WEBVTT
Kind: captions
Language: en

00:00:07.420 --> 00:00:09.420
Good morning, everyone.

00:00:09.420 --> 00:00:11.500
Thank you for -- thank you
for coming out today.

00:00:11.500 --> 00:00:16.450
To begin with, Susan has asked
that I remind everyone

00:00:16.450 --> 00:00:21.420
that ShakeOut is coming
October 15th, 10:15 a.m.

00:00:21.420 --> 00:00:23.740
The festivities will include
dropping, covering,

00:00:23.740 --> 00:00:26.880
and holding on, followed by
evacuating our buildings.

00:00:26.880 --> 00:00:30.560
[laughs]
Look forward to it.

00:00:30.560 --> 00:00:34.080
Next week, Wednesday,
October 14th, 10:30 a.m.,

00:00:34.090 --> 00:00:38.050
our speaker will be someone you’re
very familiar with, Jeanne Hardebeck.

00:00:38.050 --> 00:00:41.089
She will be discussing
stress orientations in subduction zones

00:00:41.089 --> 00:00:44.449
and the strength of
subduction megathrust faults.

00:00:44.449 --> 00:00:48.620
But today, from UC-Santa Cruz,
we have Emily Brodsky,

00:00:48.620 --> 00:00:50.890
who will be presenting
Constraints from Fault Roughness

00:00:50.890 --> 00:00:53.610
on Scale-Dependent
Strength of Rocks.

00:00:53.610 --> 00:00:57.290
Emily studies earthquakes
and is faculty at UC-Santa Cruz.

00:00:57.290 --> 00:00:59.610
She originally got her bachelor’s
from Harvard and her

00:00:59.610 --> 00:01:02.600
Ph.D. from Caltech working
with Hiroo Kanamori.

00:01:02.600 --> 00:01:05.299
And amongst many other honors,
she has received the Richter Award

00:01:05.299 --> 00:01:08.630
from the Seismological Society and
the Macelwane Medal from AGU.

00:01:08.630 --> 00:01:12.310
So please let’s give
Emily a warm welcome.

00:01:12.310 --> 00:01:15.490
[ Applause ]

00:01:17.380 --> 00:01:21.640
- Is that on?
Hey, folks.

00:01:21.650 --> 00:01:26.470
So nice to be back here.

00:01:26.470 --> 00:01:30.560
You really are all going
to sit back there. [laughter]

00:01:30.560 --> 00:01:34.490
I could fit an entire class
between me and you.

00:01:34.490 --> 00:01:36.219
All right. We’ll do it.

00:01:36.219 --> 00:01:38.299
- We’ve got hard questions.
Don't worry.

00:01:38.299 --> 00:01:39.340
- All right, good.

00:01:39.340 --> 00:01:45.140
And of course, I think I know
most of you, but I don't mind being

00:01:45.140 --> 00:01:54.220
interrupted for questions whenever.
This should be more of a conversation.

00:01:54.220 --> 00:01:59.250
I'm going to talk today about Inferring
Strength of Rocks from Fault Roughness.

00:01:59.250 --> 00:02:03.020
And that’s a title that might not
even make sense right now.

00:02:03.020 --> 00:02:05.409
How do you use the
roughness of faults

00:02:05.409 --> 00:02:09.140
to say anything about
the strength of rocks?

00:02:09.140 --> 00:02:13.680
This is a subject that I've been
partnering with Thibault Candela

00:02:13.680 --> 00:02:18.890
and Jamie Kirkpatrick, both of whom
used to be post-docs at Santa Cruz

00:02:18.890 --> 00:02:22.170
and have moved on to
greener pastures in --

00:02:22.170 --> 00:02:28.980
Thibault is now in the Netherlands
at TNO, and Jamie’s at McGill.

00:02:28.980 --> 00:02:33.370
And the three of us have been thinking a
lot about how to measure fault roughness

00:02:33.370 --> 00:02:36.670
and what it can tell us about
something as fundamental

00:02:36.670 --> 00:02:42.069
as the strength of rocks -- one of the
big quantities we need to know

00:02:42.069 --> 00:02:46.529
to have a first principle
understanding of earthquakes.

00:02:48.260 --> 00:02:55.819
So the story really begins about a
decade ago when another former

00:02:55.819 --> 00:03:03.770
post-doc and I -- Amir Sagy and I started
measuring fault service geometry.

00:03:03.770 --> 00:03:08.940
We would go out to --
oh, I got to use this mouse thing.

00:03:08.940 --> 00:03:11.880
We would go out to expose faults,
mainly in quarries.

00:03:11.880 --> 00:03:18.080
It’s a very common process
to quarry, for instance,

00:03:18.080 --> 00:03:20.390
gravels until you
hit a hard surface.

00:03:20.390 --> 00:03:24.090
And that exposed surface,
very often, is a fault plane

00:03:24.090 --> 00:03:27.220
in certain parts
of the world.

00:03:27.220 --> 00:03:30.280
And so here is a fault plane that is --

00:03:30.280 --> 00:03:32.940
Oh, that was exciting.

00:03:32.950 --> 00:03:35.340
So much for me using
the little pointer thing.

00:03:35.340 --> 00:03:38.560
I’m going to --
what happened?

00:03:38.560 --> 00:03:40.680
Oh, we’ll hit escape.

00:03:40.680 --> 00:03:42.379
- Brand-new.
- That’s why we [inaudible] . . .

00:03:42.379 --> 00:03:46.640
- Oh, there we go.
We’re back. We’re good.

00:03:46.640 --> 00:03:49.030
That was fun.
- Woo hoo!

00:03:49.030 --> 00:03:52.319
- And so I hope that
wasn’t too distracting.

00:03:52.319 --> 00:03:57.150
This here is a fault surface --
this relatively smooth, shiny surface.

00:03:57.150 --> 00:04:00.629
And this is kind of an interesting
picture where you can look up

00:04:00.629 --> 00:04:02.599
at the fault surface,
and at the same time,

00:04:02.599 --> 00:04:06.459
see the cross-section
of the fault zone beneath it.

00:04:06.459 --> 00:04:10.300
And so we went out to
surfaces like this one, and this --

00:04:10.300 --> 00:04:15.390
which is in Oregon,
and this one, which is in Italy.

00:04:15.390 --> 00:04:19.150
So we went all over the world,
and we brought with us

00:04:19.150 --> 00:04:26.939
our handy ground-based LiDAR,
which is a laser-ranging instrument

00:04:26.939 --> 00:04:31.849
that collects -- that sends out a laser,
measures the time of flight,

00:04:31.849 --> 00:04:39.430
and then scans that laser so that
we can collect a point cloud of data with,

00:04:39.430 --> 00:04:45.330
in optimal conditions, as much
as 3- to 4-millimeter resolution.

00:04:45.330 --> 00:04:48.719
And so we walk up to a fault,
and we walk away with a data set

00:04:48.719 --> 00:04:53.039
that looks something like this,
where that square -- that rectangle

00:04:53.039 --> 00:05:01.479
on this -- on the photograph has become
the data you see in the bottom panel.

00:05:01.479 --> 00:05:04.729
Okay.
And at the time,

00:05:04.729 --> 00:05:09.210
I remember lots of people
asking us why are we measuring

00:05:09.210 --> 00:05:11.430
the topography
of fault surfaces?

00:05:11.430 --> 00:05:14.419
Why do we want to know
the roughness of fault surfaces?

00:05:14.419 --> 00:05:22.369
And I have to say, Amir and I kind of
flubbed that question an awful lot.

00:05:22.369 --> 00:05:26.020
We knew that this was
the surface on which

00:05:26.020 --> 00:05:28.879
much of the slip
of earthquakes happen.

00:05:28.879 --> 00:05:32.759
And so we thought that there
must be some sort of fingerprint

00:05:32.759 --> 00:05:36.129
of the processes
controlling slip on the surface.

00:05:36.129 --> 00:05:39.210
We weren't quite sure
what we were looking at.

00:05:39.210 --> 00:05:43.520
We were also clear that,
since this was a failure surface,

00:05:43.520 --> 00:05:49.129
there must be some sort of information
of strength in there somewhere.

00:05:49.129 --> 00:05:53.039
That’s the process that
makes the surface, right?

00:05:53.039 --> 00:05:58.539
But I’m not sure we had a very
well-articulated answer beyond that.

00:05:58.539 --> 00:06:00.499
So it was a little bit
of a fishing expedition.

00:06:00.500 --> 00:06:04.580
That’s sometimes
how science works.

00:06:04.580 --> 00:06:11.699
And so when we went fishing,
we came back with this.

00:06:11.699 --> 00:06:19.879
What you’re looking at is power
spectra of fault surface topography

00:06:19.879 --> 00:06:23.680
in the direction
parallel to slip.

00:06:23.680 --> 00:06:28.020
So the basic issue
in looking at fault surfaces

00:06:28.020 --> 00:06:32.089
is that faults are
rough at all scales.

00:06:32.089 --> 00:06:36.029
And therefore, if you wanted to
come up with some sort of measure

00:06:36.029 --> 00:06:39.699
of roughness, you need to do it
in a scale-dependent way.

00:06:39.699 --> 00:06:44.759
To think about that a little bit,
you can look at this little cartoon here

00:06:44.759 --> 00:06:49.899
for a single line, a profile,
along a fault surface.

00:06:49.899 --> 00:06:54.460
Say H is schematically
the average deviation --

00:06:54.460 --> 00:06:57.800
the average asperity height
from a best-fit line.

00:06:57.800 --> 00:07:04.319
And L is the scale of observation
of this little blue cartoon.

00:07:04.319 --> 00:07:07.860
If we had taken a smaller scale of
observation, say this little chunk

00:07:07.860 --> 00:07:14.339
right here, and did a best-fit line,
H would have been much smaller, right?

00:07:14.339 --> 00:07:18.219
So the RMS roughness, H,
the average asperity height,

00:07:18.219 --> 00:07:22.319
is a function of scale --
of observation scale, L.

00:07:22.319 --> 00:07:26.279
And that’s critically important
in thinking about fault roughness.

00:07:26.279 --> 00:07:29.849
Since we have things that are --
we have a measurement that has

00:07:29.849 --> 00:07:33.719
a scale-dependent feature,
we don't really want to talk about

00:07:33.719 --> 00:07:36.399
just average asperity height
anymore, therefore.

00:07:36.399 --> 00:07:39.919
We don't want to say the average
roughness of this fault is 1 centimeter.

00:07:39.919 --> 00:07:41.729
That wouldn't make any sense.

00:07:41.729 --> 00:07:47.479
You'd have to say the average roughness
at a meter of observation is 1 centimeter.

00:07:47.479 --> 00:07:54.259
And if you want to capture all of the
information in the topographic map,

00:07:54.259 --> 00:07:59.629
it might make sense
to do a Fourier analysis.

00:07:59.629 --> 00:08:09.740
That is to break up the signal
into its various wavelength components

00:08:09.740 --> 00:08:13.659
and look at the power of the
topographic signal as a

00:08:13.659 --> 00:08:20.149
function of wavelength, just like
we often do for earthquakes.

00:08:20.149 --> 00:08:25.879
And so what you’re looking at here
is a Fourier transforms

00:08:25.879 --> 00:08:28.919
of profiles in the
along-slip direction.

00:08:28.919 --> 00:08:36.060
And then all of those
spectra average together

00:08:36.060 --> 00:08:40.300
for at least 500 profiles
for each fault.

