Presets
Playback
Source and seabed
Hover over the map for depth, wave speed and ray-theory arrival time. Buoys A and B sit in the deep ocean, C and D on the shelf.
Independent checks
The science
Shallow-water (long) waves
When the wavelength is much longer than the depth the linear shallow-water equations apply: ∂η/∂t + ∇·(h u) = 0, ∂u/∂t + g ∇η = 0, giving the speed c = √(g h). With g = 9.81 m/s², h = 4000 m gives 198 m/s = 713 km/h and h = 40 m gives 19.8 m/s = 71 km/h. The solver is a staggered-grid (Arakawa C) explicit scheme on a 2.5 km grid with sponge layers on three sides and a reflecting wall at the coast.
Travel time and isochrones
The travel time along a path is T = ∫ dx / √(g h(x)). The isochrones are a shortest-time (Dijkstra, 16-neighbour) search on the depth grid, which is ray theory for the wave front. The graph on the right compares the integral along the centre line with the crest times seen by the solver at buoys A and B.
Shoaling: Green's law
Away from sharp depth changes the wave energy flux ½ ρ g A² c b is conserved, so A ∝ h-1/4 for a plane wave: a drop from 120 m to 40 m raises the height by 31/4 = 1.32. A 2.5 km grid cannot resolve a 20 km wavelength on the shelf, so the shelf buoys use a 250 m one-dimensional zoom driven by the buoy-B record, as in the 3D page.
Source
Rupture length, width and slip come from the Wells and Coppersmith (1994) regressions for moment magnitude, with a peak uplift of one quarter of the average slip (adjustable). The initial surface is a Gaussian hump with a trailing depression along the rupture. Run-up on the beach uses the Synolakis (1987) formula for a solitary wave on a plane beach, R/d = 2.831 √(cotβ) (H/d)5/4.
Honest simplifications: a generic synthetic basin (a coast, a mid-ocean ridge and a trench), not a real ocean; linear equations (no breaking, friction, run-up inundation or dispersion); a single idealised rupture; the Synolakis estimate is only a guide for small waves (it overestimates once the wave steepens). This lab is a classroom model, not a forecast. If you ever receive an official tsunami warning, follow your local authorities and move to higher ground.
What to try
- Press the Deep 7 km trench preset: the first part of the wave runs faster and the isochrones spread.
- Compare Steep shelf 1:150 with Wide shelf 1:1200 and watch the arrival time at buoy D and the shore crest (readout) change.
- Press Skip to end to run the checks, then change the magnitude and see the ratios stay at x1.32.