[inaudible background conversations]
Okay, everyone. I guess we’ll get started.
Before we get started with today’s seminar, a couple of announcements.
Please remember that this coming Monday at 2:00 p.m. is the memorial
celebration for Dave Hill, and it’ll be here in this room at 2:00 p.m.
For next week for seminar, we’re going to have Kathryn Materna
from UC-Berkeley will come to talk to us.
And I think that’s it for announcements. And so then it’s my pleasure to
introduce today’s speaker, Kris Pankow. She got her Ph.D. at UC-Santa Cruz
working on deep subduction zone stuff and then took a – kind of a big career
change to go to University of Utah and start working on more –
much more crustal-related problems. So at University of Utah,
she’s the assistant director – is it assistant director or associate …
- The associate …
- Sorry. Associate director of the seismographic stations,
and she’s also research faculty there. And she does research on a number
of interesting topics including things like mine-induced earthquakes.
And today, she’s going to be talking about dynamic triggering. Thanks.
- Let’s see if this works. Okay. All right. Thanks, Jeanne.
And thanks for everyone – for coming today.
I’m going to talk about – oh, I have to be tall. Okay.
Talk about some work that I’ve been doing for a while on
dynamic earthquake triggering. And these are more sort of
thoughts that I’ve had, and I hope that this spawns some discussion.
So that we’re all on the same page, when I’m talking about remote
dynamic triggering, I’m talking about, when an earthquake occurs someplace
in the world, and at a distant location, we start seeing small earthquakes.
And this is a little cartoon version of this.
The surface waves come by, and you start to see earthquakes occurring here.
Maybe it’s body waves. So this is what I’m talking about
when I’m talking about dynamic earthquake triggering.
And this has been studied for a long time now.
And there’s a lot of big-picture questions.
We’re really trying to get at, you know, what is the state of stress in the crust?
And can these dynamic earthquakes tell us something about that?
And even sort of more specific questions – why do some seismic waves
trigger earthquakes and others don’t? Is it a function of the seismic waves?
Is it a function of the peak dynamic stress, the frequency,
the orientation, or, say, the particle motions?
Or is it something specific to the location of the fault
that’s being triggered? Is it the orientation of that fault?
Is it the crustal stress in that fault? Are there fluids involved?
What – so what I’m hoping in terms of my looking at this research is, what can
we learn about the earthquake process by, in a sense, these controlled
experiments that aren’t so well-controlled, right?
They don’t happen all the time, but I think there’s really good
information that we can learn about the process by studying these earthquakes.
So I didn’t realize you were having a memorial for Dave, so this is some of
Dave’s pioneering work following the 1992 magnitude 7.3 Landers earthquake.
It was found – if this is the epicenter of the earthquake, where we’d expect
the aftershocks to be is sort of in this red circle here.
And in the first paper published on dynamic earthquake triggering by Hill
and others, what was found was that, following this earthquake, there were
earthquakes in the western U.S. So not located in that area where
we’d typically see aftershocks. And I would say that probably at
this time, if you would have asked anyone if this could happen, they
probably would have said no. Okay? So here we are with this empirical
evidence that this is what’s going on – the first paper.
I got pulled into this topic in 2002 following the Denali Fault
earthquake in Alaska. It was a right-lateral strike-slip fault
with very strong directivity to the southeast. And, in fact, if you follow the
propagation here, it goes right through Yellowstone National Park in Utah –
sort of the areas of peak dynamic stress. This is from work of Velasco and et al.
where we actually went through and measured the peak dynamic stress
in the western U.S. following this earthquake.
And, at the time, Stephan Husen was a postdoc working on Yellowstone.
And he came in, and he said, Yellowstone’s going crazy.
I think we have dynamic triggering. If – you know the old helicorders,
the drum records? Sometimes they were really nice
because you could look at the drum, and you could just see earthquakes
going on all the time. And even more so, the water features
in Yellowstone were starting to bubble, and there was just a lot of activity
in Yellowstone. And that made me look at the data in Utah.
And so this is the timing of the arrival of the surface waves – the body waves
and the surface waves of the Denali Fault earthquake, and you can
see this longer-period energy being from the main shock.
And then, all of the sudden, each one of these red spikes in the spectrogram
is a small local earthquake. This is a station in northern Utah.
This is – this is pretty atypical for Utah. This would be more than we’d see in
a typical aftershock sequence, okay? So we had a lot of activity going on
in Utah as well that led me into this study to start looking at this question –
or these multiple questions.