00:08:40.300 --> 00:08:44.210
And because we have lots of data
for each fault, we can do this

00:08:44.210 --> 00:08:47.760
averaging operation that results
in very smooth spectral estimations.

00:08:47.760 --> 00:08:51.190
These are probably much smoother
than you’re used to seeing,

00:08:51.190 --> 00:08:55.190
say, source spectra
at earthquake.

00:08:55.190 --> 00:09:02.580
And -- okay, and since power spectral
density is a function of wavelength

00:09:02.580 --> 00:09:07.280
might not be the most obvious thing
to sort of get your head around,

00:09:07.280 --> 00:09:15.580
I have for reference here,
as a dashed line right here,

00:09:15.580 --> 00:09:18.550
the line of what the power
spectral density would be

00:09:18.550 --> 00:09:24.410
if the asperity height is 1% -- 0.01
of the observation scale at all scales.

00:09:24.410 --> 00:09:29.090
A [inaudible] surface
with a constant aspect ratio --

00:09:29.090 --> 00:09:32.410
a constant ratio
of H over L.

00:09:34.720 --> 00:09:36.980
It’s a useful reference line.

00:09:36.980 --> 00:09:40.520
As we will see later in the talk,
it’s more than a useful reference line.

00:09:40.520 --> 00:09:44.860
It turns out to be
quite fundamental.

00:09:44.870 --> 00:09:49.650
And what you see in this data -- what we
saw, at least in our first pass through the

00:09:49.650 --> 00:10:01.770
data, is that a lot of the faults cluster near
that 1% line, at least at the field scales.

00:10:05.020 --> 00:10:09.120
This is the scale of -- at which we
have observations with LiDAR.

00:10:09.120 --> 00:10:13.460
Down here are laboratory
measurements on hand samples.

00:10:13.460 --> 00:10:16.320
More about them later.

00:10:16.320 --> 00:10:21.020
And I’ll -- for faults that have
not slipped enough -- a lot --

00:10:21.020 --> 00:10:28.180
and in this -- in this particular study,
not -- immature, not slipping a lot,

00:10:28.180 --> 00:10:31.320
was much less
than 100 meters.

00:10:31.320 --> 00:10:44.360
So we had the lines clustering
quite closely next to the 1% line.

00:10:44.360 --> 00:10:48.140
And then there was a
population of faults

00:10:48.150 --> 00:10:53.630
that had slipped a lot
that were somewhat smoother.

00:10:54.320 --> 00:10:56.320
And ...

00:10:58.460 --> 00:11:00.820
...that was our
first take on it.

00:11:00.830 --> 00:11:03.730
And I was sort of excited at this point
because, you know, here we were

00:11:03.730 --> 00:11:07.490
in this fishing expedition, and we
were getting some systematics.

00:11:07.490 --> 00:11:10.180
And thought, oh, we’re going to
be able to figure out the displacement

00:11:10.180 --> 00:11:13.660
and offset of faults by looking
at the roughness of their surfaces.

00:11:13.660 --> 00:11:18.870
And that’s going to be a neat way
to sort of work out the history

00:11:18.870 --> 00:11:20.630
and geological
history of faults.

00:11:20.630 --> 00:11:24.510
That’s what I -- where I thought
this project was going.

00:11:24.510 --> 00:11:27.420
So I tried to do that.

00:11:27.420 --> 00:11:31.690
And it didn't work out
all that well.

00:11:31.690 --> 00:11:36.450
What is here is an expanded
data set from the original paper

00:11:36.450 --> 00:11:42.240
where I got more faults with
a greater variety of displacements.

00:11:42.240 --> 00:11:47.900
And what we see is that -- here I am
showing you an average asperity height

00:11:47.900 --> 00:11:50.450
at a reference wavelength,
just so we have a single number

00:11:50.450 --> 00:11:55.240
to compare at different faults --
in this case, at 1/2 a meter.

00:11:55.240 --> 00:11:59.750
And what we see is, as a function
of total offset on the fault, yes,

00:11:59.750 --> 00:12:05.090
the more mature faults, the ones
that have slipped more, as a population,

00:12:05.090 --> 00:12:08.200
have -- are smoother than the ones
that haven't slipped all that much.

00:12:08.200 --> 00:12:11.820
But, wow, is that a small variation.

00:12:11.820 --> 00:12:15.040
I mean, if you were
really, really ambitious,

00:12:15.040 --> 00:12:20.340
you might try to fit a straight line
in this long, linear -- long, long plot.

00:12:20.340 --> 00:12:24.470
And you'd get a tiny little
exponent of minus 1/10th.

00:12:24.470 --> 00:12:30.070
But that’s -- what that’s really telling
you is this is a very weak trend.

00:12:30.070 --> 00:12:33.040
And once you get to the high slip,
you know, any kind of slip

00:12:33.040 --> 00:12:37.290
that we would normally care about
on an earthquake fault that

00:12:37.290 --> 00:12:44.780
has mappable earthquakes, there
really wasn't any trend in the data.

00:12:44.780 --> 00:12:48.100
Huh.
Well, that was interesting.

00:12:48.100 --> 00:12:52.000
So then,
back to the drawing board.

00:12:52.010 --> 00:12:56.540
Faults are -- so faults are
smoothing gradually during slip

00:12:56.540 --> 00:13:01.510
rather than continually
or in any catastrophic way.

00:13:01.510 --> 00:13:06.760
And so back to the drawing board.
Let’s look again at our full data set.

00:13:06.760 --> 00:13:11.100
And at this point, our full data set
now includes 22 faults.

00:13:11.100 --> 00:13:15.480
Each of those faults
mainly are those little light blue lines

00:13:15.480 --> 00:13:16.880
you see -- the light blue, thin lines.

00:13:16.880 --> 00:13:20.100
And then a couple of those --
three of those faults we have highlighted

00:13:20.100 --> 00:13:24.760
as the thicker colored lines
just so you can see how data matches up

00:13:24.760 --> 00:13:32.180
for a single fault, just to be able to kind
of get the systematics of individuals.

00:13:33.980 --> 00:13:39.820
And what we noticed
about this data is that

00:13:39.820 --> 00:13:44.880
all 22 faults seem to have roughness
in this incredibly narrow range.

00:13:44.880 --> 00:13:56.450
At field scale, say 1 meter -- at 1 meter,
we have roughness between 0.1%

00:13:56.450 --> 00:14:07.400
and 1% at most of -- a little bit less
than 1% of aspect ratios, okay?

00:14:07.400 --> 00:14:14.560
Again, the red lines are
for reference -- are what you would get

00:14:14.560 --> 00:14:20.370
in power spectra if the aspect ratio,
H over L, average height

00:14:20.370 --> 00:14:23.720
over observation scale,
is constant.

00:14:23.720 --> 00:14:31.500
Okay, so data is telling us that
fault roughness is very restricted.

00:14:31.500 --> 00:14:34.080
Surprisingly restricted.

00:14:34.080 --> 00:14:39.260
And that’s good news for people who
just want to empirically use this data.

00:14:39.260 --> 00:14:43.540
And we do actually have
end users of this data set.

00:14:43.540 --> 00:14:45.550
Even though we went out there
on this fishing expedition,

00:14:45.550 --> 00:14:53.180
it turns out that we found a customer
base that -- numerical modelers

00:14:53.180 --> 00:14:58.330
who are interested in doing things
like predicting strong ground motion

00:14:58.330 --> 00:15:08.290
have used our measurements of fault
roughness to make rough faults into --

00:15:08.290 --> 00:15:12.900
and dynamically rupture those faults
and then predict the seismic waves

00:15:12.900 --> 00:15:15.110
that come off those faults.

00:15:15.110 --> 00:15:21.060
And what they find is they can make --
well, “they” being, in this case,

00:15:21.060 --> 00:15:27.520
Eric Dunham and his students
have found that they can make realistic

00:15:27.520 --> 00:15:33.470
high-frequency strong ground shaking
by using realistic roughness on faults.

00:15:33.470 --> 00:15:41.320
That using these 1% to 0.1% aspect
ratios, here he’s calling alpha,

00:15:41.320 --> 00:15:47.710
the aspect ratio, corresponds to
realistic strong ground motion.

00:15:47.710 --> 00:15:57.380
So this is -- again, so this is an
end user who is assuming

00:15:57.380 --> 00:16:01.960
that the range of roughnesses
that we measure does capture the range

00:16:01.960 --> 00:16:05.490
of the real earth and is able to
make realistic-looking seismograms.

00:16:05.490 --> 00:16:08.380
And if you think about it in reverse,
it also is a little bit of confirmation,

00:16:08.380 --> 00:16:12.589
maybe, that we really do have this
very restricted range of roughnesses

00:16:12.589 --> 00:16:17.040
in the earth if this is an accurate
explanation for strong ground motion.

00:16:17.040 --> 00:16:23.640
Okay. So that’s observation
number one, really.

00:16:28.750 --> 00:16:35.839
Looking at the data again,
you may also notice that

00:16:35.839 --> 00:16:40.660
the slope of these spectras is
not actually a constant aspect ratio.

00:16:40.660 --> 00:16:43.589
It is somewhat shallower.

00:16:43.589 --> 00:16:55.880
The best-fit slope would be for a X --
if the average height went

00:16:55.880 --> 00:17:03.170
as length scale to the 0.6 --
so, in other words, if you put --

00:17:03.170 --> 00:17:08.260
instead of H over L, H over L
to the 0.6 as constant --

00:17:08.260 --> 00:17:12.019
I’m not sure you should get that excited
about exactly what that exponent is,

00:17:12.019 --> 00:17:18.740
but the main point I’m trying to make
here is that those are shallower slopes,

00:17:18.740 --> 00:17:25.920
and they cross over the red lines
of constant aspect ratios.

00:17:25.920 --> 00:17:29.840
And just to make sure this isn't some
funky artifact of doing things

00:17:29.840 --> 00:17:37.639
in spectral space, let’s think about
what this means in the spatial domain.

00:17:37.639 --> 00:17:41.580
So what this would mean
in the spatial domain

00:17:41.580 --> 00:17:48.129
is that aspect ratio is smaller for
larger wavelengths -- larger scales.

00:17:48.129 --> 00:17:51.659
And at smaller scales
the mountains get steeper.

00:17:51.659 --> 00:17:55.179
The very big mountains
on the surface of the fault --

00:17:55.179 --> 00:17:58.939
not so big,
but they do get steeper.

00:17:58.940 --> 00:18:01.800
And that is, in fact,
what we see in the spatial domain.

00:18:01.809 --> 00:18:06.090
If we sit there and look at
individual profiles and zoom in,

00:18:06.090 --> 00:18:10.080
we do see that the aspect ratio
measured in the spatial domain

00:18:10.080 --> 00:18:13.129
does increase
with decreasing scale.

00:18:13.129 --> 00:18:17.089
So we’re not deluding ourselves
in spectral space.

00:18:22.850 --> 00:18:27.220
So that’s interesting. Aspect ratio
increases with decreasing scale.

00:18:27.220 --> 00:18:29.869
And that seems to be
a pretty robust observation.

00:18:29.869 --> 00:18:36.259
And, you know, it even looks like
you get some sort of consistent scaling

00:18:36.259 --> 00:18:40.879
with at least a best-fit line
over a large range of scales here --

00:18:40.879 --> 00:18:44.049
scales from millimeters
to tens of meters.

