1. Structure of Earth as imaged by seismic waves
crust
upper mantle
transition zone
lower mantle
D”, core-mantle boundary layer
core-mantle boundary
outer core
inner core
2000
4000 km
6000
8000
10,000
12,000
radius of earth = 6371 km

2. Seismic waves involve stress, strain, and density
Two important types of stresses and strains:
Pressure, P and volume change per unit volume, DV/V
Shear stress and shear strain

3. stress = elastic_constant x strain
For linear elasticity, Hooke’s law applies:
stress = elastic_constant x strain

4. For elastic waves, two elastic constants are key:
And density of the material, r
r = mass/volume

5. Two types of elastic waves
Compressional or P waves
involve volume change and shear
Shear or S waves
involve only shear
Click on these links to see particle motions:
P wave particle motions
S wave particle motions

6. Elastic wave velocities determined by material properties
P wave velocity
S wave velocity

7. ray perpendicular to wavefront
epicenter
Earth surface
ray perpendicular to wavefront
expanding wavefront at some instant of time after earthquake occurrence
seismograph station
Earth
center

8. D = epicentral distance in degrees
epicenter
tt(D) = total travel time along ray from earthquake to station
Earth surface
ray
D = epicentral distance in degrees D
seismograph station
Earth
center

9. Globally recorded earthquakes during the past 40 years
earthquake depth
0-33 km
33-70
70-300

10. Partial map of modern global seismograph network

11. 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km.
time, minutes
These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page
distance, degrees

12. click on link to P and S phases in the earth
PKPPKP
SSS
PPS
PPP PS SS
PKKP
SKKS
water waves
surface waves
SKS
PKS
PKP
PPP
PKIKP S PP
ScS
diffracted P
PcS
PcP P
These lines represent plus or minus one minute errors in reading arrival times

13. Nomenclature for seismic body phases
P wave segments in blue
S wave segments in red
P or S
mantle K
outer core
I or J
inner core
i = reflection at inner core-outer core boundary
c = reflection at core mantle boundary

14. Single path refracted through mantle
seismic wave source
Inner core
Outer core
Mantle

15. S P P diffracted around core
2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km.
time, minutes S
P diffracted around core P
These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page
distance, degrees

16. Single reflection at surfacePP SS
Inner core
Outer core
Mantle

17. 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. SS
time, minutes PP
These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page
distance, degrees

18. Single reflection at core-mantle boundary
PcP
reflection

19. Single reflection at core-mantle boundary
ScS

20. Single reflection with conversion of P to S
PcS

21. 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km.
time, minutes
ScS
PcS
PcP
These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page
distance, degrees

22. P in mantle, refracting to P in the outer core (K) and out through the mantle as P
PKP K P

23. P segments in mantle, P segments in outer core (K), and P segment in inner core (I)
PKIKP P K I K P

24. 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km.
time, minutes
PKP
PKIKP
These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page
distance, degrees

25. S in mantle, refracting and converting to P in outer core, then refracting back out and converting back to S in the mantle
SKS S K S

26. S in mantle, refracting and converting to P in outer core, P reflects once at inner side of core-mantle boundary, then refracting back out back with conversion to S in the mantle
SKKS S
reflection K K S

27. 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km.
time, minutes
SKKS
SKS S
These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page
distance, degrees

28. Compressional (P) and Shear (S) wave velocities, Vp and Vs
seismic wave velocity
km/sec
upper mantle
depth
transition zone km
lower mantle
D’’ layer
outer core
inner core

29. From Vp and Vs to seismic parameter f

30. For self compression of homogeneous material
f (R) = k/r
k = - dP/(dV/V) = dP/(dr/r)
dP = - g r dR
where
R = radius to a point in the earth, and
g = gravitational acceleration at that radius
g = GMR/R2
where MR = mass within sphere of radius R
dr/dR = -f/rg

31. For self compression of homogeneous material
dr/dR = -f/rg
This is the gradient in density determined by the seismic wave velocities. To obtain density, one must integrate by fixing the density, r, and gravity, g, at the top of the layer and calculating both r and g as one proceeds downwards.
The calculation assumes
a simple compression of material that does not change chemistry or phase.
the compression as one goes deeper produces an adiabatic temperature increase.

32. For self compression of homogeneous material
dr/dR = -f/rg
The method is applied to the following layers:
upper mantle
lower mantle
outer core
inner core
To determine the jumps in density between these layers, the following constraints are used:
Mass of earth
Moment of Inertia of Earth
Periods of free oscillations of Earth

33. Density, r
kg/m3 km
core-mantle boundary
depth, km

34. Gravitational acceleration, g
m/s2 km
core-mantle boundary
depth, km

35. Pressure, P
GPa. km
core-mantle boundary
depth, km

36. Density vrs pressure
kg/m3
GPa.

37. Density vrs pressure compression liquid to solid composition change
Inner core/outer core boundary
core-mantle boundary
kg/m3
compression
liquid to solid
composition change
phase changes
compression
mantle density
crustal density
GPa.

38. chemical stratification and differentiation
basaltic-granitic crust
phase changes
Mg(Fe) silicates
fluid, 90% iron
solidified iron
2000
4000 km
6000
8000
10,000
12,000

39. Earth’s convective systems
cool, strong lithospheric boundary layer
crust
slowly convecting mantle:
plate tectonic engine
seafloor spreading
core-mantle thermo-chemical boundary layer
subduction
rapidly convecting
outer core:
geomagnetic dynamo
solid inner core
2000
4000 km
6000
8000
10,000
12,000

40. near surface thermal boundary layer = lithosphere
Temperature in mantle
Temperature, degrees C
1000
2000
3000
4000
5000
near surface thermal boundary layer = lithosphere
conductive heat flow
upper mantle
transition zone
mantle melting
mantle convection
advective heat flow
lower mantle
Adiabatic gradient
Adiabatic gradient
D” = Lower mantle thermo-chemical boundary layer D”
conductive heat flow ?
CMB
iron melting
outer core

41. Temperature profile through entire earth

42. Mantle convection, hot spots and plumes
Lowrie, Fundamentals of Geophysics, Fig. 6.26

43. abstract
Average P-wave velocity perturbation in the lowermost 1000 km of the mantle

44. Generation of Earth’s magnetic field in the outer core
crust
Generation of Earth’s magnetic field in the outer core
mantle
outer core
The geomagnetic dynamo:
turbulent fluid convection
electrically conducting fluid
fluid flow-electromagnetic interactions
effects of rotation of earth
inner core
2000
4000 km
6000
8000
10,000
12,000

45. Geomagnetic field