And so there’s been a lot of work done on this, and there’s been many review
studies at this time, but there’s a couple of really nice figures
from some Hill and Prejean work. And, in this first one, which was
published in 2007 – so sort of early – I would say early in the study of
dynamic earthquake triggering, you can see – let’s see. Where did my mouse go?
There it is. It’s very touchy.
Sort of a collection of four earthquakes where we were pretty sure we had
dynamic earthquakes triggering. So following Landers, you can see
the green triangles here showing that Landers triggered earthquakes
in the western U.S. Hector Mine – the magnitude 7.2
in southern California – triggered events primarily in California.
Primarily in these geothermal systems. The Denali earthquake triggered events,
again, through much of western United States.
And then the Sumatra earthquake – it was shown that the – it triggered
events at Mount Wrangell. And these events were found in the
surface waves, and they were in phase with the peak dynamic stress. Okay?
So a couple of observations that I want to come back to later.
So some of these first cases of dynamic earthquake triggering.
These aren’t small, localized areas of triggering.
These were triggering large areas. We were triggering much of the
western United States with these studies. So, in the next review study, or –
from Hill and Prejean 2015, there’s another summary figure. Okay, so from
2007 to 2017, now all the symbols on these plots are places where
there is dynamic triggering documented.
If they’re big circles, they were larger events – 5-1/2 and larger.
If they’re orange, people went back and looked at the pre-instrumental catalog.
The smaller circles are smaller earthquakes, and with instrumental data,
we start to see triggered tremor. And people – in some work,
we started enhancing catalogs, and that was done in this work with
Velasco where we had blue. So we weren’t just looking at catalog data.
We were starting to enhance the catalogs.
Okay, so all this work has been done. Why am I still looking at this, okay?
Is there something that still needs to be done?
So – and I failed to say this at the beginning.
This is work that I’m doing with Debi Kilb from Scripps.
And the questions we’re going after is – and motivating this particular study is
we – from that previous figure, we see all these documented cases.
And if you actually go and look in the literature, we’re calling dynamic
triggering different things depending on different statistics and different criteria.
And so one of the things that I would like to look at is,
what are the indicators of dynamic triggering?
From those first studies from Landers and Denali, it seemed to be this wide,
spatial extent of increased rates. Okay? And then, if you look at those dots
from 2015, maybe it’s not so wide. Maybe you can get localized triggering.
But, as a community, I think we need to decide, what are really
the indicators of this? Is it enough to have events coincident
with the passage of the surface waves? Or do they have to be in phase?
Do we have to have a rate increase? What’s the spatial extent?
And so this is one of the questions motivating this study.
But if we’re going to talk about rate increases being an indicator of dynamic
triggering, what are we going to say about rates?
How are we going to measure rates, and how are we going to measure
a statistically significant rate change? Okay?
And this is what I’m going to spend much of my time talking about in this –
in this talk. And it’s one thing that we have a curated catalog to
talk about statistical significance. But a lot of the work being done
in dynamic earthquake triggering now is using enhanced catalogs with
really short time windows. So I’ve been thinking about this
for a while, and I think it’s a timely time for us,
as geophysicists and seismologists, to be thinking about this.
This is from a couple weeks ago – March 20, 2019, in Nature.
The statisticians – or a group of statisticians want to get rid of this
concept of statistical significance. Okay, this particular comment
has 800 signatories, okay? And this was on the 20th.
By the 27th, there were at least three letters saying that
we can’t get rid of statistical significance. Okay?
So this is something that’s happening in the statistical community, where
they’re really having this discussion. And what these people want to do is,
they want to take the idea of statistical significance and put it in the closet with
things like the ether and the cyclops. And so that’s what this cartoon
is showing us, is that maybe it has served its purpose and has
brought us as far as we can get with this particular idea.
And let’s just put it in the closet for now.
So a few quotes from this paper that I think are important for our discussion
on dynamic earthquake triggering and how we use statistics is, unfortunately,
the false belief that crossing the threshold of statistical significance is
enough to show that a result is real. Okay?
Just because we say it’s statistically significant, based on
whatever statistics we decide to use, we then decide that it’s real.
And I think we need to think about that more.
Like the 0.05 threshold – and this is talking about a P value – from which it
came the default 95% used to compute intervals is an arbitrary convention.
It is based on the false idea that there is a 95% chance that the computed
interval itself contains the true value. So when we talk about statistical
significance, we are somewhat picking these arbitrary values
for which to measure things across.
And then what they’re trying to get at is these – they want to
talk about compatibility versus statistical significance.
