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Are both okay:

Are there a lot of earthquakes here?

and

is there a lot of earthquake here?

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anon006Is there a lot of earthquake here?

Impossible. "earthquake" is countable. You are using it as uncountable.

This is like treating 'earthquake' like a substance.

Is there a lot of sugar here? OK
Is there a lot of water here? OK
Is there a lot of earthquake here? NO
Is there a lot of table here? NO

anon006Are there a lot of earthquakes here?

Perfect.

CJ