WEBVTT
Kind: captions
Language: en

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[ Silence ]

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Welcome, everyone.

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I think we’re going to
get started here.

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One quick announcement
for next week.

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Same time, same place –
10:30 on Wednesday in this room.

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We’ll have Khalid Mosalam
from UC-Berkeley giving a talk

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on Hazard Analysis: Seismologists
Building the Foundation for

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Performance-Based
Earthquake Engineering.

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And now to introduce today’s
speaker, we have Tom Holzer.

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- Thanks. I’m delighted
to introduce Jon Stewart today.

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It’s traditional for the Joyner lecturer
to say a few words about Bill Joyner.

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Jon had, I thought, some
really nice reflections on Bill,

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so I won’t steal Jon’s thunder,
but I will say a few words about

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the Joyner lecture for those of you
who are not familiar with it.

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Jon is the 13th Joyner lecturer.
And it was established by friends

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and colleagues of Bill
after he passed away in 2001.

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And the endowment is at SSA.

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And as far as I know,
it continues to grow.

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Without much solicitation,
people are still donating to it,

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which is a real tribute to Bill
and the impact he had.

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Now for a few
words about Jon.

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John is one of the leading
earthquake geotechnical engineers

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in the – in the U.S.
So he’s – and he’s had a big impact,

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actually, on a broad range of topics,
including site response.

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He’s one of the busiest people I know,
and I just assume that you must either

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not sleep or have a twin
brother named Jon. [chuckles]

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He’s chairman of civil
engineering at UCLA.

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He’s been an editor of several
journals and did a good enough job

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that he got called out of
retirement once to handle

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one of the more controversial topics
in geotechnical engineering.

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And he’s just been a
very productive researcher.

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He’s received quite a few
accolades for it.

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And there’s one I don’t think
you even know you got.

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Recently I was at a symposium to
honor Ed Idriss up at UC-Davis.

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And the seismologist with
one name – Norm –

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was parsing uncertainty,
as he usually does in his talks.

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And when he got to ergodic uncertainty,
he just turns to the audience and says,

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well, you need to
listen to Jon Stewart’s talk.

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So Jon?
Ergodic uncertainty.

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I see your title is up there,
so I won’t repeat.

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- All right. Thank you.

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[loud static]

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Was that me?
[loud static]

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- I’m going to turn this off.
[loud static]

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- I’m hoping that will stop
as soon as I stop moving that box.

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All right.

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Thank you very much for the kind
introduction, for having me her today.

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I don’t know if I should stand up here to
look taller or stand down here. [laughs]

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So I just want to initially
thank EERI and SSA

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for awarding me the Joyner lecture,
which is a great honor.

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I will have more to say about that
in just a moment, as Tom alluded to.

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Prediction – they’re doing
hazard analysis.

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And they are often viewing
that process as a black box.

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And the reason for that is that
hazard analysis consists of

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source modeling and
ground motion modeling.

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Now, the source modeling is
often predetermined, more or less,

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by experts – many of them in the
USGS – in products like UCERF3.

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Ground motion models –
kind of the same thing.

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Project like NGA comes out
with a series of models.

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Pretty much
everybody adopts them.

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So once you’ve got the source model
determined, the ground motion models

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determined, you just put in your
site coordinate, and you’re done.

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And that is basically
a black box to most engineers

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who are actually
using these tools.

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So basically, then,
the ground motion is a given.

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And you can’t do
a whole lot about it.

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But those ground motion ordinates
are extremely important.

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And small changes in those ordinates
can actually make a pretty big difference

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in whether you choose to retrofit
a building or you don’t.

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And if you are retrofitting,
how costly that’s going to be.

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So given that reality,
what do engineers do?

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Well, we come up with
all kinds of ways to

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try to change the ground
motions after the fact, right?

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So we use things like
conditional mean spectra

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to drop off the hazard away
from a conditioning period.

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Or we do soil structure interaction
in order to reduce ground motions,

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particularly at high frequencies,
which has some cost benefit.

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My message today is that the hazard is
not fixed, even if you are going with

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a pre-selected source model and a pre-
selected set of ground motion models.

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Because the site amplification
does not have to be the function

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that is in the
ground motion models.

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One can do something
that is site-specific.

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And that’s really the key point that
I’m going to try to develop today.

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And more often than not,
when you do that,

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you will see the
ground motions come down.

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And it will be coming down oftentimes
by factors considerably bigger

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than the other ones I mentioned –
conditional means spectra

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or soil structure interaction –
for a lot of applications.

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Okay. So I do want to
comment on Bill Joyner.

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This is a picture of Bill that I
got from Dave Boore, who I’ve

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worked a lot with in recent years.
So thank you, Dave.

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You’re out here somewhere, right?
There you are. [laughs]

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So Dave, of course, worked
closely with Bill for many years.

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Produced a huge number of
seminal contributions to our field.

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Now, my own introduction to
Bill occurred on this committee.

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The Building Seismic Safety Council
site and geotechnical committee.

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I was getting involved,
starting in 1997, to do some work

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on soil structure interaction
for that committee.

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Now, to understand the context here,
you have to realize, in 1997,

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I was 29 years old.

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I was a brand-new assistant
professor at UCLA.

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Nobody knew
who I was.

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I was just volunteering to see if I could
do something for this committee.

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Bill, on the other hand,
was famous – [chuckles]

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very famous in the
earthquake community.

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Kind of an elder statesman.

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So we were at completely
opposite ends of the spectrum.

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Yet, when I came into this committee
as a volunteer, he welcomed me.

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He was humble.
He was encouraging of me to

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invest time in this sort of public service
and to try to make a difference.

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And, you know, he couldn’t have been
nicer for a new person coming in.

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And I think his attitude in dealing
with me, you know, has had an impact

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on me continuing in that kind of
work in the years since then.

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Unfortunately, he died not too long
after I got started with this effort.

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And I never really
had a chance to work

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on a substantive technical
level with Bill.

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So my impressions are more just,
you know, working with him

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in the context of this committee.
And that was very positive.

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I have come to know Bill’s
work quite a bit over the years

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through reading his
many papers and reports.

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And of course his contributions are
enormous on a wide spectrum of areas,

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but a couple that I’ll just mention here
that are directly relevant to the

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presentation today are that Bill
recognized the shortcoming of using

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site categories to
deal with site effects,

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which is really the dominant way that
we did it through the ’90s and before.

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And was the first to
look at V-S30 as a site parameter

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to use in
ground motion models.

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He also introduced, with Dave,
this concept of regressions –

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two-stage regressions where different
sources of variability and

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ground motions are dealt with
a statistically rigorous way,

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which was ahead of its time and
was really a great contribution.

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And again, that’s something that
is relevant to the talk today.

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As you all know,
Bill passed away in 2001.

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In 2004, this lecture
was established.

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I think mostly due to efforts
of people here at the Survey,

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and many of whom
are in this room.

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And I think it’s worth noting
that the concept behind the award,

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aside from honoring Bill,
was to recognize research

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at the interface of science
and engineering.

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Which certainly
is what he did.

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And that spirit of the award
is inspiring to me.

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You know, that’s something
I’ve tried to do in my own work.

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And so I’m deeply honored
to be the 13th Joyner lecturer.

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And let’s get on with it.

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So the subject today of site response
is something I’ve worked on

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for really my whole academic career
since I became a faculty member.

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I’ve had a lot of
students working on it.

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These are their names in
approximate chronological order.

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And so obviously what I’m
talking about is not my own work.

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It’s benefited a lot
from these students

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and also many colleagues
outside of UCLA.

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And the ones that are
highlighted here

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contributed directly to figures or
equations that will be presented today.

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The report behind this, and some of
the ongoing work in this area

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have been supported by the PEER
Center at Berkeley, Caltrans,

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and the California Strong Motion
Instrumentation Program.

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One of the tools to come
out of this is OpenSHA.

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And that’s Open Seismic
Hazard Analysis.

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And that was supported by SCEC
and especially Kevin Milner,

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a Ph.D. student there who does
coding, was instrumental, and I want

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to acknowledge his contributions,
along with Christine Goulet.

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So some terminology
as we get started.

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I’ll use these different symbols
as we go throughout the talk,

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so I’ll just kind of
define them now.

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So IM is intensity measure.

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So it’s things like PGA or spectral
acceleration of ground motion.

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X and Z are intensity measures
for a particular site condition.

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So X is for a reference site condition.
That’s usually going to be rock.

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But it doesn’t need to be.

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Could be firm soil at some horizon
for very, very deep basin sites.

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Z is what we’re looking for.
That’s the ground motion

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at the surface.

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Again, usually
for a soil site.

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And Y is just the
ratio of the two – Z over X.

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So that’s the
site amplification.

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GMPE, sometimes being
called ground motion model now,

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that’s equations for
predicting ground motions.

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They’re largely empirical,
but they can have elements

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of simulations
in them as well.

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And they’re used to predict –
they can be used to predict X,

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or they can be
used to predict Z.

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PSHA – I think we all
know what that is –

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probabilistic seismic
hazard analysis.

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Now, the term “ergodic” –
this is the Wikipedia definition.

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Random process for which
the time average of

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one sequence of events is
the same as the ensemble average.

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Which is a little bit hard to
conceptualize, actually,

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what exactly that means.
So let me try to give you an analogy

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to ergodic that is maybe
a little more understandable.

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And for that, I’ll use
a baseball analogy, okay?

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So let’s go back a few months and
imagine we didn’t have the first half

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of the baseball season
already over with, and we were

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trying to predict how the Giants
were going to do this year.

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Now, for anybody who knows anything
about baseball, you know that one of

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the biggest factors that causes you
to be successful or not is pitching.

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Okay, pitching – pitchers make the
most money. That’s for good reason.

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They have huge influence
over the games they appear in.

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So if you wanted to predict how
the Giants were going to do,

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you’d probably want to predict how
their pitchers were going to do.

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So if you’re trying to make
that prediction, an ergodic way

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of doing that would be to say,
okay, let’s collect data

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on major league pitchers,
let’s say over the last 50 years.

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And we’re going to collect
their performance stats.

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So I’m going to get
their win/loss records.

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I’m going to have their
earned run average,

00:13:48.299 --> 00:13:51.869
strikeout-to-walk ratios –
all these sorts of things.

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I got lots and lots of pitchers
over 50 years over all the

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different teams in
major league baseball.

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So I’m going to have those statistics,
and I’m going to then say, all right,

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so those are the numbers I predict
for the Giants pitchers in 2016.

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That’s essentially an ergodic
model for that performance.

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And you might be sitting there thinking,
but that’s a terrible prediction.

00:14:15.300 --> 00:14:17.720
Because the Giants have
Madison Bumgarner.

00:14:17.720 --> 00:14:19.560
He’s not an
average pitcher.

00:14:19.560 --> 00:14:21.720
And they spent on this money
on free agents to get a bunch of

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other guys who are pretty good –
you know, not average pitchers.

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So what you have there
is a poor prediction.

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It doesn’t account for the
specifics of the Giants rotation.

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And of course,
you’d be right.

00:14:34.619 --> 00:14:36.230
So you could then
do something that is

00:14:36.230 --> 00:14:39.100
specific to the conditions
the Giants have.

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You could say, all right, well, what is
Madison Bumgarner’s statistics?

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And what are the stats for all these
other pitchers starting for them?

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And then make
a prediction of how they’re

00:14:46.829 --> 00:14:48.459
going to do this
year based on that.

00:14:48.459 --> 00:14:51.939
You’d reach a very different outcome,
which would have been accurate,

00:14:51.939 --> 00:14:55.009
as it turns out, because the
Giants are having a great year.

00:14:55.009 --> 00:14:57.290
So that’s the difference.
Right? Do you do something

00:14:57.290 --> 00:15:00.820
that’s specific to the
condition – non-ergodic?

00:15:00.820 --> 00:15:03.559
Or something very general
using a large population

00:15:03.560 --> 00:15:08.580
of seemingly similar
characteristics – that’s ergodic.

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Okay, and that same principle
holds very nicely in a lot

00:15:11.020 --> 00:15:14.160
of venues for
ground motion.

00:15:15.420 --> 00:15:19.480
So my objectives in the meeting
today are – or, sorry, in the talk today

00:15:19.489 --> 00:15:24.009
are to understand the difference
between non-ergodic and ergodic

00:15:24.009 --> 00:15:30.369
in the area of site response to present
a framework for building what are

00:15:30.369 --> 00:15:37.709
essentially site-specific ground motion
models for use in hazard analysis.

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To show that it has a pretty
appreciable effect on hazard –

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and that’s significant because that’s
what engineers are going to care about.

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And as you start to
see hazard change,

00:15:46.029 --> 00:15:50.999
that creates the financial incentive
to actually do this on projects.

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And my sort of broader point here
is I will acknowledge from

00:15:56.339 --> 00:15:59.279
the outset that this is not easy.
It takes effort.

00:15:59.279 --> 00:16:02.470
It takes additional site characterization
and engineering time.

00:16:02.470 --> 00:16:06.699
There’s no question.
It is more expensive, more difficult,

00:16:06.699 --> 00:16:10.729
to do what I’m talking about than
the standard engineering analysis.

00:16:10.729 --> 00:16:14.910
Okay? But the tools are there.
And it’s worth it.

00:16:14.910 --> 00:16:17.419
It’s, more often than not, going to
reduce the hazard enough

00:16:17.419 --> 00:16:22.999
to more than pay for itself in
an overall project cost standpoint.

00:16:22.999 --> 00:16:29.479
So this outline is what we’ll go through.
We’ll talk about site response physics.

00:16:29.479 --> 00:16:31.579
Ergodic site
amplification a little bit.

