Deep divefrom Episode 3New physics & chemistry29 September 202624 min

Lab Earthquakes Put the Slip-Pulse Theory to the Test

A deep dive into one paper: what was known before, what the researchers did, what the numbers say and what they don't.

The paper: Lab earthquakes confirm the theory of frictional slip pulses (arXiv)

Chapters

Transcript

The script the two AI voices read from. The times are worked out from the script, not heard, so a line can start a few seconds early or late.

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Cold open

Host 1You heard the trailer — this is the whole story. Welcome to the Hastrup Review of Science — where artificial intelligence reads real science, so you don't have to pretend you understood the paper. One paper today: a set of earthquakes made in the lab, between two plates of acrylic, used to test a theory of how many real earthquakes actually move.

Host 2The paper is called Lab earthquakes confirm the theory of frictional slip pulses. It is by Alina Shafir and Tom Gabrieli, who contributed equally, with Yuval Tal and Eran Bouchbinder, from the Weizmann Institute of Science and Ben-Gurion University of the Negev in Israel. It is a first version posted on the arXiv, so it has not yet been through peer review.

Host 1And the claim is in the title. A theory was made, and now the lab says it holds.

Host 2That is the claim, and the evidence is good but narrower than the title. It is twelve lab pulses in the main figures, analysed carefully, testing the shape of the predictions rather than exact numbers. We will get to why that distinction matters.

Why this field exists

Host 1Start with the basics. What is an earthquake, physically?

Host 2An earthquake is a frictional rupture. Two blocks of rock are pressed together along a fault, and slow tectonic loading stores elastic energy in them, like a stretched spring held in place by friction. When the contact fails somewhere, a rupture runs along the fault, the rock slides, and the released energy radiates as seismic waves.

Host 1And there are different ways for that rupture to run.

Host 2The paper describes two families. In a crack-like rupture, the slipping region keeps expanding behind the rupture front, so the longer it runs, the longer every point stays sliding. In a pulse-like rupture, a slip pulse, only a compact patch is sliding at any moment: the fault unlocks at the front, slides briefly, and locks again behind.

Host 1Like a ruck in a carpet that you push across the floor.

Host 2That is the classic picture, yes. The carpet only moves where the ruck is, and the ruck has a characteristic size that does not grow with distance travelled. The paper's key definition is exactly that: in pulses, the slipping zone and the slip duration at a point are independent of how far the rupture has gone.

Host 1How do we know real earthquakes do this?

Host 2As established background: in nineteen ninety, the seismologist Thomas Heaton argued from seismic inversions that slip at any point in large earthquakes lasts much shorter than the whole rupture, which points to self-healing pulses. The paper cites that work, and also cites pulse-like behaviour reported in the twenty fifteen Gorkha earthquake in Nepal, the twenty nineteen Ridgecrest earthquakes in California, and pulse-like ground motion in the twenty twenty-three Pazarcık earthquake in Türkiye. The paper's own summary is that slip pulses are a dominant rupture mode in natural earthquakes.

Host 1Why would anyone outside seismology care which mode it is?

Host 2Because the mode shapes the shaking. Pulse-like ground motion is a recognised category in earthquake engineering, with its own spectral shapes and record selection methods; the paper cites work on that. The authors also say pulses likely occur in many engineered systems, anywhere two surfaces stick and slip.

What was known before

Host 1So what did we understand before this theory came along?

Host 2Crack-like rupture is comparatively well understood, largely by analogy with ordinary tensile cracks in solids. When a glass plate cracks, the two faces separate and stop interacting. That analogy carries a long way for frictional cracks.

Host 1And for pulses it breaks.

Host 2It breaks because a pulse has a trailing edge. Behind the pulse, the two surfaces are still pressed together, the slip rate falls to zero, and the contact re-strengthens and re-locks. Nothing like that happens in bulk fracture, and it is this healing that sets the pulse's finite size, which is why they are called self-healing pulses.

Host 1Have pulses been seen in the lab before?

