Hello. I’m Rachel Abercrombie from Boston University.
Today it’s my pleasure to share with you an overview of my
recent work on small earthquakes at Parkfield.
This work was performed with Xiaowei Chen and her recently
graduated student Jiewen Zhang from the University of Oklahoma.
It also benefited from collaboration with numerous colleagues.
The aim of the work is to analyze the source processes of the numerous
small earthquakes to improve our understanding of the controls on
earthquake rupture, including the distribution of slip and stress release,
how earthquakes interact, and what they can tell us about
the faults on which they occur.
I present the results of two recent studies – one small-scale and one larger.
As you’ll see, this work is pushing the resolution limits of the available data
and so also includes investigation of the real uncertainties and resolution limits.
The San Andreas Fault at Parkfield is a fascinating place to study for
a number of reasons. It is a place where the fault goes from the primarily
creeping zone to the northwest to the primarily locked zone to the southwest,
through the transition zone, which hosts fairly regular
magnitude 6 earthquakes. The last of these was in 2004.
It is a well-studied and densely instrumented area,
including with the drilling and instrumentation of the SAFOD
deep hole and also the shallow borehole seismic HRSN network.
Parkfield is where repeating earthquakes were first noted
by the Berkeley group. Since then, they and others have
identified many sequences of highly correlated repeating earthquakes
at Parkfield and on other faults undergoing some level of aseismic slip.
The regular recurrence rates of repeating earthquakes have been
used to estimate the fault slip rate. For example, shown here are the
three sequences targeted by the SAFOD hole – San Francisco, L.A., and Hawaii.
They repeated regularly. Then, following the magnitude 6
earthquake in 2004, the rate speeded right up
before the recurrence rate returned to more normal gradually.
Most work using repeating earthquakes to monitor the slip rate
and strain rate depends on assuming the circular rupture
of fixed area, but how good is this?
Can we do better and actually estimate these parameters
for the individual events concerned?
Clearly, to understand earthquake interactions, their rupture dynamics,
and also the ground motions they and their larger cousins produce,
we need to go beyond thinking of the small earthquakes as simply points
or circular ruptures of assumed radius.
Two closely located earthquakes may indicate neighboring rupture
or overlapping rupture patches, depending on the rupture area.
Alternatively, if the slip areas are more complex, then all manner of
complex interactions are possible, clearly affecting our interpretations
and estimates of cumulative slip and temporal variation and stress.
Increasingly realistic models from points to circular rupture to asymmetric
propagation and irregular slip involve increasing numbers of unknowns
and require increased small-scale resolution,
and consequently better quality and quantity of data.
For magnitude 4 and 5 earthquakes, we can resolve slip distributions with
some degree of consistency, but there are still significant variations between
the different models of the 2004 magnitude 6 earthquake, for example.
For smaller events, we are still often struggling to resolve simply the area
of a circular rupture or maybe the direction of a simple line source.
So how do we estimate source dimension and stress drop?
Where do these estimates used to determine source strain,
predict ground motion, and monitor fault slip come from?
An earthquake of a given rupture dimension radiates its maximum energy
at wavelengths that correspond to that dimension.
A large earthquake with a rupture length of, say, tens of kilometers
will radiate its maximum energy a wavelength of similar size.
This corresponds to a velocity amplitude spectrum that’s peaked
at low frequencies. A smaller earthquake with
a smaller rupture area will radiate energy peaked at shorter wavelengths
and higher frequencies. Hence, the peak in the velocity
spectrum is proportional to 1 over the source dimension.
When we integrate the velocity spectra to displacement, the peak becomes
a corner frequency above the flat long period level, which is proportional
to the seismic moment. Combining these highly
model-dependent estimates of rupture length with the seismic moment
enables us to estimate the slip and the corresponding strain and stress drop.
But we need to remember all the model assumptions
that underlie these values before interpreting them.
Also most earthquake seismograms do not have signal
with as wide a range as in this figure.
Because the corner frequencies of large earthquakes are lower,
we analyze them typically with relatively long-period data.
To study and resolve the corner frequencies of smaller earthquakes,
we need to use much higher-frequency signals.
A fundamental problem with estimating source parameters is that seismograms
are a convolution of the radiation leaving the source with the attenuation and
other effects on the waves as they travel to the seismometer.
To isolate the source, we need to model or otherwise correct for attenuation.
Common methods include using smaller co-located earthquakes as empirical
Green’s functions, if available, or inverting large data sets
of earthquakes recorded at multiple stations to use the
common geometries to separate the source and path.
Most modeling uses simple circular source models and relatively simple
attenuation structures. In reality, the Earth is much more complex.
We know from analysis of large earthquakes that they can involve
multiple patches of slip, resulting in source time functions
or moment rate functions with separate sub-events and corresponding
to bumps in the source spectra. This could make fitting
a simple corner frequency model ambiguous.
Also, the attenuation in the Earth is far from homogeneous
and exhibits significant spatial and even temporal variation.
So, in practice, we have significant tradeoffs between source and path
that can be hard to resolve with the limited frequency data that are
typically available, leading to ongoing controversies.
Previous earthquake source analysis at Parkfield demonstrates
the relation between the frequency range of available data
and the resulting source parameter resolution.
Imanishi and Ellsworth studied the two events in the SAFOD repeating
sequences, SF and LA, that were recorded in the deep pilot hole.
These data are exceptionally high frequency.
Even magnitude 2 earthquakes are above noise to over 300 hertz.
The corner frequency of the SF event is well-constrained, whereas the LA event
is clearly more complex, making the corner frequency more ambiguous.