And this hinges on the correctness of the statistical assumptions.
I would also say it depends on whether or not you are using –
following the assumptions in the statistics that you’re using.
So they want to get rid of statistical significance and talk about confidence
intervals as compatibility intervals. So I just want to throw this out there
because we often use statistics in seismology and geophysics.
And I think this is a discussion – a broader discussion that’s
happening that maybe we should be paying attention to.
So back to dynamic earthquake triggering.
And some of the statistics we’ve used. And the first one, and probably the
one that’s most widely cited, in the beta statistic.
This was developed by Matthews and Reasenberg in 1988.
And it measures the difference in seismicity rate between the number of
earthquakes – and sorry, this is a typo – in a post-interval time.
And you subtract the number of earthquakes you’d predict for that
time using a pre-interval time. And then you normalize by the
standard deviation. You must have an earthquake in the time that you’re
using to establish the rate. Okay, there must be at least one earthquake.
So I don’t know how many of you have read Matthews and Reasenberg.
It’s a pretty dense paper with lots of mathematical notation.
And this is how they define the beta statistic in terms of a moment
and some probabilities. If we put it into something that
we can actually plug some numbers into in terms of earthquakes, it’s really
the number of earthquakes and what I’m calling the after window.
So that’s what A is standing for. You subtract the number that
you’d predict by measuring the rate – so the number before divided by
the time before, multiplying by the time.
And then you multiply by the variance in this prediction. Okay?
So it’s pretty clear to see here, if the number of earthquakes in
your before window is zero, your computer is not going to like it when
you try and calculate this equation, okay?
You get lots of things like undefineds and such.
Okay, so that’s a big – a big clue here is,
you have to have a long enough time window to have this value.
If you go through and you read the paper, it actually assumes
a declustered catalog and a Poisson catalog.
So it’s assuming earthquakes happen at a constant rate and are independent.
So you’ve done some type of declustering.
I actually think we need to have a discussion here because the
statistic is also really trying to tell us when the earthquake
is varying from an independent catalog.
Importantly here, in this paper, they say significant anomalies
located by this test in very short intervals should be treated suspiciously.
So if you’re using the really small windows and you get
significant values, it should be a suspicious result.
Significance is found by looking at a distribution of beta over an interval.
[inaudible] talk about this being an asymmetric function.
You’re only normalizing by the variance of the before window.
So this isn’t going to collapse to a nice Gaussian, even with lots of n.
So it’s not clear that you can just say beta greater than 2 is significant.
And, in this original paper, Matthews and Reasenberg,
they suggest contouring the values of beta to look at
where you really have peaks or applying other statistical values.
And to show this, in a recent paper by Prejean and Hill, where they
were looking at volcanic systems, where they are sure they aren’t
looking at Poissonian-type distributions, to get around this, they re-sampled their
catalog multiple times and then used the distribution of beta
to find when it was significant. And they found that,
for 95% of the time, in each volcanic center, your beta range
at the significance level could be 2.7 or it could be 16.
And to further illustrate this, in a paper – and there’s lots of examples.
This was just a nice figure. This is by Johnson and Bürgman from 2015.
They were looking at the Indian Ocean earthquake on the Blanco Fault Zone.
And you can see their distribution of beta values here at the start
of the surface waves coming in – or, at the start of their study window –
sorry – at this red curve is around 5. And then it jumps up to 9.
So this goes to the question of, what do we mean by statistical
significance, and how are we using our statistics to get there?
A second statistic – the Z statistic – I actually wasn’t familiar with this
statistic, and still I read the Prejean and Hill paper, and they actually required
that their triggering passed both the beta statistic and the Z statistic.
And so I went and looked at this more, and this is really a symmetrical
version of the beta statistic. It’s depending on a rate before and after.
And so here’s a formulization of it from the Aron and Hardebeck paper.
And the Z statistic is the difference in the means between two time intervals,
normalized by their variances.
So the sum – the square root of the variances there.
And so just, again, if you want to plug some numbers in, and we use the same
terminology, you can look at the number of events after and times before,
it’s some algebra to go from here to here, but it’s pretty straightforward.
And so key here is that this – you’re looking at the variance over
two different time windows surrounding the time that you’re looking at.
Okay, so this is a symmetric function. So if you’re looking at the limits here,
you can actually – if you have large n, probably 30 or larger, this will collapse
to a Gaussian, and you can talk about significance in sort of
our standard way of talking about significance at 1.96 and 2.57
for 95 and 99 – these arbitrary values.