Host 2Yes, and this is established background from the paper's reference list. Lykotrafitis, Rosakis and Ravichandran reported self-healing pulse-like shear ruptures in the lab in Science in two thousand six, and Lu, Lapusta and Rosakis showed pulse-like and crack-like ruptures in experiments mimicking crustal earthquakes in two thousand seven. So pulses exist in the lab; the question is whether anyone can predict how they evolve.

Host 1And that is where the theory comes in.

Host 2The paper says only recently has a comprehensive theory of self-healing pulse dynamics been developed. Its citations run from a twenty eighteen Physical Review Letters paper by Brener, Bouchbinder and colleagues, through a twenty twenty-three paper in the Proceedings of the National Academy of Sciences on unsteady pulses, to a single-author paper by Bouchbinder this year giving an equation of motion. It also draws on work by Brantut, Garagash and Noda on pulse stability.

Host 1Worth noting now: the senior author here is also the main author of the theory.

Host 2Yes. This is a theory group testing its own predictions, together with an experimental group, Gabrieli and Tal, who built the lab earthquake setup for earlier work on fault bends. That is common in physics and not a problem in itself, but it is a reason to want independent replication.

The theory

Host 1Walk me through the theory. What does it actually predict?

Host 2Picture two large elastic blocks pressed together, with a normal stress pushing them together and a shear stress trying to slide them. A pulse is described by a few numbers at each instant: its size, its peak slip rate, meaning the fastest sliding speed inside it, and its propagation speed along the fault. The challenge is to predict how those few numbers evolve.

Host 1Where do you start?

Host 2With steady-state pulses: idealised pulses that travel forever without changing shape. For a fixed normal stress, each value of shear stress gives one steady pulse with a particular size and peak slip rate. Plot peak slip rate against size for all of them and you get a single curve, the steady-state line.

Host 1And those steady pulses are what real pulses look like?

Host 2No, and this is the first surprising prediction. Every steady pulse on that line is unstable, whatever the stress. Nudge one and it either shrinks or grows away from steady state, so the paper calls pulses categorically unstable rupture modes.

Host 1So the steady line is a list of states no real pulse can sit in.

Host 2It cannot sit at its own steady point, no. But the second prediction is that the line is an attractor. An unsteady pulse born from some nucleation event moves toward the line in the size versus peak slip rate plane, and once it reaches it, it stays on the line while it drifts along it.

Host 1That sounds contradictory. Unstable, yet attracting.

Host 2An analogy of our own, not the paper's: think of a ball on a mountain ridge that slopes down to either side along the crest. Pushed off the crest, it rolls back to the ridge line, but along the ridge it rolls away from the balance point in one direction or the other. The steady line is the ridge; each stress sets one balance point on it.

Host 1And which way it rolls is the third prediction.

Host 2Exactly. Pulses that sit above their steady-state point on the line are growing pulses, and those below it are decaying pulses. So the steady point splits the line into a growing branch and a decaying branch.

Host 1Why is that line a big deal?

Host 2Because it means you do not need the full detailed field of sliding to describe the pulse. Once you know the family of steady solutions, the whole unsteady pulse is described by one time-dependent function, and every other property follows. The paper calls this an equation of motion expressed in discrete observables, and says the same structure holds for any pair of pulse properties, for instance speed versus size.

Host 1And the fourth prediction?

Host 2That growing pulses grow slowly. The rate of change of size divided by the propagation speed stays much smaller than one. In practice, a growing pulse travels several times its own length without appreciably changing, so the authors call these sustained pulses, and argue this is why pulses keep their compact shape on faults.

Host 1How solid was the theory before this experiment?

Host 2It had been checked numerically, using rate-and-state friction, the standard lab-derived friction law, but in a simplified geometry called anti-plane shear, where the motion is out of the plane. An analytic version of the equation of motion was verified in that case, and there are strong indications it also holds with thermal pressurization, where frictional heating raises fluid pressure in the fault. From that, the authors expect the predictions to hold broadly, including in in-plane geometry, which is what the experiment has.

