WEBVTT
Kind: captions
Language: en-US

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Morning, everyone.

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Thank you very much for
the invitation to be here today.

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I’m going to be talking about
a recent project on Bay Area

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site effects from kappa and
site spectral parameters.

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And this work is mainly from
UO undergrad Elias King and

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graduate students Tara Nye
and Alexis Klimasewski

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with collaborators for various parts
of it being Annemarie Baltay,

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Joe Fletcher,
and Jack Boatwright.

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What is kappa?

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Kappa is the decay of high –
at high frequencies of

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the acceleration spectrum,
which you can see in this

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cartoon here as the orange line,
the decay being the teal line.

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It could also be fit with this form,
which shows the acceleration spectrum

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as a function of a-naught and some
exponential decay with kappa.

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And this is usually fit after some
frequency, f-e, which is above f-max,

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that you can see labeled
on this diagram.

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Why do we care about kappa, and what
does it have to do with site effects?

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We think of kappa as likely
as an effect of site conditions.

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And it’s been used in estimating
ground motions since the ’90s.

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It’s also been found to
correlate with PGA as of late.

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That can be seen in the top right here
in this figure, showing kappa

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as a function of PGA for sites in
New Zealand where you can see that

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higher values of kappa tend to
correlate with lower values of PGA.

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And this makes sense because kappa
is a decay at high frequencies,

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so faster decay at the high frequencies
seems to make sense that produces

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lower PGA, as we think of PGA
as coming from this range.

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Klimasewski et al. 2019
found the same thing.

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Here, the axes are flipped.
Kappa is on the X axis, and the

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Y axis is plotting a ground motion
model site residual for predicting PGA.

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And what we find is that higher values
of kappa tend to correlate with lower

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site residuals, meaning correlate
with lower PGA than expected.

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And recently, ground motion
models have started to include kappa

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as a site term, such as
Laurendeau et al. 2013.

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And there are other applications.
So, for example, these could be used

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in nonergodic spatially varying models,
one of which is shown on the right,

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where each panel shows the map
variability of coefficients for

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a ground motion model
from Landwehr et al. 2016.

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Kappa could be included as
an additional constraint to these.

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They’re also often – it’s often also
featured in simulations as a site effect.

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And so these simulations
could directly include

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measured values of
kappa for the region.

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However, we don’t actually
have any measured values

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or computed values of
kappa in the Bay Area.

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And it could be useful for a lot
of things, so, as I mentioned,

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to adapt the existing ground
motion models or for future spatially

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varying ground motion models.
But, because it’s also a site condition

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in the shallow surface and has a form
similar to t-star and seismic attenuation,

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it could perhaps be used to inform
updates to community velocity models

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in the shallow subsurface
and simulations.

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And it could also be used
as a constraint in a variety of

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different seismological
studies in the area.

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It’s typically computed
in a few different ways.

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The first, from Anderson and
Hough, was to fit this A-naught

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times e to the minus pi of kappa
form to the acceleration spectra

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of any single recording
past some frequency.

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But it was determined that these
values changed as a function

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of distance away form a site.
And so another way of doing this

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that’s common is computing kappa for
a number of different records and then

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representing kappa as a function
of a kappa at the particular site,

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which is considered to be a site kappa,
as well as how that varies with distance

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away from the site, which is more
representative of the path attenuation.

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And then some have also
simultaneously solved for source and

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site, such as Anderson and Humphreys.
And you can see that here where this

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is the original form from Anderson
and Hough in natural log space.

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And this is the source
that’s being solved for.

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We’ve taken a slightly
different approach.

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This is showing Klimasewski et al.
2019, where we first take a data set

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of a number of different records
from any earthquake, i, and station, j,

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and we decompose that record
into its contributions from the event

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and the site for all
given events and sites.

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That’s in the cartoon here on the right,
where the record is in blue,

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and any particular event in the
data set here is represented in green,

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and the site is in red.
When we run this inversion,

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the resulting event and site spectra
that come out are unconstrained,

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as there is a degree of freedom.
And Andrews 1986, who started

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this method – or, who used
this method commonly,

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constrained the inversion by taking
a reference site and dividing

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all the other sites and multiplying
events by that reference value.

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This, however, yields
one of the sites ineffective.

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And so, to preserve all of them,
what we have done is constrain

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the inversion with
a theoretical Brune spectra.

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So we’ve found an event in the
data set that looks to have the

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shape closest to a Brune spectra –
and these are the velocity spectra,

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remember,
in this cartoon.

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And we then compute what its
theoretical spectra would be for

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a stress drop of 5 megapascals.
The constraint function is then the

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difference between these two spectra.
So between the unconstrained single –

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that single event and its
theoretical Brune spectra.

