# Isostasy

Now that we have addressed the concept of lithosphere and asthenosphere, we can consider the principle of  isostasy (or, simply, “isostasy”), which is an application of Archimedes’ law of buoyancy to the Earth. Knowledge of isostasy will help you to understand the elevation of mountain ranges and the nature of gravity anomalies. To discuss isostasy, we must first review Archimedes’ law.

Archimedes’ law states that when you place a block of wood in a bathtub full of water, the block sinks until the mass of the water displaced by the block is equal to the mass of the whole block
 The concept of isostasy. (a) Blocks of wood of different thicknesses float at different elevations when placed in water. Therefore, the pressure at point A is the same as the pressure at point B. (b) In the Earth, isostasy requires that the mass of a column drilled down to the level of compensation at A equals the mass of a column drilled at B, if isostatic equilibrium exists at both locations
(Figure a). Since wood is less dense than the water, some of the block protrudes above the water, just like an iceberg protrudes above the sea. When you place two wood blocks of different thicknesses into the water, the surface of the thicker block floats higher than the surface of the thinner block, yet the proportion of the thick block above the water is the same as the proportion of the thin block above the water. Thus, the base of the thick block lies at a greater depth than the base of the thin block. Now, imagine that you put two wood blocks of the same thickness but of different density in the water; this will be the case if one block is made of oak and the other is made of pine. The dense oak block floats lower than the less-dense pine block does. Note that, in the experiment, the pressure in the water at the base of the tub is the same regardless of which block floats above. Also, if you push down on or pull up on the surface of a block, it will no longer float at its proper depth. If we make an analogy between the real Earth and our bathtub experiment, the lithosphere plays the role of the wooden blocks and the asthenosphere plays the role of the water. For a given thickness of lithosphere, the surface of more buoyant lithosphere floats higher than the surface of less buoyant lithosphere, if the lithosphere is free to float. Further, the pressure in the asthenosphere, at a depth well below the base of the lithosphere, is the same regardless of thickness and/or density of the lithosphere floating above (if the lithosphere is floating at the proper depth). We call a depth in the asthenosphere at which the pressure is the same, regardless of location, a depth of compensation. With this image of floating lithosphere in mind, we can now state the principle of isostasy more formally as follows: When free to move vertically, lithosphere floats at an appropriate level in the asthenosphere so that the pressure at a depth of compensation in the asthenosphere well below the base of the lithosphere is the same. Where this condition is met, we say that the lithosphere is “isostatically compensated” or in “isostatic equilibrium.”

Another way to picture isostatic equilibrium is as follows. If a location in the ocean lithosphere and a location in the continental lithosphere are both isostatically compensated, then a column from the Earth’s surface to the depth of compensation at the ocean location has the same mass as a column of the same diameter to the same depth in the continental location (Figure b). Ocean basins exist because ocean crust is denser and thinner than continental crust, and thus ocean lithosphere sinks deeper into the asthenosphere than does continental lithosphere. Low-density water fills the space between the surface of the oceanic crust and the surface of the Earth.

Note that with isostasy in mind, we see that changing the relative proportions of crust and mantle within the lithosphere will change the depth to which the lithosphere sinks and thus will change the elevation of the lithosphere’s surface. This happens because crustal rocks are less dense than mantle rocks. For example, if we increase the proportion of buoyant crust (by thickening the crust beneath a mountain range or by underplating magma to the base of crust), the surface of the lithosphere lies higher, and if we remove dense lithospheric mantle from the base of the plate, the plate rises. If the lithosphere doesn’t float at an appropriate depth, we say that the lithosphere is “uncompensated.” Uncompensated lithosphere may occur, for example, where a relatively buoyant piece of lithosphere lies embedded within a broad region of less buoyant lithosphere. Because of its flexural rigidity, the surrounding lithosphere can hold the buoyant piece down at a level below the level that it would float to if unimpeded. The presence of uncompensated lithosphere causes gravity anomalies. Positive anomalies (gravitational pull is greater than expected) occur where there is excess mass, while negative anomalies (gravitational pull is less than expected) occur where there is too little mass.