Earth, Our Environment - Class Notes
Chapter 5, Earth Processes: Physical Principles

We can directly sample a small fraction of earth

Radius of Earth: 6371 km

Deepest Drill Hole: 15 km

We rely on indirect imaging techniques that use seismic waves, gravity and magnetic variations to "see" beneath Earth's surface. These techniques form the core areas of study in the field called geophysics - the merging of geology and physics.We will examine:


Recall that the density is the mass per unit volume:

Density = Mass/Volume

The density of Earth generally increases with increasing depth. The values of density range from about 2.7 g/cm3 near the surface to about 13 g/cm3 near the center.


Density, Pressure, and Temperature

Within Earth, both pressure and temperature increase with depth. The density of a material will increase if pressure is applied to the material (the volume decreases). If a material is heated, it expands and the density decreases.

The pressure can become so great that a mineral becomes unstable and changes to another. For example, olivine, a major component of the upper mantle, converts into a compact polymorph called spinel at about 410 km into Earth. We call this change a "phase transition". Another important transition occurs at 660 km depth.

[Study Figure 5.2 on page 110 of the text]


Elastic material like rubber bands or sponges are materials that return to their original shape after a "deforming force" is relieved. In the geosciences, the most important deforming forces are stresses. Stress is a force per unit area, and can be compressional (squeeze) or tensional (pull), or shear (twist). Compressional and tensional stress cause a material to change volume, shear stresses cause an object to change shape (without a volume change). The term for the measure of deformation of a material, either a volume change or a shape change, is call strain.

Elastic Moduli

Different elastic materials respond to stresses with a different degree of strain. For example, if I pull on a sponge it deforms much more easily than a rock. The elastic modulus is the measure of a material's resistance to strain.

Elastic Modulus = Stress / Strain

Just like density, the elastic moduli change with pressure and temperature. Pressure tends to increase the modulus, temperature tends to decrease the modulus. A rock's elastic moduli are characteristic of that rock type and are controlled by the rock's mineral content. We can measure a rock's elastic moduli in a laboratory.

If the stress is a shear, we call the modulus the shear modulus; if the stress is a compression, we call the modulus the bulk modulus.

Seismic Waves

In elastic material, disturbances that transmit energy called elastic waves. Seismic waves are elastic waves that travel through Earth.

The speed, or velocity at which these waves travel depends on the elastic moduli and the density of the rock

Equation for Seismic Velocity

There are three main types of seismic waves:

P waves travel fastest and thus are the first waves to arrive. They are sound waves that travel through Earth.

S waves are also called "shear waves" because they transmit shear strains through Earth. They travel slower than P waves but are usually larger than P waves.

Both P and S waves travel through the "body" of Earth and are collectively known as "body waves".

Surface waves travel along Earth's surface and are the largest waves observed at distance from shallow earthquakes.

The different seismic waves transmit different types of ground motion (or strain).

[Study Figure 5.5 on page 112 of the text]


Seismometers and Seismographs

To record seismic waves, seismologists operate a global network of seismic recording systems. A seismic recording system consists of two parts: a sensor and a recording system. The sensor is call a seismometer and it is the instrument that detects ground vibrations (it's like a microphone). The recording system records the vibrations picked up by the seismometer. It may save the record to a sheet of paper or directly to a computer disk. A plot of a ground motion with time varying along the horizontal axis is called a seismogram.

Wave Propagation

Like a pebble dropped in water, an earthquake (or explosions) radiates waves in all directions. These waves can be recorded on seismic systems and then analyzed to provide details about the part of Earth through which they propagated. By collecting seismograms from many earthquakes and many places, we have been able to unravel the internal structure of Earth. Seismic waves are influenced by Earth geology in several ways. Two important interaction between the rocks and the waves are refraction and reflection.

Many observed waves are combinations of reflections and refractions.

Travel Times

Two ways that we study Earth using seismic observations are travel time and normal mode analyses. The travel time is the time a wave takes to travel from the "source" to a seismometer. By collecting many travel times, we can perform an "ultra-sound" of Earth and identify relatively fast and slow regions within the planet. For the most part, Earth is radially symmetric (velocity is more or less constant at a particular depth). Even a wave that take 10's of minutes to travel through Earth generally arrives only a few seconds "off" from the time predicted using a simple Earth model. Those small differences are used to identify the variations in subsurface geology (or temperature) within Earth. That process is called seismic tomography.

[ Study Figures 5.8, 5.9, 5.14, 5.15, and 5.16 in the text]

Normal Modes

"Normal Modes" are slow, global vibrations of Earth excited by earthquakes. They change Earth's shape very slowly over broad regions, and they can last for many days (sometimes months) after a large earthquake. The time it takes a normal mode to complete an oscillation tells us information about Earth. For example, we know the inner core is not fluid because we have observed normal modes that indicate that the inner core can sustain shearing motions (i.e. it is not fluid).

[Study Figures 5.10 and 5.11 on pages 117-118 of the text]

Seismic Velocity Variations in Earth

The Crust

We live on the continental crust and we can see variations in rock type on the surface. Thus, it is not surprising that we see variations beneath the surface as well, but the average properties of the crust are important. The boundary between the crust and mantle is called the Moho - short for Mohorovicic "discontinuity". This region of rock transition greatly affects waves traveling 10's to 100's of kilometers.

