SUPPORTING MATERIAL

Terminology of Rheology

Advection	Type of heat transport. This phenomenon occurs when water from a boiler flows through pipes and the pipes heat up. The water carries heat with it, and the heat conducts from the water into the metal. Thus, advection is the process by which a moving fluid brings heat into a solid or removes heat from a solid. In the Earth, heating by advection occurs where hot water or hot magma passes through fractures in rock, and heats the surrounding rock. Cooling by advection occurs where cold seawater sinks into the oceanic crust, absorbs heat, and then rises, carrying the heat back to the sea.
Brittle-ductile transition	Commonly used term that describes depth in the Earth below which brittle behavior is replaced by plastic processes (see under “behavior” below). The use of ductile is not correct, as brittle processes, like cataclasis, can also be ductile (= distributed strain) phenomena.
Brittle-plastic transition	Depth in the Earth where the dominant deformation mechanism changes from fracturing to crystal plastic processes (see under “mechanisms” below).
Competency	Relative term comparing the resistance of rocks to flow
Conduction	Type of heat transport. This phenomenon occurs when you place one end of an iron bar in a fire; heat gradually moves along the bar so that the other end eventually gets hot too. We say that heat flows along the bar by conduction. Note that iron atoms do not physically move from the hot end of the bar to the cool end. Rather, what happens is that the atoms nearest the fire, when heated, vibrate faster, and this vibration, in turn, causes adjacent atoms further from the fire to vibrate faster, and so on, until the whole bar becomes warm.
Convection	Type of heat transport. This phenomenon occurs when you place a pot of soup on a hot stove. Conduction through the base of the pot causes the soup at the bottom to heat up. The heated soup becomes less dense than the overlying (cold) soup; this density inversion is unstable in a gravity field. Consequently, the hot soup starts to rise, to be replaced by cold soup that sinks. Thus, convection is driven by density gradients that generate buoyancy forces and occurs by physical flow of hot material. Convection occurs when (1) the rate at which heat is added at the bottom exceeds the rate at which heat can be conducted upward through the layer, and (2) the material that gets heated is able to flow.
Failure stress	Stress at which material failure occurs.
Fracturing Deformation	Mechanism by which a rock body or mineral loses coherency.
Crystal plasticity	Deformation mechanism that involves breaking of atomic bonds without the material losing coherency.
Strength	Stress that a material can support before failure.
Ultimate strength	Maximum stress that a material undergoing work softening can support before failure.
Work hardening	Condition in which stress necessary to continue deformation experiment increases.
Work softening	Condition in which stress necessary to continue deformation experiment decreases.
Yield stress	Stress at which permanent strain starts to accumulate.

Material behavior

Brittle behavior	Response of a solid material to stress during which the rock loses continuity (cohesion). Brittle behavior reflects the occurrence of brittle deformation mechanisms. It occurs only when stresses exceed a critical value, and thus only occurs after the body has already undergone some elastic and/or plastic behavior. The stress necessary to induce brittle behavior is affected strongly by pressure (stress-sensitive behavior); brittle behavior generally does not occur at high temperatures.
Ductile behavior	A general term for the response of a solid material to stress such that the rock appears to flow mesoscopically like a viscous fluid. In a material that has deformed ductilely, strain is distributed, i.e., strain develops without the formation of mesoscopic discontinuities in the material. Ductile behavior can involve brittle (cataclastic flow) or plastic deformation mechanisms.
Elastic behavior	Response of a solid material to stress such that the material develops an instantaneous, recoverable strain that is linearly proportional to the applied stress. Elastic behavior reflects the occurrence of elastic deformation mechanisms. Rocks can undergo less than a few percent elastic strain before they fail by brittle or plastic mechanisms, and conditions of failure are dependent on pressure and temperature during deformation.
Plastic behavior	Response of a solid material to stress such that when stresses exceed the yield strength of the material, it develops a strain without loss of continuity (i.e., without formation of fractures). Plastic behavior reflects the occurrence of plastic deformation mechanisms, is affected strongly by temperature, and requires time to accumulate (strain rate–sensitive behavior).
Viscous behavior	Response of a liquid material to a stress. As soon as the differential stress becomes greater than zero, a viscous material begins to flow, and the flow rate is proportional to the magnitude of the stress. Viscous deformation takes time to develop.

Deformation mechanisms

Brittle deformation	Mechanisms by which brittle deformation occurs, namely fracture growth and frictional sliding. Fracture growth includes both joint formation and shear rupture formation, and sliding implies faulting. If fracture formation and frictional sliding occur at a grain scale, the resulting deformation is called cataclasis; if cataclasis results in the rock “flowing” like a viscous fluid, then the process is called cataclastic flow.
Elastic deformation	Mechanisms by which elastic behavior occurs, namely the bending and stretching, without breaking, of chemical bonds holding atoms or molecules together.
Plastic deformation	Mechanisms by which plastic deformation occurs, namely dislocation glide, dislocation creep (glide and climb; including recovery, recrystallization), diffusive mass transfer (grain-boundary diffusion or Coble creep, and diffusion through the grain or Herring-Nabarro creep), grain–boundary sliding/superplasticity.

Creep Parameters

Rock type	A	n	E*
	(MPa–ns–1)		(kJ⋅mol–1)
Albite rock	2.6 × 10–6	3.9	234
Anorthosite	3.2 × 10–4	3.2	238
Clinopyroxene	15.7	2.6	335
Diabase	2.0 × 10–4	3.4	260
Granite	1.8 × 10–9	3.2	123
Granite (wet)	2.0 × 10–4	1.9	137
Granulite (felsic)	8.0 × 10–3	3.1	243
Granulite (mafic)	1.4 × 10–4	4.2	445
Marble (< 20 MPa)	2.0 × 10–9	4.2	427
Orthopyroxene	0.32	2.4	293
Peridotite (dry)	2.5 × 104	3.5	532
Peridotite (wet)	2.0 × 103	4.0	471
Plagioclase (An75)	3.3 × 10–4	3.2	238
Quartz	1.0 × 10–3	2.0	167
Quartz diorite	1.3 × 10–3	2.4	219
Quartzite	6.7 × 10–6	2.4	156
Quartzite (wet)	3.2 × 10–4	2.3	154
Rock salt	6.29	5.3	102
Experimentally-derived creep parameters for common minerals and rock types. From Ranalli (1995) and other sources.

MORE EXPLORATION

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.

FIGURE S10.1. 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.

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 (Figure S10.1). 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 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.

FIGURE S10.2 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.

[14.12]

Animation (isostasy.swf)

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 S10.2). Ocean basins exist because ocean crust is denser and thinner than continental crust, and thus ocean lithosphere sinks deeper into the asthenosphere than continental lithosphere. Low-density water fills the space between the surface of the oceanic crust and the surface of the Earth.

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, 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 that it would float to if unimpeded.

SUPPORTING MATERIAL

Terminology of Rheology

Creep Parameters

MORE EXPLORATION

Isostasy

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