00:18:44.049 --> 00:18:52.580
And that’s a little surprising, I think,
to a geologist because -- you know,

00:18:52.580 --> 00:18:55.440
if you actually go out and look at a fault
surface, there are lots of different

00:18:55.440 --> 00:18:59.470
processes happening at these
different scales on fault surfaces.

00:18:59.470 --> 00:19:04.710
You can look at, you know, the
millimeter scale, and you can see grain

00:19:04.710 --> 00:19:09.340
fracture and slickenlines at intermediate
scale -- at sort of centimeter scales.

00:19:09.340 --> 00:19:11.990
And at meters or tens of meter scale,
you see mullions.

00:19:11.990 --> 00:19:15.429
They're really different features.
So why are we getting something

00:19:15.429 --> 00:19:20.190
that at least, at first blush,
is like a line on a long, long plot --

00:19:20.190 --> 00:19:24.940
a consistent scaling
over many scales?

00:19:24.940 --> 00:19:29.440
Okay, so these are the puzzles
about the fault roughness data.

00:19:29.440 --> 00:19:33.960
And I think an answer
might have to do with

00:19:33.970 --> 00:19:39.830
how these rough surfaces
interact with each other.

00:19:39.830 --> 00:19:45.450
If you are going to shear
two rough surfaces past each other,

00:19:45.450 --> 00:19:50.610
the first thing that has to happen
as those surfaces shear past each other

00:19:50.610 --> 00:19:55.700
is they start to deform
to make room, right?

00:19:55.700 --> 00:20:07.330
And the strain required to
completely flatten this bump --

00:20:07.330 --> 00:20:13.159
the shear strain required, by definition,
is the displacement in one direction --

00:20:13.159 --> 00:20:15.690
in the, say, Z direction --
divided by the length scale,

00:20:15.690 --> 00:20:19.169
that displacement’s accommodated
in the opposite direction.

00:20:19.169 --> 00:20:22.350
So H over L.

00:20:22.350 --> 00:20:27.570
So if, for instance,
this strain is accommodated elastically,

00:20:27.570 --> 00:20:32.239
the stress would be
proportional to H over L.

00:20:32.239 --> 00:20:34.809
And the first process
that is in play

00:20:34.809 --> 00:20:42.470
as two surfaces slide past each other
is the elastic deformation.

00:20:42.470 --> 00:20:47.400
The first, I say,
at small deformations.

00:20:47.400 --> 00:20:49.320
Okay.
Everybody with that thought?

00:20:49.330 --> 00:20:54.600
Because the entire rest of this talk
is based on that thought.

00:20:54.600 --> 00:20:57.060
I’m going to take a pause here.

00:20:57.060 --> 00:20:58.860
We’re all good?

00:20:58.869 --> 00:21:00.869
- But it’s not going to be elastic.

00:21:00.869 --> 00:21:05.880
- No, it’s not.
Thank you, Wade.

00:21:05.889 --> 00:21:10.590
At some point, when that strain
becomes too large,

00:21:10.590 --> 00:21:15.269
something inelastic
will have to happen.

00:21:15.269 --> 00:21:17.200
It will fail.

00:21:17.200 --> 00:21:20.739
It can fail brittle-y.
It can fail plastically.

00:21:20.739 --> 00:21:24.350
There are varieties of ways
to make rock fail.

00:21:24.350 --> 00:21:26.559
But the important point is
that there will be

00:21:26.559 --> 00:21:32.059
a critical strain
at which failure occurs.

00:21:32.060 --> 00:21:35.940
Once it fails, that’s the
end of the asperity.

00:21:35.950 --> 00:21:41.610
So the maximum aspect ratio --
the maximum strain possible

00:21:41.610 --> 00:21:48.539
in a fault surface is going to be
governed by this critical strain,

00:21:48.539 --> 00:21:52.159
which is the
threshold for failure.

00:21:52.160 --> 00:21:56.400
- It’ll fail way before that.

00:21:56.400 --> 00:22:00.360
- Why?
That’s the definition of failure.

00:22:00.369 --> 00:22:03.860
The definition of failure
is the strain at which it fails.

00:22:06.760 --> 00:22:09.140
Okay?
- Actually, Emily, since you did

00:22:09.149 --> 00:22:11.899
ask about that relationship,
is that just a scaling relationship,

00:22:11.899 --> 00:22:14.350
or is that based upon
elastic contact mechanics?

00:22:14.350 --> 00:22:16.039
The H over L scale.

00:22:16.039 --> 00:22:18.409
- Right now, I’m using it
as a scaling relationship.

00:22:18.409 --> 00:22:21.179
You can get exactly the same thing
out of a Hertzian contact.

00:22:21.179 --> 00:22:22.789
- Okay.
- Yeah.

00:22:22.789 --> 00:22:26.919
If you sit there with a Hertzian contact,
A over R goes as H over L.

00:22:26.919 --> 00:22:29.770
- But that’s for normal displacement
as opposed to shear.

00:22:29.770 --> 00:22:30.390
- Right.
- Okay.

00:22:30.390 --> 00:22:32.549
- But the shear is proportional
to the normal for a Hertzian contact.

00:22:32.549 --> 00:22:33.929
- Okay. So it’s that kind of scaling.
Okay, thanks.

00:22:33.929 --> 00:22:35.820
- Okay. So it’s a scaling.
And we’re going to use it as

00:22:35.820 --> 00:22:38.320
a proportionality because
of those details.

00:22:38.320 --> 00:22:41.610
I did ask for it, right?
- Yeah.

00:22:41.610 --> 00:22:44.029
- Because of those details,
I am going to use this strictly as a

00:22:44.029 --> 00:22:50.700
proportionality statement and -- because
it is rigorously correct in this way.

00:22:50.700 --> 00:22:53.989
But working through what the
constants are in front would require

00:22:53.989 --> 00:22:57.320
a more detailed model of
both the failure process

00:22:57.320 --> 00:23:02.080
and the geometry in that
long-range elastic attractions.

00:23:02.080 --> 00:23:03.600
- Okay, thanks.

00:23:03.600 --> 00:23:05.300
- Okay.

00:23:05.300 --> 00:23:14.540
Okay, so what I am proposing here
is that the elastic --

00:23:14.549 --> 00:23:21.369
that the observed aspect ratio
is capped by some sort of failure strain.

00:23:21.369 --> 00:23:25.600
And that failure strain
varies as a function of scale

00:23:25.600 --> 00:23:29.800
because we see the aspect ratio
vary as a function of scale.

00:23:32.900 --> 00:23:39.119
So for instance, if I fit a line --
I fit the power spectra --

00:23:39.119 --> 00:23:42.459
the observed roughness for a
particular fault -- I’m going to use for --

00:23:42.459 --> 00:23:45.559
as this example, 
the Corona Fault in San Francisco.

00:23:45.570 --> 00:23:51.840
This is a fault in the Castro district about
10 minutes from the Moscone Center,

00:23:51.840 --> 00:23:57.649
should you ever want to take a break
from AGU. Lovely fault.

00:23:57.649 --> 00:24:02.700
And it is -- in that case,
the dashed line

00:24:02.700 --> 00:24:07.609
is aspect ratio as a
function of scale as observed.

00:24:07.609 --> 00:24:14.789
And as advertised, the aspect ratio
increases at smaller scale.

00:24:14.789 --> 00:24:17.090
The mountains are
steeper at smaller scale.

00:24:17.090 --> 00:24:23.129
And so in this case, the observed
scale dependence is that

00:24:23.129 --> 00:24:29.970
the aspect ratio goes as observation
to the -- observation scale to the 0.6,

00:24:29.970 --> 00:24:35.460
which means the aspect ratio
goes as -- divide both sides by L --

00:24:35.460 --> 00:24:38.730
goes as L to the minus 0.4.

00:24:38.730 --> 00:24:40.499
Okay?

00:24:41.820 --> 00:24:46.899
So what I’m suggesting
is that we can interpret

00:24:46.899 --> 00:24:54.399
that aspect ratio
as a yield strain.

00:24:56.950 --> 00:25:00.149
Or at least proportional
to a yield strain.

00:25:00.149 --> 00:25:03.590
And though we have
different processes that are governing

00:25:03.590 --> 00:25:07.649
that yield at different scales,
and this is schematic --

00:25:07.649 --> 00:25:10.859
that we might have fractures
or tool marks or ledges.

00:25:10.859 --> 00:25:13.509
There are different processes
that are geologically identified

00:25:13.509 --> 00:25:18.960
at different scales -- they're all
yielding in some form or another.

00:25:18.960 --> 00:25:21.960
And so therefore,
we translate that

00:25:21.960 --> 00:25:27.800
dependence of aspect ratio
to a scale dependence of yield strain.

00:25:32.560 --> 00:25:36.980
Okay, so now I said that we’ve
looked at the roughness of faults

00:25:36.989 --> 00:25:42.590
and found scale-dependent strength --
or the scale dependence of strength,

00:25:42.590 --> 00:25:45.590
defined as yield strain.

00:25:45.590 --> 00:25:54.140
And does this dependence make any
sense based on anything else we know?

00:25:54.140 --> 00:25:58.960
Well, at least it -- it says --
there’s a negative exponent there.

00:25:58.970 --> 00:26:03.789
So that says that, at smaller scales,
rocks are stronger.

00:26:03.789 --> 00:26:06.580
That is the common
wisdom on rocks.

00:26:06.580 --> 00:26:10.619
They have decreasing strength
as a function of scale.

00:26:10.619 --> 00:26:17.139
That’s commonly thought to be
because there is a larger probability

00:26:17.139 --> 00:26:23.470
of hitting a flaw of a given size
for larger rocks.

00:26:23.470 --> 00:26:28.840
And so therefore, you have decreasing
strength as a function of scale.

00:26:28.840 --> 00:26:32.100
And so that’s a
feature captured here.

00:26:32.100 --> 00:26:34.489
What other measurements
on real rocks do we have

00:26:34.489 --> 00:26:39.189
to compare this
interpretation to?

00:26:43.940 --> 00:26:46.080
Well . . .

00:26:55.420 --> 00:26:59.660
There are measurements in the
laboratory of rock strength

00:26:59.669 --> 00:27:05.019
as a function of scale that generally
come up with scalings of 1/2.

00:27:05.019 --> 00:27:07.230
So 0.4 is pretty close to 1/2.

00:27:07.230 --> 00:27:12.350
Certainly within the precision
of any of these measurements.

00:27:12.350 --> 00:27:17.879
So perhaps that’s a little bit of
confirmation that, empirically,

00:27:17.879 --> 00:27:24.399
we are recreating a scaling that is
thought to apply to rocks in the lab.

00:27:24.400 --> 00:27:28.320
To the best of my knowledge,
there is not a similar data set

00:27:28.330 --> 00:27:31.639
in nature doing strength
as a function of scale.

00:27:31.639 --> 00:27:36.940
So as I hunt around for something else
to compare this to at field scales,

00:27:36.940 --> 00:27:39.429
I don't think there’s a lot out there.

00:27:39.429 --> 00:27:43.680
And I’m sure somebody will correct me
in this audience if I am wrong.

00:27:43.680 --> 00:27:48.419
I’d love to hear about it.

00:27:48.419 --> 00:27:51.570
But part of the reason this
is a valuable measurement

00:27:51.570 --> 00:27:57.440
is because this is a hard thing to
measure on real rocks at field scales.