Allmann and Shearer performed a much larger-scale study to investigate spatial
and temporal variation of stress drop. They used the longer-term surface
network to analyze over 4,000 earthquakes.
However, the small-earthquake seismograms recorded at these surface
stations are only above noise to about 20 hertz, so the resolution
is limited for earthquakes with higher corner frequencies,
leading to large uncertainties.
I used the higher-frequency recordings from the HRSN shallow borehole
network to analyze the SAFOD repeating events.
For the relatively simple spectra, the LA repeating sequence,
I found good resolution and agreement with Allmann and Shearer
and also analyses by Doug Dreger and others at UC-Berkeley.
The stress drops were fairly constant prior to the magnitude 6 in 2004 and
then decreased before gradually recovering over the following years.
This suggested that the earthquakes were responding to the magnitude 6,
not just in their timing and moment,
but also in the area ruptured and the average slip.
The complex spectra of the events in the LA sequence led to
much more variation and uncertainties in my estimates
as in those of Allmann and Shearer.
Clearly we are struggling to resolve the rupture parameters and their response,
if any, to changes in strain rate following the magnitude 6 earthquake.
So the obvious next event is to analyze larger-magnitude
repeating sequences that were well-recorded by the HRSN.
I searched the relocated catalog of Waldhauser and Schaff for repeating
earthquakes that were large enough to have better resolution at the source
and small enough to have multiple repeats to see time dependence.
I found three sequences between magnitude 2 and 3 – A1, A2, and A3.
They also had plenty of smaller earthquakes to use the empirical
Green’s functions. And, as you can see, the waveforms are extremely similar.
The variation and recurrence time of the three sequences shows the familiar
speeding up after the magnitude 6 and then gradually recovering.
I color by recurrence time with the dark and red colors being the rapid
repeats just after the magnitude 6. And I used the same color scheme
in the following plots to identify the different earthquakes.
I used the closest small earthquakes as empirical Green’s functions
to calculate the P wave spectral ratios and hence the source spectra.
At each station, I calculate the spectral ratios – think of them
as source spectra – for all events in the sequence and plot them
colored by their recurrence times.
I then plot these spectra at each station at the corresponding station azimuth
so we can see the behavior of all events together.
You can see the strong similarities
of the different earthquakes at each station, even to high frequencies.
Sequence A1 earthquakes show little variation with time.
Bumps in the spectra suggest multiple sub-events,
so it is not well-fit by the simple Green’s source model.
Sequence A2 shows more temporal variation.
The spectra at the long recurrence times are fairly flat and find the
corner frequencies out of range. More rapid repeaters have less high-frequency
energy, suggesting a lower corner frequency and lower stress drop.
The magnitude 2.3 sequence is somewhere in between.
We tried different methods of removing attenuation to see
whether the temporal variation could be, in part at least,
the result of increased attenuation following the magnitude 6.
We can account for some of the variation this way, but it’s hard to count
for all it, suggesting some, at least, is real source variation.
We can then transform back the time domain and resolve the actual moment
rate or source time functions of each event at each station.
These, again, reveal the remarkable similarity of the repeating sources,
down to the azimuthal variation and observation of distinct sub-events.
We can use the azimuthal variation in duration to estimate directivity.
The post-duration recorded from an earthquake rupture coming
towards you has a shorter pulse than from one moving away.
Because this pattern shown at all the earthquakes in Sequence A1
have shorter pulses to the northwest, then modeling the variation
shows strong rupture directivity towards the northwest.
Sequence A3 shows a reverse distribution.
And these earthquakes all rupture to the southeast.
For Sequence A2, the shorter duration of those earthquakes means that many
pulses are at the minimum duration resolution, and we cannot clearly
identify the rupture direction. This remarkable repeatability
before and after the magnitude 6 event suggests spatial heterogeneity
rather than temporal heterogeneity has
a dominant effect on the rupture processes.
But these are only a few specific events. What about more generally?
Jiewen Zhang recently performed a similar large-scale spectral
decomposition analysis to that of Allmann and Shearer at Parkfield,
but using the shallow borehole data.
These example stacked spectra show the improved resolution
at the shallow borehole. The high-frequency limit of the
original study was 20 hertz, whereas, using the borehole data,
we are now able to go up to 60 hertz and can resolve
corner frequencies of smaller earthquakes much better.
Here I show the spatial variation in stress drop from three time periods from
this analysis – before the magnitude 6, one year following the magnitude 6,
and the 11 years following that. We observed strong spatial
heterogeneity in stress drop at a scale of a few kilometers. The patterns are stable
throughout the time periods, implying relatively low temporal variation.
The pattern does now show any dependence
on the first order transition from creeping to the locked fault.
We quantify the temporal variation by calculating the
differences between the earthquakes in Periods 2 and 1 and 3 and 2.
The temporal changes are relatively small – much less than 50% of the
spatial variation, and they don’t show clear, consistent patterns.
This supports the results from the repeating earthquakes that the spatial
heterogeneity, maybe geometric or material properties, has more control
on rupture processes than temporal variation in stress or slip rate.
So, in conclusion, we are resolving now useful information from
well-recorded small earthquakes. The best-recorded repeating sequences
have remarkably similar ruptures with consistent rupture direction
and complexity relatively unaffected by the magnitude 6.
The larger-scale study also reveals stable spatial variation in stress drop
on a scale of a few kilometers. The pattern appears unrelated to
the transition from creeping to locked zones along strike.
Again, the temporal variation is much smaller than the spatial.
Together, this suggests that the structural heterogeneity,
for example in geometry or material properties, has a greater influence
on earthquake rupture than temporal changes in stress or strain rate.
Thank you.