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Jan 21, 2016
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are needed to see this picture.
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? ???