Laudator Temporis Acti

Homer, Iliad 13.43 (my translation):

earth-bearing, shaking-earth

γαιήοχος ἐννοσίγαιος

Both epithets are used exclusively of the god Poseidon. Juxtaposed like this, they make a convenient hexameter ending (also Iliad 9.183, 13.59, 13.677, 14.355, 15.222, 23.584; Odyssey 11.241; sometimes in oblique cases). The presence of γαῖα (gaia = earth) in both compounds, at the beginning in γαιήοχος and at the end in ἐννοσίγαιος, creates a sort of chiastic arrangement.

Stephanie West on Odyssey 1.68:

γαιήοχος: in Homer this title is Poseidon's alone. Its origin and meaning are controversial, mainly because of uncertainty about -οχος. The poet and his audience, like the tragedians (cf. A. Supp. 816, S. OT 160), probably connected it with ἔχω and understood the compound as 'earth-holding, the Earth Sustainer', but Laconian Γαιάϝοχος (IG V i 213, 9, etc.) rules out this etymology. The usual assumption that the second element is related to ὀχέω, Lat. veho etc., leaves the interpretation of the compound debatable: 'he who rides (as a river) beneath the earth (and thereby shakes it)' Nilsson, 'husband of Gaia' Borgeaud. Meillet's suggestion that the root is *wegh- 'shake', cf. Lat. vexare, is attractive. Cf. Hainsworth on viii 322 and see further Frisk GEW s.v. γαιάοχος, Chantraine, Dictionnaire, s.v. γῆ, LfgrE.

J.B. Hainsworth on Odyssey 8.322:

Ποσειδάων γαιήοχος: the form and etymology of the divine name are discussed by C.J. Ruijgh, 'Sur le nom de Poseidon et sur les noms en -α-ϝων, -ι-ϝων,' REG lxxx (1967), 6-16. It is probable that the name consists of Ποσει- (an ossified vocative, cf. Iuppiter) +δα- 'earth', a calque of various oriental divine titles derived ultimately from the Sumerian EN.KI, 'Lord of the Earth': see Palmer, Interpretation, 255-6. The epithet γαιήοχος (< *wegh-, not *segh-, cf. Γαιάϝοχō IG V i 213), 'earth-bearing', is perhaps another version of the same title, with the nuance that the god is 'Lord of the Earth' because he is, or personifies, the 'water under the earth' on which the terrestrial disc, in Near Eastern cosmology, was conceived to float. Further literature in Burkert, Greek Religion, 402.

Martha Krieter-Spiro on Iliad 14.135:

Ἐννοσίγαιος 'Earth-shaker' (from γαῖα and ἔνοσις 'tremor') for Poseidon is probably a more recent metrical variant (20× Il., 6× Od., 10× Hes., 1× h.Hom.) of the synonym Ἐνοσίχθων (at 150, 384, etc.; with one exception always in the nom., in total 23× Il., 18× Od., 4× Hes.), since in contrast to Ἐνοσίχθων it is used as a noun and is better adapted to oblique cases. Ἐννοσίγαιος has been linked to both Mycenaean e-ne-si-da-o-ne, attested on tablets from Knossos (M 719, Gg 704), which likely denotes a deity, and Ἐννοσίδας attested at Pind. Pyth. 4.33 and 173 (etc.) (Simon 1980, 70; LfgrE s.v. Ποσειδάων 1470.52 f., 1474.1 ff.).