantly lower amplitudes

00:28:49.759 --> 00:28:52.240
of ground motion relative to
other regions for the same

00:28:52.240 --> 00:28:55.780
magnitude and distance range.
And therefore, we don’t want to

00:28:55.780 --> 00:28:59.659
recommend an empirical
Cascadia-specific constant that

00:28:59.659 --> 00:29:03.200
produces really low ground motions.
Instead, we recommend to use

00:29:03.200 --> 00:29:09.859
the global constant and then
Cascadia-specific attenuation

00:29:09.860 --> 00:29:13.120
breakpoint and site
amplification terms.

00:29:13.120 --> 00:29:17.980
And I’m briefly going to show you the
Cascadia-specific site amplification.

00:29:19.540 --> 00:29:23.279
So this is the same global
model that I showed earlier.

00:29:23.279 --> 00:29:28.519
And here is the Cascadia
data highlighted in pink.

00:29:28.519 --> 00:29:31.200
So you can see we have a
decent number of stations

00:29:31.200 --> 00:29:34.760
in Cascadia to develop a
site amplification model.

00:29:36.980 --> 00:29:42.480
Here it is plotted alone with the
global model still shown in solid black,

00:29:42.480 --> 00:29:47.340
and the dashed line shows
our regional recommendation.

00:29:47.340 --> 00:29:51.039
So the Vs30 scaling is
slightly weaker in Cascadia

00:29:51.040 --> 00:29:55.539
than it is from –
on average globally.

00:29:57.180 --> 00:30:00.340
And that’s also shown here.
So this is the same plot of that slope,

00:30:00.340 --> 00:30:06.119
and you can see Cascadia is added.
So it’s – the slope is steeper than in

00:30:06.120 --> 00:30:13.020
central/eastern North America, but, for
the most part, shallower than globally.

00:30:14.680 --> 00:30:18.280
One more thing we considered was
a further regionalization

00:30:18.289 --> 00:30:22.749
of the Cascadia basin terms.
So there are multiple basins in the

00:30:22.749 --> 00:30:27.200
Pacific Northwest that populate our
database, including the Georgia,

00:30:27.200 --> 00:30:30.100
Everett, Seattle, Tacoma,
Portland, Tualatin,

00:30:30.100 --> 00:30:33.500
and North Willamette
Valley – or, basins.

00:30:35.280 --> 00:30:39.820
And so the model I showed earlier
used data from all of these basins,

00:30:39.880 --> 00:30:42.900
or anywhere that has
a sediment depth estimate.

00:30:42.909 --> 00:30:47.789
But we do expect the amplification to
be very specific to each structure due to

00:30:47.789 --> 00:30:52.520
the unique geometry and tectonic
mechanisms that control the basins.

00:30:53.450 --> 00:30:57.860
So one of the things we were wondering
going into this project is, can we

00:30:57.860 --> 00:31:03.820
develop basin terms for specific
structures or groups of structures?

00:31:05.789 --> 00:31:10.200
And the answer is, we don’t really have
enough data to truly flush this out.

00:31:10.210 --> 00:31:15.679
So here is our model using
data from all those basins.

00:31:15.679 --> 00:31:19.710
For the most part, we don’t have
enough sites in each of them.

00:31:19.710 --> 00:31:26.190
But we do have a decent number
of recordings in the Seattle Basin,

00:31:26.190 --> 00:31:29.610
shown here in blue.
So we’re in the process of developing,

00:31:29.610 --> 00:31:35.180
perhaps, an additional
regionalization for the Seattle Basin.

00:31:40.540 --> 00:31:45.220
So, in conclusion, we’re developing
two ground motion models for

00:31:45.220 --> 00:31:48.059
subduction zones – one for
interface and slab.

00:31:48.059 --> 00:31:51.820
And the models truly are
semi-empirical, so multiple elements

00:31:51.820 --> 00:31:57.600
are constrained by simulations
in geometry in addition to data.

00:31:57.600 --> 00:32:02.600
Multiple model terms are
regionalized, including the amplitude,

00:32:02.600 --> 00:32:07.130
the anelastic attenuation,
the breakpoint, and the site term.

