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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/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 = √(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