1. science
2. physics

惑星地球科学
プレートテクトニクス１
April 15, 2015
Planets in our solar system
outer solar system
(giant planets and planet-wannabes)
inner solar system
(terrestrial planets)
Plate tectonics does not
occur on other terrestrial planets
Plate tectonics is essential for
life in many ways
One example: long-term carbon cycle
Exoplanets and planetary
habitability
4
Can plate
tectonics
take place on
those planets?
Can we explain
why it takes
place on Earth?
Solid earth science and
natural science at large
in 21st century
• Connection between life and various geological
processes
• Origin of life and its evolution on Earth
• Uniqueness of plate tectonics on Earth
• Comparative planetology
• Earth is immensely more accessible than any other
planets (cf. ‘single-pixel’ astronomy of exoplanets)
Today’s lecture:
some warm-up stuff
Present-day structure of Earth
metallic core
silicate mantle and crust
oceans
atmosphere
The evolution of these components
are all connected through mantle
dynamics.
The core
• Inner solid core and outer liquid core
• ~16% of Earth’s volume and ~32% of total
mass
• Composition: Fe-Ni alloy with some light
elements (H, O, Si, S, ...)
• Age of the core as a whole ~ 4.5 Ga
How to denote ages in
Earth sciences
Ga = billion years ago（10億年前）
Ma = million years ago（100万年前）
100 Ma = 1億年前
4.5 Ga = 45億年前
kilo (10^3), mega (10^6), giga (10^9),
tera (10^12), peta (10^15), exa (10^18)
万(10^4)、億(10^8)、兆(10^12)、京(10^16)
Speaking of the age of the core...
The age of Earth
• The oldest rock on Earth ~ 4.0 Ga
• The oldest mineral on Earth ~ 4.4 Ga
• Cosmochemical argument ~ 4.56 Ga (this is
usually referred to as the age of Earth, or
more precisely, “solar system initial”)
• cf. the age of the universe ~ 13.7 Ga
Geodynamo
• Geomagnetic field is generated by
convection in the outer core
(positive feedback between E and B)
• Convection in the core is driven by
cooling from above.
• Geomagnetic field shields cosmic
rays and prevents atmospheric
escape.
• Geomagnetic field is known to
change its polarity for ~0.5 Myr (on
average).
Insulating mantle
• The core cannot cool by
itself. Mantle cooling
controls core cooling.
• The evolution of
geomagnetic field is
regulated by mantle
dynamics.
The mantle
• The mantle is made of silicate
rocks (i.e., solid), but it can
flow.
• So, like the outer core, it
convects (with much longer
time scale), and this is the main
engine for almost all kinds of
geological phenomena.
Viscosity (粘性率)
a measure of how easily things can flow
• water ~ 10^(-3) Pa s
• maple syrup ~ 0.1 Pa s
• peanut butter ~ 100 Pa s
• mantle ~ 10^(21) Pa s
How fast can mantle flow?
Gravitational
instability results in
convection.
(slow)
(but significant)
Velocity field of Earth’s surface
Present-day Absolute Plate Motion
Earth’s surface is broken into a dozen or so pieces (”plates”),
each of which moves coherently with a velocity of a few cm/yr.
Tectonic Plates
North
American
Eurasian
Arabian
Indian
Pacific
African
Australian
Carib.
Cocos
Nazca
South
American
Antarctic
Note: Smaller plates are missing in this map
(Juan de Fuca, Philippine Sea, Scotia).
The number and size of plates are time-dependent
(e.g., Cocos and Nazca used to be one plate called Farallon).
Global Positioning
System (GPS)
•
Developed by US Department of
Defense
• A constellation of >24 GPS
satellites broadcasts precise
timing signals by radio.
• GPS receivers tell us their 3-D
coordinates (longitude, latitude,
and altitude) in any weather, day
or night, anywhere on Earth, with
accuracy of ~15 m.
Continuous GPS record
(example from some station in Northern CA)
[Station BRIB]
Where earthquakes occur
or how crust responds to mantle dynamics
Preliminary determination of epicenters
358,214 events, 1963-1998.
Continental drift, supercontinent formation,
continental breakup, mountain building
How crust responds to mantle dynamics (in a longer term)
[www.scotese.com]
Continental drift, supercontinent formation,
continental breakup, mountain building
How crust responds to mantle dynamics (in a longer term)
(note: sea level was a bit higher than present.)
