WEBVTT
Kind: captions
Language: en-US

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Hello. I’m Rachel Abercrombie
from Boston University.

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Today it’s my pleasure to share
with you an overview of my

00:00:07.040 --> 00:00:09.976
recent work on small
earthquakes at Parkfield.

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This work was performed with
Xiaowei Chen and her recently

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graduated student Jiewen Zhang
from the University of Oklahoma.

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It also benefited from collaboration
with numerous colleagues.

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The aim of the work is to analyze
the source processes of the numerous

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small earthquakes to improve our
understanding of the controls on

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earthquake rupture, including the
distribution of slip and stress release,

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how earthquakes interact,
and what they can tell us about

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the faults on
which they occur.

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I present the results of two recent
studies – one small-scale and one larger.

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As you’ll see, this work is pushing the
resolution limits of the available data

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and so also includes investigation of the
real uncertainties and resolution limits.

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The San Andreas Fault at Parkfield
is a fascinating place to study for

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a number of reasons. It is a place
where the fault goes from the primarily

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creeping zone to the northwest to the
primarily locked zone to the southwest,

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through the transition zone,
which hosts fairly regular

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magnitude 6 earthquakes.
The last of these was in 2004.

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It is a well-studied and
densely instrumented area,

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including with the drilling and
instrumentation of the SAFOD

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deep hole and also the shallow
borehole seismic HRSN network.

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Parkfield is where repeating
earthquakes were first noted

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by the Berkeley group.
Since then, they and others have

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identified many sequences of highly
correlated repeating earthquakes

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at Parkfield and on other faults
undergoing some level of aseismic slip.

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The regular recurrence rates of
repeating earthquakes have been

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used to estimate the fault slip rate.
For example, shown here are the

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three sequences targeted by the SAFOD
hole – San Francisco, L.A., and Hawaii.

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They repeated regularly.
Then, following the magnitude 6

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earthquake in 2004,
the rate speeded right up

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before the recurrence rate returned
to more normal gradually.

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Most work using repeating
earthquakes to monitor the slip rate

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and strain rate depends on
assuming the circular rupture

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of fixed area,
but how good is this?

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Can we do better and
actually estimate these parameters

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for the individual
events concerned?

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Clearly, to understand earthquake
interactions, their rupture dynamics,

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and also the ground motions they
and their larger cousins produce,

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we need to go beyond thinking of
the small earthquakes as simply points

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or circular ruptures
of assumed radius.

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Two closely located earthquakes
may indicate neighboring rupture

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or overlapping rupture patches,
depending on the rupture area.

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Alternatively, if the slip areas are
more complex, then all manner of

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complex interactions are possible,
clearly affecting our interpretations

00:02:45.680 --> 00:02:50.080
and estimates of cumulative slip
and temporal variation and stress.

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Increasingly realistic models from
points to circular rupture to asymmetric

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propagation and irregular slip involve
increasing numbers of unknowns

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and require increased
small-scale resolution,

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and consequently better
quality and quantity of data.

00:03:05.520 --> 00:03:09.120
For magnitude 4 and 5 earthquakes,
we can resolve slip distributions with

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some degree of consistency, but there
are still significant variations between

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the different models of the 2004
magnitude 6 earthquake, for example.

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For smaller events, we are still often
struggling to resolve simply the area

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of a circular rupture or maybe the
direction of a simple line source.

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So how do we estimate source
dimension and stress drop?

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Where do these estimates used to
determine source strain,

00:03:35.200 --> 00:03:38.856
predict ground motion,
and monitor fault slip come from?

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An earthquake of a given rupture
dimension radiates its maximum energy

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at wavelengths that
correspond to that dimension.

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A large earthquake with a rupture
length of, say, tens of kilometers

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will radiate its maximum energy
a wavelength of similar size.

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This corresponds to a velocity
amplitude spectrum that’s peaked

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at low frequencies.
A smaller earthquake with

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a smaller rupture area will radiate
energy peaked at shorter wavelengths

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and higher frequencies.
Hence, the peak in the velocity

00:04:06.240 --> 00:04:11.816
spectrum is proportional
to 1 over the source dimension.

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When we integrate the velocity spectra
to displacement, the peak becomes

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a corner frequency above the flat
long period level, which is proportional

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to the seismic moment.
Combining these highly

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model-dependent estimates of rupture
length with the seismic moment

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enables us to estimate the slip and the
corresponding strain and stress drop.

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But we need to remember
all the model assumptions

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that underlie these values
before interpreting them.

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Also most earthquake
seismograms do not have signal

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with as wide a range
as in this figure.

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Because the corner frequencies
of large earthquakes are lower,

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we analyze them typically with
relatively long-period data.

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To study and resolve the corner
frequencies of smaller earthquakes,

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we need to use much
higher-frequency signals.

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A fundamental problem with estimating
source parameters is that seismograms

00:05:06.560 --> 00:05:10.640
are a convolution of the radiation leaving
the source with the attenuation and

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other effects on the waves
as they travel to the seismometer.

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To isolate the source, we need to model
or otherwise correct for attenuation.

