This is Geology Bites with Oliver Strumpel.
In a couple of earlier podcast episodes, we've talked about
using seismic waves to make images of the Earth's interior.
Barbara Romanowitz introduced the topic, and Anna Ferreira
talked about using anisotropy of seismic waves to see flows in
the mantle. In both of these episodes, it
was on the one hand, exciting to be able to image the lithosphere
and mantle at all, and on the other hand, somewhat frustrating
that our images were still so blurry.
Clearly, having a sharper view of the mantle would be immensely
desirable and help us answer all sorts of geological questions.
In this episode, we explore the latest developments in the field
and the obstacles that stand in the way of rapid progress.
Andreas Fischner and his team develop and apply new techniques
for converting seismic data into 3 dimensional pictures of the
mantle. Recently, he has used fibre
optic cables to provide information about Earth's
structure and seismicity with unprecedented resolution.
He is a professor in the Department of Earth and
Planetary Sciences at the Federal Institute of Technology
in Zurich. Andreas Fischner, welcome to
Geology Bites. Thank you very much.
Can you refresh listeners on the basic principles of seismic
imaging or seismic tomography? The standard and still most
useful way of explaining seismic tomography is with the analogy
of medical ultrasound that many of us can relate to.
In medical ultrasound, small loud speakers act as the sources
of ultrasound waves. And those ultrasound waves, they
travel through the human body. As they travel through different
types of tissue, the tissue properties affect the properties
of those waves. These properties include the
speed of those waves, but also the amplitudes.
And then we can record those ultrasound waves and knowing
where they propagated, that knowing the physics of
ultrasound wave propagation, we can reconstruct a 3D image
provided that we have sufficient data.
Now what is interesting to note here is that even in medical
ultrasound, the positions of the transducers can essentially be
arbitrary. Those medical ultrasound images
have, compared to the size of the Earth, still a much poorer
resolution than we can achieve for our planet.
So actually our images are not that blurry.
We are, in fact, doing pretty well.
What is the best resolution the state-of-the-art methods can
achieve today? This is difficult question and
it depends a lot on the spatial scale of the experiment and on
the data that we are collecting. So just to give you an example,
with dedicated seismic experiments we can image the
upper 200 meters of the earth, which are very relevant for
seismic hazard, for example, with a resolution of about 10
meters. Of course, in global tomography
this is very different. I would say that order of
magnitude, we can see details with spatial scales of about 10
kilometres in the crust, about 100 kilometres in the upper
mantle and maybe a few 100 kilometres in the lower most
mantle close to the core mantle boundary.
Our problem has always been and actually continues to be the mid
mantle, but is also exciting because it means that there's
actually still structure to discover in that part of the
Earth. But let me mention another issue
that seismic tomographers are struggling with, which is what
exactly do geologists actually mean when they say resolution?
And is that something that we can really quantify in a way
that is useful for them? But first of all, I think it is
important to find a more quantitative language so that we
as tomographers understand which quantification of resolution a
geologist would actually like. Is it more complicated than then
when you talk about the resolution of an image, say
where you talk about how much you can resolve or how many
pixels you have in your X direction and Y direction?
Yes, it is a lot more complicated.
I will try to explain this intuitively.
If your pixel or your voxel is very small, then resolution
essentially means two things. One is the size of the voxel
that you have. This is the the amount of detail
you may see with your eye. But the other aspect of
resolution that you're interested in is how well can
you constrain A parameter inside that voxel.
For example, how well do you know the P wave speed inside
that voxel? And so the problem is that you
can't have both 1 trades off against the other, meaning the
larger you make the voxel, the more accurately you can say what
P wave speed is inside the voxel.
If you make your voxel smaller so that you see more detail, the
consequence is that you see the properties of the voxel.
For example, it's P wave speed with less accuracy.
And part of the art of seismic tomography is to find a
reasonable balance between the two.