00:16:31.580 --> 00:16:33.579
Non-ergodic.

00:16:33.579 --> 00:16:35.799
How it’s implemented in PSHA.

00:16:35.800 --> 00:16:37.940
And then I’ll have
a summary at the end.

00:16:39.429 --> 00:16:40.879
The physics are
important to start with,

00:16:40.879 --> 00:16:44.559
and of course, this is well-known
to this particular audience.

00:16:44.559 --> 00:16:48.459
So [chuckles] maybe I didn’t
need to include it for all of you.

00:16:48.459 --> 00:16:53.040
But I’ll go through this anyway
because the physics and understanding

00:16:53.040 --> 00:16:56.939
the different processes that contribute
to site response is quite important

00:16:56.939 --> 00:16:59.799
as we get to the conclusions
near the end of the talk

00:16:59.799 --> 00:17:03.139
and what limitations we have
with some of the models we use.

00:17:04.559 --> 00:17:11.150
So I am distinguishing site
response from ground response.

00:17:11.150 --> 00:17:15.230
Site response is the over-arching
effect we’re trying to simulate.

00:17:15.230 --> 00:17:20.120
And there’s various subsets underneath
it, one of which is ground response.

00:17:20.120 --> 00:17:22.079
Ground response has the
advantage of it’s something

00:17:22.079 --> 00:17:24.620
that geotechnical
engineers can predict.

00:17:24.620 --> 00:17:29.850
And within ground response, there are
several subsets of effects that go on.

00:17:29.850 --> 00:17:31.740
So there’s impedance
and damping, is one.

00:17:31.740 --> 00:17:35.179
So as the ground motion through
an S wave is coming up

00:17:35.179 --> 00:17:40.000
through this layer, it has a certain
velocity and a certain amplitude.

00:17:40.000 --> 00:17:44.720
And as it goes through a velocity
contrast and slows down,

00:17:44.720 --> 00:17:50.110
indicated by a shorter vector here,
its amplitude, if there were no damping,

00:17:50.110 --> 00:17:54.409
will go up in order to have
a conservation of energy

00:17:54.409 --> 00:17:59.549
across that boundary.
So that’s an impedance effect.

00:17:59.549 --> 00:18:03.320
So if we were to define a ground
motion at the surface as U-zero,

00:18:03.320 --> 00:18:07.370
and at the bottom as U-r, and basically
take the intensity measures for

00:18:07.370 --> 00:18:11.250
surface over the base, for a
high-frequency ground motion

00:18:11.250 --> 00:18:16.960
or a low-frequency ground motion,
if the strength of the input is very weak,

00:18:16.960 --> 00:18:20.559
which is going to cause damping
to be low, these ratios will always

00:18:20.559 --> 00:18:24.399
be positive due to
that impedance effect.

00:18:26.400 --> 00:18:31.600
Now, a characteristic of soil is that,
as you go to larger strains,

00:18:31.600 --> 00:18:34.130
the damping goes up.
And that damping is going to

00:18:34.130 --> 00:18:37.899
chew up energy as the waves are
propagating through these layers.

00:18:37.899 --> 00:18:41.029
And the effect of that damping is not
the same at different frequencies.

00:18:41.029 --> 00:18:44.789
So high frequencies, you’re going to
see the damping starting to attenuate

00:18:44.789 --> 00:18:49.100
the motions reflected by even
a less than 1 amplification.

00:18:49.100 --> 00:18:52.659
And low frequencies, there’s barely
an effect of that damping

00:18:52.659 --> 00:18:57.330
because the wavelength is so long,
the waves may hardly even see

00:18:57.330 --> 00:19:01.700
the damping within those layers.
So this is a nonlinear effect,

00:19:01.700 --> 00:19:05.529
which is not the same across
all these different frequencies.

00:19:05.529 --> 00:19:08.669
So all that’s contained within this
impedance and damping effects.

00:19:08.669 --> 00:19:12.730
It’s also resonance effects, of course,
where sites will tend to respond

00:19:12.730 --> 00:19:16.460
at certain resonant frequencies,
just like structures do.

00:19:16.460 --> 00:19:19.100
So we have a first, second,
and third mode and so on

00:19:19.100 --> 00:19:22.130
that can happen
within this.

00:19:22.130 --> 00:19:25.490
So ground response really
encompasses all of these things.

00:19:25.490 --> 00:19:28.930
And we have calculation methods
that can capture this.

00:19:30.020 --> 00:19:36.340
Another type of site response is
basin effects where we basically

00:19:36.350 --> 00:19:41.460
can have a ruptured fault bringing
energy directly underneath a basin,

00:19:41.460 --> 00:19:45.070
which is pretty much the
ground response type of problem.

00:19:45.070 --> 00:19:48.409
Or we can have the energy coming
across and entering through the edge

00:19:48.409 --> 00:19:53.000
as well as from underneath,
getting critical body wave reflections

00:19:53.000 --> 00:19:56.880
converting into surface waves
traveling across the basin,

00:19:56.880 --> 00:20:00.019
which can’t be modeled through
ground response type of processes.

00:20:00.019 --> 00:20:02.679
But it’s a physical
process that is there.

00:20:02.679 --> 00:20:07.000
And it’s definitely contributing
to the ground motions.

00:20:07.920 --> 00:20:10.879
There’s other types of basin effects
as well like focusing,

00:20:10.879 --> 00:20:16.240
where a lens-type structure can
focus energy in a particular area.

00:20:16.240 --> 00:20:19.480
And there’s topographic effects,
where ground motions may be

00:20:19.480 --> 00:20:21.990
higher at the top of a slope
than near its base.

00:20:21.990 --> 00:20:26.100
So all these things
are possible.

00:20:26.100 --> 00:20:30.210
So if we look at all these different
factors contributing to a site response –

00:20:30.210 --> 00:20:33.520
local ground response,
basin, topographic effects –

00:20:33.520 --> 00:20:36.340
they’re all there in the real
Earth to varying degrees.

00:20:36.350 --> 00:20:40.259
And, you know, the ground motion
databases that we work with to build

00:20:40.259 --> 00:20:45.450
models are from real sites that have,
to varying degrees, all of these things.

00:20:45.450 --> 00:20:46.899
So they’re in the ground motions.

00:20:46.899 --> 00:20:50.730
And since the ground motions
are used to build ground motion models,

00:20:50.730 --> 00:20:53.309
they’re in the
ground motion models.

00:20:53.309 --> 00:20:57.639
So the affect the GMPEs,
mostly in the site term.

00:20:57.639 --> 00:21:04.929
And the average of these effects
across all kinds of different sites

00:21:04.929 --> 00:21:08.799
are in our site terms, and our site
terms are parameterized

00:21:08.799 --> 00:21:12.980
on the basis of V-S30, and to
a lesser extent, basin depth.

00:21:12.980 --> 00:21:16.190
So the average effect
of each of these is contained

00:21:16.190 --> 00:21:19.740
within our models
parameterized by those terms.

00:21:20.900 --> 00:21:25.120
So let me just say a
little bit about V-S30 scaling.

00:21:25.129 --> 00:21:32.120
So we have here schematically a
firm site in red, kind of a transitional

00:21:32.120 --> 00:21:39.250
site in green, and a softer site in blue.
Here’s some schematic velocity profiles.

00:21:39.250 --> 00:21:44.409
So 3 will have a low V-S30,
2 intermediate, and 1 a high V-S30.

00:21:44.409 --> 00:21:48.960
If we were to record ground motions
from some distant earthquake

00:21:48.960 --> 00:21:54.679
at those three sites and plot the
acceleration response spectra,

00:21:54.679 --> 00:21:57.600
we might expect to see the red –
the rock, intermediate,

00:21:57.600 --> 00:22:00.850
and the soil plotting
something like this.

00:22:00.850 --> 00:22:04.610
And the point I want to make is,
if I was to draw a line

00:22:04.610 --> 00:22:08.929
through the spectral ordinates at
different periods and just

00:22:08.929 --> 00:22:14.399
sample the ground motions here,
and then plot that now as a function

00:22:14.399 --> 00:22:19.110
of V-S30, we would see that,
for this long-period case,

00:22:19.110 --> 00:22:24.110
there’s a fairly abrupt rapid
change in the ground motion.

00:22:24.110 --> 00:22:28.269
There’s a change at short
periods too, but it’s not as strong.

00:22:28.269 --> 00:22:31.940
And that’s kind of a characteristic
of V-S30 scaling, particularly in

00:22:31.940 --> 00:22:35.509
active crustal regions,
that the site response as

00:22:35.509 --> 00:22:42.019
parameterized through this, is stronger
at long periods than it is at short periods.

00:22:42.019 --> 00:22:44.730
And in fact, it’s often,
you know, peaking at a

00:22:44.730 --> 00:22:49.370
quite long period, say 1 to 3 seconds
or something like that.

00:22:49.370 --> 00:22:54.500
That is another point that I’ll refer
back to later, okay, that the site response

00:22:54.500 --> 00:23:00.000
revealed empirically is most
concentrated at long periods, typically.

00:23:00.000 --> 00:23:04.529
Okay, for the low V-S30s that would
be characteristic of soil sites.

00:23:06.740 --> 00:23:12.140
All right. So now a little bit
about ergodic site amplification.

00:23:12.149 --> 00:23:18.610
So these are models for ground motion –
in this case, side effects that are

00:23:18.610 --> 00:23:22.440
evaluated from a diverse
global data set, which is what

00:23:22.440 --> 00:23:25.690
we’re pretty much using
in NGA-type projects these days.

00:23:25.690 --> 00:23:30.570
We’re drawing as much data
as we can from all over the globe.

00:23:30.570 --> 00:23:32.690
These ergodic models,
as I’ve mentioned before,

00:23:32.690 --> 00:23:40.179
are dependent on V-S30 and depth
and most of the contemporary GMPEs.

00:23:40.179 --> 00:23:41.919
And those same
types of considerations

00:23:41.919 --> 00:23:45.939
go into the site factors
that are in building codes.

00:23:47.970 --> 00:23:51.519
So let’s explore this a little bit in
terms of how GMPEs are formulated.

00:23:51.519 --> 00:23:58.119
They’re usually a sum of a series
of terms in natural log units.

00:23:59.490 --> 00:24:05.279
So these first two terms – F-E and F-P –
these are ergodic models.

00:24:05.279 --> 00:24:09.580
So, again, average
globally for the source.

00:24:09.580 --> 00:24:13.289
That would be F-E.
E for event.

00:24:13.289 --> 00:24:14.840
And the path – F-P.

00:24:14.840 --> 00:24:17.840
So ergodic models
for source and path.

00:24:17.840 --> 00:24:21.440
Could we do non-ergodic
models for source and path?

00:24:21.440 --> 00:24:23.149
The answer is yes,
we could.

00:24:23.149 --> 00:24:26.769
But that’s not really the
subject of today’s lecture.

00:24:28.440 --> 00:24:30.800
F-S is the site term.

00:24:30.800 --> 00:24:33.240
And that’s an
ergodic model for site.

00:24:33.240 --> 00:24:39.759
So if I plug in a certain V-S30, say 300
meters per second, into the F-S term,

00:24:39.759 --> 00:24:47.539
what actual condition is reflected by the
site amplification that comes out of that?

00:24:47.540 --> 00:24:49.659
Well, it’s going to be
the global average

00:24:49.659 --> 00:24:52.720
shear wave velocity
given that V-S30, right?

00:24:52.720 --> 00:24:56.679
So if you take a global average across,
you know, thousands of profiles,

00:24:56.679 --> 00:24:58.460
it’s going to smooth out,
and you’re probably going to

00:24:58.460 --> 00:25:02.640
have something that goes like this
as the global average V-S30 –

00:25:02.640 --> 00:25:06.780
or, velocity given V-S30 that is
more or less associated with

00:25:06.789 --> 00:25:10.460
the amplification returned
by the ergodic model.

00:25:10.460 --> 00:25:13.300
Now, if your V-S profile
looks like that, then you’re fine.

00:25:13.309 --> 00:25:16.480
Your ergodic model
is going to work well.

00:25:16.480 --> 00:25:21.260
But you may have the same V-S30 but
a different velocity profile at your site.

00:25:21.260 --> 00:25:24.220
Okay, so you have a different
condition that’s site-specific.

00:25:24.230 --> 00:25:31.779
As a result of that, your site response is
not going to match the ergodic model.

00:25:31.779 --> 00:25:35.480
In order to represent that
mathematically, we say, all right,

00:25:35.480 --> 00:25:39.029
we stick with the ergodic model,
but we’re going to add something to it.

00:25:39.029 --> 00:25:41.899
And this difference is
the effect of those

00:25:41.899 --> 00:25:44.999
site-specific considerations,
whatever they may be.

00:25:45.000 --> 00:25:46.440
Those are called
fixed effects.

00:25:46.440 --> 00:25:50.980
And in the case of site,
we’ll call that eta-sub-S for site.

00:25:50.980 --> 00:25:54.450
So if we could figure out eta-sub-S,
then we would have,

00:25:54.450 --> 00:26:00.129
through its sum with F-S, these site-
specific or non-ergodic site response.

00:26:01.860 --> 00:26:04.380
Now, as we go through this problem,
it’s very important to keep in mind

00:26:04.389 --> 00:26:08.210
standard deviation too, so I’d
like to dwell on that a little bit.

00:26:08.210 --> 00:26:12.019
So the sigma-lnZ there at the end
is the total standard deviation

00:26:12.019 --> 00:26:16.440
that goes with
these ergodic models.

00:26:16.440 --> 00:26:20.389
And that total standard deviation has
two very well-known components.

