The ABC's of Plate Tectonics

Buoyancy and Floating Continents

by Donald L. Blanchard

 

  Preface:
Introduction to "The ABC's of Plate Tectonics"

Remedial Reading:
The Basics of Plate Tectonics

Lesson #1:
Buoyancy and Floating Continents

Lesson #2:
Sedimentation and Continental Growth

Lesson #3
When Continents Collide

Lesson #4
The Mechanism of Plate Tectonics

The Formation of Pangaea: The Making of a Supercontinent

Earth Sciences Home Page

    Introduction: Buoyancy.
Buoyancy is what makes a piece of wood float in water. It is also what makes a battleship float on the high seas, or a block of steel float in a pool of liquid mercury. The first principle of buoyancy is very simple: (1) If a solid immersed in a fluid weighs less than an equal volume of the fluid, the solid will float. Another way of saying the same thing is, if a solid has a lower specific gravity than a fluid, the solid will float in that fluid. Specific gravity is defined as the weight of a substance divided by the weight of an equal volume of water (specific gravity of water = 1).

If the first condition is met, then the level at which the solid will float is determined by the second principle: (2) A floating object will displace its own weight in a fluid. Thus, the percentage of the solid immersed in the fluid will be equal to the specific gravity of the solid divided by the specific gravity of the fluid. For a block of wood having a specific gravity of 0.7 floating in water (specific gravity 1.0), 70% of the block will be below the water's surface.

Continents are made up of solid rock, and float in the fluid (a very viscous fluid) of the Earth's mantle. If the specific gravity of the mantle and the specific gravity of continental material are known, it should be possible to calculate how continents float in the Earth's mantle.


Floating Continents:
Specific gravities of various Earth substances are listed in table 1.

TABLE I
Typical Specific Gravities of Earth Materials
SubstanceSpecific Gravity*
Sea Water1.02
Limestone2.68-2.76**
Granite2.64-2.76**
Sandstone2.14-2.36**
Slate2.6-3.3**
Basalt2.4-3.1**
Average Specific Gravity of Continents2.7
Average Specific Gravity of SiMa (Mantle Material)3.3
* Actual specific gravities vary slightly, depending on chemical composition.
(** Source: Handbook of Chemistry and Physics)

The average continent is made up primarily of limestone, granite, or eroded granitic byproducts such as shale, siltstone, and sandstone, as well as metamorphics like slate, schist, and gneiss. However, most continents also have substantial amounts of andesite and basalt added in, from a past history of various volcanic events. The addition of these denser materials raises the average specific gravity for continental material to around 2.7. SiMa (from Silicon/Magnesium - its principal elements) is the material of the Earth's mantle - the 'fluid' in which continents are floating. To all appearances, this material is solid rock, but under the extreme pressure and temperature to which it is subjected, it actually flows like a liquid, albeit very slowly. Its specific gravity of 3.3 is high enough to insure that continents cannot sink.

Given these figures, it should be possible to calculate the thickness of an average continent. Hypothesize a continent that is absolutely flat and whose surface is exactly at sea level. (Substantial portions of Australia and parts of the Canadian shield come very close to this description.) The effective 'surface' of the SiMa fluid is actually the floor of the oceans, averaging approximately 13,000' (~4 km) below sea level. The weight of 13,000' of ocean water pressing down on the mantle wherever continents are not present complicates the formula somewhat. It becomes easier to think in terms of pressures, rather than the percentage of floating object that are submerged in the fluid.

To refer back to the example in Section 1, if a rectangular block of wood 10" thick, having a specific gravity of 0.7, is floating in water having a specific gravity of 1.0, 70% or 7" of the block will be submerged and 3" will be above the surface. In terms of pressures, the 3" above water is pushing down with a force proportional to 3" times its specific gravity (0.7), while the submerged 7" are being pushed up by water pressure with a force proportional to 7" times the difference in specific gravity between the water and the wood (1.0 - 0.7). Thus:

3" x 0.7 = 7" x 0.3

Floating Continent In the case of a sea level continent (e.g. the image at right), the 13,000' between the sea floor and its surface is pushing down with a force proportional to 13,000' x 2.7, but that force is partially offset by the force of 13,000' of sea water pushing down elsewhere on the mantle, 13,000' x 1.0. Thus the effective downward force from the continent is 13,000' x 1.7. This is equal to the force generated by the buoyancy of that portion of continent submerged into the mantle, S, times the difference in specific gravities (3.3 - 2.7, or 0.6). Thus:

1.7 x 13,000 = 0.6 x S

Then S = 36,833, or ~ 37,000', and the total thickness of our hypothetical continent is 37,000' + 13,000', approximately 50,000' or ~15 km.

