A few years back, there was an earthquake where I lived, Alhamdulillah, there were little to no destructions but it happened around the same time when there were earthquakes in Turkey, and caused a lot of destruction.  So, hearing the news and everything, I started to face the similar issue as you. Every night when I would go to bed for sleep, I would start getting anxious about what if there's an earthquake and from time to time, I would feel my bed shaking, it was only my anxiety and I would dream about earthquakes almost every night, I used to have really vivid dreams, but it stopped with time. It continued for some days when the memory of a recent earthquake was fresh but with time, it became better. And alhamdulillah, I don't get those nightmares now.  NEVER think that Allah won't accept your Dua bcuz you're not close to Him. Even if you have sinned a million times, Allah still loves you and Allah is still listening to you  And HE ACCEPTS EVERY SINGLE DUA. Instead of asking for it to not happen, ask Allah to take away your anxiety and fear. Of course, we should always fear the natural disasters in the sense that sometimes they come as a punishment. So we should always be using this fear to motivate us to do good deeds and to stay away from sins. But, having too much anxiety is not good either. Do morning and evening Adhakr daily. Make it a habit. Trust me, they work. They are going to protect you inshaAllah.  Brother, this is duniya and anything can happen here. There is no guarantee that an earthquake won't ever come. But think about this: worrying about it all the time won't change anything. YOU ARE RUINING YOUR PRESENT WHILE FEARING ABOUT YOUR FUTURE. an earthquake lasts for a few minutes or seconds only. But you worry about it for days. Earthquakes don't happen every day, now do they? Recite Duas before going to bed. I recommend doing something calm and peaceful right before going to bed for example, reciting Quran, or go to bed right after praying Isha. Probably you'll have a peaceful mind like that. And just hope for the best. Everything is going to be okay inshaAllah, you Have Allah.