00:26:20.389 --> 00:26:28.769
So there’s tau and phi, where tau
is the event-to-event variability.

00:26:28.769 --> 00:26:35.330
So it’s basically accounting for the fact
that F-E is an ergodic model for source.

00:26:35.330 --> 00:26:37.710
Actual sources look different.
There are event terms that

00:26:37.710 --> 00:26:42.490
go various directions, and the
standard deviation of those is tau.

00:26:44.920 --> 00:26:48.179
And then phi is
the within-event variability.

00:26:48.179 --> 00:26:50.690
And there are a
number of contributors to phi.

00:26:50.690 --> 00:26:55.039
And this is the one we’re really
going to be working with mostly here.

00:26:55.039 --> 00:27:00.049
So as we look at the variability that
can occur for a given earthquake,

00:27:00.049 --> 00:27:04.970
we have the possibility of many
different source-to-path –

00:27:04.970 --> 00:27:10.259
source-to-site paths that are being
sampled as you look at a global model.

00:27:10.259 --> 00:27:12.509
So there’s
path-to-path variability.

00:27:13.100 --> 00:27:16.860
There’s site-to-site variability,
which is this one.

00:27:17.820 --> 00:27:21.659
That’s accounting for what I was talking
about earlier, that there’s lots of different

00:27:21.659 --> 00:27:25.049
sites having the same V-S30, and they
all have different site responses.

00:27:25.049 --> 00:27:30.940
So the variability across all of those
is phi-S2S – site-to-site variability.

00:27:30.940 --> 00:27:36.330
And then what’s left over,
basically, is, for a given site,

00:27:36.330 --> 00:27:39.230
what is the variability given
different attributes of the ground

00:27:39.230 --> 00:27:43.320
motions coming in at the bottom,
heterogeneity in the site, and so on.

00:27:43.320 --> 00:27:50.120
That would be phi-lnY, or the
site amplification variability.

00:27:52.200 --> 00:27:54.780
Does this sigma matter?

00:27:54.780 --> 00:27:57.980
Well, if it didn’t matter, I wouldn’t
have much of a talk, so it does matter.

00:27:57.980 --> 00:28:00.299
But let me
demonstrate that for you.

00:28:00.299 --> 00:28:02.590
So the importance of sigma –
so I’m just going to run

00:28:02.590 --> 00:28:06.879
a hazard analysis for a site
here with just two faults.

00:28:06.879 --> 00:28:11.889
There’s a close-by fault with maybe
magnitude 6 or so and a little further

00:28:11.889 --> 00:28:17.429
away fault with a larger magnitude –
not atypical of conditions in California.

00:28:17.429 --> 00:28:24.669
If we use an NGA model for V-S30 760
for this condition and run the

00:28:24.669 --> 00:28:28.690
hazard with the as-published sigma,
we get this hazard curve.

00:28:28.690 --> 00:28:31.249
So annual frequency of
exceedance this is

00:28:31.249 --> 00:28:34.240
1 second pseudo-acceleration
ground motion.

00:28:34.240 --> 00:28:38.860
If I then just artificially reduce sigma –
and I’m not saying you should

00:28:38.860 --> 00:28:41.889
ever do this, of course. We don’t want
to artificially reduce sigma.

00:28:41.889 --> 00:28:45.529
We have to be doing things
that are defensible. [chuckles]

00:28:45.529 --> 00:28:48.610
But just for illustrative purposes,
if I artificially reduce sigma

00:28:48.610 --> 00:28:53.559
by 0.1 and 0.2, you can see that’s
a pretty big effect on the hazard.

00:28:53.559 --> 00:28:59.249
Now, a ground motion level we use a lot
is 2% in 50 years, which is about here.

00:28:59.249 --> 00:29:03.509
So as I go – actually,
it’s more like here.

00:29:03.509 --> 00:29:11.299
As I go from the original sigma to minus
0.1, you’re going from about 0.4 to 0.3.

00:29:11.299 --> 00:29:16.389
That’s a big change.
And then maybe at 0.2 to 0.25 or so.

00:29:16.389 --> 00:29:18.019
Those are big changes
in ground motion.

00:29:18.019 --> 00:29:20.350
And those are the kind of
changes that will get engineers

00:29:20.350 --> 00:29:25.150
really excited if that could
be done in a defensible way.

00:29:26.120 --> 00:29:29.080
Given that, and this is not exactly
a new thing – we’ve known sigma

00:29:29.080 --> 00:29:35.149
matters for a long, long time –
one of the things that ground motion

00:29:35.149 --> 00:29:38.220
modelers have tried to do,
but we’ve almost given up on

00:29:38.220 --> 00:29:42.710
at this point, is to build
better and better GMPEs

00:29:42.710 --> 00:29:46.100
with the idea that we
should be able to reduce sigma.

00:29:46.100 --> 00:29:49.039
So if you could come up
with a GMPE that was done properly

00:29:49.039 --> 00:29:54.200
and had a lower sigma than
everybody else, you’d be a hero.

00:29:54.200 --> 00:29:57.110
The trouble is, it’s really
hard to do that. [chuckles]

00:29:57.110 --> 00:30:00.759
Fleur Strasser and some of her
colleagues published this figure,

00:30:00.759 --> 00:30:03.850
which is a few years old,
but it makes the point.

00:30:03.850 --> 00:30:08.789
These are sigma terms plotted as a
function of publication year starting

00:30:08.789 --> 00:30:14.829
in about the early ’70s and going up
to pretty close to the present, to 2009.

00:30:14.829 --> 00:30:18.679
And if you plot the more recent ones,
it doesn’t really change the trend,

00:30:18.679 --> 00:30:20.769
which is that it’s
pretty much flat.

00:30:20.769 --> 00:30:23.529
So as – over that period of time,
from the early ’70s, you know,

00:30:23.529 --> 00:30:27.399
ground motions have gone from a few
tens to, you know, tens of thousands.

00:30:27.399 --> 00:30:31.519
Our level of sophistication and
the analysis, the processing –

00:30:31.519 --> 00:30:34.879
every conceivable part
has gotten much, much better.

00:30:34.879 --> 00:30:39.600
Yet the sigma is persistent.
You can’t really bring it down.

00:30:41.180 --> 00:30:43.620
That’s another whole discussion
as to why that’s the case,

00:30:43.629 --> 00:30:45.559
but it’s factually true.

00:30:45.559 --> 00:30:49.440
So it’s very hard to bring it down as
long as you’re using ergodic models.

00:30:50.240 --> 00:30:53.720
Okay, so that brings us
to non-ergodic models.

00:30:56.149 --> 00:30:58.940
So non-ergodic
site amplification.

00:30:58.940 --> 00:31:03.749
So here, as I’ve mentioned before,
what we’re talking about is now

00:31:03.749 --> 00:31:09.379
site amplification that is computed
on a site-specific basis.

00:31:09.379 --> 00:31:12.029
And there’s two
main parts of this.

00:31:12.029 --> 00:31:18.460
So the first is, assuming that the default
is an ergodic model, which would have

00:31:18.460 --> 00:31:23.629
bias, by going to a non-ergodic model,
we would be removing that bias.

00:31:23.629 --> 00:31:26.789
So that’s changing the mean.

00:31:26.789 --> 00:31:30.549
And the second part of this is having
to do with the standard deviation.

00:31:30.549 --> 00:31:33.299
So we’re going to
reduce the standard deviation.

00:31:33.299 --> 00:31:38.239
We want to do both these things together
as part of our non-ergodic analysis.

00:31:39.580 --> 00:31:43.230
I will argue that we
have two ways of doing this.

00:31:43.230 --> 00:31:47.169
They both have
pluses and minuses.

00:31:47.169 --> 00:31:50.999
And I think the tension between these
two will continue to play out over time,

00:31:50.999 --> 00:31:54.320
but we should at least recognize that
there are two possibilities.

00:31:54.320 --> 00:32:01.610
Okay, so one is to use on-site
recordings of ground motion.

00:32:01.610 --> 00:32:03.690
Which has obvious
practical limitations because

00:32:03.690 --> 00:32:08.590
a lot of engineering sites
don’t have an instrument. Okay.

00:32:08.590 --> 00:32:11.899
But some do, and sites
could be instrumented,

00:32:11.899 --> 00:32:15.929
especially if you have some time
horizon in which to do the study.

00:32:15.929 --> 00:32:19.110
If it’s playing out over
several years for a critical project,

00:32:19.110 --> 00:32:21.169
you’d get an instrument
out there right away.

00:32:21.169 --> 00:32:23.019
You can probably start
recording ground motions

00:32:23.019 --> 00:32:26.330
and get something useful
during the project life.

00:32:26.330 --> 00:32:28.500
So I don’t think it’s
completely impractical.

00:32:28.500 --> 00:32:29.700
In fact, I know it’s
not because there are

00:32:29.700 --> 00:32:33.509
several projects I’m
involved with that are doing it.

00:32:33.509 --> 00:32:37.629
And then there are
geotechnical simulations as well.

00:32:38.869 --> 00:32:45.070
Our goal in the end is we want a mean.
And the mean here – I’m being

00:32:45.070 --> 00:32:50.950
quite specific in the notation – I want
a mean site amplification, so it’s Y.

00:32:50.950 --> 00:32:55.950
And to go with that, I need the phi –
the within-event variability.

00:32:55.950 --> 00:32:59.419
Not really for Y, although I do
need that as part of the process,

00:32:59.419 --> 00:33:03.440
but my end goal is I want the phi
for the predictive ground motion Z.

00:33:03.440 --> 00:33:08.440
So as we go through it, we’ll have
ways of working those two things out.

00:33:10.040 --> 00:33:13.060
I’m actually going to
start with the dispersion part.

00:33:13.070 --> 00:33:19.299
So let’s just recall that the desired
standard deviation for Z is just – the

00:33:19.299 --> 00:33:24.539
variance for that is the sum of all these
other variances, as I mentioned before.

00:33:26.100 --> 00:33:31.720
The phi-lnZ – this one – is what
we already know from a GMPE.

00:33:31.720 --> 00:33:35.499
So GMPEs will almost always,
in modern models,

00:33:35.499 --> 00:33:38.480
give you the tau
and the phi together.

00:33:38.480 --> 00:33:42.190
So we already have that, and it’s
usually a function of magnitude,

00:33:42.190 --> 00:33:46.050
sometimes distance,
and sometimes site condition.

00:33:47.830 --> 00:33:52.710
So if the site response that you’re
calculating is non-ergodic,

00:33:52.710 --> 00:33:57.500
you can take advantage of the fact that
you don’t need the phi-S2S anymore.

00:33:57.500 --> 00:34:01.100
That’s a site-to-site variability that
you have removed by adding

00:34:01.110 --> 00:34:05.119
all this additional knowledge into
your prediction of the site response.

00:34:05.119 --> 00:34:07.779
So there’s no reason
to account for uncertainty

00:34:07.779 --> 00:34:12.080
in site response that
isn’t present in your case.

00:34:12.080 --> 00:34:14.070
There are two ways
of dealing with that –

00:34:14.070 --> 00:34:17.609
of removing that –
in sort of a very practical way.

00:34:17.609 --> 00:34:20.700
So one is to simply subtract it.
And I put an approximation here

00:34:20.700 --> 00:34:22.609
because it’s a little bit
more complicated than that.

00:34:22.609 --> 00:34:25.079
But at least conceptually,
you’re pretty much just

00:34:25.079 --> 00:34:29.339
subtracting the
variance of phi-S2S.

00:34:30.659 --> 00:34:35.389
The second approach is you just
scrap this whole term and

00:34:35.389 --> 00:34:39.329
replace it with another one,
which has been archived

00:34:39.329 --> 00:34:43.899
in some reports, and I’ll
present some figures for that.

00:34:43.899 --> 00:34:46.659
And that’s called
the single-station phi.

00:34:46.659 --> 00:34:49.369
And there’s a number of
publications related to that

00:34:49.369 --> 00:34:54.530
which have been assembled
essentially to form models for it.

00:34:54.530 --> 00:35:00.180
So looking at the two – so this is
some work by Adrian Rodriguez-Marek

00:35:00.180 --> 00:35:04.060
and several others.
So this is Rodriguez-Marek et al. 2013.

00:35:04.060 --> 00:35:12.920
And trying to remember what the K is
there. That’s Kaklamanos et al. 2013.

00:35:12.920 --> 00:35:16.800
And several others –
Atkinson, Lin.

00:35:16.809 --> 00:35:21.530
So we’ve assembled a bunch of
phi-S2S values as a function of period.

00:35:21.530 --> 00:35:23.770
And there is a good deal
of variability as you look at

00:35:23.770 --> 00:35:26.520
different studies from
around the world.

00:35:26.520 --> 00:35:30.059
But most of the numbers
are between about 0.3 and 0.5.

00:35:30.059 --> 00:35:36.139
Which is a lot. That’s a – that’s a big
number in standard deviation land.

00:35:36.150 --> 00:35:40.730
And so we can take a
pretty big reduction here.

00:35:42.200 --> 00:35:45.880
This is that second approach where
you just have a single-station sigma.

00:35:45.890 --> 00:35:50.869
These are three different models for it
that were developed for a major project

00:35:50.869 --> 00:35:55.630
in the western U.S. – southwestern U.S.
published by GeoPentech.

00:35:55.630 --> 00:36:00.130
And so different assumptions were used
to develop these three different models.

00:36:00.130 --> 00:36:03.680
And there are differences, obviously.
But the difference between –

00:36:03.680 --> 00:36:10.500
excuse me – this and the ergodic
within event variability is quite large.

