17.2: Isostasy, Eustasy, and Sea Level

Essential to Know

• The level at which a solid floats in a liquid is determined by the relative densities of the solid and the liquid.
• Solids of equal density float in a liquid with the same percentage of their volume submerged.
• Two solids of different densities will float in a liquid in such a way that the solid with the greater density has a greater fraction of its volume submerged than the less dense solid.
• Lithospheric plates float on the asthenosphere. Because oceanic crust is denser and thinner than continental crust, the surface of the oceanic crust is always lower than the surface of the continental crust.
• Changes occur in the density and thickness of lithospheric plate sections as a result of various processes. The affected plate section rises or falls in response to such changes in a process called “isostatic leveling.”
• Isostatic leveling is slow. Equilibrium may not be achieved for millions of years after an event, such as the start or end of an ice age, that changes the distribution of glaciers.
• Sea level changes on a section of coast as the section of the plate rises or falls isostatically. Isostatic sea-level changes occur at different rates on different coasts.
• Eustatic sea-level changes are caused by changes in the volume of ocean water or in the volume of the ocean basins that occur as a result of a variety of plate tectonic and climatic change processes.
• Eustatic changes of sea level take place simultaneously and uniformly throughout the world. Eustatic equilibrium is easily and quickly attained.
• Changes of sea level on different sections of the world’s coasts occur at different rates, and even in different directions, because of the interaction of eustatic and isostatic changes.

Understanding the Concepts

Solid objects will sink through a fluid in which they are placed if the density of the solid is higher than that of the fluid. For example, a rock thrown into a pond sinks to the bottom. Solid objects whose density is less than that of the fluid will float. For example, wood or Styrofoam will float on water, and helium balloons will float on air.

When a solid object floats on a liquid, the depth to which the object is immersed is determined by its density and the density of the liquid. A simple principle describes this relationship. Called Archimedes’ principle, it states that the floating solid will be immersed in the liquid deep enough that the water it displaces has exactly the same total mass as the solid.

We can understand Archimedes’ principle by considering a rectangular block of wood floating on water (Fig. CC2-1). If the wood has a density of 0.5, or half the density of water, the wood floats with exactly half of its volume underwater and half exposed. If the wood has a density of only 0.1, or one-tenth the density of water, the wood floats with only one-tenth of its volume underwater and nine-tenths exposed (Fig. CC2-1a). If we place a weight on top of the less dense piece of wood, the wood is forced to sink into the water. It sinks until the mass of the total volume of water displaced is equal to the total mass of the wood plus the weight (Fig. CC2-1b).

Figure CC2-1. Archimedes’ principle determines how much of a floating solid’s volume is below the surface. The solid floats at a depth such that the weight of the volume of water or other fluid that it displaces (that is, the volume of the part of the solid that is below the water or fluid surface level) equals the total weight of the solid. (a) Lower-density materials will float higher than higher-density materials. (b) Adding weight to a floating, low-density solid increases its mass and causes it to float lower and thus displace more water. The volume of water displaced will have a weight that is equal to the total weight of the floating solid plus the added weight that it supports.

If two pieces of wood have the same density but different thicknesses, the thicker piece will float with its upper surface higher above the water surface than the thinner piece, and it will extend deeper into the water (Fig. CC2-2). The two pieces have the same percentage of their individual volumes submerged. If we have two pieces of wood of identical dimensions but different densities, the wood with higher density will float lower in the water (Fig. CC2-1a). This effect can be observed in a river, lake, or ocean. For example, most logs or driftwood pieces float with much of their volume immersed below the waterline. In contrast, Styrofoam and balsa wood seem almost to sit on the water, because their low density means that only a small percentage of their volume is immersed.

Figure CC2-2. Solids of the same density but of different thicknesses always float with the same proportion of their volume below the surface. Thicker blocks float with their upper surface higher above the surface of the fluid on which they float, and their lower surface deeper below.

Lithospheric plates float on the fluid surface of the asthenosphere in the same way that wood floats on water. Therefore, a buoyancy equilibrium is established in which the plates float freely on the material beneath them at a level that is determined by their density and thickness. This level is called isostasy, or “isostatic equilibrium.”