Okay. There’s a second equation in the Aron and Hardebeck paper
for the beta statistic. And I wanted to talk about this a little bit.
This is what they used in the Prejean and Hill paper to calculate beta.
And it’s really nice because it gets rid of this singularity, right?
We aren’t counting the events just in a before window.
You’re looking at the windows over the full time, okay?
So if N is the number of events in the full time window you’re looking at,
and T is the full time window, you’re still looking at the number of
events in an after window and subtracting the expected value.
But you’re actually normalizing by essentially a variance in both windows.
So I’m not sure this is strictly follows the beta statistic that we saw in
Matthews and Reasenberg, but it does a really nice job of dealing with
this singularity issue. And I just wanted to point out that,
if you actually have a symmetric window – so your time before and
your time after are equal, okay, and you – and here I’m just
substituting in N equals N-A plus N-B, and T equals T-A plus T-B.
This beta version reduces, and if your time windows are equal,
it’s equivalent to the Z statistic. Okay? There’s nothing to say you have to
use symmetric windows. You can have different time windows.
But, again, I think – this isn’t a strict beta statistic.
It might actually work a little bit better, and I’ll show you that going forward.
Mainly because we don’t have that singularity.
I do want to point out that, in the original formulations of the
Z statistic by Haberman in the 1980s, these were also assuming a Poisson
catalog and an independent catalog, so looking at declustered catalogs.
So a third statistic that I’ll just briefly talk about is, if we just simply assume
a Poisson distribution, which means that we have a constant rate, and we grab
any window, and we measure the mean in that window, we can compare
windows by looking at how far away it is in terms of standard deviation.
And this is what I’ve used in a number of studies.
I probably won’t be using it again, but that was the basis.
So you’re really just looking at the difference in the means.
Okay.
So what we set out to do was we wanted to find a new way to do this without
fewer assumptions. And that’s what I was going to come talk to you about.
But then I found out there’s lots of good things out there.
And so it – sort of the nature of what I’ve been doing has been
changing some. But this statistic looks at an empirical distribution.
So we take long windows of time to establish rates.
By looking at long windows, we aren’t – the assumption is, we don’t have to
decluster because the dependent times are going to show up on the tail.
And what we’re really going to see in terms of the primary distribution,
or where most of the events are, is the independent part, and that
will allow us to define what’s happening in the catalogs.
The one thing we do require is that we have a magnitude of completeness.
And similar magnitudes. And then we take this distribution,
and we explore ways to measure the significance.
We use the Chebyshev Inequality Theorem, which is five times the
standard deviation. Should give you at least 96% – another arbitrary value.
We looked at the percentiles within the distribution.
And advantages here is we have few assumptions.
I’m going to show you it doesn’t matter what the length of our windows are
because we’re looking at the catalog, and we’re defining the character of the
catalog. And then we also aren’t limited, as in many dynamic earthquakes studies,
of just looking around the time windows of teleseismic arrivals.
We’re looking across the entire catalog.
So first thing we do is we look at magnitude of completeness.
And we’re just approximating this – the maximum curvature.
I can show you later that I don’t think this is critical to our work, but it does
get rid of some of the small events that might bias our distributions.
And then what we do is, for our time window – and we settled on three-year
windows because that gave us somewhat constant magnitude of completeness –
we start at the beginning of the three-year window,
and we pick a time interval. Five hours, 12 hours, a day, five days –
whatever you want it to be, and you just start counting.
So if you’re using a five-hour window, you count all the earthquakes from
zero-zero to zero-five. And then you slide your
window by an hour, and you count again.
This gives us 26,000 data points.
And then we put this on a distribution histogram here.
And what should surprise no one in this room is that, for most catalogs,
at a five-hour time window, what you mostly count is zero. Okay?
We don’t typically see that many earthquakes happening.
But you get earthquakes – you can get going out to 5, 6, 7.
This is just using the Utah catalog as an example.
And then we can look at sort of what the character of these distributions are.
We can find the mean. We could get the standard deviation.
We can find five times the standard deviation and get the
threshold that the Chebyshev Inequality Theorem tells us.
We can look at the distribution of itself and find out where 95% of the data
is in the solid red or 99% of the data is in the dashed red.
And we can start looking at the full character of this and
start defining thresholds based on these characters.
And it’s going to change if you have different windows.
So using that and these thresholds, we define thresholds where the
catalog is anomalous at our arbitrary significance levels of 95 and 99%.
And so every dot on here is one of our windows.
If it’s red, it was above the threshold value.
