Learn English – Why “out to sea”

"Under the sea" is short for "under the surface of the sea"; the phrase is meant to evoke the romantic image seeing the waves passing while standing on the deck of a ship, say.

There are relevant sections in 'Multi-Word Verbs in Early Modern English: A Corpus-Based Study' by Claudia Claridge, précised at http://linguistlist.org/issues/12/12-698.html which contains:

Chapter 5 examines the history of these types of multi-word verbs from Old English through to Modern English. ...Chapters 6 and 7 describe the particular multi- word verbs found in the Lampeter corpus, and attempt to describe the patterns found among them. Chapter 6 treats the data synchronically, while chapter 7 looks at diachronic developments during the 100 year period covered by the corpus.

I've accessed various portions online, but had to order a copy via my local central library.

In an article by Catherine Browman at http://web.haskins.yale.edu/Reprints/HL0594.pdf , it is stated that the transformational grammarians Absalom (1973), Chomsky (1957) and Fillmore (1965) considered the contiguous form to be basic and the separated form a movement-transformation derivative, whilst Edmonds (1972) believed it was the other way round. Other grammarians, such as Gazdar, Klein, Pullum and Sag (1985) retain the verb and particle as separate constituents, but seem neutral with regard to direction of transformation (if any).

(Still other grammarians regard the verb-particle combination as more or less unanalysable, in any given example.)