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This constraint, which you can see
in the arrows here, is then applied

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to all other events and sites as a
multiplication or division factor.

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And, because it doesn’t change
the shape of the spectra,

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it really only shifts
them up or down.

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And then finally, we obtain kappa
by fitting this traditional form

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to each site’s respective
acceleration spectra,

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and that’s how we –
how we get it for each site.

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We applied this in southern California
when developing the method, so you

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can see some examples from that here,
where here, the two horizontal

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components of the waveform,
the record spectra with their

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uncertainties in the spectral
computation process with mtspec,

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the event and site spectra,
and you can see that the event

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and site multiplied back so that
we can get some level of misfit.

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We have uncertainty in many
different levels in this process,

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so we propagate them all through,
and that allows us to obtain

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an uncertainty of
kappa in the end.

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And we were fortunate in that
we did this is an area that

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many other studies have focused on.
So many of our sites had kappa values

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computed from
several different studies.

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We compared our values to those
studies, and we found that they’re

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actually pretty similar
in the region.

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So we take this as a good sign that
the method is robust, at least here.

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And lastly, one of the benefits of
this method is that we do preserve

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the entire site spectra.
So, in addition to obtaining kappa,

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we can obtain spectral levels,
or the average of the spectra in

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given frequency bins, and these
can be really useful to compare

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to different intensity measures.
Kappa, of course, is a function of

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decay at high frequencies, but because
we are preserving the spectra for all of

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these sites, would could, for example,
determine if these lower frequencies

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correlate with different
intensity measures.

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And that’s shown here from the
study where we compared it to

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a PGA ground motion model residual.
And you can see that the lower

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frequencies do not correlate,
however the spectral level

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at the higher frequencies
does seem to correlate.

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In the Bay Area, where we’re
doing this, we were using data

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from 30 broadband
stations on three networks.

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You can see that on the map over
here where the stations are triangles

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that are colored by the number
of events that they record.

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And we have almost 4,000 earthquakes
of magnitude 2.5 and greater.

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And those are the circles on this
map colored by the number of stations

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that record them to show
the robustness of the data set.

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We split it into several different
data sets based on signal-to-noise

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ratio cutoffs. So, for example, if we
leave it at a signal clearance ratio of 3,

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we have about 20,000 records or more.
And, if we cut it – if we only

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keep events that have a
signal-to-noise ratio of 5 or greater,

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then we still have nearly
15,000 records.

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One thing that we do in this process
that we didn’t do in the original study

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is look at how different
parameters affect the inversion,

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and do they have a large
impact on the kappa values.

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So we look at not just signal-to-noise
ratio, but we also look at the number

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of bins that we use in
the frequency inversion.

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The spectral decomposition
is done in each frequency bin.

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And so, by performing it on, say,
150 bins as opposed to 75, we will

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get a spectra that is less smooth and
has more features to it – or variability.

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And then finally, in the original study,
we used a record length of 60 seconds

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after the S wave arrival.
And so, in this one,

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we tried a more
traditional value at 15.

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On the bottom here, you can see
the results for these six different

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runs for three different stations.
For example, the purple line is

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for Run 6, which is 15 seconds,
150 bins, SNR 5.

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And you can see that it is less
smooth than some of the other –

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the other runs or some
of the other parameters.

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And it does show more features.
And so, in the end, we use this

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run as our preferred, or final, model to
make sure we have the best quality

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data set and we are using these –
using this S wave cut length of 15.

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And then lastly, for some of the results,
here’s our map of kappa values.

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The warm colors are
higher kappa values,

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and the more green colors
are lower kappa values.

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And there’s a lot of variability
in the area, but there are some

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features that pop out. So, for example,
we see relatively high values in

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the Sacramento-San Joaquin
River Delta over here.

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But we see slightly lower
values towards the coast.

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Down here by the San Andreas Fault,
we see fairly low values of kappa

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in the Gabilan Range
west of the San Andreas Fault.

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And we see higher values at
a station just to its east,

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suggesting that perhaps this fault
is creating sufficient difference

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in geology from west to east that
is reflected in the site conditions.

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One of the caveats,
or a downside here,

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is that our kappa values
are a little too high.

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A typical reference kappa value
is somewhere around 0.04 seconds

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for a hard rock site, whereas,
soft rock is generally considered

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to be something like 0.02 seconds.
But what you can see here is that

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our kappa values are a little higher
than that, so more like 0.06, even 0.08.

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And we think that this is
possibly because there’s

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a path component
included in there.