Seismic Velocity Variations in the Mantle

As you might expect, the phase transitions near 410 and 660 km cause an increase in seismic velocity at those depths (that's how we first hypothesized that those transitions exist).


Mineral Transition

Effect of Temperature


Olivine -> [beta]-spinel

Cooler makes transition shallower


[beta]-Spinel -> [gamma]-spinel


[gamma]-spinel -> Perovskite

Cooler makes transition deeper

Seismic Velocity in Earth's Core

The outer core is a fluid, which by definition cannot transmit shear waves. The P-velocity in the outer core is also substantially lower than that in the lower mantle. The decrease in velocity from lower mantle into core produces an effect called the "Shadow Zone". This shadow is really a distance range where direct P and Waves are "blocked out". It's as if an earthquake was a flash bulb briefly illuminating Earth, but the core casts a shadow on the far side of Earth.

[Study Figure 5.13 on page 119]

The inner core is believe to be solid, based on normal mode observations. We can however, see the boundary between the inner and outer core with seismic body waves.



Gravity is an attraction between two masses. It is one of the four fundamental force types we discussed in chapter 2.

The strength of "gravitational attraction" is proportional to the product of the two masses, and inversely proportional to the square of the distance between the masses. In Symbols:

Force of Gravity

where Fg is the force of gravity, G is the Gravitational Constant, M and m are the masses of the two objects, and r is the distance between the masses.

On Earth's surface, the attraction is approximately

mass x 9.8 m/sec2

(we call this our weight). The value varies by about 0.5% between the equator and poles, due to the effects of Earth's rotation.

Gravity Anomalies

As you might expect, since gravity depends on the attraction of masses, more mass in a given region will result in stronger gravity. That's true, and we use small observable variations in gravity to investigate the variation in mass distribution within Earth. Generally, we work with maps or diagrams of gravity anomalies, which are differences between the observed gravity field and that predicted by simple models of Earth. We generally "correct" measured gravity values for differences in elevation (Free-Air Correction), and differences in topography (Bouguer Correction).


A very important application of gravity in geoscience investigations is the concept of isostasy. The basic concepts of isostasy can be understood by studying floating wooden blocks in water. The height of the block above the water surface depends on two factors:

[Study Figures 5.22 and 5.23 on page 126 of the text]

We can calculate relative heights of two blocks of different thickness using the concept of depth of compensation and principle of isostasy.

Isostatic Calculations

Essentially, you must balance the weight of a "column". First, you pick the depth of compensation - a depth within the fluid that is beneath all the "blocks". Then you compare the weight in each column, they should be equal.

[Study Focus box 5.2 on pages 128-129 of the text]


Isostasy and Topography

How do we apply these ideas to Earth? The density of continental crust is about 2.7 g/cm3, the density of the upper mantle is about 3.3 g/cm3. Think of the crust as the blocks, and the mantle as a fluid (that's how it behaves over long time periods).

It turns out that many mountain ranges are elevated because they have crustal "roots". Just like the tall wooden blocks they are riding high because the crust beneath mountains is thicker than typical crust.

In some cases, elevated land may not have any substantial "root", but is may simply be composed of lighter rocks. In yet other cases, a small feature on the crust can be supported by the rocks beneath it. We call that regional compensation.


Compensation Mechanism


Variation in "root" thickness


Variation in density

Regional Compensation

Small mass supported by underlying "plate"



If you have seen a compass, you have seen the result of Earth's Geomagnetism. Fluid motions in the outer core produce a magnetic field that we observe at Earth's surface. The motion of the electrical-conducting liquid iron produces a self-sustaining electro-magnetic system called the geodynamo. Similar to gravity, we can also measure variations in Earth's magnetic field. They change with time and position on Earth. Temporal changes reflect changes in the geodynamo. Spatial changes reflect the inherent nature of the geomagnetic field and variations in subsurface geology.

Geoscientists use geomagnetic measurements in several ways:

Historical studies of the strength and orientation of Earth's magnetic "field" document changes in the magnetic field. These changes suggest that convection in the core proceeds at a rate of 10's of km per year - about a million times faster than the tectonic plates move.


Inclination and Declination

Earth's magnetic field" has a direction - that's why compasses point "northward". But that's only the horizontal direction of the field. The magnetic field also has a "vertical component".

In truth, the direction a compass points varies from place to place on Earth. The deviation of the magnetic field from true north is called declination. The steepness with which the magnetic field points toward Earth's center is called inclination.

Because Earth's magnetic field resembles that of a bar-magnet (with a north and south pole), the inclination angle tells us approximately what latitude (how far north) we are. The magnetic field flows into Earth at the north magnetic pole (points down), and out of Earth at the south magnetic pole (points up). At the equator, the field is horizontal.

Rocks are Magnets

Many rocks, because they contain iron, have an "intrinsic" magnetization. Their magnetic "strength" is usually very small, but measurable. The useful feature of rock magnetization, is that the orientation of a rock's intrinsic magnetization is "frozen" in while the rock forms (or is metamorphosed). For example, when a magma cools, there is a specific temperature (called the Curie temperature, which varies with rock the minerals) at which the rock "records" the orientation of ambient magnetic field.

In essence, rocks maintain records of the magnetic field throughout Earth's history. We will see that the magnetic field has changed throughout geologic history, and many times actually flipped its "polarity" (exchange the north and south poles).

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Prepared by: Charles J. Ammon
March 1997