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
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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 = √(𝐾 +
4𝐺
)
3
/ρ =
𝐸 1−𝜈
ρ 1+𝜈 1−2𝜈
• S-Wave Velocity =
𝐺
ρ
=
𝐸
√(
2𝜌 1+𝜈
)
Information Where We Need It Most
Properties of the Deep Earth
• P- and S-wave Velocities give us E, 𝜈
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