Good morning. I’d like to thank you for inviting me to give a talk
at the Northern California Earthquake Hazards Workshop.
Today I’d like to talk about moment tensors, state of stress,
finite-source scaling, and characterizing a pseudo fracture
network from microearthquakes at the Geysers, California.
This is work that I’ve done with Ronald Gritto from Array Information
Technology and Sierra Boyd and Taka’aki Taira from the Berkeley
Seismological Laboratory over the last several years.
What I’m going to focus on today is the seismicity swarm in the
Northwest Geysers Enhanced Geothermal System Experiment.
This red outline is showing the northwestern extent of the Geysers
geothermal field. And this 1-kilometer-by-2-kilometer rectangle
shows the study area for today’s talk.
And this study area is centered on the Prati-32/Prati-31 wells.
The purpose of the enhanced geothermal system experiment was to
deepen the Prati State 31 and Prati-32 wells into the high-temperature
reservoir and introduce water – inject water and stimulate fracture generation.
This plot is showing the average monthly water injection rate
beginning on October 6th, 2011 – the blue curve.
And the asterisks are showing a very strong correlation with
monthly seismicity rates within our study area.
So I’d like to give an overview of our seismic source analysis
at the Prati-32 EGS injection site.
Give some examples of seismic moment tensor analysis to obtain
waveform-constrained estimates of Mw and fault plane orientations.
We use that information to invert for the stress tensor
to investigate temporal variation in stress during injection.
We’ve done some finite-source analysis to determine the causative
plane and the scaling of rupture parameters such as average slip,
rupture area, and stress drop.
And I’d like to finish up by showing how you can integrate all of this
information to characterize seismicity in terms of a pseudo fracture network,
which is illustrated here, where, instead of a distribution of dots
in a box, we can actually start to think about the dimensions of the
microearthquakes in the study area and the degree of interconnectivity
of the – of the stimulated fractures.
So, for the moment tensor analysis, we used instrument-corrected
waveforms filtered between 0.7 to 1.7 hertz. We used a grid search
to optimally align the waveforms with the Green’s functions.
And, for some of the events, we perform a joint waveform
first-motion source-type inversion based on the work of Sean Ford et al.
and Avinash Nayak, in which we search for the optimal moment tensor
solution in the source-type space. So this takes into the account the
full moment tensor, including volumetric terms.
We’ve analyzed 160 events inside the 1-by-2-kilometer
study area, and the smallest event was moment magnitude 0.6.
So this shows the results, spanning approximately
a five-year period of time. So about a year, year and a half,
before the stimulation experiment began, we collected – well, we collected
about 20, 25 moment tensor solutions. The rate in the study area was
very low prior to injection. The red curve is showing the
injection rate in gallons per minute. And you can see, in late 2011 –
in October 2011, there’s a marked increase in the numbers of earthquakes
and – as we saw in the previous slide.
And then also the magnitudes of these microearthquakes.
The color scaling is showing the percent CLVD.
So there are non-double-coupled components as well as double-coupled
moment tensor solutions. And we see a variety of mechanisms
which are, you know, more or less distributed between strike-slip
and normal-type faulting. In fact, when we look at the distribution
with source depth, this red bar is showing the interval over which the
well casing is perforated, allowing water to enter the surrounding rock.
The seismicity is peaked at this depth range. And you can see that there’s a –
roughly a – almost a 50/50 mix between strike-slip and normal types of events.
The brackets down here are showing overlapping time windows that we
used to sample the moment tensor catalog for stress inversion.
We used a stress inverse methodology of Vaclav Vavryčuk 2014, and this
shows the results as a function of time for each of those
staggered time windows. So pre-injection,
we find the maximum compressive stress, red,
and the minimum compressive stress, blue, are in the horizontal.
So consistent with a strike-slip regime.
And then, during the injection, this remains the case, but you can
see evidence of a slight rotation of the minimum compressive
stress orientation. So it’s almost east-west.
And, mid-2012, injection was halted, and there was a dramatic rotation
in the stress direction. So, for example, the maximum
compressive stress, red, is horizontal. It rotates 90 degrees into the vertical.
So this stress regime is most consistent with normal-type faulting.
When injection restarted, the maximum principal stress
rotated back into the horizontal. So we see a very profound change
in the state of stress at the initiation of injection
and during changes in injection rate.
For finite-source analysis, we use a moment rate function
finite-source inverse method.
This is based on the method of Mori and Hartzell 1990.
We use empirical Green’s function deconvolution term in the seismic
moment rate functions at multiple stations.
Here I show an example for Parkfield.
This is for a magnitude 2.1 earthquake.
There’s a nearby moment magnitude 0.68 earthquake.
We can perform Fourier transform on both of these traces, take the ratio
of these, and common terms cancel as long as the two events are
co-located and have the same mechanism.
Of course, recorded on the same instrument.
Then G and I are going to cancel out. They’re in common.
And what’s left is the – an estimate of the main shock, or the target event,
source spectrum. We can inverse FFT and obtain a pulse in the time domain,
which represents the moment rate. So what Mori and Hartzell did was
take these moment rate functions – here’s a cartoon depicting one at
one station – and devised a finite-source model in which these
moment rate functions are modeled in terms of the superposition of
slip-distributive or finite fault rupture plane and with timing controlled by a –
by a rupture velocity. So I’m going to give you several examples.
This first one is for a magnitude 1.5 earthquake.
It’s located in the center of the study area.
The moment rate functions are shown in black.
Since we’re using a spectral domain deconvolution procedure,
we interpret the moment rate functions from the zero crossing –
zero to positive, positive back down to zero crossing.
And the red traces are showing the model fit.
This is a very small earthquake. And we find a very compact source.
