The earth, ca. 1800

Nevil Maskelyne and the Schiehallion experiment (1774) Schiehallion (‘Sidh Chailleann’) Scotland Nevil Maskelyne doing his impression of Ben Franklin MsMs  F = m. g. tan(  ) = G. m. M s /d 2 F m.gm.g d m. g = G. m. M E /R E 2 M E = (R E 2 /d 2 ). (M s /tan(  )) ~ kg R E = m; V E = m 3  ~ 5.5 g/cm 2 (initially found ~ 4.5)

Densities of common substances (all in g/cc) Ice0.917 Water1.000 Seawater1.025 Graphite2.200 Granite~2.70 Titanium4.507 Iron7.870 Copper8.960 Mercury13.58 Gas: proportional to P/RT Two options: sub-equal mix of metal and rock or… an ideal gas, w/ high density at high P (B. Franklin)

Period of precession Period of spin Torque (sun and moon trying to pull earth’s tidal bulge into plane of ecliptic) Moment of inertia I =  i m i. r i 2 mimi riri Higher Lower Earth has I much less than expected for homogeneous sphere Mass distribution in earth’s interior

Kraemer, 1902 View combining known density, moment of inertia, oblateness, rigidity of surface rocks, and topography Note bad for a bunch of turn-of-the-century quacks!

Earthquakes! The sources of seismic waves

Earthquake nomenclature Ground Hypocenter (‘focus’) Fault plane Epicenter Anticenter Other side of the earth

Basic types of faults Normal: Hanging wall down Thrust (‘reverse’): Hanging wall up Strike-slip Left lateral Right lateral Ground Fault plane Foot wall Hanging wall Fault trace (bird’s eye view) Dip-slip (cut-away view)

Focus 0 Seconds Rupture expands circularly on fault plane, sending out seismic waves in all directions. 5 Seconds Rupture continues to expand as a crack along the fault plane. Rocks at the surface begin to rebound from their deformed state. 10 Seconds The rupture front progresses down the fault plane, reducing the stress. 20 Seconds Rupture has progressed along the entire length of the fault. The earthquake stops. Fault cracks at surface Fault crack extends

The fault plane of the Landers earthquake (eastern California shear zone; 1992) Displacement on fault plane

Brittle Ductile Fault plane; episodic rupture Broad zone; continuous plastic shear Ca km deep The broader context of faulting

Focus Mantle Seismograph Core SP “sample” outer ca. 200 km, but most energy in upper 10 km

A mechanical seismograph

Minutes Surface waves 0 PS ‘Primary’ (first to arrive) ‘Secondary’ (second to arrive) Anatomy of a seismic signal

Wave direction P waves — analogous to sound

Wave direction S waves—analogous to light

Wave direction Love wave (analogous to a snake or shaken rope) Rayleigh wave (analogous to ocean surface) Wave direction Surface waves

Real data is more complicated…

Normal modes (‘natural’ or ‘harmonic’ oscillations) Toroidal (torsional, shearing motion) Spheroidal (radial motion) On earth, periods are ca. tens of minutes

Speeds of seismic waves Surface and normal modes have complex velocity dependencies; take 11d to learn about these! Body waves are simpler (and more important for studying earth’s interior) Velocity is proportional to elastic modulus’ (stiffness) density (momentum) Elastic modulus = stress strain Unitless; e.g., ∂Volume / Volume F/m 2 — kg/s 2 m Two elastic moduli: Bulk modulus (  ): isotropic compression; springiness of bonds Shear modulus (  ): resistance to change in shape

Speeds of seismic waves V = (modulus/  ) 0.5 V P = ([  +4/3  ]/  ) 0.5 General relation: V S = (  /  ) 0.5 For finite  and , V P must be faster than V S  = 0 in fluids, so V P drops sharply and V S goes to 0 when waves hit a solid/fluid boundary

Seismograph Focus Seismograph Epicenter Locating the hypocenter using networks of multiple seismographs

Distance traveled from earthquake epicenter (km) Time elapsed after start of earthquake (min) 3-minute interval at 1500 km , Seismogram A 11-minute interval at 8600 km 8-minute interval at 5600 km Seismogram B Seismogram C S wave P wave

Amplitude =23 mm Richter magnitude Amplitude (mm) Interval between S and P waves (s) Distance (km) P S S-wave interval = 24 secondsP-wave measure the amplitude of the largest seismic wave… …and the time interval between the P- and S-waves (I.e., the distance from the epicenter. Connect the points to determine the Richter magnitude.

Moment magnitude Moment = Slip x Area x Elastic modulus N. meters Meters Meters 2 Kg/s 2. m Log 10 of moment

The Mercalli Intensity scale (earthquake intensities for people who don’t like numbers and are easily scared) Board

Mg 2 SiO 4 in upper mantle Mg 2 SiO 4 in lower mantle

The core’s density is less than that of pure Fe. Requires a low-mass Alloying agent. S? O? H? ???