## Internal structure and densities of the solid worlds II - physical evidence

### Seismology

Deformation of solids:
• Stress: A mechanical force applied to a solid
• Strain: The resulting change in the solid's shape
Suppose we have a bar of stiff nylon suspended by one end. If we suspend weights from the free end, the force of the weights pulling on the bar is stress. When the bar responds by stretching slightly, the change in its length is strain.

Stiffness: A graph of this relationship shows a line whose slope is Young's modulus, which represents the solid's stiffness.

Strength: The amount of stress required to make the solid break, its tensile strength, represents the solid's strength.

Note: Stiffness and strength are not necessarily linked.
• A biscuit (1) is brittle - stiff but weak.
• Steel rebar (2) is stiff but strong.
• Nylon (3) is elastic but strong.
• Silly Putty (4) is elastic but weak.

Objects can be strained in three different ways:

Rubber band loaded in tension from Journey South.
• Elastic deformation: Generally, when a solid is strained, it will return to its original shape when the stress is removed. This is because its chemical bonds, although stretched, have not broken. E.G. stretch a piece of nylon and its shape changes as chemical bonds are stretched, storing energy, but when you stop pulling, the energy is released in the form of the work needed to restore the solid to its original shape.

Folded quartz veins and foliation.
• Ductile deformation: (A.k.a. "plastic" deformation) A solid that is strained past its zone of elastic deformation retains its new shape. This is because it has been strained to where chemical bonds have begun to break. In the Earth, we see ductile deformation manifested as folds. E.G. Silly-putty, when pulled, quickly loses its elasticity and deforms ductilely. In this case, energy is released in small increments on a microscopic scale as bonds are broken.

• Brittle deformation: Break enough chemical bonds, and the entire object breaks on a macroscopic scale, releasing large amounts of energy. In the Earth, we see breaks physically manifested as faults. The released energy is perceived as an earthquake.

Yield strength: In a typical trial, a solid would deform elastically up to a point, then ductility, then brittlely (it would break.) This gives us two measures of strength:
• Tensile strength: the transition to brittle deformation (i.e. breaking.)
• Yield strength: the transition from elastic to ductile deformation.

The real fun is that all of these parameters can vary depending on:

• Pressure: Increased pressure from all sides encourages ductile deformation rather than brittle.
• Temperature: Increased temperature encourages ductile deformation.
• Rate of deformation: A stress, when applied slowly, causes ductile defamation, but applied quickly causes brittle deformation. (Think of Silly Putty and other "non-newtonian fluids.")

Crater Glacier on Mt. St. Helens from Wikipedia
Thus in the planets we see:
• In a planet's uppermost layers, deformation quickly transitions from elastic to brittle.
• Below this, at sufficient pressure and temperature, materials primarily deform ductilely.
On a human scale, we see this transition in glacial ice (right). On a larger, scale, the same relationship holds for planets' rocky crusts.

Earthquakes result from the quick release of energy when brittle deformation occurs. As a result, they occur within a few tens of km of the surface.

### Earthquakes and Seismology:

Types of energy released when earthquake occurs - waves

• Body waves: Earthquake occurs at the focus, causing energy to propagate outward as body waves - waves that move through solids in three dimensions. There are two types:

• P-waves: Primary or pressure waves. As the wave passes, each particle of the substance it's passing through moves forward an back in line parallel with the direction of the wave's propagation. These can be thought of as push pull waves.
• S-waves: Secondary or shear waves. As the wave passes, each particle of the substance it's passing through moves forward an back in line perpendicular to the direction of the wave's propagation. - shake waves, if you will.

• Surface waves: Waves that propagate only along a surface or interface. Again, there are two types:

• R-waves: Short for Rayleigh-waves. Surface waves that cause particles on a surface or interface to oscillate up and down. The waves that cross the surfaces of bodies of water are Rayleigh-waves.
• L-waves: Short for Love-waves. Surface waves that cause particles on a surface or interface to oscillate from side to side.

Link to video of August 23, 2011 Virginia Earthquake seismic waves.

Wave speed: Each wave type travels with a characteristic speed.

• P wave: fastest
• S-wave: somewhat slower
• Surface waves: Slowest.

Thus, if you stand some distance from an earthquake epicenter, you feel P waves first, then S waves, then surface waves. The farther away you are, the longer the lag time between these waves. This lag can be used to locate the epicenter, provided three observers at separate locations keep track.

Seismic waves as emmissaries to Earth's interior: Early study of seismic waves revealed that they were both reflected and refracted by inhomogeneities within the Earth. The foremost observation, however, was that they didn't travel at uniform speed. The image at right indicates changes of wave velocity with depth for P and S waves. Note:

• Seismic waves propagate faster through denser material
• P waves propagate slower through liquids, and S waves aren't transmitted through liquids at all.

Some items of interest:

• The Moho: Near the turn of the 20th century, Croatian geophysicist Andrija Mohorovičić noted an abrupt acceleration of P and S waves between 20 and 90 km below the surface. This Mohorovičić discontinuity (mercifully known as the Moho) marks the interface between Earth's crust and mantle and was the first evidence leading to the mantle's discovery.

• The Low Velocity Zone (LVZ): Around 220 km depth, both P and S waves decelerate and weaken, indicating a zone of partial melting. We will explore its significance later.