But, in order to explain the impulsive nature of these moment rate functions,
the slip is non-uniform. So there’s a peak slip at the
center of the fault, and it tapers out to the edges, not surprisingly.
The dimensions here is about 100 meters.
So roughly a 50-meter radius for this magnitude 1.5 earthquake.
We can take this slip distribution, using the method of Ripperger and Mai,
estimate the coseismic stress change.
And that’s what’s shown in this diagram here.
Red indicates a stress drop. Blue indicates a stress increase.
And what we find is an average stress drop for this event, which is
0.4 megapascals, and a peak stress drop of about 1.8 megapascals.
So a little bit on the low side, but squarely within the observed
range of earthquake stress drops.
The next event is a magnitude 2.9 located at the southeastern corner
of the study area. The moment rate functions have slightly larger duration,
perhaps a little bit more complexity – evidence of multiple sub-events.
Two peaks here at MCL. Two peaks here at AL5.
There does seem to be a directivity effect in terms of the overall shape
of these moment rate functions. The slip has a slightly larger dimension.
The long dimension is about 200 meters.
The short dimension is quite narrow – only about, say, 100 meters at the most.
There’s evidence of two primary asperities, perhaps a third.
We take this slip distribution and, using the Ripperger and Mai approach,
we can map it to stress change. And what we find is that the average
stress drop is 11.4 megapascals, or 110 bars.
Peak stress drop is 69.1 megapascals. I guess the point to make here is that
these microearthquakes are not simple, uniform slip ruptures. They’re complex.
They do have sub-events and various variations in slip amplitude, and
therefore, variations in the stress drop across the fault surface.
The next event is a 4.4 event. This one’s actually outside
the study area but within the Geysers geothermal area.
And, for this case, we used stations recorded by the
Berkeley Seismological Network.
And the dimensions for the model space is considerably higher.
It’s about 9 square kilometers – so 3 kilometers on a side.
We see evidence of two primary asperities.
At the Hopland station, you can see the dual pulses here.
There’s a very pronounced directivity effect in the moment rate functions.
When we – when we convert the slip distribution to stress change,
we find an average stress drop of 11.4 megapascals.
The peak is about 46.9 megapascals. So the average for this 4.4 is very
similar to what we just saw for the 2.9. All right. So we put all of this together.
Of course, we’ve looked at many more earthquakes.
We also looked at a magnitude 5, which was just outside the study area –
about 600 meters south-southwest of the study area.
And, for this case, we had to use theoretical Green’s functions.
This was a very complicated rupture for a magnitude 5 earthquake.
But what we’re after here is to try to get an idea of the rupture area scaling
and the average slip scaling – so there’s a typo here.
So we have moment magnitude on the X axis, and we have rupture area.
This is 1 square kilometer. That corresponds to about
a magnitude 4.0 earthquake. The red curve is the Wells
and Coppersmith relation. The blue curve is the Leonard 2010
relationship. And this dashed curve is the two-sigma error for Leonard 2010.
And the bold dashed lines are showing the 0.1 megapascal
to 100 megapascal range.
We see stress drops that are consistent with what we’ve seen for larger
earthquakes on a global scale. Maybe there’s some evidence
of lowering of stress drop towards the smaller magnitudes,
but a lot more work – many more events are needed
to see if this is actually borne out by the data.
So, given high-resolution event locations, the seismic moment tensors
are used for insight into the mechanism type and to determine the stress tensor.
Finite-source scaling is used to determine rupture area
and fault dimension for a given Mw.
And the stress tensor is used to randomly sample fault orientations
that are optimally aligned with the stress field.
The fault orientation and rupture dimensions are assigned to the
seismicity cloud to characterize a pseudo fracture network.
Or we sometimes call it a statistical fracture network.
So what’s meant by that is we can actually plot the dimensions
of these microearthquakes.
This blow-up region is shown by the bold square here.
This is the Prati-32 injection well. This is the Prati-31 recovery well.
And what we can start to do with the finite-source scaling is look at
the degree of interconnectivity of these microearthquakes.
So we refer to this as a pseudo fracture network because it’s not a direct
estimation of parameters for the many thousands of events.
But the orientation of the faults and the – and the rupture dimension
scaling is constrained by analysis of earthquakes in the – in the study region.
What can we do with this? Well, we can – we can show
what the seismicity cloud looks like. So this is the many thousands –
I think it’s over 7,000 earthquakes that were produced by the stimulation.
If we look at 100-meter bins, we can bin up the number of
earthquakes and we find that, you know, the greatest density
of earthquakes lies below the injection well.
And, with the scaling parameters, we can start to say, okay, well,
what is the distribution of fracture area? It’s basically a way of getting towards
fracture density from these seismic observations.
All right. To summarize, I’ll leave you with a video –
an animation of this pseudo fracture network.
Small earthquakes at the Geysers and elsewhere display complex
rupture like larger counterparts. Slip and stress drop are non-uniform.
The 2016 magnitude 5 event is very complex and suggests discrete
sub-events rather than a more typical connected rupture.
We have been able to obtain seismic waveform-based moment tensor
solutions for the Geysers events moment magnitude 0.6.
This gives insight into activated faults, assisting in calibrating the
LBL P wave spectrum-based Mw estimates and enabling
inversion for the moment tensor.
The finite-source models demonstrate complexity, scaling consistent with
Leonard 2010, and stress drop between 1 and 10 megapascals.
We’ve illustrated a pseudo discrete fracture network approach for the
Prati-32 EGS site, utilizing the focal mechanism-based in situ stress,
moment tensor, and finite-source scaling results.
This can be used to infer the degree of interconnectivity
of microearthquake fractures.
Thank you for your attention, and I’m happy to take any questions.