00:32:07.130 --> 00:32:11.110
For Cascadia interface events,
we are recommending the use of

00:32:11.110 --> 00:32:14.109
the global constant and
anelastic attenuation term.

00:32:14.109 --> 00:32:15.799
And for slab events, we’re
recommending the use of the

00:32:15.799 --> 00:32:19.820
global constant. The rest of
the terms can be regionalized.

00:32:19.820 --> 00:32:23.059
And for forward use in regions
not considered, we recommend

00:32:23.059 --> 00:32:26.809
using a range of epistemic
uncertainty on the coefficients

00:32:26.809 --> 00:32:31.540
that captures, at the least,
the regional variation observed.

00:32:33.460 --> 00:32:38.500
And I also have now
a few slides on my work

00:32:38.500 --> 00:32:42.120
at the USGS related
to earthquake early warning.

00:32:44.380 --> 00:32:50.620
So this is a schematic showing the
earthquake early warning process,

00:32:50.620 --> 00:32:56.320
where, once a earthquake
is detected, we use a sensor network

00:32:56.320 --> 00:33:00.280
to determine the magnitude
and location of the event.

00:33:01.020 --> 00:33:04.320
And, once we have that,
we can use ground motion models

00:33:04.330 --> 00:33:09.309
to estimate the shaking at distributed
locations around a region and send out

00:33:09.309 --> 00:33:14.340
alerts that an earthquake is
occurring and to expect shaking.

00:33:17.020 --> 00:33:21.379
So, like I mentioned, ground motion
models are used to translate that

00:33:21.379 --> 00:33:26.169
information about the source,
path, and site into shaking measures –

00:33:26.169 --> 00:33:30.110
so PGA and PGV in
the case of ShakeAlert.

00:33:30.110 --> 00:33:35.900
And then, GMICEs are used to convert
that shaking into seismic intensity.

00:33:36.830 --> 00:33:40.240
And those intensity predictions
guide the zone of warning.

00:33:40.259 --> 00:33:44.250
But there are large uncertainties
in ground motion models,

00:33:44.250 --> 00:33:49.269
as I’m sure you saw in the variability
in the some of the plots I showed.

00:33:49.269 --> 00:33:53.119
And those uncertainties
propagate into the alerts.

00:33:53.119 --> 00:33:56.879
So this is a figure from a recent paper
by Minson et al. that shows,

00:33:56.879 --> 00:34:02.749
for different alerting thresholds –
this is shaking – the portion of

00:34:02.749 --> 00:34:08.950
correct alerts can increase
dramatically if you reduce

00:34:08.950 --> 00:34:12.760
the uncertainty, or sigma,
or your ground motion model.

00:34:15.360 --> 00:34:21.240
And one of the ways to do that is to start
considering partially nonergodic ground

00:34:21.240 --> 00:34:29.460
motion models. And I showed this slide
at the recent ShakeAlert workshop.

00:34:29.460 --> 00:34:32.399
But there’s a spectrum of ground
motion models that exist –

00:34:32.400 --> 00:34:35.460
some that are completely ergodic.
So what that means is they

00:34:35.460 --> 00:34:39.000
consider data from
all regions together.

00:34:39.010 --> 00:34:41.950
They assume that there are no
differences in ground motion properties

00:34:41.950 --> 00:34:46.260
between California and Japan,
Pacific Northwest, et cetera.

00:34:46.260 --> 00:34:50.940
And, as you might expect, those
models have the largest variability.

00:34:50.940 --> 00:34:54.800
On the opposite side, you can
have a fully nonergodic model.

00:34:54.800 --> 00:35:00.319
So that means the model is event-
specific, path-specific, and site-specific.

00:35:00.319 --> 00:35:02.589
And that has the
smallest variability.

00:35:02.589 --> 00:35:08.089
And there exists options along
this spectrum, so you could

00:35:08.089 --> 00:35:10.630
have different ground motion
models for different regions.

00:35:10.630 --> 00:35:13.970
So, for example,
NGA subduction is doing this.