If it’s green, it’s below the threshold value.
And then we compare that to the timing of teleseismic waves,
which are the green lines. And for this window –
I picked this window because, if we didn’t see Denali in Utah
as significant, we had a problem.
But we also found two other events. We found the Kuril event,
which I’m going to talk about in just a couple minutes, actually happened
within the window that we originally said we had increased seismicity
from the Denali earthquake. So, in our original study,
we didn’t discriminate between these two main shocks.
And then we also found this Molucca Sea event,
which I will come back to at the end of the talk.
The other thing about this method that I’ll just put a plug in
for right now is it also finds other time periods in the catalog
where there’s significant changes.
These are probably related to main shock/aftershock sequences.
I had a high school statistics teacher working for me this summer on
a research project, and she took and applied this technique to
the Yellowstone data, just looking for subtle changes, so maybe
small swarm-type events. And that’s work we’re still looking at.
But I think there’s other applications than dynamic earthquake triggering.
So here’s that Kuril event I talked about. The Denali Fault earthquake.
The primary – the original one that we said we had dynamic
earthquake triggering came in here on the 3rd of November.
We had a magnitude 3 and some aftershocks spiking things here.
It looks like it was starting to roll over, and then energy from the 7.3 event,
which we partly discarded because it’s – this is a deep event – 459 kilometers.
But, you know, this comes to the question of, what do we mean by
statistical significance, and what are the indicators of dynamic triggering?
And if we’re just going to use rates, then is this dynamic earthquake triggering?
Did this event further the excitation in Utah, or was it just by chance?
So that’s the method. We applied it to four catalogs in the western U.S.
We looked at 500 main shocks from the world – 11 sort of more regional events.
The catalogs we looked at – we chose catalogs that we had
some experience with, which is always kind of
a good idea if you want to blindly dig into catalogs, we have the
ANZA catalog, Utah catalog, Yellowstone, and Montana.
Reasons why you might want some experience with the catalog is,
we know, in Utah, to get rid of the mining seismicity.
So this polygon here of white is where we have coal mines in Utah.
And while there might be dynamic earthquake triggering going on in the
coal mines, decoupling the production history and the things that generate
mining seismicity from incoming waves was more than we wanted in this study.
We then calculate the magnitude of completeness for these
33-year-long catalogs in three-year windows.
Pink and red are Utah and Montana, respectively.
And they’re relatively consistent across the board.
ANZA is in green, and in 2004 here, there was
a large drop in the magnitude of completeness.
This plays into the threshold values. So if you start seeing – if there’s –
if the magnitude of completeness drops, your threshold’s going to go up
because there’s more earthquakes. And then, in Yellowstone,
it’s a little bit more scattered, but there’s also a drop here in about 1996.
Just a reminder, we count the events in five- or 12-hour windows.
And then we look – I’m going to show the results in the – from either the 99%
threshold primarily. Will also be some results from the 95% threshold.
So if we just look at thresholds for the 33-year catalogs for the four different
regions, not surprising, the magnitude of completeness was pretty stable
for Utah and Montana, and the threshold values are pretty stable.
ANZA had that drop in the magnitude of completeness, and you can see
this bimodal change in the threshold values that accompany that.
Yellowstone is all over the board. And so one question we had was,
well, maybe our assumption that, with 26,000 windows,
we could not really worry about the independent versus dependent events
when we look at rates is not valid here because of the swarms
and other activity going on. So we actually took two windows –
Before ’96 and after ’96 – and calculated magnitude of completenesses and did –
ran through the rest of the analysis with those values.
I don’t have time to go into that too much, other than to say
we get almost the same results when we’re looking for significant increases.
There’s just a couple changes.
For those of you who don’t want to count 33 years’ worth of data,
and you’re doing enhanced studies, we also went through and said,
well, we have 500 earthquakes, and we’re looking at pre-event windows
as well, so let’s count the number of earthquakes in the pre-event windows
and look at the distributions just from the 500 earthquakes we looked at.
And that’s what you see here for the four different catalogs.
When I’m comparing the statistics against our results, I don’t do any
magnitude of completeness correction because, in a lot of the dynamic
earthquake triggerings, especially – studies, especially if you’re looking at
enhanced studies, they don’t have enough of a catalog to get a magnitude
of completeness, so they just count all the events they see.
So that’s what we’re going to compare our statistics here –
sort of the curated catalog versus an enhanced-type catalog.
