There's an animation of the antipode from this eruption arriving in northern Africa and it's interesting how distorted the incoming wavefront is.

https://twitter.com/weather_models/status/148300643675002880...

Sounds like the hairy ball theorem (https://en.m.wikipedia.org/wiki/Hairy_ball_theorem)

The earth is (almost) an oblate ellipsoid so most geodesics on earth aren't closed and even if they all meet (do they? I need to to think about this or play with GeographicLib) at one point they are of different lengths (imagine a point on the equator, the latitudinal path is quite different from the longitudinal path). And then there are different propagation velocities due to pressure, terrain, etc. So probably not.

> But there would be a spot where the pressure waves would cross [simultaneously]?

There could be, but it's not immediately obvious that there has to be.

It does seem like certain points would need to be on 'cusps' of the wavefront, though, so something like getting the wave from the north and the northeast 'simultaneously'.

Not necessarily. The set of points reached last by the waves could be multiple points, or a line, or multiple lines.

I think it’s highly unlikely that even half the pressure waves would simultaneously reach a single point on earth. The waves get reflected in all kinds of ways by the ground, mountain ranges, difference in air temperature, etc.

If they did, however, I wonder how strong the force would be at its focus (if that’s the proper name)

(If I did my math right, the antipodes of Tonga live in the south of Algeria, near the Niger/Mali/Algeria tripoint. I haven’t heard of weird phenomena happening there, but then, I don’t think that is the most populated and most twitter-addicted part of the world)

I think so. I think there is necessarily a circle "eversion" (turning it inside-out) with a crease. Whatever is the point of the crease would hear sound from all directions. Even with something like a figure 8 collapsing wavefront, eventually one or more creases should form.