[www.scotese.com]
Continental drift, supercontinent formation,
continental breakup, mountain building
How crust responds to mantle dynamics (in a longer term)
Appalachian mountains were formed
~350-300 Ma during Pangea assembly.
Note: changes in continental configuration affect
ocean circulation and thus climate.
[www.scotese.com]
The crust（地殻）
Chemical consequences of mantle dynamics
Young (< 200 Ma), mafic (rich in Mg and Fe) oceanic crust
and old (~2 Ga), felsic (rich in Si and Al) continental crust
Both are products of mantle melting induced by mantle
convection.
（中央海嶺）
Mid-ocean ridges - the world’s largest volcanic system
where new oceanic crust is created
Mid-Atlantic
Ridge
East Pacific Rise
Southwest
Indian Ridge
Southeast
Indian Ridge
Pacific-Antarctic
Ridge
Global Rates of Cenozoic Magmatism
（新生代：恐竜が絶滅してから今まで）
Location
Rate (km3/yr)
Volcanic
Plutonic
Oceanic ridges
3
18
Convergent plate boundaries
0.4-0.6
2.5-8.0
Continental intraplate regions
0.03-0.1
0.1-1.5
Oceanic intraplate regions
0.3-0.4
1.5-2.0
Global Total
3.7-4.1
22.1-29.5
[after Crisp (JVGR, 1983)]
Kilauea eruption, September 1983
The atmosphere
Product of volcanic degassing
Present-day atmospheric
composition
Component
Volume %
N2
78.088
O2
20.949
Ar
0.934
CO2
0.035
Ne
1.8E-03
He
5.24E-04
CH4
1.4E-04
• Earth’s atmosphere is not
primordial (i.e., its
composition is very different
from solar nebula).
• It is the accumulated effect
of volcanic degassing from
the mantle.
• Earth’s atmosphere is NOT
in a static equilibrium with
other subsystems.
Atmospheric composition:
Comparative planetology perspective
present-day
Earth
Venus
Mars
N2
78.1
1.8
2.7
O2
20.9
-
-
Ar
0.9
0.02
1.6
CO2
0.035
98.1
95.3
Atmospheric
pressure
1 atm
90 atm
0.006 atm
average surface
temperature
15 °C
450 °C
-30 °C
Atmospheric
composition
Atmospheric composition:
Comparative planetology perspective
present-day
Earth
Earth*
Venus
Mars
N2
78.1
1
1.8
2.7
O2
20.9
-
-
-
Ar
0.9
0.01
0.02
1.6
CO2
0.035
99
98.1
95.3
Atmospheric
pressure
1 atm
~80 atm
90 atm
0.006 atm
average surface
temperature
15°C
~200°C
450°C
-30°C
Atmospheric
composition
* Present-day Earth composition - (life-origin O2) + (CO2 in sedimentary rocks)
At least more than one ocean worth of water is
contained in Earth’s mantle.
subduction of hydrated crust
(mantle gains water)
volcanic degassing
(mantle loses water)
Plate tectonics (mantle dynamics) controls
global water and carbon cycles (long-term behavior of oceans
and atmosphere).
Earth system interactions
through mantle dynamics
How Earth began
• Very early Earth was
probably hotter than
present-day Earth.
• Why?
Solar system formation
Nebular hypothesis
1. Presolar nebula (formed by the
gravitational collapse of part of a
molecular cloud in an interstellar
medium)
2. Protoplanetary disk (formed
due to centrifugal force and internal gas
pressure)
3. Condensation results in
tiny solid particles
4. Planetesimals
5. Present-day planets
[Tarbuck and Lutgens, “Earth Science”, 2004]
Planet formation
Planetary growth is not
monotonic.
N-body numerical
simulation studies suggest
the following three stages:
1. Runaway growth
2. Oligarchic growth
3. Late-stage accretion
and giant impacts
[Kokubo, 2000]
Heating by Giant Impact
Artist’s rendition for the Giant Impact
that created Moon
• We’d like to get a rough
estimate for delta T.
• Mars-size impactor (~0.1
earth mass)
[check dimension!]
Note: an impactor should glance off Earth
in order to result in Earth-orbiting Moon.
Gravitational potential energy
and kinetic energy
Conservation of energy
v~11 km/s (=25,000 mph)
Heating by Giant Impact
Order-ofmagnitude
estimate:
(cf. condensation temperature for
silicates is <~2000K in vacuum.)
•
•
•
Impact velocity depends on orbital dynamics.
Not all of kinetic energy is converted to heat.