00:27:57.440 --> 00:28:01.500
And so I think we
might be heading there.

00:28:05.500 --> 00:28:13.940
One other piece of possible
corroboration is, when we actually

00:28:13.950 --> 00:28:22.999
look at larger -- at scales of --
field scales, for instance,

00:28:22.999 --> 00:28:30.549
on the Corona Fault, we find evidence
for failure at multiple scales.

00:28:30.549 --> 00:28:37.129
Remember the pictures of intragranular
fracture and slickenlines and mullions.

00:28:37.129 --> 00:28:42.169
There are non-elastic processes
making failure at multiple scales.

00:28:42.169 --> 00:28:47.480
So this idea that failure happens
at all scales is not crazy.

00:28:47.480 --> 00:28:51.320
And in fact, if we go in detail --
for instance, on Corona,

00:28:51.320 --> 00:28:59.509
we looked at the orientation of
slickenlines around topographic bumps

00:28:59.509 --> 00:29:04.879
and found that the topographic bumps
did not, in fact, deflect the slickenlines,

00:29:04.879 --> 00:29:09.169
that the slip went straight on over
the topography as if it wasn't there,

00:29:09.169 --> 00:29:12.989
which implies a relative
weakness of that topography.

00:29:12.989 --> 00:29:16.450
So at least that’s somewhat
confirmatory with this view

00:29:16.450 --> 00:29:20.519
of failure at multiple scales.

00:29:20.519 --> 00:29:22.719
Okay.

00:29:22.720 --> 00:29:24.840
So . . .

00:29:30.700 --> 00:29:35.480
One conundrum that comes out
of this analysis is that --

00:29:35.489 --> 00:29:37.220
what happens at small scales?

00:29:37.220 --> 00:29:42.899
I've just proposed to you that we have
observed a scale dependence of

00:29:42.899 --> 00:29:48.330
aspect ratio, and we’re interpreting it
as a scale dependence of strength.

00:29:48.330 --> 00:29:55.809
This has an obvious problem at
L equals zero. Right? It blows up.

00:29:55.809 --> 00:29:59.330
One could argue that it is
probably truncated at some level

00:29:59.330 --> 00:30:04.879
by the intrinsic unflawed
strength of rocks.

00:30:04.879 --> 00:30:08.339
That may well be the case.

00:30:08.340 --> 00:30:16.679
However, I’d like to actually look at
small scales, and let’s see what happens.

00:30:16.679 --> 00:30:21.649
So when we look at small scales,
if we take samples into the laboratory,

00:30:21.649 --> 00:30:24.950
we find something very curious.

00:30:24.950 --> 00:30:28.479
What you’re looking at
for this example is

00:30:28.479 --> 00:30:32.379
a piece of fault
from Mount St. Helens.

00:30:32.380 --> 00:30:37.280
All right. Mount St. Helens Fault
may not be everybody’s favorite fault.

00:30:37.280 --> 00:30:39.140
It’s actually one of
my favorite faults.

00:30:39.149 --> 00:30:45.799
It’s actually the shear edge of
one of the 2004 eruption spines.

00:30:45.799 --> 00:30:53.299
As that spine pushed its way up past the
crater wall, there’s this highly grooved,

00:30:53.299 --> 00:30:58.570
striated surface with fault gouge
piled up at the bottom of the spine.

00:30:58.570 --> 00:31:00.489
It’s really a neat place.

00:31:00.489 --> 00:31:02.749
And part of
what makes it neat

00:31:02.749 --> 00:31:08.470
is this particular sample was collected
in 2008, was extremely fresh.

00:31:08.470 --> 00:31:10.509
It clearly had just formed.

00:31:10.509 --> 00:31:13.109
There are earthquakes associated
with the extrusion of that spine.

00:31:13.109 --> 00:31:16.809
We know a fair amount about it.
The earthquakes are shear --

00:31:16.809 --> 00:31:22.149
are thought to be shear failures
on that slip surface.

00:31:22.149 --> 00:31:29.289
So it hasn't had a long
and complicated history past that.

00:31:34.599 --> 00:31:39.349
When you take this obviously
striated sample into the laboratory

00:31:39.349 --> 00:31:42.190
and stick it under
a white light interferometer,

00:31:42.190 --> 00:31:46.999
and take a small-scale
picture of the surface, there is a

00:31:46.999 --> 00:31:52.459
scale somewhere below a millimeter
at which you no longer see grooves.

00:31:52.460 --> 00:31:56.740
As shown on the
topography image there.

00:31:56.749 --> 00:32:03.940
So another way of thinking about it is
that this surface is clearly anisotropic.

00:32:03.940 --> 00:32:07.000
Right, the slip-parallel roughness
is different than the

00:32:07.009 --> 00:32:10.499
slip-perpendicular.
That’s what grooves are.

00:32:10.499 --> 00:32:19.210
And this surface is isotropic.
Roughness is the same in all directions.

00:32:19.210 --> 00:32:27.659
And that is a feature. We can capture
the power spectral density that is not --

00:32:27.659 --> 00:32:33.580
that we -- here we are at Corona Heights
again -- Corona Fault again.

00:32:33.580 --> 00:32:36.679
And same deal.
Is we are looking at power

00:32:36.679 --> 00:32:44.109
spectral density, but now we are looking
at much smaller scales than prior.

00:32:44.109 --> 00:32:47.309
Between a micron and a millimeter.

00:32:47.309 --> 00:32:55.739
And the spectra diverge in the
slip-parallel and slip-perpendicular

00:32:55.739 --> 00:33:01.929
direction at large scales, but they
come together at some small scales.

00:33:01.929 --> 00:33:05.609
And you can -- again, to guard
against deluding ourselves,

00:33:05.609 --> 00:33:09.029
we can see the same feature in
just the raw maps,

00:33:09.029 --> 00:33:13.029
that at the tens of microns scale, it is --
you wouldn't know which way

00:33:13.029 --> 00:33:17.590
this thing was flipping, or certainly
you'd have to look at it pretty carefully.

00:33:17.590 --> 00:33:21.410
Whereas, it’s pretty obvious at this scale.

00:33:28.500 --> 00:33:33.260
When Thibault first showed this to me,
I was sure he had done some

00:33:33.269 --> 00:33:36.059
horrible experimental thing
with the white light interferometer,

00:33:36.059 --> 00:33:40.859
and it was some sort of artifact.
But he kept doing it.

00:33:40.859 --> 00:33:48.529
And we kept finding it
on lots of different slip surfaces.

00:33:48.529 --> 00:33:55.090
Here’s a suite of faults where
he’s looking at the spectra and

00:33:55.090 --> 00:34:00.369
marking with the circles
where the spectra come together.

00:34:00.369 --> 00:34:02.499
And we’re going to
call that the

00:34:02.499 --> 00:34:06.159
minimum grooving scale,
or the transition scale.

00:34:08.780 --> 00:34:11.720
And it seems to be,
for most faults that he was measuring,

00:34:11.720 --> 00:34:14.600
somewhere between
tens and hundreds of microns.

00:34:17.850 --> 00:34:22.620
And at that point, we started trying
to understand why the scale existed.

00:34:22.620 --> 00:34:24.100
What’s it telling us?

00:34:24.100 --> 00:34:27.220
And we started trying to relate it
to various properties of the rocks.

00:34:27.220 --> 00:34:31.510
And, you know, we spent
about a year looking at grain size,

00:34:31.510 --> 00:34:35.110
but that didn't work out.

00:34:35.110 --> 00:34:40.980
And it doesn't seem to be correlated
with grain size as far as we can tell.

00:34:40.980 --> 00:34:49.270
But we just have this suite of,
you know, almost -- you know,

00:34:49.270 --> 00:34:53.530
about an order of magnitude and a half
of wavelengths of different --

00:34:53.530 --> 00:35:01.020
for different faults that we observe
this onset scale on.

00:35:01.020 --> 00:35:06.800
I think the big breakthrough came
when we dropped a line on this graph.

00:35:06.800 --> 00:35:13.330
This line of constant aspect ratio that
we’ve been playing with -- in this case,

00:35:13.330 --> 00:35:19.360
for reference, a 1% line -- actually
went through the data pretty well.

00:35:19.360 --> 00:35:23.620
That all these different transition scales
seemed to be corresponding to a similar

00:35:23.620 --> 00:35:30.440
aspect ratio at the scale of transition --
at the minimum grooving scale.

00:35:30.440 --> 00:35:37.600
As it turns out, that result held up,
even for a more peculiar observation.

00:35:37.600 --> 00:35:47.720
That the -- if we look at individual
faults, samples from different places

00:35:47.720 --> 00:35:51.520
on the same fault, or even --
you take the same hand sample

00:35:51.520 --> 00:35:58.120
and do different spots with the white
light interferometer, you will, in fact,

00:35:58.120 --> 00:36:02.400
get different transition scales
at different places on the fault

00:36:02.400 --> 00:36:05.930
or even at different places
on the sample.

00:36:05.930 --> 00:36:08.910
Spectral estimation
is a statistical quantity.

00:36:08.910 --> 00:36:12.770
And roughness is not really the
same everywhere on the fault.

00:36:16.330 --> 00:36:22.390
So, however, if you mark the
transition scale at different --

00:36:22.390 --> 00:36:25.800
from different images --
different sub-samples of the fault,

00:36:25.800 --> 00:36:31.740
for any given fault, the transition
scales all fall on the same aspect ratio.

00:36:35.750 --> 00:36:38.450
Here for Corona Fault,
it’s around 1%.

00:36:38.450 --> 00:36:42.120
For Mount St. Helens,
it’s somewhat higher.

00:36:42.120 --> 00:36:46.770
The aspect ratio is just under 10%
at which the transition scale occurs.

00:36:46.770 --> 00:36:50.240
So the physical control of this
minimum grooving scale,

00:36:50.240 --> 00:36:53.500
whatever that physical
control seems to -- is, seems to

00:36:53.500 --> 00:36:57.570
be related to aspect ratio,
not length by itself.

00:36:57.570 --> 00:37:04.070
It's the ratio of asperity height
to length that matters.

00:37:04.070 --> 00:37:08.800
So here’s the full suite of data
which Thibault has measured.

00:37:08.800 --> 00:37:13.650
Minimum grooving scale at this point.

00:37:13.650 --> 00:37:16.270
You can --
different colors on the top --

00:37:16.270 --> 00:37:20.800
so the top fault panel
is natural slip surfaces.

00:37:20.800 --> 00:37:24.010
The bottom panel is
experimental slip surface,

00:37:24.010 --> 00:37:31.170
including some that have come from
Diane Moore’s lab here in Menlo Park.

00:37:31.170 --> 00:37:35.880
And as you can -- and the
different colors -- each set of colors

00:37:35.880 --> 00:37:39.180
corresponds to --
at least within a panel --

00:37:39.180 --> 00:37:45.480
to one fault or one set of experiments --
or one experiment, sorry.

00:37:45.480 --> 00:37:48.820
And what you can see is
that you get

00:37:48.820 --> 00:37:53.480
an array of transition scales
for any given fault.

00:37:53.480 --> 00:37:55.030
But everything falls
on the same line

00:37:55.030 --> 00:38:03.000
for any fault that the critical aspect ratio
is uniquely defined for a given fault.

