Yes the logo is apparently based on Kool cigarettes which Hubbard loved. They would put a pack on his desks at his offices around the world for years.
WHY THE SYMBOLS?
Remember, these secret vaults were built as a retreat for the cult leaders in the event of a nuclear war. Should that happen Tom Cruise and others would be whisked there to be kept safe. There is food, water, guns and, in Trementina, blast proof doors.
Dianetics was written in the 1950's along with "All About Radiation." Hubbard and many other people were afraid of nuclear armageddon. Scientologists believe in reincarnation. But if everyone on earth is dead there will be nobody to reincarnate as!
This means the cultist's thetan would have to travel to another planet and reincarnate as an alien intelligence. That creature would eventually feel the pull of LRH Tech, purchase or build a spacecraft, fly to earth, locate the markings on the ground, land, open the nuclear blastproof doors, learn to read english, and re-start Hubbard Tech using the contents of the vault!
So that is why they gouged symbols in the ground.
THE REAL REASON
It makes the Scientologists feel more important to dig stuff into the ground that can be seen from space.
It is so silly that they spend so much time and money dealing with some concept like "what if i can't reincarnate?" It's as stupid as the Catholic Church, which once held a meeting to decide if Adam and Eve had bellybuttons or not.