seismology and earth’s interior. mass of the earth spherical masses behave as if all mass located...
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Seismology and Earth’s Interior
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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
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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
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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
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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
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How Seismographs Work
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Seismic Waves
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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.
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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
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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).
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Why Refraction Occurs
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Waves Travel The Fastest Path
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Seismic Waves in the Earth
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Seismic Waves
• P-Wave Velocity = /ρ = • S-Wave Velocity = =
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Information Where We Need It Most
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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
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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
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Travel Time Curve
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Inner Structure of the Earth
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The overall structure of the Earth
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Locating Earthquakes
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Locating Earthquakes
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Locating Earthquakes
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Locating Earthquakes - Depth
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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