So at the end of the day, what does this mean in terms of
structures we can say are revealed by seismic tomography
today to a high level of confidence?
There are several structural features that are being imaged
very very consistently. Basically no matter how the
tomography is set up from bottom to top.
These are the large low shear velocity provinces and the ice
cream plume, which is probably the only really plume like
structure that is consistently being imaged from the core
mantle boundary all the way to the surface.
Then we very clearly see subtracting lithospheric slabs,
some of those descending below the 660 into the lower mantle.
By 660 you mean that's the mantle transition zone?
Exactly at the 660 kilometer discontinuity inside the mantle
then we very clearly see fast continental interiors, so old
lithosphere that sometimes we image down to about 300
kilometer depths. Good examples are Debaltic and
the Canadian Shields. Also very clearly visible are
the mid ocean ridges which are very pronounced low velocity
features. And the good news is that as we
collect more and more data, the agreement on the shape of these
features in different tomographic images is becoming
better and better. You and several other groups
around the world are working on improving our imagery of the
mantle, both in terms of resolution on a global scale and
on various regional scales. Can you categorize the various
obstacles that hinder our progress towards this end?
I would say there are four different categories.
The first one is inherent or physical non uniqueness.
This is an uncertainty that we cannot remove even if we had
perfect data. The second class are the many
subjective choices that we have to make when setting up a
tomographic inversion. The third is data coverage,
especially in the oceans, polar regions, the southern
hemisphere. And the fourth top one is the
actual size of the computational problem and the fact that our
computers, although they are often portrayed as growing fast,
they actually grow too slowly for the problem that we would
like to solve. OK, there's a lot there.
Let's talk about these challenges one at a time,
starting with the non uniqueness of the solution.
What does that mean and how can we address it?
So what means non uniqueness? There's a hard mathematical
definition here, but the intuitive 1 is that there simply
infinitely many tomographic images, tomographic models that
all explain our data to within the observational errors and
there's non uniqueness essentially has two origins.
The first one is just the nature of the data.
Our data are noisy and they are sparse.
This means that for some regions in the earth, we just very few
data to actually constrain those regions, which means that in our
tomographic models in those regions we can basically do
whatever we want and our data don't really see that.
The second reason or the second origin of non uniqueness is just
the physics of the problem. One aspect of this is that some
information that the waves in principle pick up when they're
travelling through the earth is being eliminated by attenuation.
The consequence is that we do not really record, for instance,
high frequency S waves that do propagate through the earth but
just don't make it all the way from the source to our
receivers. And the absence of those high
frequencies limits the resolution that we can achieve.
And there's really nothing that can be done about it, because we
can't switch off attenuation in the Earth.
Just to butt in here, so when you say S wave, that means share
waves. Correct.
And the problem here is that in the earth shear waves are
attenuated much more strongly than P waves.
So for example for a large earthquake we can record AP wave
at a frequency of 1 Hertz, but the one Hertz S wave is not
there. So what can we do about this?
There are basically 2 clean and one dirty way of addressing non
uniqueness. The first clean 1 is just
collect more information and that information could be more
seismic information by putting more stations recording for a
longer time, but it could also be filling the seismic
information gap by independent knowledge, for example from
mineral physics or geodynamics. Then the other cleaner way of
addressing is would be to just be honest and instead of just
producing one model that people look at, produce many models
that are plausible and look at how different they are given the
data that we use. This is easier said than done
because producing many many models is computationally very
very expensive. So then comes The Dirty 1, and
The Dirty 1 is called regularisation.
And regularisation, loosely speaking, means that we make up
information that we do not actually have in order to make
our inversion algorithms stable and well behaved, and to produce
just one model in a computationally efficient way
that then people can look at and interpret.
The classic example is that we fill in information, or
artificial information, that the structure of the earth is
smooth. There's not something that we
know, but it's easy to implement.
It makes the models easier to interpret and so we smooth and
forcing our models to be smooth. This is the classic, most
widely, and in fact always used method of regularization.
