The Earthquake, Reassembled

Thirty-six NOAA DART tsunameters were in the water on 11 March 2011; one of them (46413) has no record at NCEI for that deployment, so the rack holds 35 stations. Each is a pressure sensor on the seafloor, in 1,798 to 5,923 m of water, that reports the height of the water column above it; NOAA subtracts its own harmonic tide fit, and the residual is what is drawn. The nearest, 21418, sits 552 km from the epicentre and recorded a wave 1.87 m high; the farthest with a detection, 32401 off Chile, is 15,867 km away and saw 32 mm, 20 h 37 min after the origin.

Two things the records insisted on. First, 25 of the 35 buoys felt the earthquake minutes after the origin, before any water had moved: a pressure sensor on the seabed is also a seismometer, and the surface waves that circled the planet crossed the array at 3 to 4 km/s. So the arrival detectors open only after the earliest instant a tsunami could physically arrive (the distance, less 300 km for the size of the source, over the speed of a long wave in 6,000 m of water), and the page says so rather than pretend the first wiggle was the sea. Second, the two detectors, a four-sigma threshold held for three samples and a delayed energy ratio, agree to within minutes in the far field and disagree by up to 11 minutes at the nearest buoy, where the seismic coda has not died away when the tsunami arrives. 4 detections sit within two minutes of the gate and should be read as bounds. Both rules are on the page; switch between them and watch the table move.

The model side is two engines that share no code. The fast-marching solver treats the ocean as a medium with speed √(gh) in every cell of the 8-arc-minute ETOPO 2022 grid and finds the least-time path from the whole uplifted region (every cell displaced by at least a tenth of the peak) to every other cell; on a flat ocean of one depth it is within 0.6% of the exact circle, and across a depth step it takes the refracted path to within half a per cent of Snell's law. The shallow-water solver integrates the linear long-wave equations on the sphere, on an Arakawa C-grid, forward-backward in time, with land as walls; a wave has "arrived" in a cell when the surface first moves by 10 mm, the same rule the buoy detectors use for their floor. That second engine is the one the ocean above runs on the GPU (in WebGL, 7-second steps on 3.6 million cells); the CPU copy in the verifier is the reference it is checked against, and the page prints both so a port that drifted would show. The two engines agree with each other at every buoy to a few minutes.

Against the buoys they do less well, and the shape of the failure is the finding. Inside 3,000 km the observed arrival minus the fast-marching prediction is -0.1 min (median of 7, spread 2.8 min). Beyond 3,000 km, leaving out the three buoys whose detector is known to have caught a later wave and the 3 whose detection sits on the gate itself, it is +21.6 min (median of 22, spread 10.2 min), which is +4.8% of the travel time, and it is late at 21 of those 22 buoys. The exception, 51426 (13 min early), is the rule misfiring, not the sea arriving early: there the residual creeps over a low threshold on a slow drift, and the visible rise comes later than the model like everywhere else. The rule stays as stated and the row stays in the statistic. Part of that is the detector: a rule that waits for four sigma catches a few-centimetre wave some way up its leading slope, not at its foot. Part is physics the linear equations leave out. Two independent studies of exactly this event found the observed Pacific arrivals later than the classical long-wave prediction by about one to two per cent, and traced the delay to the elasticity of the solid Earth under the moving water, the compressibility of seawater, and the water's own weight (Tsai, Ampuero, Kanamori and Stevenson, Geophysical Research Letters 40, 2013; Watada, Kusumoto and Satake, Journal of Geophysical Research: Solid Earth 119, 2014). This page does not model any of that. It prints the gap, station by station, and lets you see that it grows with distance.

141 vertical, one-sample-per-second records from the IU, II, IC and G networks of the global seismographic network, fetched as miniSEED from EarthScope and decoded by this page's own decoder (checked sample for sample against ObsPy on all 141 files), from 05:40 to 07:30 UTC. Nothing is filtered for the display beyond removing a linear trend; each trace is scaled so the five minutes around its P onset are visible under the surface waves that are ten to a hundred times larger. The gold curve is the P travel time in the ak135 Earth model for a source at the depth you choose, computed by an engine written for this page and checked against ObsPy's TauP to within 0.003 s at every distance from 5° to 120°.

The onsets are picked by a short-term/long-term energy ratio with the onset refined backwards by an information criterion (Maeda's AIC), threshold adjustable above. Against the NEIC analysts' picks at the 80 stations within 100° that both sides have, ours land a median +0.6 s later (spread 1.5 s), 47 of 76 within 2 s and 70 within 5 s; the outliers are named in the record, two of them (IU.FUNA and IU.RAO) plainly wrong picks that the robust fit below shrugs off. The agency picks are on the page too; switch to them and the location barely moves, which is the point.

Locate from records. The map searches every point of a 0.1° grid over the box for the origin time and place that best explain the picks in the ak135 model (a robust L1 fit, depth fixed at the value you choose, stations beyond 100° excluded because the first arrival there is a core phase this engine does not compute). The gold surface is the misfit; the cross is the minimum; the dots are 120 bootstrap refits with stations resampled. Click any trace to throw that station away and watch the solution answer. Then turn on only records that had arrived by the clock and drag the clock rail: at one minute after the origin only the Japanese stations have reported and the fit is a smear; the solution tightens as the P wave reaches each continent. That is not a claim about when any agency issued an alert. It is what this frozen apparatus could have known from the samples that physically existed at each instant.