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Our spectral decomposition process
does not directly invert for the path.

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It just inverts for
the event and the site.

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And this data set does have
some long distances in it –

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source-to-site distances, so we
think what may be happening

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is the path attenuation is
being wrapped into the site term.

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And the way that we are
going to try and fix this,

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or see if this makes a difference,
is by correcting each record

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by some average Q value
before inverting.

00:11:36.560 --> 00:11:39.440
We have models of
seismic attenuation here.

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This one on the right is showing
Q-p from Eberhart-Phillips 2016.

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But we also have Q-s for the region.
So, for every record in our data set,

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we will find the average Q value
and then divide it out from the record

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at the same time as correcting for
distance for geometric spreading.

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Lastly, one thing to show is that
many studies have looked for

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correlations between Vs30 and kappa.
And this is perhaps useful in going back

00:12:09.920 --> 00:12:13.040
and forth between ground motion
models if you have a measured value

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of one but not the other. And so we
look at that for our data set, where

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kappa is plotted on the X axis for every
site, and its Vs30 is on the Y axis.

00:12:23.760 --> 00:12:27.520
We don’t see a significant correlation
here that’s statistically significant.

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In fact, none at all,
seemingly.

00:12:30.320 --> 00:12:32.880
And this could be
for a couple reasons.

00:12:32.880 --> 00:12:36.720
It could be that our kappa values
are not representative of the site

00:12:36.720 --> 00:12:39.816
because we need to remove
the path attenuation first.

00:12:39.840 --> 00:12:43.920
It could be that perhaps the Vs30
values are – some of these are

00:12:43.920 --> 00:12:48.240
proxy values and not measured.
And the measured values may

00:12:48.240 --> 00:12:51.680
lead to a better correlation.
Or it could just be that this correlation

00:12:51.680 --> 00:12:55.840
is not strong here, and it is
just not a good correlation.

00:12:55.840 --> 00:12:59.416
And other studies have seen
a very weak correlation

00:12:59.440 --> 00:13:03.016
but nothing particularly
strong in the past.

00:13:03.040 --> 00:13:05.520
And where to from here?
What are some different things

00:13:05.520 --> 00:13:08.160
that we are planning on
doing or could do with this?

00:13:08.160 --> 00:13:13.256
Well, first, correcting for Q is one
big thing, and that is nearly complete.

00:13:13.280 --> 00:13:17.200
Another thing to do here is to
compare the observed ground motion

00:13:17.200 --> 00:13:20.800
model residuals – or, observe
ground motion model residuals

00:13:20.800 --> 00:13:23.256
in the region to
the kappa values.

00:13:23.280 --> 00:13:28.080
Meaning, for the kappa values
that we – that we get, how do those

00:13:28.080 --> 00:13:31.520
compare to recorded ground
motions at those stations?

00:13:31.520 --> 00:13:34.480
Does kappa actually seem to
correlate with lower PGA?

00:13:34.480 --> 00:13:36.560
What about other
intensity measures,

00:13:36.560 --> 00:13:40.560
such as spectral accelerations or
even Fourier amplitude spectra?

00:13:40.560 --> 00:13:44.880
And lastly, for the spectral levels that
we get from the same-site spectra,

00:13:44.880 --> 00:13:49.256
how do those compare to,
say, the lower frequencies

00:13:49.280 --> 00:13:51.496
of recorded
ground motion?

00:13:51.520 --> 00:13:55.200
And then last, one of the goals
for this region is to obtain

00:13:55.200 --> 00:13:59.120
a spatially interpolated map of kappa,
similar to what’s shown here

00:13:59.120 --> 00:14:03.496
on the right from Van Houtte et al.
2018 in New Zealand.

00:14:03.520 --> 00:14:09.200
This model contains not just kappa –
the variability of kappa in the region,

00:14:09.200 --> 00:14:13.896
but it also shows what the standard
deviation is in each location.

00:14:13.920 --> 00:14:17.680
With our stations and our values,
we aim to create the same kind of

00:14:17.680 --> 00:14:20.960
[inaudible] map, however,
at the moment, there aren’t

00:14:20.960 --> 00:14:24.000
quite enough stations or there
isn’t quite enough density to

00:14:24.000 --> 00:14:27.360
really come up with a robust map.
And so we would like to include

00:14:27.360 --> 00:14:31.440
more strong motion stations
in our inversion so that we

00:14:31.440 --> 00:14:33.896
have a little more
data to obtain this.

00:14:33.920 --> 00:14:35.760
That’s all that I have.
Thanks for your attention,

00:14:35.760 --> 00:14:39.120
and I’m looking forward
to questions at the end.