* Trains may stop, preventing a literal train wreck.
* People doing delicate tasks (e.g., a surgeon, someone operating heavy machinery, even someone cooking) may lock to a safer position.
* Elevators may stop and open the doors safely, so no one will be stuck inside them.
* Air traffic control may hold take offs and maybe landings.
* All traffic lights going red may slightly reduce car incidents. Seems minor, I admit.
Also, people with little experience (me!) do NOT understand that an earthquake is happening until after the fact. Some blast alert even during the earthquake is very helpful for tourists and even immigrants.
Here's another example of what you can do with ten seconds: https://www.youtube.com/watch?v=gB6-nU2nJqM
In real life, the warning such as this would catch people by surprise. That's not to say they wouldn't be useful, but I highly doubt they would be that useful as they were on that video.
Even if I'm in my own home, I imagine it would take me at least a fifth of that time to look around and come up with a plan of what is achievable in such a short time span.
10 seconds would make a huge difference to some people.
I said that it super-helps Mexico, but that because of the specific situations in both regions, we should not anticipate getting anything like their results.
You could also cut off gas and water lines, so it would probably prevent a lot of damage due fire or flooding.
Earthquake P-waves travel at 5km/s. To get 60 seconds of warning, you must be 300km (186 miles) downstream of the detector.
Mexico has a very unique situation [1]: the filled lake basins that Mexico City sits on have the same resonance frequency as buildings of a certain height. Earthquakes generate that frequency. So a serious earthquake 300km away can get the lake basin rocking, and that will knock down buildings of a certain height.
A detector is nowhere near as useful in California. Consider the Loma Prieta Earthquake. It occurred 90km from the damaged sections of San Francisco. Assuming there is a detector within 10km of Loma Prieta, that is only 16 seconds of warning. Give a few seconds for the alert to get out, and it's barely 10 seconds. That's not enough time to do anything other than hide under a desk -- which you can already do after the earthquake starts. Such a system would be excellent for bringing trains to a halt, but that's pretty much it.
[1] See preface of https://en.wikipedia.org/wiki/1985_Mexico_City_earthquake