00:35:13.970 --> 00:35:19.079
You can have models that account
for one of these repeatable effects,

00:35:19.079 --> 00:35:24.839
or two of these repeatable effects.
Currently, ShakeAlert uses ground

00:35:24.839 --> 00:35:29.990
motion models that are completely
ergodic for the Pacific Northwest and

00:35:29.990 --> 00:35:35.470
part of California, and then
a regional model – Boatwright et al. –

00:35:35.470 --> 00:35:38.960
for, I think,
southern California.

00:35:41.460 --> 00:35:47.800
But is there a way to shift this down the
spectrum towards fully nonergodic?

00:35:50.480 --> 00:35:53.520
And the other factor that comes
into play here is timeliness.

00:35:53.520 --> 00:35:57.380
So, of course, the timeliness
of the alert is important.

00:35:57.380 --> 00:36:00.701
And you can correct for an
event-specific bias in the

00:36:00.701 --> 00:36:08.260
ground motion model.
So, in other words, this term here.

00:36:08.260 --> 00:36:13.740
But, in ground motion model space,
that would be done with PGA,

00:36:13.750 --> 00:36:17.300
and you would need to wait for
the peak S wave energy to do that.

00:36:17.300 --> 00:36:20.280
And that, I think,
just would take too long.

00:36:21.660 --> 00:36:27.440
But we can know information
about site-specific site

00:36:27.440 --> 00:36:31.540
amplification before
an event happens.

00:36:33.490 --> 00:36:36.260
In other words, we can account
for nonergodic site response.

00:36:36.260 --> 00:36:42.170
And this is a example from
Stewart et al. 2014 showing,

00:36:42.170 --> 00:36:49.340
as a function of PSA oscillator period,
the ergodic NGA-West2 SS14 –

00:36:49.340 --> 00:36:53.470
Seyhan and Stewart 2014 –
site amplification prediction,

00:36:53.470 --> 00:36:58.309
and then the actual measured
site amplification recorded

00:36:58.309 --> 00:37:02.119
at Obregon Park in Los Angeles.
So you can see that, in some cases,

00:37:02.119 --> 00:37:05.099
there can be a pretty
significant difference between

00:37:05.100 --> 00:37:08.660
a model and the actual
values for a single site.

00:37:11.440 --> 00:37:16.660
So there are multiple ways that you can
compute this, including simulations,

00:37:16.660 --> 00:37:19.650
one-dimensional ground response
analysis, for example, using deep soil.

00:37:19.650 --> 00:37:25.859
Or, like in this figure, using empirical
analysis of seismic recordings.

00:37:25.859 --> 00:37:29.920
And that could potentially
push you farther down the

00:37:29.920 --> 00:37:33.280
spectrum towards a site-specific
ground motion model.

00:37:34.140 --> 00:37:38.640
There are multiple ways
that you could approach this.

00:37:38.650 --> 00:37:41.990
Many ways to look at empirical site
response exist, including a reference

00:37:41.990 --> 00:37:47.730
site approach or standard spectral ratio,
where site amplification is computed

00:37:47.730 --> 00:37:52.360
as the ratio of two nearby sites –
one on rock, and one on soil.

00:37:53.220 --> 00:37:56.930
And this method assumes that
the differences in path effects

00:37:56.930 --> 00:38:00.280
are negligible if the
sites are close enough.

00:38:00.800 --> 00:38:04.200
But it can be hard to find
a suitable reference site

00:38:04.200 --> 00:38:06.780
that’s close enough
to your site of interest.

00:38:06.780 --> 00:38:09.580
There’s also a generalized inversion
technique where you can invert

00:38:09.589 --> 00:38:15.319
for the source spectra and the site
spectra using earthquake data.

00:38:15.319 --> 00:38:21.510
And there’s also a non-reference site
approach, which is a residuals analysis

00:38:21.510 --> 00:38:25.359
using a ground motion model.
So you can take the amplification

00:38:25.359 --> 00:38:30.780
as the data minus the model
condition at a – for a rock site.

00:38:30.780 --> 00:38:35.280
And that’s pretty commonly employed
in ground motion model development.

00:38:35.280 --> 00:38:40.640
However, all of these methods
are based on seismic recordings.

00:38:40.640 --> 00:38:44.440
And therefore, you can only
estimate your site-specific

00:38:44.440 --> 00:38:47.840
site response at
a recording station.

