2. The earth, ca. 1800

3. Nevil Maskelyne and the Schiehallion experiment (1774)
Schiehallion (‘Sidh Chailleann’) Scotland
Nevil Maskelyne doing his impression of Ben Franklin d  F Ms
m.g
F = m.g.tan() = G.m.Ms/d2
ME = (RE2/d2).(Ms/tan()) ~ kg
m.g = G.m.ME/RE2
RE = m; VE = m3
 ~ 5.5 g/cm2 (initially found ~ 4.5)

4. Densities of common substances (all in g/cc)
Ice
Water
Seawater 1.025
Graphite 2.200
Granite ~2.70
Titanium 4.507
Iron
Copper 8.960
Mercury 13.58
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)

5. Mass distribution in earth’s interior
Period of precession
Moment of inertia
Period of spin
Torque (sun and moon trying to pull earth’s tidal bulge into plane of ecliptic)
I = i mi.ri2 ri mi
Higher
Earth has I much less than
expected for homogeneous sphere
Lower

6. View combining known density, moment of inertia,
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!

7. Earthquakes! The sources of seismic waves

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

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

10. Rupture continues to expand as a crack along the fault plane.
0 Seconds
Rupture expands circularly on fault plane, sending out seismic waves in all directions.
Focus
Fault cracks
at surface
5 Seconds
Rupture continues to expand
as a crack along the fault plane.
Rocks at the surface begin to
rebound from their deformed
state.
Fault crack
extends
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.

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

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

13. Surface waves Body waves
Focus
“sample” outer ca. 200 km,
but most energy in upper 10 km
Surface waves
Mantle
Body waves
Seismograph
Core S P

14. A mechanical seismograph

15. ‘Primary’ (first to arrive)
Anatomy of a seismic signal
Minutes 10 20 30 40 50
Surface waves P S
‘Primary’ (first to arrive)
‘Secondary’ (second to arrive)

16. P waves — analogous to sound
Wave direction

17. S waves—analogous to light
Wave direction

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

19. Real data is more complicated…

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

22. 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)
elastic modulus’ (stiffness)
Velocity is proportional to
density (momentum)
F/m2 — kg/s2m
stress
strain
Elastic modulus =
Unitless; e.g., ∂Volume/Volume
Two elastic moduli:
• Bulk modulus (): isotropic compression; springiness of bonds
• Shear modulus (): resistance to change in shape

23. Speeds of seismic waves
General relation:
V = (modulus/)0.5
VP = ([+4/3]/)0.5
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

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

25. Seismogram C
Seismogram B
Seismogram A
S wave 25 20
11-minute
interval at
8600 km
Time elapsed after start of earthquake (min)
8-minute
interval at
5600 km 15
P wave 10 5
3-minute
interval at
1500 km
2000
4000
6000
8000
10,000
Distance traveled from earthquake epicenter (km)

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

28. Moment = Slip x Area x Elastic modulus
Moment magnitude
Moment = Slip x Area x Elastic modulus
N.meters
Meters
Kg/s2.m
Meters2
Log10 of moment

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

36. Mg2SiO4 in upper mantle
Mg2SiO4 in lower mantle

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