The first Mediterranean Games took place in Alexandria, Egypt, in 1951, with the most recent event located in Mersin, Turkey, in 2013. The multi-sport event takes place every four years in the year following the Olympic Games.
The three rings in the symbol stand for sports, friendship, and peace in the Mediterranean, and this graphics guide from 1977 (two years before the VIII Mediterranean Games in Split, Yugoslavia — now Croatia) is the earliest document I’ve seen that features the distinctive mark.
It might’ve been in place for the 1975 event, but I can’t tell if the ’75 logo shows the same water-like detail in the lower half the three rings.
“The symbol is a symmetric graphic figure consisting of three uniform circular elements joined together to form a regular sequence. Since each of the circular elements is symmetrical along the vertical axis and the left half is mirrored in the right half, the entire symbol consists of six such halves. One-sixth of the symbol, or one half of a circular element in the upper part, may be drawn with a pair of compasses, while the bottom part is a more complex curve which must be constructed by means of a grid.”
(Quoted from the manual.)
The Games’ mascot was a Mediterranean monk seal, showing a touch more restraint than the gaudy mascots we see at more recent sporting events.
The symbol was designed by Borislav Ljubičić, and you can see more of the graphics manual on designers books. Via Aisle One.