The La Plata Mountains as seen from above the author’s

Durango Bill's

Paleogeography (Historical Geology) Research

Appendix to the Evolution of the Colorado River and its Tributaries (Part 1)

The Physics of Mountain Building

Bill Butler

   There is a popular oversimplification regarding tectonic forces and the resulting effects on surface topography. We think of all the action taking place on top of a stable foundation when in fact things are a little more complicated. If we think of two plates colliding, we tend to compare it to having two loose rugs on a slippery floor and then pushing them toward each other. One rug might slide under the other, it might drop down into a mysterious black hole, or you might just have crumples and folds in both rugs.

   Unfortunately, the earth’s crust is not as simple as the above examples. We are not resting on a stable surface. Instead the crust is akin to so much floating scum on the mantle, which underlies the crust. The mantle is a very viscous fluid. In many ways it will react to forces the same way water does although it will take millions (or billions, or whatever) times longer to do so.

   If you add weight to an object floating in water, then the object sinks lower into the water. For example, if you fill a coal barge with coal, the barge sinks lower. If the Mississippi River adds silt to southern Louisiana then New Orleans will sink lower toward the mantle (Also lower relative to the Gulf of Mexico. There is a hint here regarding long term real estate investments.). Conversely, if you remove weight by melting a large icecap that has previously depressed the earth’s surface, then that area of the crust will slowly rise back up again. If erosion removes sedimentary layers from the top of an existing mountain range, then the remaining portion of the earth’s crust will float higher. Thus, metamorphic and even deeper basement layers, which were formerly much lower in the crust, will gradually float upwards where they will form mountains that are almost as high as those that existed before erosion took place.

   Let’s perform an experiment with the coal barge. Assume a team of divers brings in balsa wood from an external source and places a 5-foot thick section under the barge. Assume balsa density equals 0.2 and water density equals 1.0. We know that the balsa wood will lift the barge higher out of the water (similar to a life jacket lifting the head of a hapless swimmer), but let’s do a little arithmetic.

   The total thickness of the barge/balsa complex has increased by 5 feet. (We have added 5 feet to the bottom of the barge.) The weight (per square foot) that we have added is equal to the density (0.2) times the thickness (5 feet). (Technically, we should also multiply by the weight of water per cubic foot, but this term cancels out – hence, for simplicity, we have ignored it.) The barge/balsa complex must displace this additional weight of water. Thus, the bottom of the barge/balsa complex must extend 0.2 times 5 feet equals 1 foot deeper into the water. We thus calculate that the barge has been lifted 4 feet higher out of the water. (5 feet thicker minus 1 foot deeper equals 4 feet higher out of the water.) It is interesting that this amount of lifting is independent of any cargo that might be in the barge.

   We could also calculate what would happen if we used another variety of wood that had a higher density. For example, if we added 5 feet of live oak, which has a density of about 0.977, then the bottom of the barge/oak complex would have to displace an additional 0.977 times 5 feet equals 4.885 feet of water. The barge would only be lifted 5 minus 4.885 equals 0.115 feet higher (about 1.38 inches). (Hint, don’t use ironwood, density equals 1.077, in life preservers.)

   We can apply these principles to plate tectonics. If two plates collide, either the two pieces of surface crust must crumple, or one of the pieces must slide under the other (usually a combination of both). In either case, we have thickened the lightweight crustal material. (If the subducting plate dives steeply taking most of its material down with it, this thickening is substantially reduced, but it is still not entirely eliminated.) When we added lightweight wood underneath the barge, the barge rose higher out of the water. When we thicken the lightweight components of the earth’s crust, we call it mountain building. In the barge example, we also noted that adding wood to the bottom of the barge caused the complex to extend deeper into the water as the added weight required a greater water displacement. When we used the higher density oak instead of the balsa wood, it caused a deeper displacement and less lifting. This is because the density of the oak (at 0.977) was much closer to the density of water (at 1.0) than was the density of balsa (at 0.2).

   The earth’s crust (and particularly the lithosphere under it) has a density only slightly less than that of the underlying mantle. Thus, when we thicken crustal material and form mountain ranges, the situation is similar to the oak experiment with the barge. The displacement taking place out of sight under the crust is ten to twenty times greater than the uplift above the surface. In order to build a mile-high mountain range we have to increase the subsurface displacement by ten to twenty miles. (In practice, there is enough rigidity in crustal material and the underlying lithosphere so that the displacement depth can be somewhat less as long as the subsurface horizontal extent is increased enough to equal the required weight displacement.)

   As noted above, this thickening of the lightweight crustal material is usually a result of plate collision (convergence). In theory, we could also thicken the crust by having a team of divers bring in balsa (or other light weight material) from an outside source, diving down under the crust (or the rigid portion of the lithosphere), and nailing it in place under the area where we want to form a mountain range. (We admit this isn’t overly practical.) Alternately, we could push or otherwise slide the earth’s crust over a forest of balsa wood, and as we pass over each tree, nail pieces of the lightweight material underneath our incipient mountain range. We will return to this alternate “sliding” process when we discuss the theory explaining all the local mountain building since the Laramide. For now, we will simply note that ten million years ago, a “hot plume” in the mantle was under the Snake River Plain in Idaho. Since then, the earth’s crust has been slowly sliding west-southwestward so that now the “hot plume” is under Yellowstone National Park.

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