Acceptance is the only way I reckon.
Accept that you live in an area that is prone to earthquakes. There is NOTHING you can do to stop them happening so you need to take the stress off yourself. easier said than done I know....it's not something I have to worry about at all in Scotland. But treat it like another aspect of life that you can't control so why worry? Sounds crazy and impossible, but acceptance is great when you master it. I used to get sooooo upset every time I saw or spoke to my mum and sister. They used to have so much power over me until I just said "enough". I know i can't change them, and I will just get more and more upset if I try to.....so I accept that they will say stupid things, insensitive things, that they said horrible and hateful things in the past, and hit me and hurt me in the past. But I can't change it so I accept it.....and it's like a huge burden lifted.
You can't change the fact that earthquakes happen in the world. What you can do is live each day to the full, make sure you tell the people you care about the most that you care for them as often as you can....and learn to live with it. Or move to somewhere without earthquakes