# Seismology and Earth’s Interior. 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.

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Seismology and Earth’s Interior

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

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

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 = 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

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

Information Where We Need It Most

Properties of the Deep Earth

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 - 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

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