Douglas Harper's Etymology Dictionary
in reference to seas covering continental shelves, 1915, from Greek epeiros "mainland, land, continent," from PIE root *apero- "shore" (cognates: Old English ofer "bank, rim, shore," Old Frisian over "bank") + -ic.\n\nAs the term "continental deposits" in this sense is now ingrained in Geology, we can no longer use Dana's "continental seas" without raising a question in the mind as to what is meant when their deposits are considered. For this reason we propose here to use epeiric seas (meaning seas that lie upon the continents) for the bodies of water that lie within the continents in the downwarps of the continental masses.
[Louis V. Pirsson, "A Text-Book of Geology," 1915]
Wiktionary
a. Describing the part of a sea that lies over a continental shelf
Usage examples of "epeiric".
Lake Manyara, epeiric Lake Eyasi, will be out on the fabled Serengeti.