Seismology and Earth’s Interior

Mass of the Earth• Spherical masses behave as if all mass located

at central point• g = GMe/R2 Me = gR2/G• g = 9.8 m/sec2

• R = 6,371,000m• G = 6.67 x 10-11 m3/(kg sec2)• Me = 9.8 x (6,371,000)2/(6.67 x 10-11)

= 6 x 1024 kg

Mass in the Earth

• Rotating bodies have a moment of inertia (I)• Corresponds to mass for linear motion• Rotational velocity used as velocity term• Generally of the form I = kMR2

• For a uniform sphere, k = 2/5• For the earth, K = 0.33• Hence, mass concentrated in center

Mass distribution in the Earth

• Model Earth as series of thin shells with given density

• Sum of masses must equal mass of the earth• Sum of moments of inertia must equal

moment of inertia of the earth

Gravity inside a Sphere• Gravitational attraction inside a spherical shell =

zero• Gravitational attraction inside a uniform sphere

drops linearly to zero at the center• In the Earth: Gravity at radius r = Gmr/r2

– Mass above radius r has no effect– Surprise – nearly constant from surface to top of core

• Pressure = weight of overlying shells– Thickness of shell x density x local gravity

How Seismographs Work

Seismic Waves

1. Assume the Earth is uniform.• We know it isn't, but it's a useful place to start. It's

a simple matter to predict when a seismic signal will travel any given distance.

2. Actual seismic signals don't match the predictions

• If we match the arrival times of nearby signals, distant signals arrive too soon

• If we match the arrival times of distant signals, nearby signals arrive too late.

• Signals are interrupted beyond about 109 degrees

3. We conclude:

• Distant signals travel through deeper parts of the Earth, therefore ..

• Seismic waves travel faster through deeper parts of the Earth, and ..

• They travel curving paths (refract)

• Also, there is an obstacle in the center (the core).

Why Refraction Occurs

Waves Travel The Fastest Path

Seismic Waves in the Earth

Seismic Waves

• P-Wave Velocity = /ρ = • S-Wave Velocity = =

Information Where We Need It Most

Properties of the Deep Earth

• P- and S-wave Velocities give us E, everywhere in the Earth

• Know density and pressure from mass-balance and moment of inertia

• Know composition from meteorites and mantle xenoliths

• Compare mechanical properties and density to rocks

Continental Drift is Impossible!

• Shear modulus of deep mantle is 300 Gpa: more than steel

• Therefore continental drift is impossible!• Fallacy: failure to recognize time scales• Seismic waves reflect properties on a scale of

seconds• Convection reflects properties on a scale of

years

Travel Time Curve

Inner Structure of the Earth

The overall structure of the Earth

Locating Earthquakes

Locating Earthquakes

Locating Earthquakes

Locating Earthquakes - Depth

Temperature: The Hard Part• Near surface gradient = 25K/km• Center of Earth would be 160,000 K at that

rate• We know mantle is solid (transmits S-waves)• Estimated mostly from experimental data– Extrapolating melting points to high pressure– Comparing observed elastic properties with lab

data