And so, if you just – if you’ve looked at 500 events,
you can form the distribution. And, while the 99% thresholds
here shown in these purple curves are not exactly what we saw in the
previous slide, they’re pretty close. So it’s saying that maybe you could do some
random sampling of your catalog with a lot of numbers, where you could actually get the
distribution, and you could form the rates in this way. Okay.
So some results. So this is results if we just assume
a Poisson process and look at the – essentially the difference in the means.
The results with our new approach are the green stars.
So we don’t get that many cases of what we’d call statistical rate changes.
In comparison to when we use – just looking at a mean and looking at
the standard deviations from the mean. Okay.
We do see a decrease at the 99% level, so telling us things are working.
And the main reason for this is, to use the statistic properly for Poisson,
we have to assume we have large n, and oftentimes, we don’t have large n.
We have quite small n. So there’s two scales here.
On the left is for the gray bars, and on the right is for the orange bars.
The gray bars would be the number of events for the black stars in the previous
slide where there was some statistical significance looking at
the number of pre-events and the number of post-events.
And then, for our new approach, we’re using this empirical distribution.
And what you can see is, many of the events from the difference in the mean
that showed up as stars that we didn’t find with our rate changes
are because there’s really just a few events.
And it’s probably not really significant because we really
didn’t properly account for the assumptions in the statistics.
But for our new rate change, you can see that, at 95%,
you can start to get significant changes at 3 and 4. At 99%, you really have to
see about six events in the post window for it to be significant.
So then I compared this with the Z statistic.
The green symbols, again, are using our empirical rates.
Stars are at 99%. Crosses are at 95%. Comparing those to a Z statistic, looking
at just five hours plus and minus when the teleseismic energy came through.
Stars, again, are at 99%. Crosses are at 95%.
And we largely get the same answer.
There are some differences. In some cases, the Z statistic finds
what would be considered significant triggering that we don’t identify.
And, in all of those cases, that’s a function of the magnitude
of completeness correction. So, in our analysis, we look at –
we remove many of the smallest events with the magnitude of completeness,
but those are counted when we do the Z statistic.
So that’s one difference there.
In the cases where we see triggering – or, we have a statistical rate increase
that are not found by the Z statistic is where there’s a subtle change in rates,
like what we saw with the Kuril event in Utah.
And I’ll show a few more examples of this.
So the Z statistic is not picking up what might be a subtle rate change
where the actual number of events is larger than you’d expect to see.
So just going through some examples and coming back to, what are the
indicators of dynamic earthquake triggering, and what do we mean
by statistical significance, if we start with the three events that are
well-documented as triggering, and we look at the character
of the cumulative earthquake plots – so this is the cumulative number
of earthquakes with time. Where the red bars are,
that’s – those are our five-hour windows.
You can see, for Landers, Denali in Utah, and Denali in Yellowstone,
you had pretty constant rates. Then these huge changes.
And, in each of these catalogs, you can see that we had events
widespread throughout the region – maybe not quite as much in Utah
for Landers, but there were a couple locations that were triggered here.
So really clear – nothing, something.
If we look more closely at some of the results from Yellowstone – and I’m just
showing a few of the examples here. Excuse me – we see that, at the
99% confidence level – this arbitrary value again – we see,
following the 1985 Mexico City event, pretty much nothing.
A big step. Again, spatially distributed throughout Yellowstone.
It’s a pretty – the scale over here is quite large because, a few weeks later,
we had the start of a Yellowstone swarm. Okay?
But I would argue that this is a pretty distinct step.
In these two other cases, which were flagged at 95% confidence by both
our method and the Z statistic, you know, it looks like you have
a pretty constant rate, and then you do see these bumps in seismicity.
In these cases, it seems to be isolated regionally within the catalog.
But then, if we look at this, right, we have an increase here.
We have something that looks about the same here.
Something that looks about the same here.
You can say the same thing down – following this 2003 event,
where you have sort of these repeating types of increases.
And so, if we’re talking about an indicator for dynamic earthquake
triggering, is this dynamic earthquake triggering?
It doesn’t fit our classical model of the original studies.
And, in some of the more recent studies, we don’t look at things over a long
time period, so we just look at these rate changes.
So what does it mean to be dynamically earthquake triggered,
and how are we going to separate this? How can we actually get to
that causative nature versus just looking at a rate change?
If we look at ANZA, this is following the Baja earthquake.
95% confidence interval.
I would say we had a pretty steady rate. We have a bump in the number
of events. Widely distributed. I’m not aware of this being documented.
But – so I think maybe we saw some limited triggering
in ANZA following the Baja event.