00:36:10.500 --> 00:36:14.500
And so that’s the reduction
that we’re able to take.

00:36:16.290 --> 00:36:18.450
So going back to that
previous schematic, if I use

00:36:18.450 --> 00:36:24.329
that single-station phi, it works out
to a sigma reduction of about 0.15,

00:36:24.329 --> 00:36:26.109
and so that’s what
you would have.

00:36:26.109 --> 00:36:30.799
Okay, not changing the mean at all.
Just changing the standard deviation.

00:36:30.799 --> 00:36:34.930
And that is a big deal.
Okay, that’s a big change right there.

00:36:34.930 --> 00:36:39.700
Now, there are other uncertainties
that come along with it, but just as a –

00:36:39.700 --> 00:36:45.160
to give you an idea that this matters,
you know, there you have it.

00:36:46.540 --> 00:36:50.140
Okay. So that’s the standard deviation
part. What about the mean?

00:36:50.140 --> 00:36:53.589
So I’m going to talk about these
two ways of getting towards that.

00:36:53.589 --> 00:36:56.480
One is through the use of recordings.
And the other is through

00:36:56.480 --> 00:37:00.349
the use of simulations.
We’ll start with recordings.

00:37:00.349 --> 00:37:04.020
So obviously we have to start
by instrumenting the site.

00:37:04.020 --> 00:37:08.560
So we do that, and then we
start recording earthquakes.

00:37:09.140 --> 00:37:11.799
Magnitude zero earthquakes
aren’t really going to be useful to us,

00:37:11.799 --> 00:37:13.790
at least with the
models we have now.

00:37:13.790 --> 00:37:18.630
Okay, we’re going to have to have
earthquakes that are at least about 3.

00:37:19.060 --> 00:37:25.000
Now, just as an aside,
when the NGA-West2 project

00:37:25.000 --> 00:37:29.670
was underway, which Dave and I
were involved in pretty heavily,

00:37:29.670 --> 00:37:37.970
we made the decision to lower the range
of data from about 4-1/2 to 5 down to 3.

00:37:37.970 --> 00:37:40.609
Which brought in a
huge number of additional records,

00:37:40.609 --> 00:37:42.700
mostly from California.

00:37:42.700 --> 00:37:46.940
And a lot of people have really
wondered why in the world

00:37:46.950 --> 00:37:52.720
did we do that. It made a lot of work
to digitize and create all these records.

00:37:52.720 --> 00:37:55.690
I have been mocked
by certain structural engineers.

00:37:55.690 --> 00:37:58.730
Why are you guys doing this?
This is totally irrelevant.

00:37:58.730 --> 00:38:01.859
We never seen damage from
magnitude 3 and 4 earthquakes.

00:38:01.859 --> 00:38:06.339
You’re wasting everybody’s
time by doing all of this.

00:38:06.339 --> 00:38:08.369
So why did we do that?

00:38:09.240 --> 00:38:12.460
Well, for a variety of reasons,
but one of them relevant to this talk

00:38:12.470 --> 00:38:17.200
is that, if I have a model that
works down to magnitude 3,

00:38:17.200 --> 00:38:21.240
I can do the sorts of calculations
I’m going to talk about here.

00:38:21.240 --> 00:38:25.099
Which is I can compare observations
that will happen fairly frequently –

00:38:25.099 --> 00:38:28.780
because, of course, we get
a lot of magnitude 3s and 4s –

00:38:28.780 --> 00:38:30.180
to my ergodic model.

00:38:30.180 --> 00:38:33.250
That’s really going to be
the key as we go through this.

00:38:33.250 --> 00:38:38.930
So by NGA going down in magnitude
and up in distance, it just ups the range

00:38:38.930 --> 00:38:42.450
of motions that we can be considering.
And that has some very practical

00:38:42.450 --> 00:38:45.850
benefits from a site response
point of view.

00:38:47.880 --> 00:38:49.589
So I record some ground motions.

00:38:49.589 --> 00:38:53.069
They need to be in the usable range of
the GMPE, as I was just talking about.

00:38:53.069 --> 00:38:54.730
And now I’m going to
calculate residuals.

00:38:54.730 --> 00:38:58.630
So that’s going to be the difference
between the recorded ground motion

00:38:58.630 --> 00:39:03.520
and the mean that you would predict
for that ground motion, given that

00:39:03.520 --> 00:39:08.940
source and the path and so on.
And that is this residual R-ij.

00:39:10.660 --> 00:39:16.580
I then need to partition residuals
because that residual, R-ij,

00:39:16.700 --> 00:39:20.680
if I go over to this side,
has event terms contributing to it

00:39:20.680 --> 00:39:23.920
and within-event
variability, delta-W here.

00:39:23.920 --> 00:39:26.740
And I’m really
interested in this part.

00:39:26.740 --> 00:39:32.299
I need to know this to help me
get at the within-event variability.

00:39:32.299 --> 00:39:34.880
Otherwise I’m not particularly
interested in the event term.

00:39:34.880 --> 00:39:38.440
So I do need to go through a process
of partitioning the residuals

00:39:38.440 --> 00:39:41.670
to get the within-event
variability for my site.

00:39:41.670 --> 00:39:44.480
And if I have this,
I can then plot it

00:39:44.480 --> 00:39:48.680
for all the different events
as a function of period.

00:39:48.680 --> 00:39:53.280
And this is actually doing that for a site
in southern California – Los Angeles

00:39:53.290 --> 00:39:57.760
Obregon Park, which has recorded,
I think, 15 or 16 earthquakes.

00:39:57.760 --> 00:40:02.270
And if you look at all those within-event
variabilities, you see a fair amount of

00:40:02.270 --> 00:40:06.450
scatter, but one thing that’s persistent
is that these residuals are positive.

00:40:06.450 --> 00:40:09.270
Okay, and pretty
significantly positive.

00:40:09.270 --> 00:40:10.359
And this is typical.

00:40:10.359 --> 00:40:12.369
We’re always going to
have a lot of scatter.

00:40:12.369 --> 00:40:15.990
But if you have enough
observations like we had here,

00:40:15.990 --> 00:40:19.480
you can get a
pretty decent mean.

00:40:19.480 --> 00:40:22.799
Okay, a mean that is
reasonably well-constrained.

00:40:22.799 --> 00:40:24.950
And that’s really
what we’re trying to do.

00:40:24.950 --> 00:40:29.680
So we take the mean of the
within-event residuals at each period,

00:40:29.680 --> 00:40:31.799
which is these
thicker symbols here.

00:40:31.799 --> 00:40:35.390
Those are just confidence
intervals on that mean.

00:40:35.390 --> 00:40:44.790
And that essentially comprises the fixed
effect, eta-sub-S, okay, for that site.

00:40:48.210 --> 00:40:51.750
So now, if I know that eta-sub-S –
so this is just repeating the figure

00:40:51.750 --> 00:40:53.859
from the previous slide here.

00:40:53.859 --> 00:40:58.319
So I can take that eta-sub-S, which is
just the distance from zero up to that

00:40:58.319 --> 00:41:03.770
mean, and I can add the ergodic site
term, okay, which is depicted here.

00:41:03.770 --> 00:41:06.700
The ergodic site term, given these
are probably weak motions,

00:41:06.700 --> 00:41:10.180
is the linear part of the ergodic
site amplification model.

00:41:10.180 --> 00:41:13.089
Perhaps a depth term
in that ergodic model.

00:41:13.089 --> 00:41:17.839
And then I’m adding the eta-sub-S.
So the ergodic model is here.

00:41:17.839 --> 00:41:21.430
This is the bias that was observed
through the recordings.

00:41:21.430 --> 00:41:26.910
And the sum of the two gets you
this total site response here.

00:41:26.910 --> 00:41:32.430
Now, probably those recordings are
mostly for fairly weak motions,

00:41:32.430 --> 00:41:35.789
not necessarily suitable for site
response in engineering applications

00:41:35.789 --> 00:41:38.650
where you have nonlinearity.
[static] And that’s all right.

00:41:38.650 --> 00:41:42.900
But at least we’ve got a good
handle on the more or less linear,

00:41:42.900 --> 00:41:46.690
or small strain, site response
through a process like this.

00:41:46.690 --> 00:41:49.789
And we can simply add in
the nonlinear term later

00:41:49.789 --> 00:41:53.869
by running
suitable simulations.

00:41:55.160 --> 00:41:57.700
I’ll illustrate that process
a little later on.

00:41:57.700 --> 00:42:02.530
Okay, so all of this essentially
is for bias removal.

00:42:02.530 --> 00:42:08.109
And it’s going to help give me what
I seek, which is the mean, mu-lnZ.

00:42:08.109 --> 00:42:11.410
So I’m going to take this, I’m going to
add it in with the source and path terms,

00:42:11.410 --> 00:42:17.059
and I’ll have a GMPE now
that is site-specific in its mean.

00:42:19.200 --> 00:42:21.820
Okay, well, what if you don’t
have recordings at your site?

00:42:21.820 --> 00:42:23.540
What do you do then?

00:42:23.560 --> 00:42:27.500
Well, you do what geotechnical
engineers have done since the 1970s,

00:42:27.500 --> 00:42:29.160
maybe even before.

00:42:29.160 --> 00:42:33.780
We run geotechnical, one-dimensional
ground response analysis.

00:42:33.780 --> 00:42:38.970
And in those analyses, we take some
input motions, usually on rock.

00:42:38.970 --> 00:42:43.069
We run them up –
assuming that they are S waves.

00:42:43.069 --> 00:42:46.809
They pass through a soil column
with a shear wave velocity profile.

00:42:46.809 --> 00:42:48.650
Certain nonlinear properties.

00:42:48.650 --> 00:42:51.400
And we calculate
the motions up at the top.

00:42:51.400 --> 00:42:55.420
There’s a whole series
of assumptions that go into that.

00:42:55.420 --> 00:42:59.200
And it’s important for us to
recognize what we’re modeling

00:42:59.210 --> 00:43:02.490
in the true site response physics
and what we’re not modeling.

00:43:02.490 --> 00:43:06.220
So what we are modeling
is impedance effects.

00:43:06.220 --> 00:43:10.380
We’re getting damping effects.
We’re getting resonance effects.

00:43:10.380 --> 00:43:12.690
Might be overdoing the
resonance effects a little bit,

00:43:12.690 --> 00:43:16.740
but we at least have that
physical process in there.

00:43:16.740 --> 00:43:20.650
We don’t have surface waves.
We don’t have the effects

00:43:20.650 --> 00:43:23.640
of deeper geologic structure.
We don’t have basin effects.

00:43:23.640 --> 00:43:26.460
Don’t have topography
if it’s present.

00:43:26.460 --> 00:43:27.609
So it’s an imperfect model.

00:43:27.609 --> 00:43:30.220
It models some parts of the
site response and not others.

00:43:30.220 --> 00:43:33.200
It’s quite important
to keep that in mind.

00:43:33.200 --> 00:43:36.080
Again, this is not an audience that’s
probably going to argue that point

00:43:36.089 --> 00:43:39.220
with me very much because you’re
seismologists and geologists.

00:43:39.220 --> 00:43:42.750
But those are fightin’ words to a lot of
geotechs, okay, who have been doing

00:43:42.750 --> 00:43:46.790
this for a long, long time and
assuming it’s the right answer.

00:43:48.700 --> 00:43:52.500
When we run those calculations,
we do it for a range of input motions

00:43:52.500 --> 00:43:55.619
with many different amplitudes,
ideally. That’s X.

00:43:55.619 --> 00:43:57.609
And for each one of
those input motions,

00:43:57.609 --> 00:44:02.750
we compute the ratio Z over X
to get the amplification.

00:44:02.750 --> 00:44:06.650
Now, another one- or two-hour lecture
could go into how you’re supposed

00:44:06.650 --> 00:44:09.280
to do all that.
That is not trivial.

00:44:09.280 --> 00:44:11.560
The way you select the
parameters and details

00:44:11.569 --> 00:44:16.579
of that are pretty nuanced
and complex and evolving.

00:44:16.579 --> 00:44:21.809
And I’m not going to go there at all,
okay, but I’ll just point to a 2014 report

00:44:21.809 --> 00:44:26.510
that lays all that out in great detail and
underwent a great deal of peer review.

00:44:26.510 --> 00:44:32.550
So it represents a good standard
of practice guideline.

00:44:34.799 --> 00:44:41.150
What I do want to talk about is how
effective those sorts of calculations are.

00:44:41.150 --> 00:44:44.700
And before getting into
these vertical array studies,

00:44:44.700 --> 00:44:48.150
I should just mention that
there’s any number of studies,

00:44:48.150 --> 00:44:53.420
some of which I’ve written, where we’ve
gone to a particular site, studied it

00:44:53.420 --> 00:44:57.829
very carefully, and found that ground
response analysis works quite well.

00:44:57.829 --> 00:45:01.349
So you find individual sites
where everything’s great.

00:45:01.349 --> 00:45:05.730
Okay? There’s many
papers of that sort.

00:45:05.730 --> 00:45:10.089
Only a few papers have looked at
large inventories of vertical arrays –

00:45:10.089 --> 00:45:14.510
so surface and downhole instruments –
analyzed them in a consistent way,

00:45:14.510 --> 00:45:19.440
and looked and seen, well, overall,
how are things coming out?

00:45:19.440 --> 00:45:23.400
Are these calculations
working well, not well, and so on.

00:45:23.400 --> 00:45:28.819
Okay, and really one of the
seminal works doing that was

00:45:28.819 --> 00:45:30.369
published by
Thompson et al.

00:45:30.369 --> 00:45:34.560
One of the et als is Rob Kayen,
who is here – in 2012.