Continental crust has a lower density than oceanic crust (Chap. 4). Therefore, lithospheric plates covered with continental crust float with a smaller percentage of their volume “submerged” than plates covered with oceanic crust. If the plates with continental crust and oceanic crust were the same thickness (Fig. CC2-3), the upper surface of the continental crust plate (the land surface) would be higher than the surface of the oceanic crust plate (the seafloor). In addition, the lithosphere-asthenosphere boundary would be shallower (farther from the Earth’s center) under the continents than under the seafloor. However, lithospheric plates with oceanic crust are thinner than those with continental crust. Because the two types of crust are of different thicknesses, the lithosphere-asthenosphere boundary is shallower below ocean crust than it is below continental crust (Fig. CC2-3), and the continent surface is more elevated above the oceanic crust surface than it would be if ocean and continental crust were the same thickness.

Figure CC2-3. Isostasy is the condition in which blocks of lithosphere float on the asthenosphere at the equilibrium level determined by Archimedes’ principle. Above the compensation level (the depth at which the asthenosphere behaves as a fluid such that it can be displaced by floating lithospheric plates), the total weight of a column of continental crust plus mantle at isostasy will equal the total weight of a column of water, sediment, oceanic crust, and mantle. They do not quite do so in this figure, because the numbers are rounded.

If the density and thickness of the lithospheric plates were invariable, the continents and seafloor would always remain at a fixed equilibrium height above the asthenosphere. However, both the density and the thickness of lithospheric plates are altered by a variety of processes. First, the crust can be heated, which reduces its density; or cooled, which increases its density. Second, the thickness of the crust can be increased by the formation of mountains or volcanoes or by the deposition of large amounts of sediment, or it can be thinned by the erosion of mountains or stretching of the lithospheric plate. Third, the thickness of the lithospheric plate can be increased by the cooling and solidification of upper mantle material. This material is added to the bottom of the plate. Conversely, the plate can be thinned by the heating and melting of mantle material on the underside of the plate. Finally, the volume and mass of the continental crust can be increased by the development of glaciers, or decreased if glaciers melt, or altered by several other means, such as the growth of coral reefs.

If the density of a section of lithospheric plate is increased, it sinks until it reaches its new equilibrium level in a process known as isostatic leveling (Fig. CC2-4). Similarly, crust whose density has decreased will rise isostatically. Changes in thickness of the crust will also cause isostatic leveling (Fig. CC2-4).

Figure CC2-4. Isostatic leveling takes place in response to crustal density changes, plate thickening, and plate loading processes. (a) As oceanic crust moves away from an oceanic ridge, it cools, its density increases, and it sinks lower in the asthenosphere. The plate also thickens as mantle material solidifies and is accreted to the cooling underside of the plate. (b) Volcanoes formed at hot spots add mass to the crust. The increased mass causes the plate to bend and sink lower under the volcano, especially after the old volcano moves away from a hot spot and cools, thus increasing its density. (c) A section of continental crust on which glaciers are formed will sink to a new isostatic equilibrium because of the additional weight of the glacier (like the wood in Figure CC2-1b). If the ice melts, the continent will rise in a process called “isostatic rebound” until it reaches its new equilibrium level. Isostatic changes take place very slowly compared to the climate changes that can cause large variations in the area of the continents that is covered by glaciers.

Isostatic leveling is very slow because the asthenosphere is very viscous and flows extremely slowly to accommodate the rising or sinking lithospheric plate. The processes that cause changes in isostatic level are often localized to certain sections of a lithospheric plate and its overlying crust. Therefore, one section of a plate may be rising while another is sinking. Lithospheric plates can bend to accommodate this process. When the section of a lithospheric plate that supports the edge of a continent changes its isostatic level, sea level rises or falls along this coast but does not necessarily change on other coasts.

Sea level can be altered not only by isostatic leveling of the continents, but also by processes that increase or decrease either the volume of ocean water or the volume of the ocean basins. Changes in water volume or in ocean basin volume cause changes in sea level that occur simultaneously and almost uniformly along all the world’s coasts. Simultaneous worldwide changes in sea level are called eustatic changes (Fig. CC2-5b).

