in our university project, we are developing a tsunami simulation using the Shallow Water Equations. For our project, we have decided to allow users to enter an epicentre and the magnitude of an earthquake, then put in the coordinates of a coastal city, and calculate a rough estimate saying when the tsunami resulting from the earthquake (we handle seafloor earthquakes) should reach the city. The first step to get there is to figure out how to get from magnitude to the resulting wave. The ground displacement caused by the earthquake has relatively little correlation to its magnitude (at least not if you consider the range, height etc.). Where the correlation is way higher tough, is between earthquake magnitude, and maximum height of the resulting tsunami.
It's also worth noting that in examples 3 and 4, the earthquake was near the coast so the tsunami didn't have time to properly build up before reaching the shore which is where the max height usually evolves.
Knowing this relationship, we were wondering: what is the best way to add a starting wave into our simulation (we can f.e. create a high water column at the epicentre and let that create the wave) that results in our desired outcome. Options we have thought about are:
- Creating a high point of water in the middle and letting it "drop"
- Getting some "standardized" displacement charts that result in a wave with max height x
Sadly, none of us are physics students. Since there are cases, where the epicentre is near the shore (see examples 3 and 4) we have to let the wave evolve, so the displacement idea would be better.
Any ideas on how to calculate something like that or any relationships we can use for further research are greatly appreciated!