00:38:48.340 --> 00:38:51.599
But, for ShakeAlert purposes,
we’re interested in shaking

00:38:51.600 --> 00:38:56.280
at a specific user location or
dispersed locations across a region.

00:38:57.250 --> 00:39:02.560
So you could use spatial
interpolation to create some

00:39:02.569 --> 00:39:08.369
gridded map at locations between
seismic recording stations.

00:39:08.369 --> 00:39:14.380
And this might be easier in areas
where you have dense networks

00:39:14.380 --> 00:39:17.180
and more difficult in
areas where you don’t.

00:39:17.180 --> 00:39:23.800
So, in particular, what I’m interested in
is, how can prior or outside information

00:39:23.800 --> 00:39:28.270
help constrain the spatial correlation
of this computed site response.

00:39:28.270 --> 00:39:34.260
And some of the things we are starting
to look at are geologic conditions,

00:39:34.260 --> 00:39:38.369
sediment depth models,
and then dominant site frequencies

00:39:38.369 --> 00:39:41.089
from horizontal to
vertical spectral ratios

00:39:41.089 --> 00:39:44.960
from both microtremors
and earthquakes.

00:39:47.380 --> 00:39:50.480
And with that,
I’d like to say thank you,

00:39:50.480 --> 00:39:55.480
and I’m happy to take any
questions on either part of the talk.

00:39:55.480 --> 00:40:00.160
[Applause]

00:40:00.860 --> 00:40:02.360
- That was a great talk.
Thanks, Grace.

00:40:02.360 --> 00:40:05.100
Who has a question
for Grace?

00:40:08.820 --> 00:40:11.260
- Okay, since I have a microphone,
I’ll ask a question.

00:40:11.260 --> 00:40:12.680
- Mm-hmm.

00:40:12.680 --> 00:40:15.240
- When you – when you have –
with your magnitude scaling, you have

00:40:15.240 --> 00:40:18.630
that corner – the magnitude corner?
- Yep.

00:40:18.630 --> 00:40:22.910
- And you were putting both types
of earthquakes together, right,

00:40:22.910 --> 00:40:27.099
the interface and the slab events?
Or did you have separate corners?

00:40:27.100 --> 00:40:29.180
- They’re separate.
- Okay, great.

00:40:29.720 --> 00:40:30.720
- Yeah.

00:40:32.300 --> 00:40:32.800
Yeah.

00:40:32.800 --> 00:40:34.550
- Yeah. Because obviously,
there’s different geometries,

00:40:34.550 --> 00:40:36.760
so there’s going to be
different limitations and …

00:40:36.760 --> 00:40:38.200
- Yep.
- … what the scaling of

00:40:38.200 --> 00:40:40.930
those could be. Okay.
- Yeah. So the slab breakpoint

00:40:40.930 --> 00:40:44.150
is constrained by some work that
Archuleta and Ji have done,

00:40:44.150 --> 00:40:47.349
and I think that’s published as a
conference paper at the moment.

00:40:47.349 --> 00:40:52.160
And then the interface breakpoints
are based on work that

00:40:52.160 --> 00:40:57.480
Ken Campbell has done,
and that paper is still in review.

00:40:57.480 --> 00:40:59.680
- Okay. Great. Thank you.

00:41:01.400 --> 00:41:03.680
[Silence]

00:41:04.180 --> 00:41:10.560
- All right. So since Jeanne already
brought this up, so the – particularly

00:41:10.560 --> 00:41:14.560
for Cascadia, that’s not constrained
by any of the data. Is that correct?

00:41:14.579 --> 00:41:18.109
- No. This value is not constrained
by data for any region.

00:41:18.109 --> 00:41:21.279
- Oh, for any region. Okay.
- It’s really just looking at –

00:41:21.279 --> 00:41:28.660
so magnitude saturation is geometrical,
and one of the mechanisms that causes it

00:41:28.660 --> 00:41:33.539
is when you have a rupture propagating,
and it hits some end of the seismogenic

00:41:33.539 --> 00:41:37.210
zone down-dip, and then
only propagates along strike.