OK, so you mentioned other subjective choices one has to
make, in this case to do with selecting the physical
properties that one would like to image and how they limit the
quality of the results. So why does one have to select
different data types and what are the implications of the
choices one has to make? So the underlying problem is
that seismic waves are sensitive to a very large number of
physical properties in the Earth. 2 that we all know are
the P and the S wave speed inside the Earth.
But here's more. There's the attenuation of P
waves and S waves. There's density, there is
topography of the internal discontinuities, for example,
the four hundred 10660 discontinuities and the core
mental boundary, and there is a total of 19 additional
parameters that describe seismic anisotropy in the Earth.
Now it is intuitively clear that we can't constrain all of those
physical properties at the same time, and as a consequence we
need to make choices. For example, a scientist
interested in attenuation in the Earth, which closely links to
the distribution of temperature inside the Earth, may add
attenuation to the standard P&S wave speed of a tomographic
model. This is nice and good, but in
doing so, the person also chooses to ignore all the other
parameters. Now the issue here is that of
course all of the other parameters have individually a
small influence on the data, but there are many and they
collaborate and their combined effect may actually be pretty
large. And admittedly, so far we have
no good technical solution for this problem.
So I would say this is an open methodological challenge how to
actually address this. And it is one of the reasons why
tomographic images of attenuation are much more
different than tomographic images of P and South wave
speed, which are resolved much more robustly.
There's also the question about how you parameterize the
tomographic model. Can you explain that and why
this presents a challenge to making better and more
trustworthy imagery? So this is actually closely
linked to the regularization issue that we just discussed,
because the parameterization can be seen as a more subtle, more
invisible way of regularizing A tomographic inversion.
Now to explain this, it's a matter of fact that the Earth is
a continuum, but all the methods that we are using and more
fundamentally the computers that we use to run the inversion can
only handle discrete things. And as a consequence, we somehow
need to discretize the earth. And how this is done, again is a
subjective choice. So some may partition the earth
in two voxels that we already discussed, others may use
polynomials, and again, others may use a combination of these
or whatever basis functions they like, or they can plug into
their numerical solver. And of course, in making
different subjective choices on how to discretize the earth
leads to slightly different tomographic images.
And these differences just between the parameterization,
they may be small, but the important thing here is that
they add to the differences that we already get from explicit
regularization, from data selection and many other things.
The other kind of problem that you mentioned is data coverage.
Does this apply both to the sources of seismic waves, IE
where the earthquakes occur, as well as to the distribution of
seismometers that detect the seismic waves from the
earthquakes? Yes, absolutely.
It is both. Obviously, we cannot move to
earthquakes. There's nothing to be done.
They are where they are. But in the past decades, we have
seen really fast progress in improving coverage of seismic
stations, for example, in the oceans, in the polar regions and
in the Southern Hemisphere, although there are still far
less seismic stations than in Europe, North America and China.
Interestingly, currently due to its size, Russia is probably the
biggest problem here as there are very few openly available
data from there. Is that because the data has
potential military implications? To some extent, yes.
Lastly, you mentioned the computational problem, and I
assume that's to do with the scaling of the numerical methods
as you try and improve the imagery.
So I suppose the amount of computation does not scale
linearly with the quality of the imagery.
This is absolutely true, and this is a tough one.
The first part to the answer here is that resolution scales
approximately with frequency. So this means, intuitively
speaking, if I want to see a feature that is half as small
inside the earth or inside the human body, I need to use
frequencies that are twice as high.
And so for example, if I have a 10 kilometer feature in the
earth, I have a resolution of 10 kilometers somewhere and I would
like to see a resolution of five kilometers, so a sharper image.
Then I need to use frequencies that are twice as high as the
ones that I have used before. Now the issue here is that
computational cost does not scale linearly with frequency.
In fact, the computational cost of the imaging problem.
