Australia and Arizona rock layers

No, they're not even close. However, similar processes exist everywhere and this results in a similar appearance. It's called "Uniformitarian" -- "the present is the key to the past"

The theoretical system Lyell presented in 1830 was composed of three requirements or principles: 1) the Uniformity Principle which states that past geological events must be explained by the same causes now in operation; 2) the Uniformity of Rate Principle which states that geological laws operate with the same force as at present; 3) the Steady-state Principle which states that the earth does not undergo any directional change. The three principles form a single thesis called “uniformitarianism” [...]

But it also means that the same processes can be active in multiple places independently at the same time.