00:38:03.000 --> 00:38:07.910
And it’s different for
different faults interestingly.

00:38:07.910 --> 00:38:17.250
We see the same behavior in the lab,
which is reassuring because it means

00:38:17.250 --> 00:38:19.740
we’re not looking at some
funky weathering artifact

00:38:19.740 --> 00:38:25.860
or something related to exhumation.
It happens in the lab as well.

00:38:25.860 --> 00:38:29.560
So what we conclude at this stage is
there exists a critical aspect ratio

00:38:29.560 --> 00:38:32.790
at each fault that governs
the minimal scale of grooving.

00:38:34.820 --> 00:38:36.680
All right.

00:38:37.860 --> 00:38:41.360
You all have been very quiet.

00:38:41.360 --> 00:38:45.460
Ten microns.
Does that get anybody thinking?

00:38:45.470 --> 00:38:46.970
Ten microns.

00:38:46.970 --> 00:38:51.630
Is that a scale of interest
to anybody in this room?

00:38:53.940 --> 00:38:57.000
Who has not already
read the manuscript?

00:38:59.520 --> 00:39:01.780
No?
Ten microns doesn't do it for anyone?

00:39:01.780 --> 00:39:03.680
A hundred microns?
Somewhere in there?

00:39:03.680 --> 00:39:05.360
Doesn't make you
think of something?

00:39:05.360 --> 00:39:07.820
Made me think of something.

00:39:07.820 --> 00:39:11.640
No? No?
No rate-and-state fanatics here?

00:39:14.300 --> 00:39:20.480
D-sub-c? Yeah?
No? Yeah? Maybe?

00:39:23.450 --> 00:39:31.110
That when people do laboratory
experiments and look at the

00:39:31.110 --> 00:39:39.920
displacement required for
weakening a fault as --

00:39:39.920 --> 00:39:43.740
or weakening a surface
as velocity changes,

00:39:43.750 --> 00:39:51.260
they -- there is often observed a critical
slip distance over which faults --

00:39:51.260 --> 00:39:55.010
over which laboratory experiments
weaken where friction changes.

00:39:55.010 --> 00:40:00.900
And this is known as D-sub-c
in rate-and-state friction

00:40:00.900 --> 00:40:06.010
and actually in more general
forms of slip-weakening friction.

00:40:06.010 --> 00:40:12.030
And, as I mentioned, at least some of
these examples came courtesy of Diane.

00:40:12.030 --> 00:40:20.490
And you can see that the --
that is the one set of samples

00:40:20.490 --> 00:40:23.760
for which we actually --
no, actually there’s another set.

00:40:23.760 --> 00:40:30.800
But it is one of the set of samples
for which we have both the

00:40:30.800 --> 00:40:33.150
laboratory measurements
of D-sub-c and the transition scale

00:40:33.150 --> 00:40:35.620
measured at the --
on the same sample.

00:40:35.620 --> 00:40:40.430
And we do see that at least
approximately, D-sub-c for those

00:40:40.430 --> 00:40:47.910
samples is 10 microns, which is, in that
case, pretty close to the transition scale.

00:40:47.910 --> 00:40:53.110
So maybe -- maybe these things have
something to do with each other.

00:40:56.340 --> 00:41:00.060
I’m really surprised
that you guys didn't call it out.

00:41:00.060 --> 00:41:02.360
All right.

00:41:02.360 --> 00:41:08.800
- Excuse me. Doesn't D-sub-c depend on the
roughness of the fault surface in the lab?

00:41:09.840 --> 00:41:17.880
- It does.
And it does in the observations as well.

00:41:17.890 --> 00:41:22.770
Our L-sub-c, if you will, our transition
scale depends on the roughness.

00:41:22.770 --> 00:41:25.090
Because it depends on the aspect ratio.

00:41:25.090 --> 00:41:29.420
So the aspect ratio is constant
at the minimum scale of grooving.

00:41:29.420 --> 00:41:32.030
But if you have a rougher fault,
you will therefore have

00:41:32.030 --> 00:41:36.570
the transition scale
at a larger observation scale.

00:41:36.570 --> 00:41:39.550
So that’s actually quite consistent.

00:41:42.520 --> 00:41:46.550
So what is this
D-sub-c micromechanically?

00:41:49.340 --> 00:41:53.580
Dieterich and Kilgore proposed
that it was related to a scale

00:41:53.580 --> 00:41:57.930
of plastically yielding asperities
through a very elegant set

00:41:57.930 --> 00:42:03.980
of experiments where they imaged
asperity growth and plastic -- what

00:42:03.980 --> 00:42:11.680
appeared to be a plastic process as they
grew over time or with increasing load.

00:42:11.680 --> 00:42:15.640
And so there’s a
connection between

00:42:15.640 --> 00:42:21.980
this slip weakening distance, D-sub-c,
and a scale of plastic yield.

00:42:30.830 --> 00:42:32.730
Why is there a
scale of plastic yield?

00:42:32.730 --> 00:42:40.240
I've just been talking about
asperities yielding at all scales.

00:42:40.240 --> 00:42:43.380
Asperities yielding at all scales.

00:42:45.600 --> 00:42:47.600
Well...

00:42:48.820 --> 00:42:52.100
... the reason
has to do with

00:42:52.110 --> 00:42:56.460
the micromechanics
of how asperities interact.

00:42:56.460 --> 00:43:01.900
And this was some fundamental work
done in the late ’70s, early ’80s

00:43:01.900 --> 00:43:10.310
by Lawn and co-workers where they
looked at -- underneath an indenter

00:43:10.310 --> 00:43:11.700
and they found that there was

00:43:11.700 --> 00:43:20.700
a zone at which the stresses are
high enough to have plastic yield.

00:43:20.700 --> 00:43:30.690
And beyond that, you could start to
get fractures if -- in some circumstances.

00:43:30.690 --> 00:43:38.340
And you would get fractures
beyond the plastic zone --

00:43:38.340 --> 00:43:43.590
these fractures that are growing
away from the indenter --

00:43:43.590 --> 00:43:49.910
if the stress intensity factor
at the edge of the plastic zone

00:43:49.910 --> 00:43:54.280
is high enough to be
above the toughness.

00:43:54.280 --> 00:43:57.230
Or the stress intensity factor --
I’m sorry -- on flaws at the

00:43:57.230 --> 00:44:01.690
end of the fracture zone
is above a --

00:44:01.690 --> 00:44:05.940
high enough to be above a certain
critical stress intensity factor.

00:44:05.940 --> 00:44:11.260
Since this stress in the plastic zone
is governed by the plastic

00:44:11.260 --> 00:44:18.240
failure strength of the rock hardness,
which is the definition of hardness,

00:44:18.240 --> 00:44:22.700
then we actually know
what the stress loading

00:44:22.700 --> 00:44:26.530
for the stress intensity factor is.
It's H -- for hardness.

00:44:26.530 --> 00:44:34.590
And there is a relationship between
the scale of this asperity contact area --

00:44:34.590 --> 00:44:38.420
the scale of which that stress
is getting concentrated on it edges --

00:44:38.420 --> 00:44:42.190
and the material properties.

00:44:42.190 --> 00:44:50.720
That if that indenter is large enough --
L is large enough --

00:44:50.720 --> 00:44:56.600
then fractures are
able to propagate.

00:44:56.610 --> 00:45:04.450
If it’s too small, there is only plastic
failure underneath a indenter.

00:45:04.450 --> 00:45:08.340
So small scales, indenters
make plastic failure.

00:45:08.340 --> 00:45:11.300
Large-scale indenters
also make brittle failure.

00:45:13.990 --> 00:45:16.790
So there exists a
brittle-plastic transition

00:45:16.790 --> 00:45:19.010
in asperity interaction
as a function of scale.

00:45:19.010 --> 00:45:22.050
That’s the bottom line here.

00:45:25.210 --> 00:45:31.760
And previous work certainly
has made a connection between

00:45:31.760 --> 00:45:37.390
brittle or non-brittle behavior of
asperities and the existence of grooves.

00:45:37.390 --> 00:45:39.330
Here’s another old paper.

00:45:39.330 --> 00:45:44.370
I do feel like I spend a lot of time reading
1970s papers in this field.

00:45:44.370 --> 00:45:49.730
There was a lot of wonderful stuff
that happened in that period.

00:45:49.730 --> 00:45:59.790
And the -- what Engelder and Scholz
showed is, for conditions -- for loads,

00:45:59.790 --> 00:46:10.060
and by extension,
scales that are relatively light

00:46:10.060 --> 00:46:15.040
and only make plastic failure,
you can get grooves,

00:46:15.040 --> 00:46:21.000
but they're very light.
They're really small, subtle features.

00:46:21.000 --> 00:46:25.020
And that major grooving
was associated with the existence

00:46:25.020 --> 00:46:31.190
of fractures on a surface --
a brittle feature.

00:46:31.190 --> 00:46:35.690
So what I am proposing --
come right back out to what we’re

00:46:35.690 --> 00:46:39.190
now measuring about roughness
on faults -- is that the minimum scale

00:46:39.190 --> 00:46:45.990
of grooving, as observed on faults,
is capturing an aspect ratio

00:46:45.990 --> 00:46:56.420
which corresponds to a critical pressure
at which -- a critical strain at which

00:46:56.420 --> 00:47:02.620
we are sufficient to make
this brittle-plastic transition.

00:47:06.760 --> 00:47:11.080
And so we have a brittle-plastic --
the minimum scale of grooving

00:47:11.090 --> 00:47:16.750
is a brittle-plastic transition in
the behavior of asperity attraction.

00:47:19.640 --> 00:47:24.180
I’m realizing that the silence
may have something to do with

00:47:24.190 --> 00:47:27.920
the fact that I rushed over one slide
in the first half of the talk.

00:47:27.920 --> 00:47:31.060
- [inaudible] questions at the end.

00:47:31.060 --> 00:47:34.040
- Okay. It could be cultural, too.
I get that.

00:47:34.040 --> 00:47:37.780
But, you know, let me just
pause here for a minute

00:47:37.780 --> 00:47:42.320
and give you
a little bit of context.

00:47:42.320 --> 00:47:51.920
I started out with big faults, which --
you know, and out there in the field

00:47:51.920 --> 00:47:53.430
measuring fault roughness.

00:47:53.430 --> 00:47:56.370
And, you know, we even
talked about seismic waves.

00:47:56.370 --> 00:48:02.220
And now I’m giving you a story
about micron scale grooves.

00:48:02.220 --> 00:48:07.320
Why am I so obsessed with brittle-plastic
transition on micron scale grooves?

00:48:07.320 --> 00:48:12.390
My obsession is coming
from one statement that I made

00:48:12.390 --> 00:48:15.940
very quickly in the
first half of the talk.

00:48:15.940 --> 00:48:20.780
Which is that I have said
that asperities fail at all scales.

00:48:20.780 --> 00:48:26.840
Right, that was the whole interpretation
of this roughness in a restricted range.

00:48:26.840 --> 00:48:31.060
Asperities -- bumps --
are what determine

00:48:31.060 --> 00:48:35.800
real area of contact
and what determine friction.

00:48:35.800 --> 00:48:39.280
That’s the game.
If you want to know fault resistance,

00:48:39.290 --> 00:48:43.000
what you want to know is
about real area of contact between

00:48:43.000 --> 00:48:51.130
surfaces and the process by which
that real area of contact is determined.