00:41:37.210 --> 00:41:41.510
So your site doesn’t see that.
So there should be – if you assume

00:41:41.510 --> 00:41:48.950
an aspect ratio, basically, once you
hit that depth, you can compute

00:41:48.950 --> 00:41:52.510
a magnitude associated with it.
And that’s what Ralph

00:41:52.510 --> 00:41:53.510
and Chen have done.

00:41:53.510 --> 00:41:55.280
- Okay. So, yeah, I don’t want to
quiz you on what Ralph did.

00:41:55.280 --> 00:41:56.960
But that’s generally
your understanding of …

00:41:56.960 --> 00:41:59.920
- That’s generally my understanding.
- So then I guess another question

00:41:59.920 --> 00:42:03.329
related to the model development is,
is it necessary to put that in there?

00:42:03.329 --> 00:42:07.851
Or could you – why do you have a
linear portion above that instead of just

00:42:07.860 --> 00:42:12.500
having it totally smooth through there?
Is that just GMPE model …

00:42:12.500 --> 00:42:14.840
- Convention. Yeah.
- Convention, yeah.

00:42:14.840 --> 00:42:18.900
- That’s – I mean, yes, you could
have a parabolic – I think we wanted to

00:42:18.910 --> 00:42:24.480
make sure we were enforcing saturation.
And that’s an easy way to do that

00:42:24.480 --> 00:42:26.359
because you have direct control
over that part of the model.

00:42:26.359 --> 00:42:31.109
But I agree, you could do that using
just a continuous parabolic function.

00:42:31.109 --> 00:42:34.070
- Okay. And, sorry,
a third question related to this.

00:42:34.070 --> 00:42:40.120
This is just showing two seconds, but
I’m assuming that linear portion is very

00:42:40.120 --> 00:42:43.260
different for the higher frequencies?
- Yeah.

00:42:45.820 --> 00:42:48.880
- Grace, thanks.
I was – so you have slab

00:42:48.890 --> 00:42:50.480
and interface event, but …
- Mm-hmm.

00:42:50.480 --> 00:42:54.430
- … do you make any distinction
about events that are on transform –

00:42:54.430 --> 00:42:57.960
or, fracture zones that
separate plates, for example?

00:42:57.960 --> 00:43:05.400
Like, in Cascadia, that’s some of
the highest seismicity rates are on the –

00:43:05.400 --> 00:43:09.460
you know, those faults.
So do you just ignore those events?

00:43:09.460 --> 00:43:11.500
Or do you consider them?

00:43:12.709 --> 00:43:15.039
- Can you clarify what you mean?

00:43:15.039 --> 00:43:17.800
Which types of events?
So transform …

00:43:17.800 --> 00:43:21.380
- So, like, in Cascadia, there’s the
Juan de Fuca Plate and the Gorda Plate,

00:43:21.380 --> 00:43:23.140
and they’re separated by those …
- Ah.

00:43:23.140 --> 00:43:25.520
- And there’s lots of
seismicity on both of them.

00:43:25.520 --> 00:43:29.100
- Okay. Yeah. No, we don’t.
And now that you mention it,

00:43:29.100 --> 00:43:32.800
that’s probably something
we should consider or look at.

00:43:32.809 --> 00:43:35.400
- Are those lumped
into the interface events?

00:43:35.400 --> 00:43:37.300
Or you just …

00:43:38.440 --> 00:43:40.320
- I would have to look.
- Oh, okay.

00:43:40.320 --> 00:43:41.420
- Yeah.

00:43:41.420 --> 00:43:45.120
- I’m just asking because I think there’s
some recent work that shows fairly

00:43:45.120 --> 00:43:48.200
substantial differences in source
properties on those faults.

00:43:48.200 --> 00:43:50.780
- Yeah. That doesn’t surprise me.
- Okay. [laughs]

00:43:50.780 --> 00:43:52.840
- Now that you
mention it, yeah.

00:43:57.140 --> 00:43:59.800
Yeah. I wonder if that’s one of
the reasons why we’re seeing

00:43:59.800 --> 00:44:03.620
such a difference in the
amplitude from Cascadia events.

00:44:03.620 --> 00:44:06.020
I will definitely
look at that.

00:44:07.820 --> 00:44:13.660
- Yeah, Grace. A lot happened
in a hurry here for this plot.