And then, coming back to the Molucca Sea event that I mentioned earlier,
and another example from Yellowstone following a Kermadec Islands event,
if we look at these sequences – these are ones that were not found
by the Z statistic but did get flagged using our empirical rates.
We see that a sequence started. In each case, we have some type of
sequence that began very localized, and then there is this increase in
this rate. So a significant change that goes with this.
And, again, is this significant? Is this dynamic earthquake triggering?
Are these waves further enhancing these sequences, or is this happening by chance?
So what are the indicators of dynamic earthquake triggering?
And with that, I’m going to move to the conclusions.
So what we’ve done is we developed an empirical density distribution
based on earthquake rates in a tailored time window.
I showed five-hour windows today because that’s often used in dynamic
earthquake triggering studies because that’s a pretty long window
when you’re trying to enhance the catalog.
We’ve identified past instances of dynamic triggering as well as what
I think are potentially previously undocumented cases.
I would argue that looking at these longer catalogs gives us a more robust
rate to actually form our statistics and look at what we might mean by
statistically significant rate changes. The Z statistic produces similar
results to the long-term catalog. I have no idea why.
Okay, why, if I look at a 10-hour window, with this particular statistic,
can I reproduce what we get from a long catalog?
I can’t – I’ve tried to play with some math earlier this week,
but I don’t have a good answer for that.
But I would maybe encourage people to move from
thinking about the beta statistic to the Z statistic.
And so, if we go back to the questions that I started this with,
what does it mean to be statistically significant?
What do these arbitrary values of 95 and 99% mean when we’re talking
about dynamic earthquake triggering? And should we be using these
arbitrary values to assert this? I would argue, as was originally argued
in the Matthews and Reasenberg paper, that we need to sort of further
investigate this catalog and really look at what’s going on in the background.
And then, if we’re going to go from these rate changes or earthquakes
in the surface waves or whatever we’re going to declare as these
indicators of dynamic triggering, how are we going to define those?
Is it enough to say we had a subtle increase in an ongoing sequence?
Do we have to have a large spatial extent of triggering that’s
triggering all of the western U.S.? Can it be a localized area?
And maybe all of these are correct, but I think we have to expand
what we’re thinking about and our definitions as we do this and
be maybe a little bit more specific when we’re writing our papers
in terms of what we’re using for statistics and what we’re using
as indicators for dynamic earthquake triggering.
So with that, I’ll say thank you and take any questions.
[Applause]
- Okay, thank you, Kris. Questions?
- Okay, as someone who’s actually one of the authors of the Hill et al. paper,
one of the – one of the joys of that paper was – and being you said, what were we
thinking beforehand, was that we were completely stunned when it happened.
And – because it was the largest earthquake we had after we
had installed, you know, dense seismic networks.
- Right. - So in the – you know,
we had a few decades of data and hadn’t seen anything like it.
Also the statistics are so far off the chart that I think Paul Reasenberg referred to
it as his mother’s test – the mother test.
That he showed it to his mother, and she was shocked by it. [laughter]
You know, so we were sort of saved from a lot of these details.
One thing that confused me a little bit is that you’re taking an empirical
distribution, but you’re still computing a mean and a standard deviation.
And there was one plot in the five-hour things where you had the 95 and the
99% confidence bounds – the thresholds, in the same integer bin.
And so I was sort of curious why you’re doing that versus, you know,
in an empirical distribution, just looking at the point where
you cross 95 and 99% values. - I’m sorry I was confusing things.
So first – you’re first comment. Landers, Denali, in our statistics,
are the mother of all statistics too. - Yeah.
- I mean, Yellowstone following Denali has – like, we could
actually get a beta statistic for it. It’s, like, 70 or 80 or something.
We aren’t talking 2 and 3 anymore, right?
- Yeah, no. - So, for the cases –
those well-documented cases, the statistics are all off the chart.
Regarding this, I’m sorry for the confusion.
I just put the mean up there to just show where it was.
The 95 and the 99% are based on the distribution.
They aren’t based on the standard deviation.
- Okay. In the inset, why are – my understanding was that the –
you have two thresholds that are sort of in different places
within the bin that’s marked 4. - Right. And – yes, the Chebyshev
Inequality Theorem does use five standard deviations from the mean.
And we’ve gone away from that, and I didn’t talk about any of the results
for the exact reason that you talk about. We don’t really have
a normal distribution. We aren’t really looking at
something where I’m confident talking about standard deviations.