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Common methods include using smaller
co-located earthquakes as empirical

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Green’s functions, if available,
or inverting large data sets

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of earthquakes recorded at
multiple stations to use the

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common geometries to
separate the source and path.

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Most modeling uses simple circular
source models and relatively simple

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attenuation structures. In reality,
the Earth is much more complex.

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We know from analysis of large
earthquakes that they can involve

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multiple patches of slip,
resulting in source time functions

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or moment rate functions with
separate sub-events and corresponding

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to bumps in the source spectra.
This could make fitting

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a simple corner frequency
model ambiguous.

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Also, the attenuation in the Earth
is far from homogeneous

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and exhibits significant spatial
and even temporal variation.

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So, in practice, we have significant
tradeoffs between source and path

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that can be hard to resolve with the
limited frequency data that are

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typically available,
leading to ongoing controversies.

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Previous earthquake source
analysis at Parkfield demonstrates

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the relation between the
frequency range of available data

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and the resulting source
parameter resolution.

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Imanishi and Ellsworth studied the
two events in the SAFOD repeating

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sequences, SF and LA, that were
recorded in the deep pilot hole.

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These data are exceptionally
high frequency.

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Even magnitude 2 earthquakes
are above noise to over 300 hertz.

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The corner frequency of the SF event is
well-constrained, whereas the LA event

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is clearly more complex, making the
corner frequency more ambiguous.

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Allmann and Shearer performed a much
larger-scale study to investigate spatial

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and temporal variation of stress drop.
They used the longer-term surface

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network to analyze
over 4,000 earthquakes.

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However, the small-earthquake
seismograms recorded at these surface

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stations are only above noise to
about 20 hertz, so the resolution

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is limited for earthquakes
with higher corner frequencies,

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leading to
large uncertainties.

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I used the higher-frequency recordings
from the HRSN shallow borehole

00:07:19.920 --> 00:07:23.200
network to analyze the
SAFOD repeating events.

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For the relatively simple spectra,
the LA repeating sequence,

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I found good resolution and
agreement with Allmann and Shearer

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and also analyses by Doug Dreger
and others at UC-Berkeley.

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The stress drops were fairly constant
prior to the magnitude 6 in 2004 and

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then decreased before gradually
recovering over the following years.

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This suggested that the earthquakes
were responding to the magnitude 6,

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not just in their
timing and moment,

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but also in the area ruptured
and the average slip.

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The complex spectra of the events
in the LA sequence led to

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much more variation and
uncertainties in my estimates

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as in those of
Allmann and Shearer.

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Clearly we are struggling to resolve the
rupture parameters and their response,

00:08:06.000 --> 00:08:09.736
if any, to changes in strain rate
following the magnitude 6 earthquake.

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So the obvious next event is
to analyze larger-magnitude

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repeating sequences that were
well-recorded by the HRSN.

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I searched the relocated catalog of
Waldhauser and Schaff for repeating

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earthquakes that were large enough to
have better resolution at the source

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and small enough to have multiple
repeats to see time dependence.

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I found three sequences between
magnitude 2 and 3 – A1, A2, and A3.

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They also had plenty of smaller
earthquakes to use the empirical

00:08:37.360 --> 00:08:42.376
Green’s functions. And, as you can see,
the waveforms are extremely similar.

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The variation and recurrence time of
the three sequences shows the familiar

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speeding up after the magnitude 6
and then gradually recovering.

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I color by recurrence time with the
dark and red colors being the rapid

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repeats just after the magnitude 6.
And I used the same color scheme

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in the following plots to identify
the different earthquakes.

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I used the closest small earthquakes
as empirical Green’s functions

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to calculate the P wave spectral
ratios and hence the source spectra.

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At each station, I calculate the
spectral ratios – think of them

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as source spectra – for all events
in the sequence and plot them

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colored by their
recurrence times.

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I then plot these spectra at each station
at the corresponding station azimuth

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so we can see the behavior
of all events together.

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You can see the
strong similarities

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of the different earthquakes at each
station, even to high frequencies.

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Sequence A1 earthquakes
show little variation with time.

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Bumps in the spectra suggest
multiple sub-events,

00:09:45.040 --> 00:09:49.176
so it is not well-fit by the
simple Green’s source model.

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Sequence A2 shows
more temporal variation.

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The spectra at the long recurrence
times are fairly flat and find the

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corner frequencies out of range. More
rapid repeaters have less high-frequency

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energy, suggesting a lower corner
frequency and lower stress drop.

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The magnitude 2.3 sequence
is somewhere in between.

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We tried different methods
of removing attenuation to see

00:10:14.400 --> 00:10:17.200
whether the temporal variation
could be, in part at least,

00:10:17.200 --> 00:10:21.096
the result of increased attenuation
following the magnitude 6.

00:10:21.120 --> 00:10:24.560
We can account for some of the
variation this way, but it’s hard to count

00:10:24.560 --> 00:10:31.176
for all it, suggesting some, at least,
is real source variation.