Continental material extending above sea level is not, of course, buoyed by the weight of the sea water, and adds thickness to the continent at a rate of

1 + (2.7/(3.3 - 2.7))

or 5.5 feet in thickness for every foot of elevation. Therefore, when erosional sediments are being deposited above sea level, for every 5.5' of sediments deposited, the continent will gain 1' in elevation. (Of course, this may not be immediately obvious; the mantle 'fluid' is very viscous, and flows ever so slowly.)

It is interesting to note that in many places on the Earth, marine sedimentary deposits of up to 50,000' thickness have been reported, but this author has never seen a report of more than 50,000' of marine deposits. This is predictable from the above calculations. Sediments eroded on dry land are ultimately washed out to sea, to be deposited on the sea floor along continental margins. As soon as 50,000' of sediments have accumulated, the depositional surface has reached sea level. New erosional sediments are then washed over the old deposits and farther out to sea. The old depositional surface has effectively become dry land.


Rates of Isostacy:
The mantle flows very slowly, but it moves fast enough to stay ahead of most geological processes. Thus in most cases isostatic equilibrium - the balance that keeps continents floating where calculations say they should be - is maintained. The rate of isostacy can best be illustrated in Scandinavia, which 8,000 to 10,000 years ago was covered by a large ice cap. The weight of the ice caused Northern Europe to sink some 2,300' (700 m). In the 8,000 years since the ice melted, the land has risen about 1,800' (550 m) and it is rising still, at a rate of up to 3' (90 cm) per century. The average over 8,000 years is 0.225' (68 mm) per year. Put into a geological perspective, this implies that isostacy could compensate for redistribution of continental mass at a rate of 225,000' (68 km) per million years! Of course, no geological process known can redistribute continental material at this rate sustained over that long a time span, but a few processes can get ahead of isostacy for a short while.

Rates of deposition of eroded sediments rarely exceeds 20,000' (~6000 m) within a single geological period - typically 35-60 million years, or 1/3' (10 cm) per million years or less. Over a shorter time span, however, certain forms of deposition can exceed the rate of isostacy. One example is the formation, or at least the melting, of continental glaciers, as mentioned above. Another process is volcanism. Mt. Katmai in Alaska erupted in 1912, ejecting an aerosol of molten lava at essentially the speed of sound. The "Valley of Ten Thousand Smokes" was filled with tens of feet of tuff for 6-7 miles (~10 km) in perhaps 90 seconds! 30 to 50' (10-15 m) of volcanic deposits aren't significant to the isostatic balance of an entire continent, but sustained volcanic eruptions over an extended period can be.

The big island of Hawaii sits above a plume in the mantle - a rising column of hot molten material rising from deep within the Earth. The mountain thus formed is nearly 30,000' (9000 m) high; 15,000' (4500 m) above sea level, and nearly the same below to the ocean floor. Its volcanos are active today, and the island continues to grow. The Pacific plate, on which Hawaii sits, is drifting slowly to the northwest, and eventually will carry the island away from the plume, bringing its volcanism to a halt. To the north and west are the rest of the Hawaiian island chain, each island an extinct volcano which had previously been created by the same plume. The farther these islands are from the big island, the older they are, and also the lower in elevation. For once volcanism ceases, isostacy asserts itself, and the islands slowly sink back into the mantle. Beyond the oldest island of the Hawaiian chain stretch a row of submerged seamounts - sunken islands that have at last reached their isostatic equilibrium.

It can then be safely assumed that, barring some obvious short term perturbation like glaciation or volcanism, most continents are stable and very close to being isostatically balanced in their liquid mantle medium. But isostacy is a dynamic process; mountains erode, and their sediments are washed out to sea, to accumulate as sediments along the continental shelves. Also, continents tend to move primarily as solid blocks, so what happens in one part of a continent affects the rest of the continent as well. Thus, Scandinavia is still rising, and Venice is sinking, as Europe rotates slowly in response to the dictates of isostacy.


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File created on May 3, 1998.
Last updated November 2004.