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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/R 2 Me = gR 2 /G g = 9.8 m/sec 2 R = 6,371,000m G = 6.67 x 10 -11 m 3 /(kg sec 2 ) Me = 9.8 x (6,371,000) 2 /(6.67 x 10 -11 ) = 6 x 10 24 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 = kMR 2 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 = Gm r /r 2 – 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

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Information Where We Need It Most

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Properties of the Deep Earth

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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 - 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

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