00:45:34.560 --> 00:45:40.580
And it’s worth looking at what they
found using vertical arrays in Japan.

00:45:40.589 --> 00:45:46.099
So what’s being shown here
is one particular site

00:45:46.099 --> 00:45:48.670
where they have
lots of recordings.

00:45:48.670 --> 00:45:51.490
And the thin black line here
with the shading around it

00:45:51.490 --> 00:45:56.210
is the mean site amplification in terms
of Fourier amplitude ratios

00:45:56.210 --> 00:45:58.920
across many recordings.

00:45:58.920 --> 00:46:03.470
And the thick black line is the
prediction of the site response

00:46:03.470 --> 00:46:09.460
from the bottom instrument to the
top instrument from a 1D model.

00:46:09.460 --> 00:46:13.609
And you can see that
the peak doesn’t line up.

00:46:13.609 --> 00:46:16.530
The amplitudes are not too bad
over here, but this first-mode peak

00:46:16.530 --> 00:46:25.150
is certainly pretty far off
from the actual site response.

00:46:25.150 --> 00:46:29.309
And it so happens that something
like 82% of the 100 or so sites

00:46:29.309 --> 00:46:34.349
they looked at have misfits that
are pretty profound between

00:46:34.349 --> 00:46:40.440
the prediction and the observation
for these KiK-net array sites in Japan.

00:46:40.440 --> 00:46:42.599
So they looked into
a little more detail

00:46:42.599 --> 00:46:44.589
to try and understand
why this might be happening.

00:46:44.589 --> 00:46:48.260
This is where the instrument is.
These are topographic contours.

00:46:48.260 --> 00:46:53.839
And so SASW profiles
were done by Rob

00:46:53.839 --> 00:46:57.520
at these various locations
around the site.

00:46:57.520 --> 00:46:59.970
And these are
his dispersion curves.

00:46:59.970 --> 00:47:01.829
So phase velocity
versus frequency.

00:47:01.829 --> 00:47:05.410
And what you notice is that they
don’t line up on top of each other,

00:47:05.410 --> 00:47:09.430
suggesting different velocity structures
in these different places.

00:47:09.430 --> 00:47:12.559
Which isn’t altogether surprising.
This is a fairly narrow valley.

00:47:12.559 --> 00:47:13.819
Probably shallow soil.

00:47:13.819 --> 00:47:17.710
One would expect velocity changes
as you move you way around here.

00:47:17.710 --> 00:47:21.410
The point is is that the velocity
structure isn’t one-dimensional,

00:47:21.410 --> 00:47:25.150
the site response is more complicated,
and it shouldn’t come as a great surprise

00:47:25.150 --> 00:47:30.569
that a 1D model doesn’t really work
under conditions like that.

00:47:30.569 --> 00:47:33.929
So we probably thought
before Thompson et al. that,

00:47:33.929 --> 00:47:35.560
yeah, this could happen.

00:47:35.560 --> 00:47:39.819
And maybe it’s on a small minority
of cases where you might see this.

00:47:39.819 --> 00:47:43.990
But when we saw the number 82%,
that was kind of a humbling figure.

00:47:44.600 --> 00:47:46.480
Now, this is the other 18%.

00:47:46.480 --> 00:47:50.670
This is more representative of those,
where things are lining up quite nicely.

00:47:50.670 --> 00:47:56.430
Again, multiple surface wave tests
were run, but in this case, they line up,

00:47:56.430 --> 00:47:58.770
suggesting a more
consistent structure

00:47:58.770 --> 00:48:03.710
compatible with 1D
modeling assumptions.

00:48:06.240 --> 00:48:11.400
That sort of thing is possible
on a smaller scale in California.

00:48:11.400 --> 00:48:15.140
We have, I think, 39 vertical
arrays throughout the state.

00:48:15.140 --> 00:48:18.230
These are
locations of them.

00:48:18.230 --> 00:48:21.299
And the blue ones are ones
that we’ve been looking at.

00:48:21.299 --> 00:48:27.119
We’re not done, but we have looked
at about 20 of the 39 stations.

00:48:27.120 --> 00:48:29.720
And we have similar
sorts of features.

00:48:29.720 --> 00:48:33.130
So this is an example
of a poor fit at Garner Valley.

00:48:33.130 --> 00:48:36.549
This is an example of
a pretty good fit at La Cienega.

00:48:36.549 --> 00:48:40.990
So we have poor and good fit sites.
This, again, would be the observation

00:48:40.990 --> 00:48:43.799
in blue and the
ground response prediction in red.

00:48:43.799 --> 00:48:47.980
So we have the same sorts of
features that they saw in Japan.

00:48:47.980 --> 00:48:51.549
When you look at the population so far,
we’re a little better than the Japanese

00:48:51.549 --> 00:48:56.020
are in terms of the ability of 1D to
match things, but it’s about 50/50.

00:48:56.020 --> 00:49:01.010
It’s still, you know, not as good
as we would have liked to think

00:49:01.010 --> 00:49:04.240
for our engineering procedures.

00:49:04.240 --> 00:49:09.099
So we have to recognize that there is
a pretty substantial possibility, when we

00:49:09.099 --> 00:49:13.039
run a ground response analysis,
that we’re getting the wrong answer.

00:49:13.060 --> 00:49:16.300
And our ability to know in advance
when we’re getting the wrong answer,

00:49:16.309 --> 00:49:19.720
and how far off it is,
is not very well-developed.

00:49:19.720 --> 00:49:25.160
Most people, myself included,
really can’t tell you in advance

00:49:25.160 --> 00:49:27.720
when this is
going to be the case.

00:49:27.720 --> 00:49:30.660
Working our way through this
and learning how to make those

00:49:30.670 --> 00:49:34.930
predictions in a forward sense,
I think is one of our great challenges

00:49:34.930 --> 00:49:39.660
in ground motion prediction, at least
as it relates to site response.

00:49:41.100 --> 00:49:48.460
Okay, so putting that aside – behind us
for a moment, we have our site-specific

00:49:48.460 --> 00:49:51.960
site response, either through the
recordings or through the simulations.

00:49:51.960 --> 00:49:55.869
We want to move forward now and
build a model and use it for hazard.

00:49:55.869 --> 00:50:00.329
So we have to have a site-specific
amplification function.

00:50:00.329 --> 00:50:05.200
And this is a model form
that seems to work quite well.

00:50:05.200 --> 00:50:08.599
So these F-1, F-2, F-3
become coefficients

00:50:08.599 --> 00:50:11.920
that we need to determine
on a site-specific basis.

00:50:13.180 --> 00:50:16.200
F-1 – that’s essentially
the linear amplification.

00:50:16.200 --> 00:50:19.040
That’s like the V-S30 scaling
in an ergodic model.

00:50:19.049 --> 00:50:24.809
And it would just be done – you know, a
value per period in a site-specific sense.

00:50:24.809 --> 00:50:27.220
F-2 and F-3 – I just have
a little schematic

00:50:27.220 --> 00:50:29.609
to illustrate their
physical meaning.

00:50:29.609 --> 00:50:34.020
So F-2 is a negative number
that reflects the slope of this

00:50:34.020 --> 00:50:38.140
amplification versus, say,
intensity of shaking here.

00:50:38.140 --> 00:50:42.839
It represents this slope when you
get out to strong levels of shaking.

00:50:42.839 --> 00:50:45.500
This relationship becomes
basically linear,

00:50:45.500 --> 00:50:48.750
and F-2 is the change
over a log cycle.

00:50:48.750 --> 00:50:54.250
F-3 is essentially where
you see the curve bending over.

00:50:54.250 --> 00:50:59.000
Okay, and it’s usually somewhere
between about 0.03 and maybe 0.3 –

00:50:59.000 --> 00:51:04.299
somewhere in that range.
0.1 is a pretty good number many times.

00:51:06.860 --> 00:51:10.640
All right.
So we want to fit this function.

00:51:10.640 --> 00:51:15.049
And so if we’re running simulations,
we run many simulations.

00:51:15.049 --> 00:51:18.329
Each X here is a single
ground response analysis

00:51:18.329 --> 00:51:21.670
run for a site –
in this case, Obregon Park.

00:51:21.670 --> 00:51:26.070
And we can fit that function
through it quite nicely.

00:51:27.529 --> 00:51:30.319
If we don’t do so many runs –
say we only do runs over

00:51:30.319 --> 00:51:34.410
a small range of PGA –
there are more approximate ways

00:51:34.410 --> 00:51:37.720
of essentially assuming a slope
and drawing a line through that

00:51:37.720 --> 00:51:42.599
so you still have a function to work with,
although that would obviously be

00:51:42.599 --> 00:51:47.910
carrying with it additional
epistemic uncertainty.

00:51:47.910 --> 00:51:50.260
If you have an
empirical observation,

00:51:50.260 --> 00:51:54.760
which we do for Obregon Park,
it’s good to make note of that.

00:51:54.760 --> 00:51:58.529
And in this case, as we saw earlier,
there’s a pretty big difference.

00:51:58.529 --> 00:52:03.950
So if you have this, what we think
you should do is, don’t use that

00:52:03.950 --> 00:52:07.309
red fit of the ground
response analysis results.

00:52:07.309 --> 00:52:08.849
Simply shift it up.

00:52:08.849 --> 00:52:14.130
Okay. So it’s matching the empirical
observation while retaining the slope.

00:52:14.130 --> 00:52:21.090
So retaining the F-2, F-3, and essentially
just using the observations to set F-1.

00:52:23.039 --> 00:52:25.470
On the standard deviation side.

00:52:25.470 --> 00:52:29.410
So just remembering that this is
our equation for the mean.

00:52:29.410 --> 00:52:32.640
The standard deviation
is going to be reduced.

00:52:32.640 --> 00:52:36.880
So the sigma-lnZ is going to be
reduced relative to the –

00:52:36.880 --> 00:52:40.240
phi-lnZ –
relative to phi-lnX.

00:52:40.250 --> 00:52:42.260
And there’s several
factors causing that.

00:52:42.260 --> 00:52:46.859
So I want to go through them
as we look at this equation here.

00:52:47.720 --> 00:52:50.100
So the first is
nonlinearity.

00:52:50.100 --> 00:52:53.800
Nonlinearity in the site response is
going to reduce the standard deviation.

00:52:53.809 --> 00:52:56.000
That is expressed
mathematically through this

00:52:56.000 --> 00:52:57.410
equation here
which has F-2.

00:52:57.410 --> 00:53:00.579
Remember that F-2
is a negative number.

00:53:00.579 --> 00:53:04.960
So this negative number is going to
cause this term to be negative.

00:53:04.960 --> 00:53:09.619
Plus 1 – so this term is less than 1.
Square it, and that is then being

00:53:09.619 --> 00:53:13.279
multiplied by this term over here,
which has phi-lnX.

00:53:13.279 --> 00:53:18.670
So the nonlinearity itself is going to
be reducing the within-event variability.

00:53:18.670 --> 00:53:20.789
And you can understand that
on a physical level

00:53:20.789 --> 00:53:23.039
because of the nonlinearity
in site response.

00:53:23.039 --> 00:53:27.230
So if I have an especially
weak site response – sorry –

00:53:27.230 --> 00:53:31.319
an especially weak input motion,
that’s going to produce

00:53:31.319 --> 00:53:35.179
a stronger site response
due to less damping.

00:53:35.180 --> 00:53:39.000
And you’re going to have something
a little bit stronger at the surface

00:53:39.010 --> 00:53:42.240
than you would have expected
perhaps given the weak input.

00:53:42.240 --> 00:53:44.470
Whereas, if you have a very
strong input at the bottom,

00:53:44.470 --> 00:53:47.329
that’s going to produce more
than the typical nonlinearity,

00:53:47.329 --> 00:53:49.160
bringing the motions
down at the surface.

00:53:49.160 --> 00:53:52.529
So a wide dispersion at the bottom
will become a narrower dispersion

00:53:52.529 --> 00:53:56.359
at the top due to these nonlinear
effects and the site response.

00:53:56.359 --> 00:54:00.349
And that essentially is
reflected through this term here.

00:54:02.140 --> 00:54:03.900
Then there’s the
non-ergodic part

00:54:03.900 --> 00:54:06.560
and the two approaches
I talked about earlier.

00:54:06.560 --> 00:54:09.640
This is the first of them
where we essentially subtract

00:54:09.650 --> 00:54:12.890
the phi-S2S from
the phi-lnX.

00:54:12.890 --> 00:54:17.430
And I’m putting this term F in here
because that allows the engineer

00:54:17.430 --> 00:54:23.859
to quantify their confidence
in the degree to which they think

00:54:23.859 --> 00:54:27.480
they’ve actually achieved
non-ergodic site response.

00:54:27.480 --> 00:54:32.820
If you don’t think you have it –
you don’t really trust your calculations,

00:54:32.820 --> 00:54:35.120
you’re going to
make F zero.

00:54:35.130 --> 00:54:37.680
If you are very confident –
maybe because you have

00:54:37.680 --> 00:54:42.420
recordings at your site and lots
of them, then you use F equals 1.

00:54:42.420 --> 00:54:44.220
And maybe you’re
not quite sure where you are,

00:54:44.220 --> 00:54:45.440
so you go
somewhere in between.

00:54:45.440 --> 00:54:49.200
So that’s the only reason for F.
It’s between zero and 1.

00:54:50.360 --> 00:54:54.880
Or if you use approach 2, you simply
replace that term with phi-SS.

