Download The Earth in cross-section: what`s down there and how we know it

Structure of Earth as imaged by seismic waves
crust
upper mantle
transition zone
lower mantle
core-mantle boundary
D”, core-mantle
boundary layer
outer core
inner core
2000
4000 km
radius of earth = 6371 km
6000
8000
10,000
12,000
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
For linear elasticity, Hooke’s law applies:
stress = elastic_constant x strain
For elastic waves, two elastic constants
are key:
DP

 modulus of incompressibility
DV / V
shear stress

 modulus of rigidity
shear strain
  density
And density of the material, 
 = mass/volume
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
Elastic wave velocities determined
by material properties
4
 
3
P wave velocity V p 


S wave velocity Vs 

epicenter
Earth surface
expanding wavefront at
some instant of time after
earthquake occurrence
ray
perpendicular
to wavefront
seismograph
station
Earth
center
epicenter
tt(D) = total travel time along
ray from earthquake to station
Earth surface
ray
D = epicentral
distance in degrees
D
Earth
center
seismograph
station
Globally recorded earthquakes during the past 40 years
earthquake depth
0-33 km
33-70
70-300
300-700
Partial map of modern global seismograph network
time, minutes
2,538,185 travel time observations from
International Seismological Centre (ISC), for
earthquakes with depths between “0” and 60 km.
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
click on link to P and S phases in the earth
PKIKP
ScS
PcS
PcP
These lines represent plus or
minus one minute errors in
reading arrival times
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
c = reflection at
core mantle
boundary
i = reflection at
inner core-outer
core boundary
Single path refracted through mantle
S
P
seismic
wave
source
Inner core
Outer core
Mantle
time, minutes
2,538,185 travel time observations from
International Seismological Centre (ISC), for
earthquakes with depths between “0” and 60 km.
S
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
Single reflection at surface
PP
Inner core
Outer core
Mantle
SS
time, minutes
2,538,185 travel time observations from
International Seismological Centre (ISC), for
earthquakes with depths between “0” and 60 km.
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
Single reflection at core-mantle boundary
PcP
reflection
Single reflection at core-mantle boundary
ScS
Single reflection with conversion of P to S
PcS
time, minutes
2,538,185 travel time observations from
International Seismological Centre (ISC), for
earthquakes with depths between “0” and 60 km.
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
P in mantle, refracting to P in the outer core (K) and out through the mantle as P
P
K
P
PKP
P segments in mantle, P segments in outer core (K), and P segment in inner core (I)
PKIKP
P
K
I
K
P
time, minutes
2,538,185 travel time observations from
International Seismological Centre (ISC), for
earthquakes with depths between “0” and 60 km.
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
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
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
S
reflection
K
K
S
SKKS
time, minutes
2,538,185 travel time observations from
International Seismological Centre (ISC), for
earthquakes with depths between “0” and 60 km.
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
Compressional (P) and Shear (S) wave velocities, Vp and Vs
depth
0
0
1
2
3
4
seismic wave velocity
5
6
7
8
9
10
km/sec
upper mantle
transition zone
1000
km
lower mantle
2000
D’’ layer
3000
4000
outer core
5000
6000
7000
inner core
11
12
13
14
From Vp and Vs to seismic parameter 
Vp 
Vs 
4
3
 



 2 4 2 
 V p  3 Vs      ( R )


DP

 modulus of incompressibility
DV / V
shear stress

 modulus of rigidity
shear strain
  density
 (R) = "seismic parameter" derived from Vp(R) and Vs(R)
For self compression of homogeneous material
 (R) = /
 = - dP/(dV/V) = dP/(d/)
d/dR = -/g
dP = - g  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
For self compression of homogeneous material
d/dR = -/g
This is the gradient in density determined by the seismic
wave velocities. To obtain density, one must integrate by
fixing the density, , and gravity, g, at the top of the layer
and calculating both  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.
For self compression of homogeneous material
d/dR = -/g
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
Density, 
0
0
2000
4000
6000
kg/m3
8000
10000
1000
km
depth, km
2000
3000
4000
5000
6000
core-mantle boundary
12000
14000
Gravitational acceleration, g
0
2
4
m/s2
0
1000
km
depth, km
2000
3000
4000
5000
6000
core-mantle boundary
6
8
10
12
Pressure, P
0
0
50
100
150
200
GPa.
250
300
1000
km
depth, km
2000
3000
4000
5000
6000
core-mantle boundary
350
400
Density vrs pressure
14000
12000
kg/m3
10000
8000
6000
4000
2000
0
0
50
100
150
200
GPa.
250
300
350
400
Density vrs pressure
Inner core/outer
core boundary
14000
liquid to solid
12000
core-mantle
boundary
kg/m3
composition
change
10000
phase
changes
8000
6000
4000
mantle
density
2000
crustal
density
0
0
50
100
150
200
GPa.
250
300
350
400
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
Earth’s convective systems
cool, strong lithospheric boundary layer
slowly convecting mantle:
plate tectonic engine
core-mantle thermo-chemical boundary layer
rapidly convecting
outer core:
geomagnetic dynamo
solid inner core
2000
4000 km
6000
8000
10,000
12,000
Temperature in mantle
0
Temperature, degrees C
2000
3000
4000
1000
5000
conductive heat flow
upper mantle
near surface
thermal boundary
layer = lithosphere
transition zone
mantle convection
advective heat flow
lower mantle
D”
CMB
outer core
conductive heat flow
iron melting
?
D” = Lower mantle
thermo-chemical
boundary layer
Temperature
profile through
entire earth
Mantle convection, hot spots and plumes
Lowrie, Fundamentals of Geophysics, Fig. 6.26
abstract
Average P-wave velocity perturbation in the lowermost 1000 km of the mantle
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
Geomagnetic field