Tutorial: Tsunami Travel Times

A tsunami travel-time map shows how long a tsunami takes to get from its source to each point of the ocean. The speed of a long wave depends only on the water depth ($c = \sqrt{g\,h}$), so the map is computed from a bathymetry grid and a source. Nothing else is needed: no fault model, no simulation.

The result is a new grid, Travel time (h), in hours. This tutorial computes one for a source SW of Cape São Vicente (the region of the 1755 Lisbon earthquake), draws its isochrones every 0.25 hours (15 minutes), reads the arrival times at a few ports, and compares the two methods the tool offers.

1. Load the bathymetry

The travel times are computed on the grid in the window. They come back on exactly the same nodes. The grid must be in geographic coordinates (longitude/latitude), with ocean depths negative (metres below sea level), like the GMT @earth_relief grids.

Here the grid is @earth_relief_02m cut to -20/-4/30/44: a 481 × 421 grid at 2 arc-minutes, from Galicia to southern Morocco, with Madeira in the SW corner. From the REPL:

using GMT, InteractiveGMT
G = grdcut("@earth_relief_02m", region=(-20, -4, 30, 44))
view_grid(G)

Or open the file with File → Open, or drag it onto the window. Switch the view to 2D (toolbar button) to place the source more easily.

2. Open Tsunami travel times

In the Geophysics menu, switch to the Tsunamis discipline (Geophysics › → Tsunamis), then pick Tsunami travel times….

The dialog has three parts: the source, the method, and the arrival times at stations.

3. Place the source

There is no default source. Place one with one of the two buttons at the top:

• Plot point source: click once on the map. That point is the source.
• Draw Fault source: draw a line on the map (double-click ends it). Every vertex is a point source, and so is the middle of the line. Use it for a long rupture: the waves then leave from the whole fault, not from one point.

The source is drawn as an orange circle and gets a TTT source row in Scene Objects. It can be moved like any other symbol: double-click it, then drag. Here the point is at 10.0°W, 36.3°N.

4. Choose the method

Options of the Wessel method:

Fill voids left by the wavefront applies to the Mirone method only. Save grid (optional) also writes the result to a file. The result always goes to Scene Objects, with or without it.

5. Compute

Press Compute travel times. A busy notice stays up while it runs. On this grid, the Wessel method with 120 stencil nodes took about 4 seconds.

The result is a new layer named Travel time (h), with its own axes and its own colour bar, in hours (here 0 to 3.15 h). The bathymetry (Surface) is unchecked but stays in the window. Land has no travel time and is left blank.

Already in the colours, the wave runs much faster over the deep abyssal plains to the west (blue to green) than on the shelf. It crosses the whole region westward in less than 2 hours, but needs almost 3 hours to go around Cape Finisterre into the Bay of Biscay (orange, top right).

6. Isochrones every 0.25 hours

Contour lines of the travel-time grid are isochrones: lines that the wavefront reaches at the same time. Make sure Travel time (h) is the layer on display (it is, right after Compute), then pick Grid Tools → Contours → Contour Tool….

Min and Max are read from the travel-time layer: 0 and 3.147 hours. To get a line every 0.25 hours:

1. In Custom Elevations, set Starting Elevation to 0.25 and Elevation Step to 0.25.
2. Press Generate Elevation Intervals. The list on the right gets the twelve levels 0.25, 0.5, … , 3.0.
3. Tick Plot Labels to write each time on its line.
4. Press Compute.

The isochrones are drawn on top of the travel times, under one Contours group in Scene Objects (each level is its own row inside it). Pressing Compute again redraws the whole list and replaces the previous set.

How to read the map:

• The lines are 15 minutes apart in time. Where they are far apart, the wave is fast (deep water). Where they crowd together, it is slow (shelf, shallow banks).
• The wave reaches the Algarve in about 0.6 h, Lisbon in about 0.8 h and Madeira in about 1.1 h (see the table in step 7). Cádiz, closer than Madeira, is reached later (1.2 h): the last stretch is over the shallow shelf of the Gulf of Cádiz.

7. Arrival times at ports

The lower part of the dialog reads the arrival times off the travel-time grid at a list of stations. Write them in a text file, one per line: longitude, latitude and an optional name.

-9.14 38.69 Lisbon
-8.67 37.10 Lagos
-6.30 36.53 Cadiz
-7.62 33.61 Casablanca
-16.91 32.64 Funchal
-9.60 30.42 Agadir
-8.68 41.15 Porto

Every station must be inside the grid region. Choose the file in Stations file. Optionally set an Origin time (ISO format, e.g. 1755-11-01T09:40:00), to get clock times instead of elapsed times, and tick UTC if that time is UTC. Then press Arrival times.

The table opens in its own window, sorted by arrival time:

Here the wave reaches Lagos first (36 min), then Lisbon (47 min), Casablanca (59 min), Funchal (1 h 06 min), Cádiz (1 h 13 min), Porto (1 h 19 min) and Agadir (1 h 34 min). Save… writes the table, names included, to a tab-separated text file.

The arrival times are read off whatever travel-time grid is on display, whichever method made it. They work the same way with the Mirone method below.

8. The other method: Mirone

Now compute the same source with the second method. In the dialog, select Mirone wavefront expansion (fast). The ttt options gray out, except Fill voids left by the wavefront, which belongs to this method. Leave it ticked: it fills the few water nodes the expansion can skip.

The source does not need to be placed again: it is still on the map. Press Compute travel times. The new grid replaces Travel time (h). The isochrones do not follow by themselves: press Compute in the Contour Tool again (its list of 0.25 h levels is still there) to trace them on the new grid.

The two maps are very close. Side by side:

Most arrivals agree within a minute or two. The biggest difference is at Porto, about 8 minutes. The Mirone method is several times faster, so use it to try sources quickly, and the Wessel method for the final map.