00:54:56.119 --> 00:54:59.400
We do have to add the
site response uncertainty itself,

00:54:59.400 --> 00:55:04.440
and that’s a chapter in that peer report,
which I don’t have time to go through,

00:55:04.440 --> 00:55:09.430
but I’ll just point out that when you
look at studies of ground motions

00:55:09.430 --> 00:55:14.420
from the field at many different places,
it is a surprisingly stable number,

00:55:14.420 --> 00:55:17.220
even over a pretty
wide period range.

00:55:17.220 --> 00:55:21.000
It’s about 0.3.
And it doesn’t budge much.

00:55:21.010 --> 00:55:24.670
So we think that’s a pretty good
number to use for that term.

00:55:26.260 --> 00:55:28.420
Okay, so what did I just skip?

00:55:34.069 --> 00:55:35.819
This one. Okay.

00:55:35.819 --> 00:55:37.900
And so the last point
before I move on from this section

00:55:37.900 --> 00:55:39.279
is epistemic uncertainty.

00:55:39.279 --> 00:55:43.049
So this is uncertainty
related to lack of knowledge.

00:55:43.049 --> 00:55:45.220
We can’t lose sight of that.
So even if we’re doing

00:55:45.220 --> 00:55:48.460
a non-ergodic analysis,
there’s uncertainty in that mean.

00:55:48.460 --> 00:55:52.170
There’s uncertainty
in that standard deviation.

00:55:52.170 --> 00:55:55.510
So we should be considering that,
and that’s through the use of

00:55:55.510 --> 00:55:59.109
logic trees and things like
that as you run the PSHA.

00:55:59.109 --> 00:56:03.920
So we will want to have multiple
possible realizations of what that actual

00:56:03.920 --> 00:56:08.559
mean amplification is to account for
the fact we don’t know it perfectly.

00:56:08.559 --> 00:56:13.039
And there are, as you’ve seen,
multiple models for the phi term,

00:56:13.039 --> 00:56:16.799
and we can carry those through
as well to see how impactful that is.

00:56:17.980 --> 00:56:22.640
Okay, so in terms of implementation
in PSHA, it’s pretty simple, actually.

00:56:22.640 --> 00:56:26.829
Once you’ve worked through all that,
all you’re doing is you’re calculating

00:56:26.829 --> 00:56:33.569
your desired mean through the mean
for X, which is coming from the GMPE

00:56:33.569 --> 00:56:40.340
for reference site condition and the
site-specific site amplification mu-lnY.

00:56:40.340 --> 00:56:44.000
And then we’re adjusting the phi term
like we talked about before.

00:56:44.000 --> 00:56:47.500
We don’t do anything with the tau term.
We just keep the one from the GMPE.

00:56:48.760 --> 00:56:51.760
And as I talked about,
we need to carefully consider

00:56:51.760 --> 00:56:53.630
those epistemic
uncertainties.

00:56:53.630 --> 00:56:59.450
And one of the really dicey issues is,
if you’re using ground response analysis,

00:56:59.450 --> 00:57:01.559
how sure are you
that your mean is right?

00:57:01.559 --> 00:57:04.609
We’ve seen that, at least half
the time, you’re wrong,

00:57:04.609 --> 00:57:06.819
so what kinds of
uncertainty bounds

00:57:06.819 --> 00:57:11.539
should we be putting on those
means to account for that effect?

00:57:12.700 --> 00:57:15.160
Largely, that is
unknown at present.

00:57:15.170 --> 00:57:20.870
But at least some consideration should
be given when we use these procedures.

00:57:22.040 --> 00:57:25.340
Another issue that I’ll just
raise for people who are really close

00:57:25.349 --> 00:57:28.809
to this subject – and we can talk about
it more later if you’re interested –

00:57:28.809 --> 00:57:33.930
is there’s an issue of correlation
between the soil ground motion Z

00:57:33.930 --> 00:57:39.500
and the reference ground motion X
that nobody is dealing with right now

00:57:39.500 --> 00:57:46.859
but does impact how these calculations
are run in the final answer.

00:57:46.859 --> 00:57:50.579
So all this is implemented
in OpenSHA.

00:57:50.579 --> 00:57:54.260
So if you download the tool,
there is a non-ergodic site response

00:57:54.260 --> 00:57:57.490
GMPE option under
“intensity measure relation.”

00:57:57.490 --> 00:58:00.829
So the same place that
you would pick a GMPE to use,

00:58:00.829 --> 00:58:04.210
you could
pick this instead.

00:58:04.210 --> 00:58:08.470
Underneath that tool, you can select
a GMPE, which is for the reference

00:58:08.470 --> 00:58:14.950
condition, and the V-S30 that would
be used for that reference condition.

00:58:14.950 --> 00:58:17.210
So it might be, say,
760 meters per second,

00:58:17.210 --> 00:58:22.789
or whatever is representative of the
firm material at the base of your site.

00:58:22.789 --> 00:58:25.740
You do have to enter a V-S30
and depth parameters for

00:58:25.740 --> 00:58:31.250
the surface condition as well.
I’ll explain more why we need that.

00:58:31.250 --> 00:58:34.319
We have to enter all these coefficients
I’ve talked about – F-1, F-2, F-3,

00:58:34.319 --> 00:58:38.519
et cetera, for the mean
and standard deviation models.

00:58:40.549 --> 00:58:43.849
We have set it up so that you –
you know, that if you look at the

00:58:43.849 --> 00:58:47.730
number of periods in a GMPE,
there might be 100. [chuckles]

00:58:47.730 --> 00:58:51.200
And we don’t want people to have to
enter all these data points 100 times.

00:58:51.200 --> 00:58:55.319
So you can enter just, like, 10,
and there are interpolation functions

00:58:55.319 --> 00:58:59.960
to get the other ones for you,
so that’s been worked out.

00:58:59.960 --> 00:59:04.750
And there is an option – the motivation
for which I’ll explain in a moment – for

00:59:04.750 --> 00:59:11.230
adjusting the non-ergodic model to an
ergodic model as you go to long periods.

00:59:12.980 --> 00:59:17.500
So that’s the most formal
proper implementation of all this

00:59:17.500 --> 00:59:20.970
within a hazard code.

00:59:20.970 --> 00:59:25.339
That is not the way that site response
is dealt with in typical engineering

00:59:25.339 --> 00:59:32.210
practice now, okay, which is most
often what is called hybrid.

00:59:32.210 --> 00:59:37.240
And actually, when I gave the talk
at SSA, I attributed this to Cramer,

00:59:37.240 --> 00:59:42.510
and he corrected me later, saying,
I do not advocate this approach.

00:59:42.510 --> 00:59:45.700
He coined the term. He doesn’t
actually advocate the approach.

00:59:45.700 --> 00:59:48.329
So I’m being more specific.
The term is from Cramer,

00:59:48.329 --> 00:59:52.619
but he doesn’t agree that this
is what we should be doing.

00:59:52.619 --> 00:59:54.260
The hybrid approach.

00:59:54.260 --> 01:00:01.710
Basically you take the rock
hazard curve – take the log of it.

01:00:01.710 --> 01:00:09.730
You calculate the mean site response,
given the rock ground motion.

01:00:09.730 --> 01:00:12.059
Take the log of that.
You add them together.

01:00:12.059 --> 01:00:15.099
And you’ve got the
soil ground motion.

01:00:15.099 --> 01:00:17.890
Okay, so you’re using
rock hazard with essentially

01:00:17.890 --> 01:00:22.480
deterministic site factor
that gets combined with it.

01:00:22.480 --> 01:00:27.740
Very simple. Okay?
Seems intuitive. Seems fine.

01:00:29.670 --> 01:00:32.630
This is the dominant approach
in practice, including – whenever

01:00:32.630 --> 01:00:37.170
we use site factors in the building
code, this is what we’re doing.

01:00:39.200 --> 01:00:42.490
The advantages are basically
that it’s easy and you only

01:00:42.490 --> 01:00:44.299
need to have a
single rock PSHA.

01:00:44.299 --> 01:00:47.029
And this has really been the
guiding principle for the

01:00:47.029 --> 01:00:50.769
USGS mapping program
for however many years.

01:00:50.769 --> 01:00:54.339
Calculate rock hazard,
and we’ll just deal with the soil

01:00:54.339 --> 01:00:57.660
by putting it in with
these site factors later on.

01:00:58.900 --> 01:01:01.059
Okay, now the drawbacks
when you look at this from

01:01:01.059 --> 01:01:03.029
a probabilistic point of view –
the sort of things we’ve been

01:01:03.029 --> 01:01:07.920
talking about here this morning –
is that the PSHA is based on the

01:01:07.920 --> 01:01:10.690
standard deviation
for rock – phi-lnX.

01:01:10.690 --> 01:01:16.769
Not phi-lnZ. Or sigma, actually.
Sigma-lnX, sigma-lnZ.

01:01:16.769 --> 01:01:18.160
And those two are different.

01:01:18.160 --> 01:01:22.280
And so we’re not taking advantage of
the fact that there is that difference.

01:01:22.280 --> 01:01:27.760
If we’re using these USGS or similar
standard maps, we really don’t have any

01:01:27.769 --> 01:01:35.369
way of allowing for the non-ergodic
standard deviation to enter that process.

01:01:35.369 --> 01:01:38.740
The sources that control the hazard
for a given site are determined on the

01:01:38.740 --> 01:01:40.869
basis of the rock site condition.

01:01:40.869 --> 01:01:43.819
The epsilons for the
ground motion – same thing.

01:01:43.819 --> 01:01:49.599
And those are all going to be different
for soil, and you’re not allowing for that.

01:01:49.600 --> 01:01:54.680
There’s variability in the site
amplification that isn’t being considered.

01:01:54.680 --> 01:01:59.720
And you end up producing through
this process excessive nonlinearity.

01:01:59.720 --> 01:02:04.089
And I’ll just go back
briefly to explain why that is.

01:02:04.089 --> 01:02:08.400
We enter the rock hazard curve
at very long return periods, typically,

01:02:08.400 --> 01:02:12.150
for engineering application.
That means high epsilon.

01:02:12.150 --> 01:02:16.670
And that goes in here to drive the
nonlinearity in the site amplification.

01:02:16.670 --> 01:02:21.650
Whereas, the original GMPEs
did not use a positive epsilon ground

01:02:21.650 --> 01:02:24.780
motion to drive the nonlinearity.
They used the mean.

01:02:24.789 --> 01:02:28.250
So the nonlinear term becomes much
more pronounced as it’s applied in this

01:02:28.250 --> 01:02:33.490
hybrid manner than the way the
GMPEs were intended to be used.

01:02:33.490 --> 01:02:35.579
And that produces a
pretty appreciable drop

01:02:35.579 --> 01:02:40.970
in the hazard when it is
calculated this way.

01:02:42.780 --> 01:02:44.580
Okay, so some
example applications.

01:02:44.589 --> 01:02:46.670
This is the Obregon Park site
we’ve talked about.

01:02:46.670 --> 01:02:48.769
This is where it actually is.

01:02:48.769 --> 01:02:54.609
These are the same amplification – same
amplification function I showed earlier.

01:02:54.609 --> 01:02:58.849
This is actually the soil profile.
It’s not terribly deep by L.A. standards.

01:02:58.849 --> 01:03:02.349
There is sandstone
at 60 meters.

01:03:04.059 --> 01:03:09.089
If we run ground response analysis
for that site going from that sandstone

01:03:09.089 --> 01:03:11.170
on up – I don’t know if
you can see it very well,

01:03:11.170 --> 01:03:14.460
but there isn’t much of
an impedance contrast here.

01:03:14.460 --> 01:03:16.640
So you don’t get
much of a site response.

01:03:16.640 --> 01:03:18.349
And you can see
this is log scale.

01:03:18.349 --> 01:03:25.569
We’re really far off from the observation
if we run ground response through there.

01:03:25.569 --> 01:03:31.210
If we do an ergodic model,
the ergodic model in the VS-SA GMPE

01:03:31.210 --> 01:03:36.049
does a little better, but it’s still,
by no measure, good.

01:03:36.049 --> 01:03:40.609
[chuckles] It’s still way off from
the observations for that site.

01:03:42.150 --> 01:03:46.500
This is the nonlinear function
I showed earlier and the

01:03:46.500 --> 01:03:50.180
empirical amplification,
which is higher.

01:03:50.180 --> 01:03:53.380
If we run these things
through the OpenSHA code,

01:03:53.380 --> 01:03:56.059
this is, for reference,
the uniform hazard spectra

01:03:56.059 --> 01:04:01.150
at 2% in 50 years for –
this is mislabeled here, actually.

01:04:01.150 --> 01:04:03.029
This would be
Obregon Park.

01:04:03.029 --> 01:04:07.990
This is the
2% in 50-year rock.

01:04:07.990 --> 01:04:13.859
This is the non-ergodic approach
using essentially that weak motion

01:04:13.859 --> 01:04:17.499
and the nonlinearity
implied by the red line.

01:04:17.500 --> 01:04:18.980
This would be
the non-ergodic

01:04:18.980 --> 01:04:23.320
if you base it on ground
response analysis alone.

01:04:23.320 --> 01:04:27.460
And this would be the
result of an ergodic analysis.

01:04:27.460 --> 01:04:30.019
And there’s a couple
factors at play here.

01:04:30.020 --> 01:04:33.600
These – it’s just accidental
that these line up at the long periods.

01:04:33.600 --> 01:04:39.040
That’s a trade-off between a difference
in standard deviation, with the green one

01:04:39.049 --> 01:04:46.829
being higher, and a difference in mean,
with the blue one being higher.

01:04:48.579 --> 01:04:51.519
The overall point is that these
differences are fairly appreciable.

