Albert Barnes Commentary Psalms 46:3

"Though the waters thereof roar and be troubled, Though the mountains tremble with the swelling thereof. Selah" — Psalms 46:3 (ASV)

Though the waters thereof roar and be troubled – The waters of the sea. The idea is that they would not be afraid even if everything were in commotion and as unsettled as the restless waves of the ocean. The earth might be changed, the mountains removed, and the agitated sea roar and dash against the shore, but their minds would remain calm.

The word translated “be troubled” means to boil, to ferment, or to foam; and here it refers to the ocean being agitated and lashed into foam.

Nothing is more sublime and fearful than the ocean in a storm. Nothing provides a better illustration of the peace produced by confidence in God amid the agitations that occur in the world, than the mind of a seaman who remains calm when the ocean is heaved in wild commotion.

Though the mountains shake with the swelling thereof – The rolling ocean breaking against the sides of the mountains on its shore, and seeming to shake them to their foundation.

The word translated “swelling” primarily means majesty or glory, and then pride, haughtiness, or insolence. Literally, “though the mountains tremble through their pride.” . Regarding the word “Selah,” see the notes on Psalm 3:2.