I partly left it here because we presented a poster at SSA last year where
this is the criteria we were using. But the – but these thresholds that
I talk about, and the results I talk about, are looking at where – the dashed
red line here is where in the histogram you see 99% of the data.
And the red solid line is 95. So we actually use the distribution,
not a mean or a standard deviation. - Okay. Thanks.
- Thank you. That was an interesting talk.
So these examples where you sort of discovered possible instances
of triggered seismicity, and some of them were kind of dispersed,
and some of them were kind of localized, if you put those localities on,
say, geologic maps, does anything pop out?
Do they coincide with faults of particular orientations,
hydrothermal areas, anything like that?
- We have not done that. So, in Yellowstone, they’re occurring
where we have geothermal, hydrothermal systems.
And, in Utah, probably not so much the case.
We do have some geothermal systems in central Utah,
but not in the north where we see these events.
I’m not as familiar with ANZA as Debi is, so I can’t speak to that.
[Silence]
- Hi. Thanks, Kris. So maybe this is naive,
and I’m not really up on all the dynamic triggering to date, but a lot of times,
we see these nice waveforms where you can see the surface waves
or whatever coming through. And then, when you filter at really
high frequencies, you see the little events popping off,
exactly timed with those dynamic waves. Can you –
have you looked at any of that? Or, why or why not?
Or do you see that? - Yeah. And that was what I showed
for the first slide from Denali. We filtered the data.
And I think that’s part of the question that I’m asking.
Is that enough? Okay? So … - Right. So I – do you see it for some of
these more – Denali, like you – and you were talking about – pretty clear-cut.
So what about some of the other more questionable cases or …
- I haven’t looked … - Because it [inaudible]
bolster the argument, I guess. - Yeah. And I haven’t looked in detail
at the waveforms, is the simple answer. For, like, the Mexico event
in Yellowstone, that – we aren’t going to have data to do that with, right?
Some of the older events, that data doesn’t exist.
But for some of the newer events, we could definitely look at the data.
And for Utah, we don’t filter the data, so the increases in the catalogs
aren’t including those surface wave windows exactly.
[Silence]
- Well, maybe the answer to this question is already included in
your definitions. [inaudible] statistics that I’m not – pardon me?
Right to my mouth. Oh, okay. Sorry. Excuse me.
Maybe the answer to this question is already
included in some definitions, but when is an event an event?
I mean, magnitude, orientation? You’re talking about events
as if all events are equivalent. It seems – that’s what it seems to me.
Maybe it’s something – as I say, in definitions
or statistics that I’m not familiar with.
- Sorry I’m laughing. Walter Arabasz has tried to teach
me this lesson for the last 20 years. I’m talking about small earthquakes.
- So that’s it. - So that’s it. So I’m talking about
small earthquakes, so we have P waves and S waves.
I mean, other people look for tremor, and I haven’t looked at any of that.
But what I’m looking at are earthquakes that we’ve
been located and that are in an earthquake catalog.
And that’s what we’re counting. So we’re counting everything that’s
in the catalog, which is a function of the magnitude of completeness.
Or a detection level, depending on if we’re looking at
the small time windows or the curated catalog.
Does that answer the question?
- Yeah. It answers that question. - Okay.
- I guess I would ask also, why you do that.
Is that enough? Is that sufficient?
- I – well, I guess that’s what I was going after was to find
dynamically triggered earthquakes. So that’s what I’m counting are the
earthquakes that could potentially be dynamically triggered.
And if you wanted to look at other events, you would have to
process your data separately and define what those events are.
And so I’ve not included that in this analysis.
- Thank you.
[Silence]
- From what I recall from Landers, up in Mammoth Lakes, the threshold
was something – calculated something like 1 bar dynamic stress level was –
seemed to be sort of the magic number – something in that range.
I just was wondering, have you looked at, for example, tidal triggering and
how that would compare at much lower dynamic stress levels?
- I personally have not looked at tidal triggering.
But what we see from the dynamic earthquake triggering is you’re sort of
at the same sort of stress level. So, at least from what we saw in
Denali and Landers – so the same sort of magnitude of change.
But I haven’t gone and looked for tidal changes, no.
- Any more questions?
Okay. Well, I guess we’ll wrap up. If anybody wants to join us for lunch
with the speaker, please come on up and talk to us.
I’m not sure that we’re going to go to the café because apparently
they’re on limited menu right now. So if you want to come to lunch,
come up and talk to us, and we’ll figure out what to do.
And please join me in giving Kris another
round of applause for a great talk.
[Applause]
[Silence]