The open question

Host 1So what is the open question the experiment answers?

Host 2Whether any of this happens in a real material with a real, messy friction law, rather than in a simulation with a chosen one. Nobody knows the exact friction law of these lab faults, let alone natural ones. So the question is whether real pulses show the structure the theory predicts: a single line, a split into growing and decaying pulses, and slow growth.

Host 1Without knowing the friction law, you cannot draw the predicted line in advance.

Host 2Right, and the authors say so plainly. So the test is structural. If the theory is right, pulses made under the same stress and the same fault surface should all fall on one monotonically increasing line, however they were triggered; the line should shift in predictable directions when stress or roughness change; and growing pulses should evolve slowly.

The experiment

Host 1Let us build the lab earthquake. What is the setup?

Host 2Two plates of PMMA, which is acrylic glass, cut at an angle and pressed together to form a dry, flat fault with no crushed-rock gouge. The plates are quasi two-dimensional, thin compared to their other dimensions, so they mimic the two-dimensional theory. A compressive load is applied, and because the fault sits at an angle to it, the load splits into a normal stress and a shear stress on the fault.

Host 1So you tune the stress by tuning the load and the angle.

Host 2Shear stress is given by τ = 2 P sin(2α) and normal stress by σ = P cos²α, letting them set the prestress on the fault.

Host 1Why acrylic and not rock?

Host 2The paper's reason is that acrylic has a much lower shear modulus than crustal rock, so waves travel slower and ruptures become well developed within samples tens of centimetres long. Rock would need much larger samples. The Rayleigh wave speed, a natural speed limit for these ruptures, is one thousand two hundred and thirty-seven metres per second in this material.

Host 1How do they change the friction law?

Host 2Through roughness. After cutting, the fault faces are sandblasted with aluminium oxide particles, either a mean diameter of one hundred and eighty micrometres, or roughly one hundred and twenty-five to one hundred and fifty micrometres for a smoother fault. Smoother surfaces are expected to give lower frictional resistance, which effectively changes the constitutive law.

Host 1And how do you start an earthquake on demand?

Host 2A thin nickel-chromium wire at one spot on the fault is burst with an electrical pulse, releasing energy locally. The voltage sets how hard that kick is; the values in the paper run from one point three to one point eight kilovolts. So the three control knobs are prestress, nucleation intensity, and roughness, which are exactly the variables the theory cares about.

Measuring a moving pulse

Host 1Then you have to watch something that lasts microseconds.

Host 2They use an ultrahigh-speed Kirana camera at one million frames per second, with a resolution of nine hundred and twenty-four by seven hundred and sixty-eight pixels. It frames a ten by eight centimetre window, placed one and a half to four centimetres from the nucleation point, so the rupture has time to mature before it enters the view. A typical pulse is about five centimetres wide, so it fits in the frame.

Host 1Why vary the distance?

Host 2The paper says the far end suited growing pulses, which need time to form, and the near end suited decaying pulses, which might die before reaching a distant window. Each experiment records one hundred and eighty frames, which at that frame rate is one hundred and eighty microseconds of footage.

Host 1And a camera sees the plates, not the slip.

Host 2So they use digital image correlation. The plates are painted matte white and a random pattern of black dots is printed on with an ultraviolet flatbed printer, covering about half the surface. Software tracks how small squares of that speckle pattern move between frames, giving the displacement field across the plate.

Host 1And from displacement you get slip.

Host 2They analyse the upper and lower plates separately, take time derivatives to get particle velocities, and define the slip rate as the difference in fault-parallel velocity just above and just below the fault. The analysis cannot reach the fault itself, so values are extrapolated to about two pixels from it. That means the measured slip rate is really taken a small, fixed distance off the fault, and the authors argue that is fine as long as that distance stays fixed.

Host 1Does the size of those tracking squares matter?

