The Geo Catastrope was the series of events which completely reshaped the surface of the Earth, and ended almost all previous human countries and cultures. It is a central event to the entire plot of Alita: Battle Angel.
The event occurred in ES 55.
The Geo Catastrophe begins with the asteroid Ixchel impacting off the coast of Japan. The impact instantly destroys the country, with massive tsunamis radiating outward that would devastate coastal areas all around the world.
The dust raised from this would plunge the planet into an ice-age that would persist past ES 127, but seem to have ended by, ES 173.
The Catastrophe is responsible for the creation of Merlin, founding of Starcity which would one day become Tiphares and the Scrapyard, eventually the Earth Orbital Federation, and the mass exodus of humans from Earth which led to the Terraforming Wars. Indirectly, the Geo Catastrophe has influenced every event since.
Alita: Battle Angel (film)
In the film, Alita: Battle Angel, the Geo-Catastrophe did not occur. Instead, a devastating interplanetary war known as The Fall occurred in the 23rd Century A.D.