This transcript was generated automatically and lightly edited for readability.

Oliver Strimpel: This is Geology Bites with Oliver Strimpel. In a couple of earlier podcast episodes, we've talked about using seismic waves to make images of the Earth's interior. Barbara Romanowicz introduced the topic, and Ana 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 Fichtner and his team develop and apply new techniques for converting seismic data into three-dimensional pictures of the mantle. Recently, he has used fiber 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 Fichtner, welcome to Geology Bites.

Andreas Fichtner: Thank you very much.

Oliver Strimpel: Can you refresh listeners on the basic principles of seismic imaging, or seismic tomography?

Andreas Fichtner: The standard and still most useful way of explaining seismic tomography is with the analogy of medical ultrasound, which many of us can relate to. In medical ultrasound, small loudspeakers act as the sources of ultrasound waves, and those ultrasound waves 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, and 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. And those medical ultrasound images have, compared to the size of the Earth, 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.

Oliver Strimpel: What is the best resolution that state-of-the-art methods can achieve today?

Andreas Fichtner: This is a difficult question, and it depends a lot on the spatial scale of the experiment and on the data that we are collecting. 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, to order of magnitude, we can see details with spatial scales of about 10 kilometers in the crust, about 100 kilometers in the upper mantle, and maybe a few hundred kilometers in the lowermost mantle, close to the core-mantle boundary. Our problem has always been, and actually continues to be, the mid-mantle, but that 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? 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.

Oliver Strimpel: Is it more complicated than when you talk about the resolution of an image, where you talk about how much you can resolve, or how many pixels you have in your x direction and y direction?

Andreas Fichtner: 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 amount of detail you may see with your eye. But the other aspect of resolution that you're interested in is how well you can constrain a parameter inside that voxel. For example, how well do you know the P-wave speed inside that voxel? And the problem is that you can't have both; one trades off against the other. The larger you make the voxel, the more accurately you can say what the 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 its P-wave speed, with less accuracy. And part of the art of seismic tomography is to find a reasonable balance between the two.

Oliver Strimpel: So at the end of the day, what does this mean in terms of structures we can say are revealed by seismic tomography today with a high level of confidence?

Andreas Fichtner: 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 Iceland 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 subducting lithospheric slabs, some of those descending below the 660 into the lower mantle.

Oliver Strimpel: By the 660, you mean the mantle transition zone?

Andreas Fichtner: Exactly, 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 kilometers depth. Good examples are the Baltic 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.

Oliver Strimpel: 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?

Andreas Fichtner: 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, the polar regions and the Southern Hemisphere. And the fourth one is the actual size of the computational problem, and the fact that our computers, although they are often portrayed as growing fast, actually grow too slowly for the problem that we would like to solve.

Oliver Strimpel: 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?

Andreas Fichtner: So what does non-uniqueness mean? There's a hard mathematical definition here, but the intuitive one is that there are simply infinitely many tomographic images, tomographic models, that all explain our data to within the observational errors. And this 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 have 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 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 traveling 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.

Oliver Strimpel: Just to butt in here: when you say S wave, that means shear waves.

Andreas Fichtner: 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 a P wave at a frequency of 1 hertz, but the 1-hertz S wave is not there.

So what can we do about this? There are basically two clean ways and one dirty way of addressing non-uniqueness. The first clean one is just to collect more information. That information could be more seismic information, by putting out more stations recording for a longer time, but it could also be filling the seismic information gap with independent knowledge, for example from mineral physics or geodynamics. The other clean way of addressing it would be to just be honest, and instead of 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 one, and the dirty one is called regularization. Regularization, 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 people can then look at and interpret. The classic example is that we fill in artificial information that the structure of the Earth is smooth. That's not something that we know, but it's easy to implement. It makes the models easier to interpret, and so we smooth, forcing our models to be smooth. This is the classic, most widely used, and in fact always used, method of regularization.

Oliver Strimpel: 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?

Andreas Fichtner: The underlying problem is that seismic waves are sensitive to a very large number of physical properties in the Earth. Two that we all know are the P- and the S-wave speeds inside the Earth. But there's more. There's the attenuation of P waves and S waves. There's density. There's the topography of the internal discontinuities, for example the 410 and 660 discontinuities and the core-mantle boundary. And there are 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- and S-wave speeds 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 all of the other parameters individually have a small influence on the data, but there are many of them, 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. It is one of the reasons why tomographic images of attenuation are much more different from one another than tomographic images of P- and S-wave speeds, which are resolved much more robustly.

Oliver Strimpel: There's also the question of how you parameterize the tomographic model. Can you explain that, and why this presents a challenge to making better and more trustworthy imagery?

Andreas Fichtner: 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. As a consequence, we somehow need to discretize the Earth. And how this is done, again, is a subjective choice. Some may partition the Earth into the 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 can plug into their numerical solver. And of course, making different subjective choices on how to discretize the Earth leads to slightly different tomographic images. These differences just from the parameterization 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.

Oliver Strimpel: The other kind of problem that you mentioned is data coverage. Does this apply both to the sources of seismic waves, i.e. where the earthquakes occur, as well as to the distribution of seismometers that detect the seismic waves from the earthquakes?

