This section is from the book "An Introduction To Geology", by William B. Scott. Also available from Amazon: An Introduction to Geology.
An old land-surface with well-defined topography may be deeply buried under newer accumulations, as of lava floods, great bodies of volcanic ash and tuff, sheets of glacial drift, lake deposits, or, after depression beneath the sea, by marine deposits. In each of these cases, the new surface has no reference whatever to the old; the more ancient and buried rocks may and generally do have an entirely different character, arrangement, and structure from those which overlie them. The drainage system established upon the new surface is consequent upon the initial slopes of the latter, and when the streams have cut through the mantle of newer rocks and reach the ancient surface below, they are entirely out of adjustment with that surface and its rocks. As the streams cut their trenches through the overlying mantle of newer strata, they encounter the older rocks below, first laying bare the higher ridges of the latter, which will cause waterfalls and rapids. The upper Mississippi has in many places excavated its channel through the surface sheet of glacial drift and is now engaged in eroding the ancient crystalline rocks which the drift had covered.
When the stream has everywhere cut through the newer rocks, its course will be seen to have no relation to the structure of the older rocks which it is now trenching. If, as frequently has happened, denudation has stripped away almost all the newer strata, the drainage of the country seems to be quite inexplicable and to be arranged without any reference to the structure of the rocks across which the streams flow. Such a system of drainage is said to be superimposed, inherited, or epigenetic.
Examples of superimposed streams may be found in great numbers in the United States. Almost all of the minor streams in that part of the country which is covered with glacial drift belong in this class, as do also the rivers, like the Columbia, the Snake, and the Des Chutes, which trench the great volcanic plateau of Idaho, Oregon, and Washington. An especially curious and interesting case is found in western Colorado in the valleys of the Uncompahgre and Gunnison. When these streams were first established, the region was a plateau with westerly slope largely built up of volcanic ash, beneath which an old topography was buried. The Gunnison flowed over a concealed mountain of granite, and when its valley had been cut down to the granite, it was compelled to hold the same course, and has trenched a canon 2000 feet deep in that rock. The Uncompahgre, which, though a tributary of the Gunnison, flows parallel with it for a considerable distance, followed a course which took it over an old valley buried under soft materials which were rapidly removed.
At the present time the course of the Gunnison seems to be quite paradoxical, though it is easily explained by its history.
 
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