Can we use explosives to cause small earthquakes in order to prevent having large ones?
No. Even huge amounts of explosive almost never cause even small earthquakes, and it would take hundreds and thousands of small earthquakes to equal a large one, even if it could be done. In addition, we wouldn't have any control over the size of the earthquake being created if it worked, since small and large earthquakes all start out in exactly the same way. It's just not physically possible.