Andreas Fichtner: Yes, absolutely, it is both. Obviously, we cannot move the 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 the coverage of seismic stations, for example in the oceans, in the polar regions and in the Southern Hemisphere, although there are still far fewer seismic stations there 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.

Oliver Strimpel: Is that because the data have potential military implications?

Andreas Fichtner: To some extent, yes.

Oliver Strimpel: Lastly, you mentioned the computational problem, and I assume that's to do with the scaling of the numerical methods as you try to improve the imagery. So I suppose the amount of computation does not scale linearly with the quality of the imagery.

Andreas Fichtner: This is absolutely true, and this is a tough one. The first part of the answer here is that resolution scales approximately with frequency. This means, intuitively speaking, that 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. So for example, if I have a resolution of 10 kilometers somewhere and I would like to have 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, of seismic tomography, scales with frequency to the power of at least 5. Not 5, at least 5, 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. Loosely speaking, as I 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 a P wave with a frequency of something like 0.1 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. Now let's go back to that scaling, frequency to the power of 5 at least. This means that we miss a factor of 10 to the 5, which is 100,000, in 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.

Oliver Strimpel: And I assume you're using GPUs and all the latest?

Andreas Fichtner: That is already accounted for, yes.

Oliver Strimpel: 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 fiber optic cables can give us information about Earth structure?

Andreas Fichtner: Yes. Concerning the first question, we can actually use both. For example, in cities or in the oceans, the co-use of telecommunication fibers is just very, very convenient. We don't need to deploy them; they're already there. So this is pretty nice. It 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 used as chains of densely spaced seismometers, densely spaced here meaning spaced at about 1 meter. This means that a 10-kilometer-long optical fiber 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 fibers contain teeny, tiny heterogeneities from the fabrication. The telecommunication people, of course, don't like that, 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 heterogeneities, 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 scatterer moves a tiny bit. And in response to the movement of the scatterer, the travel time of the backscattered laser pulse gets modified a tiny bit. That small modification of the travel time of the backscattered laser pulse, in response to deformation of the fiber, is actually something that can be measured. And that measurement of the travel time shift of the backscattered light can be translated back into a distributed measurement of deformation along the fiber. And so we have these seismometers that produce seismograms, and we can use them just as we use regular seismograms in our tomographic inversions.

Oliver Strimpel: Well, that's really incredible. Can you even use these super-long transoceanic fiber optic cables?

Andreas Fichtner: 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. This means that if I have a fiber that is relatively short, a few kilometers or a few tens of kilometers, I can have a very high spatial resolution, meter scale. If I have a fiber that extends through the North Atlantic, then the spatial resolution along the fiber is much, much lower. So I can't have both. And how to deal with those ultra-long fibers in tomographic inversion, or how to use them, is still very much work in progress, still something that we need to figure out.

Oliver Strimpel: Is this something to do with distinguishing between the many backscattered pulses that come from the impurities, so that if you have too many of them, it's hard to distinguish them?

Andreas Fichtner: This is one component. The more fundamental one is that the longer those backscattered pulses travel, the more they attenuate, and that attenuation eliminates some of the spatial information that you have when the fiber is shorter.

Oliver Strimpel: So it's incredible. You're getting orders of magnitude more effective seismometers than you would by traditional methods.

Andreas Fichtner: Absolutely, yes.

Oliver Strimpel: And on the episode web page, we illustrate how you've used fiber optics to study Iceland's most active volcano and the Northeast Greenland Ice Stream. We also show an example where fiber 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?

Andreas Fichtner: 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 traveling 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 we actually measure the information. As a consequence, 3D images of the inner core are really just emerging. The first ones have 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 is still a little bit open. So there's something moving, but those images are not yet as robust as those that we have for the crust and the mantle.

Oliver Strimpel: 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 in one of the categories of challenges you mentioned that we'd make significant improvements in seismic imagery?

Andreas Fichtner: I'm actually quite hopeful, and my guess is that we will see improvements mainly in two aspects: data coverage and computational methods. For example, I'm pretty sure that fiber 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 clever way, and that is really just beginning.

Oliver Strimpel: But do you think there are some fundamental physical or mathematical barriers that will ultimately limit the quality of the seismic imagery we can get?

Andreas Fichtner: Ultimately, mathematical, I think no. There, I think 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 sensors at the surface, or how big our supercomputers 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-mantle boundary, distributed 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 1-hertz S waves, so the information that is contained in those high-frequency waves we will just never have. And also, seismic noise will always be present, and that will always inherently limit the certainty that we can achieve.

Oliver Strimpel: What are you working on at the moment?

Andreas Fichtner: 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 physical quantity 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, computational component, but it also has the other component that we discussed earlier: what are measures of resolution that geologists actually find useful, that enter into 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 resolution is for them, because in many cases resolution for us applied mathematicians is something else, and this needs to be harmonized as well. And then finally, the third big topic is overcoming computational challenges, which will allow us to include more of the data that we already have.

Oliver Strimpel: Andreas Fichtner, thank you very much.

Andreas Fichtner: Many thanks to you. It was really a pleasure.

Oliver Strimpel: To see pictures and illustrations that support this podcast, go to geologybites.com, where you'll also find a subject matter index of all the episodes. There you can also give me feedback, which I welcome, as well as sign up to get my emails about new episodes.