01:04:51.519 --> 01:04:54.240
If you’re looking at 1 second,
you know, you’re talking about

01:04:54.240 --> 01:04:58.789
differences that are
a factor of 2 or more.

01:04:59.900 --> 01:05:04.220
These are the hazard curves
for PGA and 1 second.

01:05:04.220 --> 01:05:09.009
So then, again, was rock,
the non-ergodic using the recordings,

01:05:09.009 --> 01:05:12.930
the non-ergodic using ground
response analysis simulations,

01:05:12.930 --> 01:05:18.279
and the ergodic model.
So big differences.

01:05:18.279 --> 01:05:21.410
And getting rid of all the others and
just looking at the hybrid case,

01:05:21.410 --> 01:05:24.900
just to show the differences there,
it’s actually not very big in this case.

01:05:24.900 --> 01:05:29.300
They hybrid assumption is problematic
when you have a lot of nonlinearity.

01:05:29.300 --> 01:05:31.859
Otherwise, it doesn’t really matter.

01:05:33.200 --> 01:05:36.120
Okay, so this is that
mean site response –

01:05:36.120 --> 01:05:42.680
sorry, the mean seismic hazard
as represented by uniform hazard

01:05:42.680 --> 01:05:45.710
spectrum that we showed –
I showed just a moment ago.

01:05:45.710 --> 01:05:49.819
And these are the
15th and 85th percentiles,

01:05:49.819 --> 01:05:51.710
which is accounting for
uncertainties in the

01:05:51.710 --> 01:05:55.099
mean site response and the
different standard deviation terms.

01:05:55.099 --> 01:05:58.160
So you can see that these
epistemic uncertainties

01:05:58.160 --> 01:06:02.349
are still there and
are not insignificant.

01:06:02.349 --> 01:06:05.009
That’s there with
any seismic hazard analysis,

01:06:05.009 --> 01:06:07.430
and we have to
put it in here too.

01:06:08.580 --> 01:06:13.319
This is another site, El Centro
in the Imperial Valley.

01:06:13.319 --> 01:06:16.769
This is the same sort of
empirical site response in blue

01:06:16.769 --> 01:06:18.809
with its confidence interval.

01:06:18.809 --> 01:06:22.119
This is the ergodic model,
which is surprisingly good.

01:06:22.119 --> 01:06:26.230
That’s not usually the case,
but it’s lining up reasonably well.

01:06:26.230 --> 01:06:31.970
And this is the ground response analysis,
which is not too bad at short periods

01:06:31.970 --> 01:06:36.329
but becomes significantly
biased at long periods.

01:06:36.329 --> 01:06:39.599
And this bias is a point
that I want to emphasize.

01:06:39.600 --> 01:06:41.920
This is actually
quite typical.

01:06:41.920 --> 01:06:44.799
The ground response analysis
does okay for a while,

01:06:44.799 --> 01:06:48.959
and it’s usually breaking down in a
big way when you get to long periods.

01:06:48.960 --> 01:06:54.200
And there’s a very simple-to-understand
physical reason for that, which is that

01:06:54.200 --> 01:06:56.579
the depth of the column we’re
considering in a ground response

01:06:56.579 --> 01:07:02.000
analysis maybe goes to fundamental
periods of 1 or 2 seconds.

01:07:02.000 --> 01:07:06.160
Once you get beyond that,
there is no predictive site response.

01:07:06.160 --> 01:07:08.960
Yet the real Earth
does have site response.

01:07:08.960 --> 01:07:10.660
That’s the point I made
at the beginning.

01:07:10.660 --> 01:07:14.500
The real Earth, the biggest site response
is often at these long periods.

01:07:14.500 --> 01:07:18.140
But the geotechnical analysis
will very often give you nothing

01:07:18.140 --> 01:07:20.060
or very, very little.

01:07:20.060 --> 01:07:24.220
Okay, so that’s a problem, but it’s one
that we can fairly easily correct.

01:07:24.220 --> 01:07:28.039
We can correct it by using these for a
limited period range and then

01:07:28.039 --> 01:07:32.720
shifting to the ergodic model
if we don’t have observations.

01:07:34.440 --> 01:07:38.240
Okay, so the same process.
Here are the observations.

01:07:38.250 --> 01:07:42.289
And the ground response are pretty
consistent for the weak motions.

01:07:42.289 --> 01:07:44.519
The nonlinearity is
pretty strong in this case.

01:07:44.519 --> 01:07:47.519
This is a much deeper slope
than Obregon Park.

01:07:47.519 --> 01:07:52.720
And these are the uniform hazard spectra
that are produced over here with this one

01:07:52.720 --> 01:07:56.440
probably being the best estimate
with the non-ergodic site response

01:07:56.440 --> 01:08:00.400
and the nonlinearity
from simulations.

01:08:00.400 --> 01:08:02.680
This is if we’re using
ground response only,

01:08:02.680 --> 01:08:05.720
which turns out to be
lower for most periods.

01:08:05.720 --> 01:08:08.920
Not so much at short periods,
but at the long periods.

01:08:08.920 --> 01:08:14.000
And this would be the ergodic model,
which is much higher in this case.

01:08:14.000 --> 01:08:19.359
Mostly because it has less nonlinearity
than that site actually experiences.

01:08:19.359 --> 01:08:22.029
And just one more – I’ll just
show this one figure for this one.

01:08:22.029 --> 01:08:26.020
This is Apeel site near us
along the margins of

01:08:26.020 --> 01:08:29.030
San Francisco Bay –
soft clay.

01:08:29.030 --> 01:08:33.620
This is really the idea sort of site for
ground response analysis to work.

01:08:33.620 --> 01:08:38.650
It’s soft clay over something pretty firm.
Site condition is shown here.

01:08:38.650 --> 01:08:40.540
Bay mud over firmer deposits.

01:08:40.540 --> 01:08:44.770
Rock is reasonably shallow –
about 85 meters.

01:08:44.770 --> 01:08:50.100
Big resonant condition, which is reflected
by this period here of about a second.

01:08:50.100 --> 01:08:55.020
The observations and the ground
response line up pretty well.

01:08:55.020 --> 01:08:59.790
The ergodic model is not nearly as good,
although it’s not horrible.

01:08:59.790 --> 01:09:04.420
But clearly the ground response
is doing a better job.

01:09:05.620 --> 01:09:11.380
Okay, so to summarize,
I’ll make several points

01:09:11.390 --> 01:09:15.020
that I’ve made before
just to sort of emphasize them.

01:09:15.020 --> 01:09:20.810
So site response physics are
associated with a diverse array

01:09:20.810 --> 01:09:23.290
of wave propagation mechanisms.

01:09:23.290 --> 01:09:26.740
There’s the ground response with
the impedance and those things.

01:09:26.740 --> 01:09:28.720
There’s the basin effects.

01:09:28.720 --> 01:09:35.800
Effects of deep sediment structure,
rock structure, and topography.

01:09:37.680 --> 01:09:41.160
Our ergodic or global models
have all these things in them,

01:09:41.170 --> 01:09:44.460
and they’re easy to use, but they
do sacrifice precision because

01:09:44.460 --> 01:09:48.580
they don’t account for the
conditions specific to your site.

01:09:49.980 --> 01:09:53.580
And because you
lack that precision,

01:09:53.580 --> 01:09:57.460
they have inherent to them
a very large dispersion.

01:09:57.460 --> 01:10:00.430
Okay, so you’re using a
big dispersion to account for the fact

01:10:00.430 --> 01:10:06.390
that you don’t know the site-specific
condition applying ergodic model.

01:10:06.390 --> 01:10:09.300
And that has big impact
on the final result.

01:10:09.300 --> 01:10:13.430
Non-ergodic, or site-specific,
is preferred.

01:10:13.430 --> 01:10:19.500
You get to reduce the standard deviation
term, which reduces the hazard.

01:10:19.500 --> 01:10:21.200
And this isn’t
just a hypothetical.

01:10:21.200 --> 01:10:23.480
This is being done
for critical projects.

01:10:23.480 --> 01:10:26.640
Most nuclear projects now
are being done, for example,

01:10:26.640 --> 01:10:31.110
with techniques similar to
what I’ve talked about here.

01:10:32.200 --> 01:10:36.780
Full benefits of non-ergodic
are only possible when implemented

01:10:36.790 --> 01:10:38.100
in a site-specific GMPE.

01:10:38.100 --> 01:10:41.100
So you’re not going to get them
if you’re using that hybrid approach.

01:10:41.100 --> 01:10:43.650
Or there are other approaches
like convolution that are

01:10:43.650 --> 01:10:47.230
better than hybrid but not
as good as site-specific GMPE.

01:10:51.220 --> 01:10:57.300
The implementation that I’ve shown
was not possible for most engineers

01:10:57.300 --> 01:11:00.920
or seismologists until recently because
it wasn’t implemented anywhere.

01:11:00.920 --> 01:11:03.780
So that was the motivation for
working with SCEC and Kevin Milner

01:11:03.780 --> 01:11:10.760
to implement this in OpenSHA, and it
is there now and ready to be used.

01:11:13.380 --> 01:11:17.540
The use of on-site recordings is
preferred if you have them,

01:11:17.540 --> 01:11:20.800
over the use of simulations.
We call that semi-empirical.

01:11:20.800 --> 01:11:24.720
If you’re using ground response, the
drawbacks are that it is almost certainly

01:11:24.730 --> 01:11:29.040
biased at long periods – once you get
beyond the period of the soil column.

01:11:29.040 --> 01:11:33.560
Its short-period accuracy
depends on the geologic complexity,

01:11:33.560 --> 01:11:37.000
as we saw with those
examples in Japan.

01:11:38.520 --> 01:11:43.520
Okay, so a little philosophy –
philosophical points.

01:11:43.520 --> 01:11:46.380
You know, if we have more
knowledge, that’s a good thing.

01:11:46.390 --> 01:11:49.770
So basically, all non-ergodic is
is it’s a way of introducing

01:11:49.770 --> 01:11:52.660
extra knowledge into the
ground motion prediction process.

01:11:52.660 --> 01:11:57.140
If I have more knowledge,
I lower my aleatory variability,

01:11:57.140 --> 01:12:01.120
and most often, this is
going to reduce the hazard.

01:12:02.290 --> 01:12:09.910
If hazard matters in our engineering
calculations, and it surely does,

01:12:09.910 --> 01:12:12.870
then we really should be
moving ever more towards

01:12:12.870 --> 01:12:15.930
the use of these
types of procedures.

01:12:15.930 --> 01:12:21.250
And these types of procedures
are only possible through

01:12:21.250 --> 01:12:24.710
the combined work of
seismologists and engineers.

01:12:24.710 --> 01:12:30.750
Right? Exactly the sort of thing that
Bill Joyner was trying to lead us to do.

01:12:30.750 --> 01:12:35.890
You can’t do this kind of work if you’re
only running engineering simulations.

01:12:35.890 --> 01:12:39.890
Right? You have to have the
two groups working together.

01:12:39.890 --> 01:12:45.200
And so that’s the future, and that’s
what we need to be working on.

01:12:45.760 --> 01:12:48.340
Here’s the references.
And I thank you for your attention.

01:12:48.340 --> 01:12:56.000
[ Applause ]

01:13:02.160 --> 01:13:04.500
- Any questions?

01:13:11.400 --> 01:13:12.940
- [inaudible]
- All right.

01:13:12.940 --> 01:13:14.020
- Someone has to.
[laughs]

01:13:14.020 --> 01:13:15.860
- [inaudible]

01:13:15.860 --> 01:13:19.780
- While they’re thinking up questions,
Jon, do you have any idea what the

01:13:19.790 --> 01:13:24.250
cost savings associated with
the non-ergodic [loud static]

01:13:24.250 --> 01:13:26.870
[inaudible] …
- Sorry. This is really …

01:13:26.870 --> 01:13:32.140
[loud intermittent static]

01:13:32.140 --> 01:13:34.580
If I don’t move it.

01:13:35.850 --> 01:13:39.710
So I have looked into that.
I’m just trying to recall the numbers.

01:13:39.710 --> 01:13:43.580
[background static] I’ve looked into it
actually not for this problem, but for

01:13:43.580 --> 01:13:47.080
soil structure interaction problems
where the same sort of dynamic exists.

01:13:47.080 --> 01:13:50.990
So if you’re going to reduce the
ground motion by 10%, how does

01:13:50.990 --> 01:13:54.690
that translate into less concrete
and things like that? [static]

01:13:58.140 --> 01:14:03.500
It’s huge, really. I mean – I mean,
if you’re talking about a

01:14:03.500 --> 01:14:06.680
10 or 20% reduction
in ground motion,

01:14:06.680 --> 01:14:10.820
that is affecting section sizes
and amount of steel. Things like that.

01:14:10.820 --> 01:14:13.760
So if you’re actually
building a project,

01:14:13.760 --> 01:14:18.260
it has a direct translation
into member sizes.

01:14:18.260 --> 01:14:27.140
So I don’t have a multiplier for you,
but I mean, it’s like an

01:14:27.140 --> 01:14:30.680
order of magnitude difference.

01:14:30.680 --> 01:14:34.070
If – you know, so – of course it depends
on how much the reduction is, right?

01:14:34.070 --> 01:14:40.050
But if you’re talking, like, a 10 or 20%
reduction, it’s an appreciable effect.

01:14:40.050 --> 01:14:42.900
So the issue is not,
does it have an effect or not.

01:14:42.900 --> 01:14:48.120
It’s just getting structural engineers
and owners to be having a

01:14:48.120 --> 01:14:52.440
willingness to, first of all, extend the
time period of the design process –

01:14:52.440 --> 01:14:56.470
it does take more time –
and to invest more upfront.