• Olivine transformations: As one would expect, the speed of P and S waves increases with depth beneath the LVZ, as the material through which they travel becomes denser and denser through gravitational self-compression. Abrupt increases in speed occur at 400 and 670 km depth. These correspond to the depths at which olivine transforms into its high-pressure forms, wadsleyite and ringwoodite.

• 2900 km: At this depth radical changes abruptly occur. P waves slow down abruptly and S waves disappear altogether. This is consistent with their passing into a body of liquid.

• 5154 km: P waves suddenly accelerate, as if they are passing into a solid body.

Shadow zones: The presence of a molten substance starting at 2900 km is demonstrated by the S wave shadow that it casts. Moreover, refraction of P waves at the solid liquid interface "focuses" them so that a ring-shaped P wave shadow also exists.

### Moment of Inertia

This is a rotating object's tendency to resist changes in its rate of rotation and reflects the distribution of its mass around its rotational axis. You know about the effect that folding your arms has when you are spinning. This happens because when you move the mass of your arms closer to your axis of rotation, you alter your moment of inertia. Observations of how celestial bodies interact with one another gravitationally enable us to determine their moments of inertia and make inferences about the distribution of their mass.

The moment of inertia (I) of a rotating object is given by:

I = C M R2

where M is the object's mass, R is its radius, and C, the moment of inertia coefficient, is a parameter that depends on the object's internal distribution of mass.

The example at right contrasts C for hypothetical planets of identical mass and radius but different mass distributions.Observed C for some planets include:

• Moon: C = 0.39
• Mars: C = 0.365
• Earth: C = 0.33
• Saturn: C = 0.25
• Sun: C = 0.06
Thus, the moon is nearly uniform in density whereas the Sun is massively self-compressed. Earth has a significant concentration of mass at its center, in agreement with the other lines of evidence we have discussed.

### The differentiated Earth

The stratified Earth from Prentice Hall via Purdue University.
At this point, we have a developing picture of Earth's interior, divided into distinct physical and compositional regions:
• Crust: Light rocks of Earth's surface rich in Si and Al. Anywhere from 10 to 70 km. thick.

• Mantle: Bottom of crust down to 2900 km. Dense rocks rich in Fe and Mg. We occasionally see upper mantle rocks at the surface when they are brought up in volcanic conduits as xenoliths. Although we can't sample deeper layers, laboratory studies and behavior of seismic waves suggest that they consist of generally the same material at greater densities because of gravitational self-compression.

• Outer Core: From 2900 - 5154 km. Moment of inertia and Earth's overall mass tell us that it is much denser than the mantle. Seismic waves tell us that it is liquid. The abrupt seismic transition at 2900 km is the core-mantle boundary (CMB)

• Inner Core: From 5154 km to center. Moment of inertia and Earth's overall mass again suggest that it is much denser than the mantle. Seismic waves tell us that it is solid.
So, what might the inner and outer core be made of?

### Magnetic fields

Model of Earth's magnetic field from DKimages.
When an electric current travels in a circuit, it generates a magnetic field. Similarly, when a magnetic field moves or changes intensity, it induces current in nearby electrical paths. These two processes feed back on one another in active cores to sustain a planetary magnetic field. The energy to keep it going comes from movements in the fluid metallic core, driven by convection and the planet's rotation. This process requires that the core be metallic, because metals conduct electricity well. (Indeed, no known solid could support a magnetic field at deep Earth temperatures.) Thus, we know that the outer core is made of a substance that is:
• Liquid
• Dense enough to account for Earth's density paradox
• A good conductor of electricity.
Moreover, it is probably made of something that is:
• common in the galaxy
• has a relatively depleted chondritic concentration in Earth surface rocks
The most likely candidate is iron. Every line of evidence, including laboratory studies, points at the mantle being made of silicate rocks and the core of an iron alloy. specifically:
• The inner core: is a nickel-iron alloy.
• The outer core: is 5-10% less dense than pure iron. The remainder of the core must be
• lighter than iron,
• abundant in the Earth,
• likely to form a metallic alloy with iron.
Candidates include oxygen, silicon, sulfur, carbon, and possibly others, but the issue is unresolved.

### Gravitational anomalies

A final source of information about the structure of the deep Earth comes from variations in Earth's gravitational field. These indicate variations in the density of rock, as in the example at right. Their study reveals details of Earth's subsurface structure on large and small scales. For us now, they confirm that:

• Continental crust is light and buoyant compared to oceanic crust
• The crust is thicker overall beneath the continents.

And for fun, on 9/9/11, NASA's GRAIL Mission launched a pair of lunar satellites that created a detailed map of the moon's gravitational field before their mission ended in 2012.

Key concepts and vocabulary:
• Stress
• Strain
• Young's modulus
• Tensile strength
• Elastic deformation
• Ductile deformation
• Brittle deformation
• Yield strength
• Seismic waves
• Surface waves
• Rayleigh waves
• Love waves
• Body waves
• P waves
• S waves
• P and S wave lag time
• The Moho
• The Low Velocity Zone
• Olivine transfprmations
• Moment of inertia
• Moment of inertia coefficient C (Know general comparative values)
• Basic Earth layers
• Crust
• Mantle
• Outer core
• Inner core
• Core-mantle boundary (CMB)
• Mantle xenolith
• Magnetic field
• Chondritic concentrations
• Core composition - alloys of iron
• Gravitational anomalies
• Continental crust
• Oceanic crust