00:10:31.200 --> 00:10:34.720
We can then transform back the time
domain and resolve the actual moment

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rate or source time functions
of each event at each station.

00:10:39.200 --> 00:10:43.200
These, again, reveal the remarkable
similarity of the repeating sources,

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down to the azimuthal variation and
observation of distinct sub-events.

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We can use the azimuthal variation
in duration to estimate directivity.

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The post-duration recorded from
an earthquake rupture coming

00:10:56.560 --> 00:11:00.720
towards you has a shorter pulse
than from one moving away.

00:11:00.720 --> 00:11:04.720
Because this pattern shown at
all the earthquakes in Sequence A1

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have shorter pulses to the northwest,
then modeling the variation

00:11:08.880 --> 00:11:12.296
shows strong rupture directivity
towards the northwest.

00:11:12.320 --> 00:11:15.520
Sequence A3 shows
a reverse distribution.

00:11:15.520 --> 00:11:18.080
And these earthquakes
all rupture to the southeast.

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For Sequence A2, the shorter duration
of those earthquakes means that many

00:11:22.560 --> 00:11:26.800
pulses are at the minimum duration
resolution, and we cannot clearly

00:11:26.800 --> 00:11:32.080
identify the rupture direction.
This remarkable repeatability

00:11:32.080 --> 00:11:36.240
before and after the magnitude 6
event suggests spatial heterogeneity

00:11:36.240 --> 00:11:38.240
rather than temporal
heterogeneity has

00:11:38.240 --> 00:11:42.080
a dominant effect
on the rupture processes.

00:11:42.080 --> 00:11:46.856
But these are only a few specific events.
What about more generally?

00:11:46.880 --> 00:11:50.320
Jiewen Zhang recently performed
a similar large-scale spectral

00:11:50.320 --> 00:11:54.240
decomposition analysis to that of
Allmann and Shearer at Parkfield,

00:11:54.240 --> 00:11:57.416
but using the
shallow borehole data.

00:11:57.440 --> 00:12:00.960
These example stacked spectra
show the improved resolution

00:12:00.960 --> 00:12:03.280
at the shallow borehole.
The high-frequency limit of the

00:12:03.280 --> 00:12:07.120
original study was 20 hertz,
whereas, using the borehole data,

00:12:07.120 --> 00:12:10.320
we are now able to go
up to 60 hertz and can resolve

00:12:10.320 --> 00:12:14.602
corner frequencies of smaller
earthquakes much better.

00:12:15.840 --> 00:12:19.840
Here I show the spatial variation in
stress drop from three time periods from

00:12:19.840 --> 00:12:25.280
this analysis – before the magnitude 6,
one year following the magnitude 6,

00:12:25.280 --> 00:12:29.280
and the 11 years following that.
We observed strong spatial

00:12:29.280 --> 00:12:34.560
heterogeneity in stress drop at a scale of
a few kilometers. The patterns are stable

00:12:34.560 --> 00:12:39.896
throughout the time periods, implying
relatively low temporal variation.

00:12:39.920 --> 00:12:42.080
The pattern does now
show any dependence

00:12:42.080 --> 00:12:46.616
on the first order transition
from creeping to the locked fault.

00:12:46.640 --> 00:12:49.760
We quantify the temporal
variation by calculating the

00:12:49.760 --> 00:12:55.798
differences between the earthquakes
in Periods 2 and 1 and 3 and 2.

00:12:56.640 --> 00:13:01.200
The temporal changes are relatively
small – much less than 50% of the

00:13:01.200 --> 00:13:06.376
spatial variation, and they don’t
show clear, consistent patterns.

00:13:06.400 --> 00:13:09.520
This supports the results from the
repeating earthquakes that the spatial

00:13:09.520 --> 00:13:13.840
heterogeneity, maybe geometric or
material properties, has more control

00:13:13.840 --> 00:13:19.973
on rupture processes than temporal
variation in stress or slip rate.

00:13:19.973 --> 00:13:23.040
So, in conclusion, we are resolving
now useful information from

00:13:23.040 --> 00:13:27.440
well-recorded small earthquakes.
The best-recorded repeating sequences

00:13:27.440 --> 00:13:30.960
have remarkably similar ruptures
with consistent rupture direction

00:13:30.960 --> 00:13:35.096
and complexity relatively
unaffected by the magnitude 6.

00:13:35.120 --> 00:13:40.480
The larger-scale study also reveals
stable spatial variation in stress drop

00:13:40.480 --> 00:13:44.320
on a scale of a few kilometers.
The pattern appears unrelated to

00:13:44.320 --> 00:13:47.600
the transition from creeping
to locked zones along strike.

00:13:47.600 --> 00:13:51.896
Again, the temporal variation
is much smaller than the spatial.

00:13:51.920 --> 00:13:54.800
Together, this suggests that
the structural heterogeneity,

00:13:54.800 --> 00:13:58.640
for example in geometry or material
properties, has a greater influence

00:13:58.640 --> 00:14:03.600
on earthquake rupture than temporal
changes in stress or strain rate.

00:14:03.625 --> 00:14:05.054
Thank you.