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The earth, ca. 1800

Nevil Maskelyne and the Schiehallion experiment (1774)

Schiehallion (‘Sidh Chailleann’) ScotlandNevil Maskelyne doing his impression of Ben Franklin

Ms

F = m.g.tan() = G.m.Ms/d2

F

m.g

d

m.g = G.m.ME/RE2

ME = (RE2/d2).(Ms/tan()) ~ 6.1024 kg

RE = 6.37.106 m; VE = 1.1.1021 m3

~ 5.5 g/cm2 (initially found ~ 4.5)

Densities of common substances (all in g/cc)

Ice 0.917Water 1.000Seawater 1.025Graphite 2.200Granite ~2.70Titanium 4.507Iron 7.870Copper 8.960Mercury 13.58Gas: 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 mi.ri

2 miri Higher

Lower

Earth has I much less thanexpected 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

AnticenterOther 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 wallHanging wall

Fault trace

(bird’s eye view)

Dip-slip (cut-away view)

Focus0 SecondsRupture expands circularly on fault plane, sending out seismic waves in all directions.

5 SecondsRupture continues to expand as a crack along the fault plane. Rocks at the surface begin to rebound from their deformed state.

10 SecondsThe rupture front progresses down the fault plane, reducing the stress.

20 SecondsRupture has progressed alongthe entire length of the fault.The earthquake stops.

Fault cracksat surface

Fault crackextends

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. 10-30 km deep

The broader context of faulting

Focus

Mantle

SeismographCoreS P

“sample” outer ca. 200 km,but most energy in upper 10 km

A mechanical seismograph

Minutes

Surface waves

0

P S

10 20 30 40 50

‘Primary’ (first to arrive)

‘Secondary’ (second to arrive)

Anatomy of a seismic signal

Wave directionWave direction

P waves — analogous to sound

Wave directionWave 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 = stressstrain

Unitless; e.g., ∂Volume/Volume

F/m2 — kg/s2m

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

VP = ([+4/3]/)0.5

General relation:

VS = (/)0.5

• For finite and , VP must be faster than VS

• = 0 in fluids, so VP drops sharply and VS goes to 0 when waves hit a solid/fluid boundary

Seismograph

FocusSeismograph

Seismograph

Epicenter

Locating the hypocenter using networks of multiple seismographs

Distance traveled from earthquake epicenter (km)

Tim

e e

lap

sed

aft

er

sta

rt o

f eart

hq

uake (

min

)

3-minute interval at 1500 km

2000 4000 6000 8000 10,000

25

20

SeismogramA

11-minuteinterval at8600 km8-minute

interval at5600 km

15

10

5

0

SeismogramB

SeismogramC

S wave

P wave

Amplitude=23 mm

Richtermagnitude

Amplitude(mm)

Inte

rval b

etw

een

S a

nd

P w

aves (

s)

Dis

tan

ce (

km

)

P S

S-wave interval = 24 secondsP-wave

measure the amplitude of the largest seismic wave…

…and the timeinterval between the P- and S-waves (I.e., the distance from the epicenter.

Connect the points to determine theRichter magnitude.

Moment magnitude

Moment = Slip x Area x Elastic modulusN.meters Meters

Meters2Kg/s2.m

Log10 of moment

The Mercalli Intensity scale

(earthquake intensities for people who don’t like numbers

and are easily scared)

Board

Mg2SiO4 in upper mantle

Mg2SiO4 in lower mantle

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