00:44:14.280 --> 00:44:19.400
So I’ll go back to a basic question.
Is there any discernable difference

00:44:19.400 --> 00:44:27.269
in the source terms for the interslab
events versus the interface events?

00:44:27.269 --> 00:44:33.119
- Yes. So this – the slab events,
which is shown here, tend to

00:44:33.119 --> 00:44:38.819
have a steeper magnitude
scaling than interface events.

00:44:38.820 --> 00:44:43.979
The functional form is the same,
but the slope changes.

00:44:44.820 --> 00:44:49.100
- Okay. And so that difference
increases with magnitude, then.

00:44:49.100 --> 00:44:50.040
- Yes.

00:44:50.040 --> 00:44:51.040
- Okay.

00:44:52.640 --> 00:44:57.599
And, with respect to the Los Angeles
Basin, and the work you’ve done with

00:44:57.599 --> 00:45:07.549
site effects or gridding the whole basin
to help reduce site effect uncertainty,

00:45:07.549 --> 00:45:16.349
if you were to make a GMPE solely
from Los Angeles Basin data,

00:45:16.349 --> 00:45:21.069
and compare that to NGA-West2,
do you think there would be

00:45:21.069 --> 00:45:26.180
a substantial difference?
Or, put another way, is looking at

00:45:26.180 --> 00:45:31.180
the path effects in the Los Angeles
Basin alone, would that help you

00:45:31.180 --> 00:45:40.220
reduce – help you reduce …
- The variability?

00:45:40.220 --> 00:45:45.580
- Yeah. Help you reduce the
epistemic uncertainty by having

00:45:45.580 --> 00:45:51.960
a region-specific GMPE?

00:45:54.640 --> 00:45:56.520
- It’s possible.

00:45:56.520 --> 00:46:01.579
I think if you really want to
consider path-specific effects,

00:46:01.579 --> 00:46:08.460
you’d need to probably break it down
into even smaller spatial chunks.

00:46:08.460 --> 00:46:16.859
So some recent work has been done
on fitting a path model where each –

00:46:16.859 --> 00:46:22.079
they break California down into cells.
Like, a kilometer – I don’t remember

00:46:22.079 --> 00:46:26.010
the exact spacing – a kilometer,
10-kilometer cells, and each cell

00:46:26.010 --> 00:46:30.890
is allowed a different
slope with distance.

00:46:30.890 --> 00:46:36.740
So that way you can truly capture how
your path varies as a function of space.

00:46:39.960 --> 00:46:41.700
Because I …
- But those are ground

00:46:41.700 --> 00:46:44.210
motion simulations, right?
- No. It’s empirical.

00:46:44.210 --> 00:46:47.490
- No.
- It’s work done by Nico Kuehn.

00:46:47.490 --> 00:46:50.440
He’s a postdoc –
either a researcher at PEER.

00:46:52.420 --> 00:46:57.500
- But doesn’t your data set for each
and every path become pretty thin?

00:46:57.510 --> 00:47:05.400
- Yeah, so he uses a Bayesian inference.
So in locations where there’s no data,

00:47:05.400 --> 00:47:10.130
it defaults to the average model.
And then, in cells where you have

00:47:10.130 --> 00:47:14.320
lots of data, or more data,
you get some variation from that.

00:47:15.650 --> 00:47:18.640
- And what would the
average model be, then?

00:47:18.640 --> 00:47:22.000
- Based on California as a whole.
- Okay. California as a whole.

00:47:22.000 --> 00:47:24.280
- Yeah.
- Okay, thanks.

00:47:26.500 --> 00:47:30.000
[Silence]

00:47:30.340 --> 00:47:32.380
- Any other questions?

00:47:33.640 --> 00:47:35.720
Great. Well, let’s all
thank Grace again.

00:47:35.720 --> 00:47:40.460
[Applause]

00:47:40.460 --> 00:47:43.960
We’ll now be taking Grace
out to lunch, as is customary.

00:47:43.960 --> 00:47:46.599
For those of you who want to join us,
please come up to the front,

00:47:46.600 --> 00:47:50.540
and we’ll be leaving straight from
here to our lunch place. Thanks.

00:47:50.540 --> 00:48:03.160
[Silence]