Does the theory that earth quakes may be related to petrol production seems probable?

Answer 1

Not at all.
Firstly, areas that are the most prone to earthquakes are not areas where oil is extracted. Conversely, most areas where oil is pumped out are geologically stable.
And then, the amount of oil pumped out is insignificant at geological level, and most often than not, underground water seeps in and replaces the oil that was taken out.

Answer 2

Earth quakes are related to plate techtonics - basic geology.