So if the seismic tomography it scales with frequency to the
power of at least 5, not 5, at least five if all the
computations run fine. Now what does this mean
practically? In global scale waveform
tomography we still miss a factor of 10 in frequency.
So loosely speaking, as already said, we can observe seismic P
waves at a frequency of 1 Hertz, but what we can simulate and
actually bring into our seismic tomography is AP wave with the
frequency of something like .1 Hertz.
So there's this factor of 10 in frequency that we still miss
between what we can simulate and what we actually have in the
data. So now let's go back to that
scaling frequency to the power of 5 at least.
So this means that we miss a factor of 10 to the five S
100,000 in, say, the power of our computers.
So if we wanted to exploit the data that we actually have, we
would need computers that are at least 100,000 times more
powerful than the most powerful ones that we have right now.
And I assume you're using GPU's and all the latest?
That is already accounted for, yes.
In the introduction, I mentioned that you've developed methods
that use fiber optic cables. Are these existing
telecommunications cables or are these specially installed ones
for this purpose? And can you explain how fibre
optic cables can give us information about earth
structure? Yes.
So concerning the first question, we can actually use
both, for example in cities or in the oceans.
The Co use of telecommunication fibres is just very, very
convenient. We don't need to deploy them,
they're already there. So this is pretty nice.
This makes the cost of our experiments very low, provided
that we actually get access to those fibers.
In challenging terrain, which often includes glaciers or
volcanoes, it can actually be much easier to deploy a fiber
optic cable than to install many seismometers.
So people are doing both Now. How does this work?
Why does it work? The underlying idea is that
optical fibers can be transformed or can be used as
chains of densely spaced seismometers.
Densely spaced here meaning spaced at about 1m.
Which means that if one has a 10 kilometre long optical fibre,
this can act as a chain of 10,000 seismometers, which is a
lot compared to what seismologists are traditionally
used to. Now why does this work?
It works because those optical fibres, they contain teeny tiny
heterogeneities from the fabrication.
The telecommunication people, of course they don't like it
because it attenuates the waves as they propagate.
But for us this is nice because each time a laser pulse hits one
of those small heterogeneity, it backscatters a tiny amount of
the light to the beginning of the fiber.
Now when the fiber deforms, for example when a seismic wave
passes by, the scatter moves a tiny bit.
And in response to the movement of the scatter, the travel time
of the back scattered laser pulse gets modified a tiny bit.
And that small modification of the travel time of the back
scattered laser pulse in response to deformation of the
fibre, this is actually something that can be measured.
And that measurement of travel time shift of the back scattered
light can be translated back into a distributed measurement
of deformation along the fibre. And so we have those
seismometers that produce seismograms, and we can use them
just as we use regular seismograms in our tomographic
inversions. Well that's really incredible.
Can you even use these super long transoceanic fiber optic
cables? Yes and no.
There is a little bit of a trade off here, and the trade off is
between the length of the fiber that one can interrogate and the
spacing of the seismometers that I can achieve.
Loosely speaking, the longer the fiber, the coarser the spatial
resolution along the fiber, which means that if I have a
fiber that is relatively short, a few kilometers or a few tenths
of kilometers, I can have a very high spatial resolution meter
scale. If I have a fiber that extends
through the North Atlantic, then that spatial resolution along
the fibre is much, much lower. So I can't have both.
And how to deal with those ultra long fibres in the tomographic
inversion or how to use them? This is still very much work in
progress, still something that we need to figure out.
Is this something to do with distinguishing between the many
backscattered pulses that come from the impurities that if you
have too many of them it's hard to distinguish them?
This is 1 component. The more fundamental 1 is that
the longer those backscatter pulses travel, the more they
attenuate, and that attenuation eliminates some of the spatial
information that you have when the fiber is shorter.
So it's incredible. You're getting really orders of
magnitude more effective seismometers than you would by
traditional methods. Absolutely yes.
