All were rooted in uniformitarianism, as the idea was known.
They admit the occasional catastrophe, but not enough so as to cause them to utterly throw out uniformitarianism completely.
British Dictionary definitions for uniformitarianism
the concept that the earth's surface was shaped in the past by gradual processes, such as erosion, and by small sudden changes, such as earthquakes, of the type acting today rather than by the sudden divine acts, such as the flood survived by Noah (Genesis 6–8), demanded by the doctrine of catastrophism
of or relating to uniformitarianism
of, characterized by, or conforming to uniformity
a supporter of a theory of uniformity or of uniformitarianism
(y'nə-fôr'mĭ-târ'ē-ə-nĭz'əm) The theory that all geologic phenomena may be explained as the result of existing forces having operated uniformly from the origin of the Earth to the present time. See Note at Lyell.