Tsunami source of the 2011 off the Pacific coast of Tohoku Earthquake

It is two forty-six in the afternoon on March eleventh, two thousand eleven. On the seafloor off the coast of Tohoku, two tectonic plates lurch violently past each other. Nobody on the surface can see what just happened down there. But within minutes, pressure gauges bolted to the ocean bottom and GPS buoys floating in open water begin registering something strange: a slow, gentle rise in sea level — about two meters over ten minutes — and then, arriving separately, a sharp, impulsive wall of water three to five meters high. Two steps. Gradual, then sudden. That two-step signature is the puzzle at the center of this paper by Fujii, Satake, Sakai, Shinohara, and Kanazawa. Decode it, and you know exactly what the seafloor did. And what the seafloor did turns out to be far larger than anyone expected. The instruments that captured this signature were spread across a range of environments. Fujii and colleagues assembled data from thirty-three coastal tide gauges alongside three crucial offshore sensors: a GPS wave gauge called Iwate S, sitting in about two hundred meters of water, and two cabled ocean-bottom pressure gauges — TM-2 at roughly one thousand meters depth and TM-1 at about one thousand six hundred meters. Coastal gauges from the Japan Coast Guard, the Japan Meteorological Agency, and port research institutes filled in the nearshore picture. But the coastal record had a serious problem: many Pacific coast tide stations went off-scale or lost power entirely after the first tsunami wave exceeded nine meters. The offshore instruments survived. They preserved the two-step shape that the coastal network could not. Fujii and colleagues kept even the damaged coastal records in their analysis because arrival times and the initial slope of the sea-level change still carry source information, even when the peak is gone. To remove tidal drift, they fit and subtracted a polynomial from each record, then resampled everything to one-minute intervals. In total, two thousand eight hundred and eighteen data points went into the inversion. Now, here is how tsunami waveform inversion works, because the method is worth understanding. You know what the wave looked like at the gauges. You know the physics of how waves travel through water. So you run the problem in reverse: what pattern of seafloor motion would produce exactly those observations? Fujii and colleagues divided the earthquake source into forty rectangular patches — subfaults — each fifty kilometers by fifty kilometers across the plate interface. For each subfault, they computed the seafloor deformation that one meter of slip would produce, then propagated that deformation forward using the linear shallow-water equations with a finite-difference scheme, generating a predicted wave at every gauge. That gives you the building blocks. The inversion then finds how much slip on each subfault, combined, best matches reality. Two constraints kept the math honest. First, non-negative least squares: slip on any subfault can only be zero or positive; it cannot go negative, which would be physically absurd for this fault geometry. Second, a delete-half jackknife test: the team repeatedly discarded half the data at random and re-ran the inversion dozens of times. The slip features that kept showing up regardless of which data were removed are the ones you can trust. Different gauges were weighted differently to balance the dataset: nearby GPS and bottom-pressure records were upweighted by factors of ten to thirty, near-source tide gauges by two to ten, and distant DART buoys by ten to compensate for their much smaller amplitudes. What the inversion found is extraordinary. The largest slip — more than forty meters — was concentrated right at the Japan trench axis, the shallowest part of the plate interface where the Pacific plate dives beneath northeastern Japan. Subfault four returned forty-one meters of slip, subfault five returned nearly forty-eight meters. To put that in physical terms: a patch of seafloor the size of a small city moved nearly half the length of a football field in a matter of minutes. Seafloor uplift above those patches exceeded ten meters. That trench-axis slip is what produced the impulsive, sharp-peaked second wave — the one that arrived with three to five meters of amplitude at the offshore gauges. Deeper on the plate interface, a second zone of large slip straddled the epicentral region. Southern Sanriku-oki showed slips around twenty-eight to thirty-four meters. Miyagi-oki, beneath and around the epicenter, showed nine to twenty-three meters across several subfaults. Fukushima-oki had roughly ten meters of slip, and the Ibaraki-oki region at the southern end had less than three meters. The total rupture zone with slip exceeding two meters stretched about three hundred fifty kilometers along strike. This deeper interplate slip produced the initial gradual two-meter rise — the first step — and Fujii and colleagues argue it explains the catastrophic inundation on the Sendai plain, where the tsunami reached more than five kilometers inland. The total seismic moment summed to three point eight times ten to the twenty-second newton-meters, confirming the moment magnitude of nine point zero. Crucially, synthetic waveforms computed from the inverted slip distribution matched the observed records well — the two-step shape at offshore gauges TM-1, TM-2, Iwate M, and Iwate S is reproduced, as are the initial small troughs and gradual rises recorded at coastal stations like Miyako, Kamaishi, Ofunato, and Soma. The fit is the validation. Now consider what that slip distribution means against the historical record, because Fujii and Satake frame this explicitly. The eight hundred sixty-nine Jogan earthquake — more than eleven centuries ago — left tsunami deposits along the Sanriku coast, and previous modeling had shown that only a broad interplate rupture near the coast could produce the inundation those deposits implied. Trench-axis slip alone wouldn't do it. So the historical baseline was an interplate rupture model. The two thousand eleven event ruptured in exactly that interplate zone — southern Sanriku-oki and Miyagi-oki — but with substantially larger slip than any Jogan-based forecast would have required. And it simultaneously produced enormous trench-axis slip on top of that. The paper frames it clearly: the two thousand eleven event combined both rupture styles in the same earthquake and exceeded the historical templates in both. The eighteen ninety-six Sanriku earthquake offers the other historical parallel. That event was a classic tsunami earthquake — a term for earthquakes that generate disproportionately large tsunamis relative to the shaking felt on land, because the rupture is concentrated near the trench axis where soft sediments amplify displacement. The two thousand eleven trench-axis slip is analogous in style to eighteen ninety-six. It is not analogous in scale. Forty-seven meters of slip dwarfs anything that event produced. The two-step waveform recorded in two thousand eleven is, in a sense, the fingerprint of both the eighteen ninety-six style and the Jogan style operating together, simultaneously, on a scale that exceeded either. What the offshore sensor network made possible here deserves a closing thought. Without the GPS wave gauge and the two cabled bottom-pressure gauges, the two-step signature would have been buried in noisy, saturated coastal records. It was those open-ocean instruments — sitting quietly on the seafloor or bobbing in water hundreds of meters deep, far from any harbor that could distort the signal — that preserved the clean distinction between the gradual rise and the impulsive peak. And it was that distinction that allowed Fujii and colleagues to separate the trench-axis contribution from the deeper interplate contribution, to assign the right amount of slip to each zone, and to reconstruct a source model that actually reproduces what the ocean did. The shallowest part of the plate interface, long considered relatively quiet, moved the most. The waves said so. The inversion confirmed it. This lecture was created by ennepō. Go to https://ennepo.ai to Discover, Create and Follow the latest research in your field. Read when you can. Listen when you want to.