00:48:51.130 --> 00:48:55.190
And that is going to tell you about
the scale dependence of friction,

00:48:55.190 --> 00:48:58.770
should there be any
scale dependence of friction.

00:49:01.930 --> 00:49:04.190
If fault asperities are
failing at all scale,

00:49:04.190 --> 00:49:08.680
that means real area of contact is
potentially determined at all scales.

00:49:08.680 --> 00:49:10.770
And it is possible that
the laboratory experiments

00:49:10.770 --> 00:49:15.120
have no bearing
whatsoever on the real Earth.

00:49:15.120 --> 00:49:17.450
That’s terrifying, right?

00:49:17.450 --> 00:49:21.300
But it’s also a physical possibility
from what I just told you.

00:49:21.300 --> 00:49:24.970
I am now telling you
something somewhat different.

00:49:24.970 --> 00:49:30.310
I am now telling you that there
is an intrinsic length scale in this

00:49:30.310 --> 00:49:35.590
problem between a brittle and plastic
interaction of asperities that has

00:49:35.590 --> 00:49:41.000
a manifestation on real fault surfaces --
this minimum scale of grooving.

00:49:41.000 --> 00:49:44.020
And so perhaps --
and seems to correspond

00:49:44.020 --> 00:49:47.600
to some processes
that we know about in the lab.

00:49:47.600 --> 00:49:49.780
So with that said,
the real area of contact

00:49:49.780 --> 00:49:57.930
is being determined, perhaps, by
actual laboratory-simulated processes.

00:49:57.930 --> 00:50:00.330
Okay.

00:50:00.330 --> 00:50:05.370
Just to throw some numbers at it,
does this brittle-plastic transition

00:50:05.370 --> 00:50:08.140
make sense for
realistic values?

00:50:08.140 --> 00:50:12.900
If I just pick some pretty arbitrary
textbook kind of values for silica glass --

00:50:12.910 --> 00:50:17.960
not that this is that representative
of actual fault rocks -- and work through

00:50:17.960 --> 00:50:22.540
what this predicated transition scale
would be, I’d get around a micron.

00:50:22.540 --> 00:50:28.320
Which, you know,
given how rough these numbers are,

00:50:28.320 --> 00:50:32.030
actually is a kind of yes --
confirmatory that at least

00:50:32.030 --> 00:50:36.150
we’re in the right scale range to be
talking about a brittle-plastic transition.

00:50:36.150 --> 00:50:38.670
That’s a yes-question mark
because I get it.

00:50:38.670 --> 00:50:40.370
I was talking about
10 microns a minute ago,

00:50:40.370 --> 00:50:43.170
and now I’m talking
about a micron.

00:50:43.170 --> 00:50:49.970
But since I also am talking about
scale-dependent strength --

00:50:49.970 --> 00:50:55.030
that was the first half of this talk --
I don't think the laboratory values

00:50:55.030 --> 00:51:01.740
in a generic sense -- in a scale-
independent sense, are that --

00:51:01.740 --> 00:51:05.440
are necessarily the right thing
to be using for this problem.

00:51:05.440 --> 00:51:11.140
So what I am imagining
is that we have strength

00:51:11.140 --> 00:51:15.150
as measured by aspect ratio
as a function of length scale.

00:51:15.150 --> 00:51:24.130
At large scales, that is controlled for a --
addressed by the fracture toughness.

00:51:24.130 --> 00:51:28.720
At small scales, strength is
being controlled by a plastic process,

00:51:28.720 --> 00:51:31.790
which is parameterized
as hardness.

00:51:31.790 --> 00:51:39.460
We have a crossover of these strength
profiles -- strength as a function of scale.

00:51:39.460 --> 00:51:45.190
And just like in the Earth, in the crust,
where we have strength envelopes

00:51:45.190 --> 00:51:49.770
crossing over as a function of depth
to get a brittle-plastic transition,

00:51:49.770 --> 00:51:54.920
in this case, we have a
crossover as a function of scale.

00:51:54.920 --> 00:52:03.160
And so, at large scales, brittle dominates.
At small scales, plastic dominates.

00:52:03.160 --> 00:52:10.840
And their crossover scale
is being determined -- is being inferred

00:52:10.840 --> 00:52:18.900
from the minimum scale of grooving
from these -- where these power spectra

00:52:18.900 --> 00:52:24.800
come together and is being interpreted
as a brittle-plastic transition.

00:52:27.360 --> 00:52:31.140
Whew.
Which might be D-sub-c.

00:52:34.460 --> 00:52:38.360
Okay.
I think I've gone far enough here.

00:52:38.360 --> 00:52:40.720
To recap.

00:52:43.900 --> 00:52:50.920
What I have -- actually, what we
have actually observed is that fault

00:52:50.920 --> 00:52:55.610
roughness at the field scale is observed
in a narrow range of aspect ratios.

00:52:55.610 --> 00:52:57.650
That’s an observation.

00:52:57.650 --> 00:53:01.700
And I said 0.1 to 1%.
Strictly speaking,

00:53:01.700 --> 00:53:08.760
it’s 0.07 to 0.5% at 1 meter
at the field scale.

00:53:08.760 --> 00:53:11.660
The aspect ratio increases
with decreasing scale,

00:53:11.660 --> 00:53:14.380
and there exists a minimum scale
of grooving controlled by

00:53:14.380 --> 00:53:17.820
critical aspect ratio that is uniquely
defined for any given fault.

00:53:17.820 --> 00:53:19.500
Those are the observations.

00:53:19.500 --> 00:53:23.300
Those, I think -- I hope you
actually believe.

00:53:23.300 --> 00:53:28.310
After that, I jumped off the deep end,
and I interpreted them,

00:53:28.310 --> 00:53:32.710
which is that the strength
decreases with scale

00:53:32.710 --> 00:53:38.140
specifically as L to the minus 0.4
in the brittle regime.

00:53:38.140 --> 00:53:40.910
That there exists a brittle-ductile --
a brittle-plastic transition

00:53:40.910 --> 00:53:44.920
at a critical scale.

00:53:44.920 --> 00:53:53.440
And the implications here are
both macroscopic and microscopic.

00:53:53.440 --> 00:53:58.450
Macroscopically, if we’re gaining
some sort of physical understanding

00:53:58.450 --> 00:54:02.310
of the origin of this roughness, we are
on much, much firmer ground

00:54:02.310 --> 00:54:07.780
on extrapolating it to other applications
like strong ground shaking.

00:54:07.780 --> 00:54:10.880
This idea that it would be -- what
we’ve measured on these 22 faults

00:54:10.880 --> 00:54:15.050
are representative of the Earth and
that we should go out and

00:54:15.050 --> 00:54:22.710
make strong ground shaking or any other
dynamic rupture model based on this,

00:54:22.710 --> 00:54:26.310
that idea would be much more
well-founded if we understood

00:54:26.310 --> 00:54:28.970
why we had
such a restrictive range.

00:54:32.240 --> 00:54:40.980
Microscopically, I think what we’re learning
here is that the real area

00:54:40.990 --> 00:54:45.060
of contact is determined by
asperities yielding at all scales.

00:54:45.060 --> 00:54:47.760
And therefore, friction is --
I think I should have put

00:54:47.760 --> 00:54:53.440
the word “potentially”
scale-dependent in here.

00:54:53.440 --> 00:54:55.980
Because of the next line.

00:54:55.980 --> 00:54:59.960
But the process of accommodation
varies with scale -- this brittle/plastic.

00:54:59.960 --> 00:55:03.960
And so there is some hope of
being able to actually --

00:55:03.960 --> 00:55:06.460
we’re not at the
end of the road yet here.

00:55:06.460 --> 00:55:11.620
But a hope of being able to
do this scale-dependent accommodation

00:55:11.620 --> 00:55:16.110
process and actually get
resistance as a function of scale.

00:55:16.110 --> 00:55:23.350
And I think possibly we also
have evidence of a microscopic

00:55:23.350 --> 00:55:27.650
slip-weakening distance -- something
like D-sub-c on real, live faults --

00:55:27.650 --> 00:55:33.750
or real, dead faults, actually --
but actual natural surfaces.

00:55:33.750 --> 00:55:39.960
And that’s extremely exciting,
at least to me, that there have

00:55:39.960 --> 00:55:45.430
been decades of laboratory work
carefully studying

00:55:45.430 --> 00:55:50.460
and elucidating
friction laws on rocks.

00:55:50.460 --> 00:55:54.400
And it’s very hard to know whether or
not those extrapolate to real conditions.

00:55:54.400 --> 00:55:57.740
And if we can find a parameter that we
can measure in the lab and find some

00:55:57.740 --> 00:56:04.140
feature on a surface that corresponds
to that, that would be a good thing.

00:56:04.140 --> 00:56:09.620
So I will stop there, and now
you will ask questions. [laughs]

00:56:09.620 --> 00:56:13.900
[ Applause ]

00:56:13.900 --> 00:56:16.940
- Questions?

00:56:26.460 --> 00:56:28.660
- Thank you very much.

00:56:28.660 --> 00:56:33.460
I’m wondering if this assumes
that the stresses inside the asperity

00:56:33.460 --> 00:56:39.940
are uniform or if you’re really just
quantifying stress concentrations?

00:56:39.940 --> 00:56:43.300
Meaning that, as the aspect ratio
increases, you might have

00:56:43.310 --> 00:56:48.880
a situation where stresses
start to focus at certain points.

00:56:48.880 --> 00:56:51.760
- You certainly do.

00:56:51.760 --> 00:56:56.400
That’s why I’m confining myself
to these scaling arguments.

00:56:56.400 --> 00:56:59.450
The scaling arguments,
I think, are pretty robust.

00:56:59.450 --> 00:57:04.270
The maximum stress under a Hertzian
contact scale is H over L because,

00:57:04.270 --> 00:57:08.980
fundamentally, that’s the definition
of shear strain is this.

00:57:08.980 --> 00:57:17.040
But in detail, yes, I mean, if you
actually wanted to have a yield stress,

00:57:17.040 --> 00:57:22.860
not a yield strain, off of this -- or even
a yield strain in detail with --

00:57:22.860 --> 00:57:28.230
not just the scaling of yield strain
with scale, then you'd have to

00:57:28.230 --> 00:57:32.520
solve that problem, the stress
concentration problem.

00:57:32.520 --> 00:57:37.340
I think that if you’re just looking
at the scale dependence of the threshold,

00:57:37.350 --> 00:57:42.130
I don't think you necessarily
need to solve that problem.

00:57:43.220 --> 00:57:50.920
[ Silence ]

00:57:51.500 --> 00:57:53.080
- Hi, Emily.
That was a nice talk.

00:57:53.080 --> 00:57:55.040
And also we always wait
until the end because we have

00:57:55.040 --> 00:57:58.040
people watching remotely, and the
microphone helps them hear.

00:57:58.040 --> 00:57:59.500
- Okay.

00:57:59.510 --> 00:58:04.380
- So basically, what you’re saying
is that these asperities at all wavelengths

00:58:04.380 --> 00:58:08.890
are failing, and the scale dependence
is a -- as a consequence of them failing

00:58:08.890 --> 00:58:12.780
at all wavelengths, plastically and
elastically, through this transition ...

00:58:12.780 --> 00:58:14.970
- Brittle-y, yeah.
- I’m sorry. Yeah.

