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Synonyms for Deep (same or very similar meaning)

WordNet sense 1 (a long steep-sided depression in the ocean floor):
trench, oceanic abyss

WordNet sense 2 (not thin; of a specific thickness or of relatively great extent from one surface to the opposite usually in the smallest of the three solid dimensions):
thick

WordNet sense 3 (having great (or a certain) extent from one side to the other):
broad, wide

WordNet sense 4 (showing intellectual penetration or emotional depths; from the depths of your being):
profound

WordNet sense 5 (in an extreme degree):
intense

WordNet sense 6 (above average in size or number or quantity or magnitude or extent):
big, large

WordNet sense 7 (having or denoting a low vocal or instrumental range):
bass, bass

WordNet sense 8 (used of sounds and voices; low in pitch or frequency):
low, low-pitched

WordNet sense 9 (of an obscure nature):
cryptic, inscrutable, mysterious, mystifying, cryptical

WordNet sense 10 (incapable of being explained or accounted for):
incomprehensible, inexplicable

WordNet sense 11 (difficult to penetrate; incomprehensible to one of ordinary understanding or knowledge):
abstruse, recondite

WordNet sense 12 (confined to and understandable by only an enlightened inner circle):
esoteric

WordNet sense 13 ((of sleep) deep and complete):
heavy, sound

WordNet sense 14 (extremely deep):
bottomless

WordNet sense 15 (so deep as to be unmeasurable):
abysmal, unfathomable

WordNet sense 16 (separated in space or coming from or going to a distance):
distant

WordNet sense 17 (strong; intense):
rich

WordNet sense 18 (having striking color):
colorful, colourful

WordNet sense 19 (to an advanced time):
late

WordNet sense 20 (to a great depth):
deeply

WordNet sense 21 (marked by skill in achieving a desired end especially with cunning or craft):
artful


From the ODE community, based on WordNetadd/edit