Figure CC2-5. (a) Isostatic sea-level changes take place when the land rises or falls while the seafloor and ocean depth remain the same. In this case, a continent that was previously depressed by the weight of an ice sheet rises slowly, exposing more of the continent to the atmosphere. (b) Eustatic sea-level changes take place when the volume of water in the oceans changes. In this case, the ocean has cooled and the water has been transferred to an ice cap on the land, thus lowering the sea level. Notice that the continent has not sunk lower in the asthenosphere in this diagram. In the situation depicted, the continent would eventually sink isostatically, but isostatic changes are much slower than eustatic changes.

Eustatic sea-level changes can be caused by several processes. For example, the volume of water in the oceans can be increased by the addition of water from melting glaciers or by elevation of the average temperature of ocean water that causes the water to expand. Correspondingly, the volume of ocean water can be decreased by increased glaciation or by a decline in average ocean water temperatures.

The volume of the ocean basins (actually the volume available for seawater to fill below a fixed level, independent of vertical movements of the continents) can be decreased if a larger percentage of the ocean basin floor is occupied by oceanic ridges. During the parts of spreading cycles when continents are being broken up, such as at present, there are many continents moving apart and many oceanic ridges between them. Hence, the percentage of the ocean floor covered by oceanic ridge is larger than it is during periods of reassembly of the continents. As a result, the ocean basin volume tends to be diminished, and sea level is correspondingly high.

Changes in the rate of seafloor spreading within a spreading cycle also affect sea level. When seafloor spreading is fast, the young, warm oceanic crust extends far from each oceanic ridge. Therefore, the volume of the ocean basin is reduced, sea level is higher, and more continental crust is covered by oceans. When seafloor spreading is slow, a smaller amount of young, warm oceanic crust is produced, the volume of the ocean basins is increased, and sea level is lower. During periods when the Earth’s continents are assembled in supercontinents such as Pangaea, the number of oceanic ridges and the rate of seafloor spreading are reduced. Therefore, young, warm oceanic crust covers a smaller percentage of the ocean floor, the ocean basin volume is increased, and sea level is lower. The processes, just described, that affect the volume of the ocean basins are complicated and interact with each other as the various plate tectonic processes simultaneously change the thickness, relative abundance, and isostatic level of the continental and oceanic crusts. At the same time, climate changes, which themselves may be linked to tectonic processes, also change the volume of water in the oceans.

Processes that alter sea level occur on a variety of different timescales, from centuries to millennia. Eustatic equilibrium is reached quickly in response to such changes, whereas isostatic equilibrium is attained very slowly. Sea level may be rising, static, or falling on any individual section of the world’s coasts as various eustatic and isostatic changes work in concert or in opposition in different regions.

At present, there is concern that human enhancement of the greenhouse effect (Chaps. 1, 7, CC9) will lead to substantial additional global warming. One fear is that if sufficient warming occurs, it will increase the volume of ocean waters as the average temperature increases and the water expands, and as partial melting of the polar ice sheets contributes additional water. The result is likely to be an acceleration in the eustatic rise in sea level, which would have severe consequences because many coastal regions and cities would be inundated by the sea. Indeed, the acceleration of the rate of sea level rise has been observed in currently available data.  Therefore, measuring the current rate of eustatic sea-level change is considered to be critically important.

Measurement of the rate of eustatic change of sea level is complicated by the interaction of isostatic and eustatic changes that occur simultaneously on any given section of coast. For example, the sea-level change measured on the northeast coast of the United States will be the net result of several processes: rising sea level due to any greenhouse warming effect, rising sea level due to progressive cooling and isostatic sinking of the continental crust, and falling sea level due to isostatic rise caused by the geologically recent melting of the ice age glaciers that once lay on this crust. As a further complication, human activities such as groundwater and oil withdrawal cause the subsidence of certain sections of the coast. Because of these complicated interactions, we are able to measure any greenhouse-induced sea-level rise only by studying sea level change on many different coasts or by extremely precise and difficult satellite measurements.