00:58:14.970 --> 00:58:18.440
- Yeah, no. I know what you meant.
- Plastically and then brittle-y,

00:58:18.440 --> 00:58:21.120
does that really -- I’m trying to
get a sense of how that really

00:58:21.120 --> 00:58:22.250
explains the
grooving phenomenon.

00:58:22.250 --> 00:58:26.380
I mean, the grooves -- the width of the
grooves is determined by a contact size.

00:58:26.380 --> 00:58:31.010
So the asperities are loaded.
They have a real area of contact.

00:58:31.010 --> 00:58:34.500
And that is determined
by the elastic/brittle failure strength

00:58:34.500 --> 00:58:35.410
beneath the asperity.

00:58:35.410 --> 00:58:40.990
And then it’s dragged through,
producing a plow or a groove.

00:58:40.990 --> 00:58:45.110
The width of the groove is determined
by the contact -- real area of contact,

00:58:45.110 --> 00:58:48.070
but how does the wavelength along
the groove trajectory determined by --

00:58:48.070 --> 00:58:50.760
I mean, there’s a roughness
along the groove trajectory.

00:58:50.760 --> 00:58:53.230
How does that -- actually
controlled by strength?

00:58:53.230 --> 00:58:55.460
- That actually -- okay, well ...

00:58:55.460 --> 00:58:57.730
- I mean, there’s a -- the two
things diverge, right?

00:58:57.730 --> 00:59:00.930
So there’s a -- there’s a fault parallel
and a fault perpendicular roughness.

00:59:00.930 --> 00:59:04.130
- Right.
- The striation or fault parallel roughness

00:59:04.130 --> 00:59:07.560
is smaller than the fault
perpendicular, which makes sense.

00:59:07.560 --> 00:59:10.500
But how is the fault parallel
actually determined by strength?

00:59:10.500 --> 00:59:12.400
I can see why the fault
perpendicular would be.

00:59:12.400 --> 00:59:15.380
- That -- well, that -- to me, that’s one
of the most perplexing problems here.

00:59:15.380 --> 00:59:18.320
I think -- I thought you were going
somewhere else with that question,

00:59:18.320 --> 00:59:22.620
so I was -- I put this up, but that’s not --
this is not the answer to that question.

00:59:22.620 --> 00:59:24.840
- Yeah, I’m trying to explain the --
understand the anisotropy and

00:59:24.840 --> 00:59:29.100
roughness parallel and perpendicular
to the grooves as a function of strength.

00:59:29.100 --> 00:59:30.760
- Okay, so ...
- And it doesn't make sense ...

00:59:30.770 --> 00:59:37.100
- So I hear at least two questions there.
So let me try to answer both of them.

00:59:37.100 --> 00:59:42.530
One is -- let’s just kind of
look at the data again.

00:59:42.530 --> 00:59:47.750
The slip-parallel is the blue here.
The slip-perpendicular is the green.

00:59:47.750 --> 00:59:51.290
Okay? And so what Steve’s
pointing out is slip-parallel

00:59:51.290 --> 00:59:57.840
in the large-scale regime
is less than slip-perpendicular.

00:59:57.840 --> 00:59:59.640
And then they come together.

00:59:59.640 --> 01:00:04.590
And there really is blue under there.
It’s just hiding.

01:00:04.590 --> 01:00:10.490
And notice that the blue is not
that different than the green.

01:00:10.490 --> 01:00:13.270
So there’s a subtle slope change,
but it’s subtle.

01:00:13.270 --> 01:00:16.220
Whereas, there’s a really
bigger change really coming --

01:00:16.220 --> 01:00:19.910
it’s really the perpendicular
coming in -- cutting in.

01:00:19.910 --> 01:00:24.920
So what I think is that the
perpendicular is being governed

01:00:24.920 --> 01:00:26.960
by the existence
of the grooves.

01:00:26.960 --> 01:00:29.300
And when the grooves cease,
you get some of the same processes

01:00:29.300 --> 01:00:35.340
going in the parallel direction that --
in both regimes.

01:00:35.340 --> 01:00:38.660
Some of, but not all of.

01:00:38.660 --> 01:00:44.650
What I was going towards this slide
was to point out is that the slip-parallel

01:00:44.650 --> 01:00:47.680
roughness is determined -- ah.
I did it again.

01:00:47.680 --> 01:00:50.190
Very peculiar.

01:00:50.190 --> 01:00:54.990
By these slip-perpendicular
fractures that form as you do --

01:00:54.990 --> 01:00:58.180
that Engelder and Scholz
interpreted as stick-slip.

01:00:58.180 --> 01:01:02.630
So there are features
that make tensile gashes.

01:01:02.630 --> 01:01:05.300
I mean, that’s just one of
many processes,

01:01:05.300 --> 01:01:08.380
but there are features that
make perpendicular roughness.

01:01:08.380 --> 01:01:14.870
And they're not as spectacular as the
excavated grooves from the

01:01:14.870 --> 01:01:17.520
brittle failure in the slip
that make roughness

01:01:17.520 --> 01:01:21.180
in the slip-perpendicular direction,
but they do exist.

01:01:21.180 --> 01:01:22.520
Okay.

01:01:22.520 --> 01:01:24.240
I’m not sure I answered
your question here.

01:01:24.250 --> 01:01:26.690
- Well, I think you sort of did,
but I’m also wondering -- I mean,

01:01:26.690 --> 01:01:29.540
I can see a physical reason why the
roughness and the slip direction

01:01:29.540 --> 01:01:32.670
would scale with the amount of slip
during an earthquake, for example.

01:01:32.670 --> 01:01:35.960
I mean, the earthquake starts under a
certain stress condition then stops.

01:01:35.960 --> 01:01:38.630
It recurs, then, perhaps
under a different stress condition

01:01:38.630 --> 01:01:41.040
that might produce different roughness,
different contact area.

01:01:41.040 --> 01:01:44.580
I can imagine -- and this was
your original goal, hoping to get

01:01:44.590 --> 01:01:47.310
to some kind of relationship
between roughness and displacement

01:01:47.310 --> 01:01:50.350
so you can infer displacement
from past events.

01:01:50.350 --> 01:01:53.430
I’m just trying to get a sense of what
the physical reason for that would be.

01:01:53.430 --> 01:01:55.830
You know, what would
map displacement per event

01:01:55.830 --> 01:01:59.590
into roughness in the
slip-parallel direction?

01:01:59.590 --> 01:02:00.730
- Ah ...

01:02:00.730 --> 01:02:02.730
- And maybe this is something
better talked about later.

01:02:02.730 --> 01:02:07.260
- Yeah, no. I mean -- I think something
that I may have forgotten to say is --

01:02:07.260 --> 01:02:14.480
so what I think is happening here is,
as you have slip,

01:02:14.480 --> 01:02:16.640
there are two
competing processes.

01:02:16.640 --> 01:02:19.730
There is this
truncation failure process

01:02:19.730 --> 01:02:22.730
that’s controlling the
maximum roughness.

01:02:22.730 --> 01:02:25.750
At the same time, you’re always
regenerating roughness.

01:02:25.750 --> 01:02:29.480
Otherwise, you would have had
a much stronger smoothing trend.

01:02:29.480 --> 01:02:33.840
If every time you slipped, you wore
down a surface and smoothed it,

01:02:33.840 --> 01:02:36.490
you would eventually get
some sort of smoothing trend.

01:02:36.490 --> 01:02:40.380
So when you slip, you recreate
roughness through plucking,

01:02:40.380 --> 01:02:46.140
through making cavities, through --
there’s -- there is -- through piling

01:02:46.140 --> 01:02:50.420
up gouge -- there are a bunch of
processes that can create roughness,

01:02:50.420 --> 01:02:53.200
and they're always competing
and pushing yourself --

01:02:53.200 --> 01:02:58.610
you up towards
that maximum bound.

01:02:58.610 --> 01:03:02.820
And so the fact that this -- there’s a
narrow range, I am interpreting, at least,

01:03:02.820 --> 01:03:07.630
as evidence of the maximum bound and
the fact that roughness is decreasing

01:03:07.630 --> 01:03:13.630
gradually with slip, I am interpreting as
evidence of the re-roughening process.

01:03:13.630 --> 01:03:15.880
Okay.

01:03:15.890 --> 01:03:18.390
You know, my computer’s going to
prevent me from doing a bad thing here.

01:03:18.390 --> 01:03:21.800
No, it’s not.

01:03:21.810 --> 01:03:28.030
There was a slide here that I put on
hide that I wasn't going to show.

01:03:28.030 --> 01:03:32.890
But because you’re asking this question,
I’m going to try to unhide it.

01:03:38.160 --> 01:03:39.920
You know, the computer
really should have something

01:03:39.930 --> 01:03:41.820
that prevents me
from doing this.

01:03:50.340 --> 01:03:53.420
It does, right.

01:03:55.620 --> 01:03:59.860
- I think you can click it, but not put it
in view mode, it’ll show up. I think.

01:03:59.860 --> 01:04:03.860
- Here it is.

01:04:03.860 --> 01:04:10.950
For discussion only, this is my
imagination of how it works.

01:04:10.950 --> 01:04:18.000
Everybody’s really clear that
I don't necessarily believe this?

01:04:18.000 --> 01:04:27.040
That we have different parameters
controlling the slope of the

01:04:27.040 --> 01:04:30.480
roughness and different processes
at different scales.

01:04:30.480 --> 01:04:34.640
And there is both mode one and
mode two failure going on here.

01:04:34.640 --> 01:04:39.570
And the reason I put mode one on the
top -- on the slip-perpendicular branch

01:04:39.570 --> 01:04:48.790
there is because the slope of that line
is pretty much the same as the

01:04:48.790 --> 01:04:52.640
roughness slope that you get for
mode one fractures for joints.

01:04:52.640 --> 01:04:56.260
- Yeah. That answers my question.
- I knew it did. I ...

01:04:56.270 --> 01:04:58.490
- So it’s really the difference
between fracture toughness between

01:04:58.490 --> 01:05:00.119
mode one and mode two . . .
- Yes.

01:05:00.119 --> 01:05:02.360
- ... that controls the indentation
versus indentation and plowing,

01:05:02.360 --> 01:05:04.140
in your conceptual model.
- Yes.

01:05:04.140 --> 01:05:06.060
- Okay, thank you.
- Yep.

01:05:12.760 --> 01:05:16.220
- As usual, Emily, you've forced me
to think in uncomfortably

01:05:16.220 --> 01:05:20.120
different directions, and I guess
that’s a good thing.

01:05:20.120 --> 01:05:23.960
- You’re welcome.
- [laughs]

01:05:23.960 --> 01:05:28.250
One of the iconic things that I’ll
take away from your talk is this --

01:05:28.250 --> 01:05:33.270
the scale length as indicated by
these topography diagrams where

01:05:33.270 --> 01:05:37.170
at the larger scale, you see the grooving,
and at the smaller scale, you don't.

01:05:37.170 --> 01:05:44.310
And you’re saying there’s a difference
in process that’s controlling that, right?

01:05:44.310 --> 01:05:45.980
- Mm-hmm.

01:05:45.990 --> 01:05:51.330
- I’m a little confused --
probably because this isn't my field --

01:05:51.330 --> 01:05:56.060
what you mean by
plastic yielding.

01:05:56.060 --> 01:06:01.920
Isn't that, at some micromechanical
scale, also some kind of brittle fracture?

