User blog comment:Hyperborean/"The House of Hades" – official expectations blog/@comment-10867502-20130823184113/@comment-3146930-20130823200017

It has been mentioned once or twice that Poseidon is the god of Earthquakes. In fact one of Frank's ancestors was kicked out of Camp Jupiter because an earthquake destroyed it and he was blamed for it (being a legacy of Poseidon). Also, Hephaestus once referred to Poseidon as "The earth shaker."

As far as Percy having earthquake powers, I don't see it happening as that would make him very overpowered compared to other demigods. All the times that Percy has used Earthquake-like powers, it normally had to do with water somehow. The explosion of Mount Saint Helens was caused by a large explosion of water. On the bridge, Percy stabbed Riptide into the already damaged bridge and water poured through the fissures, eventually breaking the bridge completely. Same thing on the glacier; he stabbed his sword into the ice and streams of water poured out of them and ripped the glacier apart.