And on the episode web page, we illustrate how you've used fibre
optics to study Iceland's most active volcano and the Northeast
Greenland Ice stream. We also show an example where
fibre optic sensing was used to make a high resolution
tomographic image of a seismically active caldera in
California. In addition to the lithosphere
and mantle, are we also able to use seismic methods to reveal
structures within the core? I would also say that this is
work in progress. People have been interested in
the structure of the inner core for a very long time, and what
is known pretty well is the seismic anisotropy of the inner
core, which we can infer quite directly from the arrival times
of P waves travelling through the core in different
directions. Now, why is it difficult to make
a 3D image of the core just as we do for the mantle?
Well, essentially the problem is that the inner core occupies
just about 1% of the Earth's volume, actually less.
So this means we're looking at a teeny tiny volume of the Earth
that is very far away from the surface, so very far away from
where where we actually measure the information.
And as a consequence, 3D images of the inner core are really
just emerging. So the first ones have really
appeared in the past few years and they're based on very
careful data selection procedures.
And I would say that even though this goes in a very promising
direction, how robust these models are against the many
subjective choices that we already discussed, I think this
is still a little bit open. So there's something moving, but
those images are not yet as robust as those that we have put
across and the matter. So given all the numerous
hurdles we've been discussing, what sort of progress do you
think we'll be able to make, say, over the next 10 years?
And would it be mainly one of the categories you mentioned of
the challenges that would yield to our efforts to make
significant improvements in seismic imagery?
I'm actually quite hopeful and my guess is that we will see
improvements mainly in two aspects, that's data coverage
and computational methods. So for example, I'm pretty sure
that fibre optic sensing will most likely allow us to expand
coverage significantly into the oceans and to fill one of our
major data gaps there. And hopefully also some
political changes in certain countries will make a
contribution. Now, when it comes to
computation, my hope would be that the clever combination of
the classical numerical methods that we're already using and
evolving machine learning tools will allow us to overcome some
of the current computational challenges.
And here I want to stress that I think it's really the
combination of the two. I think brute force machine
learning will not bring us further.
The classical numerical methods probably won't do so either.
We need to think about how to combine them in a temper way,
and that is really just beginning.
But do you think there's some fundamental physical or
mathematical barriers that will ultimately limit the quality of
the seismic imagery we can get? Ultimately, I think
mathematical, No, I think there it is a matter of being clever
and having bigger computers. But there certainly are
barriers. No matter how densely we cover
the earth with centers at the surface or how big our super
computers become, we will not be able to place earthquakes where
we need them to be. And that would actually be deep
inside the earth. If we wanted to improve
resolution drastically, we would need to have earthquakes near
the core mental boundary, so distribute it through the
volume. But that's not going to happen.
And also we will just not be able to switch off attenuation.
As I already explained, we will not have one Hertz as waves, so
that information that is contained in those high
frequency waves, we will just never have it.
And also seismic noise will always be present and that will
always inherently the certainty that we can achieve.
What are you working on at the moment?
When it comes to seismic tomography, I would say we have
three main topics. The first one already discussed
is the incorporation of fiber optic sensing data into seismic
waveform tomography. This is a tough one because in
contrast to traditional seismometers, we don't know as
well what the physical quantity is that those optical fibers are
really recording. Then we are working a lot on the
quantification of image quality, and this actually has two
components. It has a technological
component, a computational one, but it also has the other
component that we discussed earlier, what are measures of
resolution that geologists actually find useful that enter
different types of geological interpretation?
And there this is not technological.
This is a matter of having closer interaction with
geologists who tell us more precisely what exactly they want
to know, what is resolution for them, because in many cases
resolution for us applied mathematicians is something
else, and this needs to be homogenized well.
And then finally, the third big topic is overcoming
computational challenges that allow us to include more of the
data that we already have. Andreas Fischner, thank you very
much. Many thanks to you, it was
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