Hi, I'd like to help you with your question.
A fear of earthquakes is called Seismophobia. It is considered a natural environment phobia, as opposed to an situational phobia (like fear of flying or fear of tunnels), animal phobia, or medical phobias. All phobias are related. Phobias are about the fear, not the object. That is why phobias seem unreasonable. It is not about the object or situation, it is about the fear that a person feels when they are faced with the feared object or situation.
Because of that, phobias are very easy to treat, one of the easiest disorders in mental health. Cognative behavioral therapy (CBT) has shown to be one of the most effective therapies. Seeing a therapist can help you overcome this fear. If you want to see a therapist, you can search on line for one at http://therapists.psychologytoday.com/rms/.
You can also treat your phobia through self help. Here are some suggestions:
The Anxiety & Phobia Workbook by Edmund J. Bourne
When Panic Attacks: The New, Drug-Free Anxiety Therapy That Can Change Your Life by David D. Burns
The Cognitive Behavioral Workbook for Anxiety: A Step-By-Step Program by William Knaus and Jon, Psy.D. Carlson
You can find these books on Amazon.com or your local library may have them for you.
I hope this has helped,