Host 2It does, and they show it. They used squares of forty-one pixels throughout; with sixty-one-pixel squares, the peak slip rate comes out lower and the pulse wider. But at either size the pulses still fall on a clean line, just shifted, which is why they fixed one size and kept it.

Host 1So the absolute numbers are method-dependent, but the pattern survives.

Host 2That is the honest reading. The same goes for pulse size, which they define as the distance between points where slip rate falls below five percent of the peak. With thresholds of two or eight percent, the sizes change but their time evolution looks similar.

Cleaning the data

Host 1High-speed cameras are noisy. How did they deal with that?

Host 2Two kinds of noise. Random noise was reduced with a non-local means filter, a standard image-denoising method that averages each pixel with others that have similar surroundings, applied in space and in time. That mainly smoothed the pulse tails, which improves the size measurements.

Host 1And the second kind?

Host 2A known systematic noise of this camera model that repeats every ten frames: the tenth frame of each cycle is the noisiest, the third to fifth are the cleanest. They fitted a twentieth-degree polynomial through the average displacement of only the clean frames, fifty-four out of one hundred and eighty, treated each frame's departure from that curve as noise, and subtracted it. Then, because derivatives amplify what is left, they applied a ten-frame moving average to all pulse properties.

Host 1That is a lot of processing between the camera and the plot.

Host 2It is, and it is a legitimate caveat. In their example, peak slip rate rises slowly from about five to seven metres per second over the window, with a leftover periodic wobble of about half a metre per second. The trend is bigger than the wobble, but a reader should know the curves are smoothed.

Result one: a single line

Host 1Now the results. First test: the line.

Host 2Five experiments at a normal stress of about ten megapascals, with shear stress around five, and two nucleation voltages. Three produced growing pulses, and they fall approximately on one monotonic line when you plot peak slip rate against size. The other two, at slightly lower shear stress, produced decaying pulses.

Host 1And where do the decaying ones land?

Host 2On the continuation of the same line, below the growing ones. That is the prediction: one attractor, with the steady-state point sitting somewhere between the decaying and growing groups. The authors mark an estimate of that point, and the figure closely mirrors the theoretical one.

Host 1Is there a direct example of the switch?

Host 2Yes, and it is the cleanest single result in the paper. Two pulses, both triggered at one point eight kilovolts: one at ten point three megapascals normal stress and four point eight shear decayed and eventually stopped; one at ten point one and four point nine grew. A tenth of a megapascal of shear separated a pulse that dies from one that keeps going, which is what an unstable system should do.

Host 1Were they fast?

Host 2All the ruptures in the paper travelled below the Rayleigh wave speed, the sub-Rayleigh regime. So none of this covers the faster, supershear ruptures.

Result two: shifting the line

Host 1Second test: change the stress.

Host 2Four more experiments, all growing pulses, at a higher normal stress of about twelve point two megapascals and shear of about five point eight five. The theory expects a slightly shifted attractor, and the four pulses do form a monotonic line, slightly above the first one.

Host 1Third test: change the friction.

Host 2Three experiments on the smoother faults, at about eleven point nine megapascals normal and six point zero five shear. Smoother means less resistance and so higher slip rates, which should push the line upward. It does: the three growing pulses form a line shifted upward relative to the rougher faults.

Host 1Is that shift purely from roughness?

Host 2Our observation, not the paper's: the smoother-fault stresses are close to, but not identical with, those of the second set, so stress and roughness are not perfectly separated. The direction matches the prediction, but three pulses on one alternative surface is a modest test of generality across friction laws.

Result three: slow growth

Host 1And the slow-growth prediction?

Host 2That one needs time derivatives of size and position, and with this noise, derivatives are unreliable. So the authors derived a weaker, integrated version: the change in pulse size since the first observed frame, divided by the distance the peak has travelled, should stay much smaller than one. They show in the supplement that this ratio is an upper bound on the quantity the theory actually constrains.

Host 1So if the bound is small, the real thing is smaller.