Giant impact can happen more than once.
Moon-forming Giant Impact
Numerical simulation by spherical particle hydrodynamics (SPH)
Note: Color shows temperature. This whole
simulation covers a period of a few days.
[Canup, 2004]
Moon-forming giant imapct
(from “Cosmic Collisions”)
Note: tidal dissipation led to an increase in the Earth-Moon distance.
Magma ocean and core formation
[Wood et al., 2006]
•
Part of (or most of) Earth is
likely to have been molten
owing to energy from planetary
accretion, helping dense metallic
components to segregate
(geochronology tells us the
core formed during the first
100 Myr or so).
•
High surface heat flux from the
magma ocean means rapid
cooling; the magma ocean is
expected to have lasted only for
a few tens of Myr.
How quickly can Earth cool down?
T=3000K
T=2000K
t=0
t=?
• How fast can Earth release heat into the space?
Three ways of heat transfer
• Radiation
（輻射）
Electromagnetic wave propagation or a stream of photons (‘light’)
• Conduction
（伝導）
Propagation of atomic vibration (phonons)
• Advection
（移流）
Physical transport of hot material
Radiative cooling
•
•
•
•
This mechanism depends strongly on temperature.
For radiation to be efficient, medium should be
‘transparent’.
Not efficient for heat transfer inside a planet.
Important for stars, but not for planets.
Conduction
Fourier’s law
“Heat always flows from hot to cold materials.”
• q: heat flux [W/m^2]
• k: thermal conductivity [W/m K]
Scaling for thermal diffusion
Quiz
“How long does it take
for temperature to be
homogenized by
conduction?”
Hints:
* Heat flow q = -k dT/dx has a
dimension of W/m^2.
* Specific heat Cp has a dimension
of J/(K kg).
Scaling for thermal diffusion
heat flow:
q
T
k
L
energy difference (per unit area):
E
Cp T L
diffusion time scale:
d
E
Cp 2 L2
=
L =
q
k
thermal diffusivity:
k
Cp
Check dimension for all of these!
Scaling for thermal diffusion
diffusion time scale:
L2
d
diffusion length scale:
L
t
For rocks,
10 6 m2 /s = 1 mm2 /s
Conductive cooling of a hot sphere
T
t=0
z
t>0
Lord Kelvin’s estimate on
the age of Earth (1862)
T
z
•
Deep mines - temperature
goes up with dT/dz~35 K/km.
•
Assume the initial
temperature of 2000°C.
•
Then the boundary layer
thickness is ~60 km.
•
Thermal diffusivity of
1 mm^2/s gives t~100 Myr.
Lord Kelvin
(William Thomson, 1st Baron Kelvin)
•
Superstar physicist in the 19th
century (after Newton, before
Einstein). Worked on nearly all
branches of physics
•
One of the founders of
thermodynamics
•
Also worked on a variety of
geological and geophysical
problems (as physicists and
mathematicians in those days).
Charles Lyell
Popularizer of James Hutton’s “Uniformitarianism”
•
Close and influential friend of
Charles Darwin
•
Uniformitarianism: “The Earth
was shaped by slow-moving
forces still in operation today”
--- this (somehow) led to no
definite beginning of Earth’s
history...
•
Kelvin attacked this notion on
the basis of thermodynamics:
“energy must be finite in a finite
space.”
Kelvin’s estimate on the age of
the Sun
•
•
The only ‘thinkable’
energy source (in the
19th century) is
gravitational collapse
(~2.3e41 J):
3M 2 G
U=
5R
Dividing this by solar
luminosity (4e26 W)
gives the time scale of
~20 Myr.
(currently this time scale is known as KelvinHelmholtz time scale in stellar physics.)
What’s wrong, then?
•
Discovery of radioactivity at the turn of the 19th
century: the birth of nuclear physics
•
Nuclear decay (radioactivity) and nuclear fusion both
provide energy missing in Kelvin’s estimates for the
ages of Earth and Sun, respectively.
•
... but radioactivity is only a part of story.
What’s chiefly wrong, then?
Conduction is not the only way of heat
transfer.
• Radiation
Electromagnetic wave propagation or a stream of photons (‘light’)
• Conduction
Propagation of atomic vibration (phonons)
• Advection
Physical transport of hot material
Convection（対流）
= CONduction + adVECTION
Top layer is cooled down
by conduction
Cold
advection
Direction of
gravity
Direction of
heat flow
advection
Hot
Bottom layer is heated up
by conduction
to be continued…