With every usable station and depth fixed at 30 km, the fit lands at 38.18°N 142.58°E, 22 km from the USGS official origin and +0.3 s from its time, with a bootstrap 95% radius of 13 km and a median absolute residual of 0.87 s over 92 stations. From the analysts' own picks the same code lands 6 km from the official origin. The agency origins are hidden from the fit and from the map until you reveal them.

Six published origins exist for this earthquake, from five agencies, spread over 6.0 s in time and 48 km on the map. None is ground truth. The one at the top of the rack's selector defines t = 0 for everything on the page; change it and every residual is recomputed under the new clock.

The Japan Meteorological Agency published the accelerograms of 52 of its own stations for this earthquake, 100 samples a second on three axes for six minutes. Its terms let anyone download and compute from them and forbid passing the files on, so this page stores not one sample and shows only what it computed, with the attribution JMA asks for. What it computed is the two numbers JMA itself publishes per station, from the same bytes, by JMA's own published recipe: the peak acceleration, and the instrumental seismic intensity (the 1996 algorithm: a fixed band-pass on the vector sum and the acceleration exceeded for a total of 0.3 s). The strongest record here is 大船渡市大船渡町 (47512), 102 km from the epicentre, at 1,076.4 gal against JMA's 1,076.4, intensity 5.7; the famous 2,933 gal at Tsukidate belongs to a different network (K-NET, registration required) and is not on this page.

Of 208 published peak values, 170 come out exactly the same to a tenth of a gal, and 38 come out larger, never smaller. The intensity matches at 44 of 52 stations and is a tenth higher at the other 8, never lower. Both one-sided residues have one cause, and it was tested rather than assumed: JMA quotes the peak of the sixty-second window with the highest intensity, while these numbers are taken over the whole file, and at the two stations checked by hand the window peak reproduces JMA's figure to a hundredth. The P onset was picked at 47 stations; 9 records began after the P wave had already passed, because those instruments start on a trigger, and are marked. No S onset is reported at all: on every record a pick lands a median 23 s before the S wave could arrive, inside the coda of a rupture that went on for two and a half minutes, so the detector was refused rather than its answer kept.

The file headers also carry JMA's own preliminary hypocentre, which this page adds as a sixth published origin: 38.103°N 142.860°E, 24 km, at 05:46:18.103 UTC, 6.0 s before the USGS origin and 48 km from it. Choose it at the top of the buoy rack and every clock on the page moves with it.

The plan said Japan's dense GNSS network, GEONET, was closed to us, and as a source it is: the Geospatial Information Authority gates its daily solutions behind an application, so this page stores none of its bytes and quotes only its published headline (The largest horizontal displacement detected by GEONET was 5.40 m at M-Oshika as a co-seismic deformation of the 2011 Great East Japan Earthquake, and the largest vertical displacement was an uplift of 2.08 m at Kurikoma-2, Tsuji and colleagues, 2017). But the Nevada Geodetic Laboratory reprocesses the public RINEX of about 1,200 GEONET marks and publishes daily positions for anyone to use with a citation, so the arch got built after all. 29 stations within 1,500 km were fetched by a stated rule; 23 of them have positions in the ten days after the earthquake, and 4 more went off the air for weeks and report only the offset at their first return, which is coseismic plus that many days of afterslip and is labelled so.

The offset is the difference between a linear fit to the thirty days before and the mean of the ten days after, skipping the day itself. Mizusawa (MIZU), 142 km from the epicentre, moved 2.34 m east and 1.25 m south, and sank 0.10 m, with a formal uncertainty of 6 mm; the rupture model through Okada says 2.72 m east there. The largest coseismic offset in the set is 4.49 m at J918, 96 km out; Oshika (J550), the station GSI names for its 5.40 m, returned after 29 days reading 5.61 m, larger than GSI's coseismic number by the afterslip of a month, and 1.11 m lower, against GSI's roughly 1.2 m of subsidence. Changing the windows moves a station's answer by a median 2.5 cm, and by 8.2 cm at worst (J914), almost all of it from how much postseismic creep the after-window swallows.

The finding is in the map. Observed against the rupture model's prediction at the same 23 stations, the residual is 0.23 m RMS horizontally, and the ratio of observed to modelled motion falls with distance: a median of 1.11 inside 150 km (6 stations, where the observation carries afterslip), 0.75 from 150 to 500 km (8), and 0.62 beyond 500 km (9). A model fitted to seismic waves predicts more static far-field displacement than the ground kept. That is not a defect in the map or the arithmetic: the two readings of the same model (our Okada sum and the grid USGS published) differ by 0.20 m RMS in east, which bounds our share, and the rest is the model.

The wave in the ocean above starts from the USGS NEIC finite-fault model of the rupture (Hayes, 2011, product revised 2017): 325 patches of 25 by 16.6 km on three planes striking 198°, each with a slip, a rake, a rupture time and a rise time, inverted from teleseismic body and surface waves. It is a model, the one borrowed thing on this page, and the page treats it as such: every patch is drawn, the arithmetic is audited, and the seafloor displacement is recomputed here from the patches with Okada's 1985 elastic half-space solution rather than taken from the product. That recomputation is checked against the deformation grid USGS published from the same model: the vertical component agrees to an RMS of 0.058 m over 400 points against a peak of 5.28 m, the worst point being 0.80 m off on a steep gradient near the trench. The peak uplift of the model is +11.26 m at 38.55°N 143.52°E and the deepest subsidence -5.16 m; 143.7 km³ of water is lifted and 86.5 km³ let down, and that shape, released all at once at t = 0, is the ocean's initial condition. The real rupture took about two and a half minutes, which the wave model ignores and the moment-rate curve beside the map does not.