Host 2Exactly. The main text shows two growing pulses, one from each roughness, and the ratio stays small over the roughly forty microseconds shown. The supplement says the same holds for all growing pulses they observed, but only two are plotted, so a reader has to take the rest on trust.

Host 1Anything beyond the four predictions?

Host 2The same theory also predicts that increasing nucleation intensity at fixed stress can turn a pulse into a crack. At eleven point five megapascals normal and six point four shear, a one point three kilovolt trigger produced a growing pulse, and one point five kilovolts produced a crack-like rupture, with sliding continuing at about two metres per second behind the front instead of stopping. It is a single pair, shown as an illustration.

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Why it matters

Host 1Back to the paper. Step back: why does this matter?

Host 2The principle is a reduction of complexity. A pulse is a messy field of sliding that changes in space and time, and the theory says its evolution collapses onto one curve set by the steady solutions, with one number telling you where on the curve it is. This paper provides experimental evidence that real pulses, in a real material with an unknown friction law, show that structure.

Host 1Who does that change things for?

Host 2For earthquake modellers, the authors suggest it may improve estimates of source parameters for pulse-like earthquakes and the interpretation of observations: if pulses follow such a line, a few observed quantities constrain the rest. It also offers a mechanism for why pulses stay compact, and the authors expect it to help explain complex fault slip, since unstable compact pulses are thought to contribute to it. And for engineers, the same physics applies to stick-slip in structures and machines.

Host 1And what does it not mean?

Host 2It does not predict earthquakes, and it does not tell you whether a given fault will rupture as a pulse or a crack. It does not give you the friction law of any real fault; the line itself had to be measured, not calculated. And it is acrylic, not rock: no crushed gouge, no fluids, no heat-driven pressurization, a flat fault, and effectively two dimensions.

Honest caveats

Host 1Give me the caveats in one place.

Host 2First, sample size: twelve pulses in the main figures, across three stress and roughness settings, plus one illustrative pulse-to-crack pair. Second, the test is qualitative in shape: approximately monotonic lines, shifts in the right direction, and an estimated steady-state point, not a quantitative match to a calculated curve, because the friction law is unknown.

Host 1Third?

Host 2The measurements carry method choices. Absolute slip rates and sizes depend on the tracking-square size and the size threshold, the slip rate is measured just off the fault, and the data are heavily filtered. The authors show the patterns survive those choices, but only the patterns.

Host 1And the theory side?

Host 2The prior numerical confirmation was in anti-plane geometry, while the experiment is in-plane, so the authors are extending the theory by expectation, which the experiment then supports. The slow-growth test uses an upper bound because derivatives were too noisy, with two of the growing pulses shown. And it is a preprint, written in part by the theory's author, with strong language: 'confirm' in the title and 'major progress' in the abstract.

Host 1Is the language justified?

Host 2The results are consistent with every prediction tested, across two roughnesses, several stress levels and different trigger strengths, and the growing-decaying switch is clean. 'Supports' would be the more careful word than 'confirms'. A handful of lab pulses in acrylic is solid evidence for the structure of the theory, and a starting point for testing it anywhere else.

What to watch next

Host 1What should we watch for next?

Host 2The peer-reviewed version, and whether more pulses per condition make it into the plots. Independent groups repeating this on other lab faults, ideally rock, with gouge or fluids, since the theory claims to be general across friction laws. And a direct measurement of the growth rate with less noisy imaging, instead of the upper bound.

Host 1And in the field?

Host 2Whether seismologists can use the size versus slip-rate structure when they infer how real pulse-like earthquakes slipped. Earthquakes like Ridgecrest and Pazarcık are exactly the kind of data such an equation of motion would need to describe. That is the real test, and it has not been done here.

Sign-off

Host 1That is the deep dive: Lab earthquakes confirm the theory of frictional slip pulses, by Shafir, Gabrieli, Tal and Bouchbinder, a preprint on the arXiv. The link is in the show notes.

Host 2Every Friday this same feed carries the roundup episode: five new papers as trailers, and you pick which become deep dives. This has been the Hastrup Review of Science.