01:06:01.930 --> 01:06:03.690
What’s going on in,
and is that important,

01:06:03.690 --> 01:06:05.690
or is that just
a stupid question?

01:06:05.690 --> 01:06:10.050
- Oh, it’s a very deep question.
- Thank you.

01:06:10.050 --> 01:06:12.250
[laughter]

01:06:14.230 --> 01:06:22.040
- What I mean by plastic yielding is that
there is a failure stress that results

01:06:22.040 --> 01:06:32.200
in permanent deformation
as opposed to a separation of surfaces,

01:06:32.200 --> 01:06:35.230
which is controlled
by a fracture toughness.

01:06:35.230 --> 01:06:41.530
So that is a fairly specific
definition that I’m taking here.

01:06:41.530 --> 01:06:45.100
I am making no statement
whatsoever about the micromechanics

01:06:45.100 --> 01:06:46.600
of that plastic yielding.

01:06:46.600 --> 01:06:51.880
Thibault and I have had very long
discussions about what that

01:06:51.880 --> 01:06:56.950
micromechanics might be because there
is sort of growing literature right now

01:06:56.950 --> 01:07:01.890
on trying to identify micromechanics
of plastic yielding on faults, and if it’s

01:07:01.890 --> 01:07:12.260
dislocation creep or what -- or the
little nano balls of lubrication.

01:07:12.260 --> 01:07:17.040
Shalev Siman-Tov, who is visiting here
with me, a post-doc at Santa Cruz

01:07:17.040 --> 01:07:22.010
who I believe has just gotten signed up
to give you guys a talk shortly,

01:07:22.010 --> 01:07:29.710
he can tell you about his evidence
for plasticity at very fine scales.

01:07:29.710 --> 01:07:35.960
But I don't think we have any constraint
on that from this particular study.

01:07:35.960 --> 01:07:39.460
What we have evidence for
is something that happens at --

01:07:39.460 --> 01:07:42.980
with a hardness control.

01:07:42.980 --> 01:07:45.340
Okay.
- Thanks.

01:07:51.580 --> 01:07:57.360
- Emily, just had a couple questions
for clarification, but first, you know,

01:07:57.369 --> 01:08:01.619
there’s the old observation
that the width of the fault zone

01:08:01.619 --> 01:08:08.230
is about 1% of the total slip,
which seems to fall into this as well.

01:08:08.230 --> 01:08:11.820
But I just was wondering
about two parameters.

01:08:11.820 --> 01:08:15.820
One, you finally mentioned
gouge in the last five minutes.

01:08:15.820 --> 01:08:21.589
So you’re talking about two,
more or less, surfaces --

01:08:21.589 --> 01:08:24.020
clean surfaces
in intimate contact.

01:08:24.020 --> 01:08:26.859
But in your first slide,
you show that there’s a thick

01:08:26.859 --> 01:08:32.880
gouge layer, even in your normal
faulting, in Oregon, I believe.

01:08:32.880 --> 01:08:37.029
And so you’re looking at the surface
in a snapshot in time, which,

01:08:37.029 --> 01:08:41.380
after it has slid a little bit,
that has to -- that whole surface

01:08:41.380 --> 01:08:44.520
has to evolve, and it’s all
within this thicker gouge layer.

01:08:44.520 --> 01:08:50.040
And the other is what’s the effect
of normal stress on all of this?

01:08:50.040 --> 01:08:55.040
And certainly in the lab scale,
some of these features can't evolve

01:08:55.040 --> 01:08:59.710
if you’re running it at typical very low,
normal stress, that you'll simply

01:08:59.710 --> 01:09:03.620
not create grooves
and that sort of process.

01:09:03.620 --> 01:09:08.830
So there seem to be at least two more
parameters involved in this.

01:09:08.830 --> 01:09:12.230
And certainly, you know,
when you think of gouge thickness

01:09:12.230 --> 01:09:17.359
in the laboratory scale, 10 microns
comes to mind as sort of a natural

01:09:17.359 --> 01:09:21.250
thickness if you don't start
with something thicker than that

01:09:21.250 --> 01:09:24.540
as the sort of gouge layer
that will build up.

01:09:24.540 --> 01:09:28.860
- Okay. So a couple issues here.
Right. Yes, gouge exists.

01:09:28.860 --> 01:09:31.369
I’m with you.

01:09:32.589 --> 01:09:35.950
Preserve gouge is also
known as cataclasite.

01:09:35.950 --> 01:09:42.290
And certainly for these -- indurated zone
that I showed you in Oregon.

01:09:42.290 --> 01:09:45.400
And it’s a rock.

01:09:45.400 --> 01:09:51.180
It’s a rock that deforms.
It’s a rock that fails internally.

01:09:51.180 --> 01:09:55.520
But it’s -- when I talk about failure,
I am thinking about the failure

01:09:55.520 --> 01:09:59.040
of the gouge as
one side of that.

01:09:59.040 --> 01:10:04.640
Okay, and that’s -- in other words --
to some extent, whether you

01:10:04.640 --> 01:10:09.640
call it gouge or a rock
is a function of scale.

01:10:09.640 --> 01:10:18.520
And so I -- perhaps one of the
reasons you do get failure

01:10:18.520 --> 01:10:20.640
at all scales is because
you have gouge there.

01:10:20.640 --> 01:10:23.280
That it is weak,
and it is deforming,

01:10:23.280 --> 01:10:29.180
but it is not deforming
with infinite flexibility.

01:10:29.180 --> 01:10:32.240
The depth issue.

01:10:34.180 --> 01:10:38.080
What can I say about the depth issue?
I study exhumed faults.

01:10:38.080 --> 01:10:40.220
Yeah. They're at the surface.

01:10:40.220 --> 01:10:44.740
There’s this tiny, little chip of a SAFOD
sample -- actually, two different chips

01:10:44.750 --> 01:10:52.360
of SAFOD samples that seem to follow
the same systematics, so that’s helpful.

01:10:52.360 --> 01:10:57.480
But other than that, these are
exhumed faults and laboratory faults.

01:10:57.480 --> 01:11:07.520
And so the fact that we see the same
systematics on the chip of the SAFOD

01:11:07.520 --> 01:11:13.360
sample and the -- in the laboratory
gives at least -- for the minimum scale

01:11:13.360 --> 01:11:18.960
of grooving story, some confidence that
that’s not just some funny depth effect.

01:11:18.960 --> 01:11:25.840
But it is certainly true that one would
want to study this at higher pressures.

01:11:25.840 --> 01:11:30.600
It’s just that’s not where we
get our faults preserved.

01:11:30.600 --> 01:11:35.040
I should say that some of these faults
were active at higher depths.

01:11:35.040 --> 01:11:40.590
So it is what it is.

01:11:40.590 --> 01:11:44.100
This is -- for that reason,
I would say this story probably

01:11:44.100 --> 01:11:49.560
has more bearing on rupture propagation
than it does enucleation.

01:11:56.800 --> 01:11:59.000
- Thanks, Emily.
Quick question.

01:11:59.000 --> 01:12:06.380
If one of the ultimate goals is to try to
relate displacement to properties of a

01:12:06.380 --> 01:12:10.230
fault plane -- roughness or whatever,
don't you need to know something about

01:12:10.230 --> 01:12:13.300
pore pressure at the time that
the displacement occurred?

01:12:13.300 --> 01:12:17.340
And especially in light of the some of
the -- I don't know, the Lapusta, et al,

01:12:17.340 --> 01:12:20.150
studies -- dynamic weakening
suggesting that you can, you know,

01:12:20.150 --> 01:12:23.730
propagate ruptures pretty far.

01:12:23.730 --> 01:12:26.840
- I think, in detail -- yes.
I mean, ultimately,

01:12:26.840 --> 01:12:29.900
to do the whole problem,
you need all the stresses.

01:12:29.900 --> 01:12:34.210
This is a talk about strength.
Okay?

01:12:34.210 --> 01:12:37.000
Pore pressure -- at least one
of the major effects of pore pressure

01:12:37.000 --> 01:12:39.700
is on effective stress --
what’s driving it.

01:12:39.700 --> 01:12:43.580
And that’s a whole different story that’s
for another day, and I’m happy

01:12:43.580 --> 01:12:47.150
to talk about pore pressure.
I love talking about pore pressure.

01:12:47.150 --> 01:12:50.110
But what I wanted to do
for this particular study

01:12:50.110 --> 01:12:54.750
was confine ourselves to
looking at strength. Okay?

01:12:58.690 --> 01:13:01.690
But since you’ve started --
mentioned dynamic weakening,

01:13:01.690 --> 01:13:03.690
[laughter]

01:13:05.020 --> 01:13:09.740
I’d like to just point out
one little tease in the data.

01:13:09.750 --> 01:13:14.640
Which is the laboratory --
the experimental slip surfaces,

01:13:14.640 --> 01:13:17.970
you notice there’s one that
looks like it has

01:13:17.970 --> 01:13:23.260
a smaller aspect ratio
at transition than the others.

01:13:23.260 --> 01:13:29.900
I’m scared of this mouse now,
but these guys.

01:13:29.900 --> 01:13:32.460
That’s the highest
velocity experiment.

01:13:32.470 --> 01:13:37.340
There’s -- all the gold ones are
dolomite experiments from SHIVA --

01:13:37.340 --> 01:13:39.190
from Di Toro’s lab.

01:13:39.190 --> 01:13:45.650
And they are --
and the one that --

01:13:45.650 --> 01:13:49.850
the highest slip rates,
the meter per second is the circles.

01:13:49.850 --> 01:13:53.520
And so it does suggest that
maybe we are seeing something

01:13:53.520 --> 01:13:56.940
related to the dynamic weakening,
possibly the heating of asperity

01:13:56.940 --> 01:14:01.420
is promoting plasticity in that.

01:14:01.420 --> 01:14:05.000
I think there is a potential to
sit here and -- you know,

01:14:05.000 --> 01:14:10.790
once we get off first base -- you know,
once we kind of get the framework right,

01:14:10.790 --> 01:14:13.120
we could sit here and have an
interesting conversation

01:14:13.120 --> 01:14:16.610
about the systematics
in this data set,

01:14:16.610 --> 01:14:22.200
whether deeper faults or hotter faults
have greater or less plasticity.

01:14:22.200 --> 01:14:25.300
I think that would be a
really interesting line to run after.

01:14:25.310 --> 01:14:29.210
But right now, we’re just
setting up the framework.

01:14:37.220 --> 01:14:39.600
Julian is pointing at the clock.

01:14:39.610 --> 01:14:42.070
- There are other people who
use this room at noon, actually.

01:14:42.070 --> 01:14:47.270
So -- and so I guess, since I’m --
since I’m talking,

01:14:47.270 --> 01:14:50.620
I’ll take this lull to say
we probably should clear out.

01:14:50.620 --> 01:14:53.650
But if you want to continue
this conversation, as always,

01:14:53.650 --> 01:14:54.840
we will be going to lunch.

01:14:54.840 --> 01:14:58.230
So we can meet in --
should probably meet in, like,

01:14:58.230 --> 01:15:01.969
five minutes before all of the
tech guys get in line ahead of us.

01:15:01.969 --> 01:15:05.730
- So let’s meet in five minutes
downstairs in front of building 3

01:15:05.730 --> 01:15:09.200
and walk over to the patio for lunch.
And let’s thank Emily again.

01:15:09.200 --> 01:15:12.040
[ Applause ]