01:14:56.470 --> 01:14:59.990
Because usually the work of
a geotechnical engineer

01:14:59.990 --> 01:15:04.710
and others doing ground motion work
is sort of seen as a necessary evil.

01:15:04.710 --> 01:15:07.420
Just get it out of the way, and we
want to move on to the architecture

01:15:07.420 --> 01:15:11.150
and the structural engineering and
the things we really care about.

01:15:11.150 --> 01:15:15.970
And so it’s always a bit of an uphill
battle to convince them to invest here.

01:15:16.560 --> 01:15:19.140
- It’s kind of interesting that it
would be that large because

01:15:19.140 --> 01:15:23.340
usually when people talk about the
benefits of retrofitting and the cost,

01:15:23.340 --> 01:15:28.240
those numbers, I hear, are always
quite small – you know, like 1 or 2%.

01:15:28.240 --> 01:15:32.960
But it sounds like getting ground
motion right is really important.

01:15:32.960 --> 01:15:35.260
- Well, so what I was talking about
is when you’re coming up with

01:15:35.260 --> 01:15:40.680
ground motions to build a structure,
right – so the ground motions

01:15:40.680 --> 01:15:43.180
convert to forces, right?

01:15:43.180 --> 01:15:46.610
And the members have to be
sized to resist those forces.

01:15:46.610 --> 01:15:49.520
So essentially a spectral
acceleration times the building weight

01:15:49.520 --> 01:15:53.960
is more or less a force.
That force gets distributed

01:15:53.960 --> 01:15:56.230
through the structure,
and the columns and the beams

01:15:56.230 --> 01:16:01.660
and the walls have to resist it.
So as the force goes up, or down,

01:16:01.660 --> 01:16:05.060
those can be designed
in a different way, right?

01:16:05.060 --> 01:16:08.990
If the structure is already there,
then it’s a different dynamic, right?

01:16:08.990 --> 01:16:12.800
So if you’re analyzing a structure
that’s already been built, the question

01:16:12.800 --> 01:16:17.040
isn’t about construction cost.
It’s – or at least new construction cost.

01:16:17.040 --> 01:16:18.460
It’s usually about retrofit.

01:16:18.460 --> 01:16:23.080
And you’re often looking at it
either retrofit-or-don’t decision.

01:16:23.080 --> 01:16:25.580
And if it were to actually
take you on one side or the other,

01:16:25.580 --> 01:16:28.910
obviously it’s a big deal.
If you’re already retrofitting,

01:16:28.910 --> 01:16:32.410
then maybe there again it’s affecting the
size of the walls and things like that.

01:16:32.410 --> 01:16:36.780
Probably not as appreciably as a
new structure, you know, honestly.

01:16:36.780 --> 01:16:42.620
But, you know, the cost of these sorts of
investigations is not millions of dollars.

01:16:43.680 --> 01:16:48.180
$50,000 or something like that.
It’s fairly small compared to

01:16:48.180 --> 01:16:52.180
the types of numbers we talk about
when we get to construction.

01:16:54.760 --> 01:16:55.860
Yes?

01:16:57.300 --> 01:17:03.740
[ Silence ]

01:17:04.380 --> 01:17:11.690
- As a seismologist, clearly my
sympathies lie with recording

01:17:11.690 --> 01:17:14.510
ground motion at a site.

01:17:14.510 --> 01:17:27.500
However, obviously, in order to record
larger-amplitude ground motions,

01:17:27.500 --> 01:17:33.460
you’d need to have an instrument
there for generally a longer time.

01:17:33.460 --> 01:17:37.040
So my question would be,
how confident are you

01:17:37.040 --> 01:17:42.220
in the nonlinear part
of that analysis?

01:17:42.220 --> 01:17:50.900
I mean, is it worthwhile to simply
be able to record magnitude 3s at a site

01:17:50.900 --> 01:18:05.080
and then simply put on the nonlinear
behavior basically perhaps derived from

01:18:05.080 --> 01:18:09.780
the sort of materials you feel you’re on?
- Yeah. That’s a great question.

01:18:11.360 --> 01:18:14.740
So, I mean, the short answer is,
I’m pretty confident.

01:18:14.750 --> 01:18:18.350
I think that the problems
with the site response physics

01:18:18.350 --> 01:18:21.890
are largely in
the linear response.

01:18:23.360 --> 01:18:25.320
There is a little
more to the answer.

01:18:25.320 --> 01:18:31.680
We’ve actually – we and others
have done research in which

01:18:31.680 --> 01:18:34.900
empirically derived
site amplification

01:18:34.910 --> 01:18:39.130
has been compared to
simulation-derived site amplification.

01:18:40.600 --> 01:18:44.240
And in this case, the simulations
were run by Walt Silva.

01:18:44.250 --> 01:18:48.810
And we were comparing them to
amplification observed empirically.

01:18:48.810 --> 01:18:58.040
And we found that his linear
amplification was off.

01:18:58.040 --> 01:19:04.830
But the trend of that amplification with
the strength of the shaking was okay.

01:19:04.830 --> 01:19:08.730
We couldn’t demonstrate statistically
significant differences in the trends

01:19:08.730 --> 01:19:13.810
implied by data versus what
was in his simulation results.

01:19:13.810 --> 01:19:17.330
So we actually have a paper on this
from about 10 years ago to say,

01:19:17.330 --> 01:19:21.810
be careful with the use of these
simulations for amplitude.

01:19:21.810 --> 01:19:25.400
But on the nonlinear part,
they seem to be all right.

01:19:25.400 --> 01:19:30.120
In a more recent study –
actually as part of NGA-West2,

01:19:30.120 --> 01:19:35.240
a similar thing was done.
Again, Walt was involved with

01:19:35.240 --> 01:19:39.970
Ronnie Kamai and Norm and a
few others, where they ran simulations,

01:19:39.970 --> 01:19:43.210
and they parameterized the
nonlinearity actually using a form

01:19:43.210 --> 01:19:47.050
very similar to
what I showed – F-2, F-3.

01:19:47.680 --> 01:19:53.120
We had, in the
NGA-West2 database,

01:19:53.120 --> 01:19:58.310
recordings over a very
wide range of amplitudes.

01:19:58.310 --> 01:20:02.250
And we were able to see the
nonlinearity empirically there again.

01:20:02.250 --> 01:20:06.340
And if you compare those
F-2 values derived both ways,

01:20:06.340 --> 01:20:08.680
they’re not
very divergent.

01:20:08.680 --> 01:20:14.660
There are cases where they differ,
but in totality across many periods,

01:20:14.660 --> 01:20:19.250
many different site conditions,
they’re grossly similar.

01:20:19.250 --> 01:20:23.810
And so there’s been a few investigations
like that where they seem to line up

01:20:23.810 --> 01:20:29.480
in nonlinearity if not in the overall
amplitude, and that’s really what

01:20:29.480 --> 01:20:35.020
gives me confidence in
that part of the application.

01:20:40.060 --> 01:20:44.940
- Any other questions?
- Right behind you. [laughs]

01:20:46.140 --> 01:20:49.400
- Nice talk, Jon.
Covered lots of material.

01:20:51.160 --> 01:20:56.940
How we model site – or the models
that are used for site response,

01:20:56.940 --> 01:21:00.620
to model site response,
or the physics of site response,

01:21:00.620 --> 01:21:03.440
seem to be – play a
pretty large role.

01:21:03.440 --> 01:21:07.600
Lots of little tweaks and lots of little –
whatever we can do to change that and

01:21:07.600 --> 01:21:10.780
come up with so many different things.
- Yep.

01:21:10.780 --> 01:21:14.100
- I’m going to come back to
an old issue or come back to

01:21:14.100 --> 01:21:18.760
an issue that you know very well.
But when we went from NGA-West1

01:21:18.770 --> 01:21:26.820
to NGA-West2, much larger data set,
we saw site amplifications go up, in

01:21:26.820 --> 01:21:32.860
Charlie Kirchner terms, maybe by 40%
or 45% or some pretty large number.

01:21:32.860 --> 01:21:38.240
My results showed significant
increases as well.

01:21:39.980 --> 01:21:43.980
And the only explanation
I can come up with is,

01:21:43.980 --> 01:21:49.500
is that has to be due to the models –
to the modeling because there’s a big –

01:21:49.500 --> 01:21:54.680
pretty significant modeling change
of the NGA-West1 data set

01:21:54.680 --> 01:21:59.820
versus what the developers
did for NGA-West2.

01:21:59.820 --> 01:22:06.860
Because the data set was much
larger for NGA-West1 – West2.

01:22:06.860 --> 01:22:11.100
And that would explain
some of these significant changes

01:22:11.100 --> 01:22:16.200
we saw for the softer soils
like site class E soils.

01:22:16.200 --> 01:22:23.980
It wouldn’t necessarily have such a
major impact on C or D type soils.

01:22:23.980 --> 01:22:27.400
But I was wondering if you would
comment on that aspect of this and

01:22:27.400 --> 01:22:35.140
how you think that plays into what
you’re talking about here today.

01:22:35.140 --> 01:22:39.540
- So I think your question has to
do with, you know, does the –

01:22:39.540 --> 01:22:45.960
do the NGA-West2 models
accurately reflect the data

01:22:45.960 --> 01:22:49.250
that went into their
development, more or less.

01:22:49.250 --> 01:22:52.430
And the short answer is,
yeah, they do. [chuckles]

01:22:52.430 --> 01:22:59.230
And the simple explanation is,
if you take the models and you

01:22:59.230 --> 01:23:04.750
apply them to the data set,
calculate residuals,

01:23:04.750 --> 01:23:08.480
partition the residuals properly,
take out the event terms,

01:23:08.490 --> 01:23:12.550
look at trends with V-S30,
look at trends with basin depth,

01:23:12.550 --> 01:23:16.900
look at trends with strength
of shaking, do you see bias?

01:23:16.900 --> 01:23:20.620
In other words, are there trends
where there should not be trends?

01:23:20.620 --> 01:23:23.060
And this is a standard
part of model-building.

01:23:23.070 --> 01:23:27.190
The exact same process
happens with path effects

01:23:27.190 --> 01:23:31.630
looking at distance attenuation
and all sorts of other things.

01:23:31.630 --> 01:23:33.790
So all that stuff was done, right?

01:23:33.790 --> 01:23:40.240
And the – each GMPE developer
did that more or less independently.

01:23:40.240 --> 01:23:43.500
Of course, there was
checking between us.

01:23:43.500 --> 01:23:45.580
And each one of us
showed residual plots

01:23:45.580 --> 01:23:49.580
that showed our models weren’t biased
with those predictive parameters.

01:23:49.580 --> 01:23:51.940
Then, at the end of the day,
if you plot them up

01:23:51.950 --> 01:23:58.040
one against the other,
the site terms were pretty close.

01:23:58.040 --> 01:24:01.860
A lot closer than
you get in other domains.

01:24:01.860 --> 01:24:04.520
This isn’t an area that maybe
you’ve looked at as much,

01:24:04.530 --> 01:24:09.430
but we’re dealing with the east now.
And I know that we had all kinds of

01:24:09.430 --> 01:24:15.200
back-and-forth with you and
Charlie on differences in the west.

01:24:15.200 --> 01:24:19.910
Those are tiny compared to differences
we encounter in other regions.

01:24:19.910 --> 01:24:27.230
So on that central question of whether
the models accurately reflect the data

01:24:27.230 --> 01:24:31.330
used in their derivation, I don’t
think there’s any question.

01:24:32.120 --> 01:24:36.460
Now, the first part of your question is,
you know, simulations and stuff,

01:24:36.470 --> 01:24:40.090
and yeah, there are details about that that
I didn’t get into that are very important.

01:24:40.090 --> 01:24:44.140
But that’s actually not the issue
behind your second question.

01:24:44.140 --> 01:24:48.880
Because your second question is
more about empirical models, right?

01:24:48.890 --> 01:24:52.090
And that is, did you do
your regression properly?

01:24:52.090 --> 01:24:55.820
If you’re going to compare one set
of empirical models to another set

01:24:55.820 --> 01:25:00.660
of empirical models, there’s all kinds of
things you have to be careful to control.

01:25:00.660 --> 01:25:03.480
And as you know very well –
we don’t want to hash this out again

01:25:03.480 --> 01:25:08.340
in front of all these good people – it’s
very easy to get those things incorrect.

01:25:08.340 --> 01:25:11.640
Right, and a lot of the differences
you’re talking about can be explained

01:25:11.650 --> 01:25:16.000
through carefully dissecting how
you’re making the comparisons.

01:25:16.000 --> 01:25:19.980
When that’s done properly,
those models line up very well.

01:25:19.980 --> 01:25:23.150
And that was really what
gave us confidence in

01:25:23.150 --> 01:25:27.610
the models themselves and
in the use of them since that time.

01:25:33.960 --> 01:25:36.120
- Any other questions for Jon?
[loud static]

01:25:38.160 --> 01:25:40.220
We’re going to put Jon
to work at lunch,

01:25:40.220 --> 01:25:44.700
so [chuckles] we won’t be
taking him out to the patio.

01:25:44.700 --> 01:25:47.930
And those of you who have signed up
on the Google Drive spreadsheet,

01:25:47.930 --> 01:25:53.640
we’ll give a copy to Jon, and he’ll
be coming by at [distortion].

01:25:53.640 --> 01:25:55.700
And with that, if we could
give Jon another hand.

01:25:55.700 --> 01:25:56.980
- Thanks.

01:25:56.980 --> 01:26:01.080
[ Applause ]

01:26:01.080 --> 01:26:05.460
[ Silence ]