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The deep inner Earth
Global Geophysics 2015
Deep interior of the Earth
David Stevenson (nature, 2003):
2003
1864
Seismic velocity-depth model
Discovering the inner structure of Earth
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•
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Crust
Mantle
Outer core
Inner core
Ray-path coding within the Earth
P
S
K
I
J
c
i
p
s
LR
LQ
P-wave in the mantle
S-wave in the mantle
P-wave through the outer core
P-wave through the inner core
S-wave through the inner core
reflection from the mantle-outer-core boundary
reflection from the outer-core-inner-core boundary
P-wave reflected from the surface of the Earth close to the
earthquake focus
S-wave reflected from the surface of the Earth close to the
earthquake focus
Rayleigh wave
Love wave
Shadow zones
Crust-Mantle boundary (Moho)
Andrija Mohorivicic - 1909
A chemical boundary – and seismic boundary
Crust-mantle transition in Kohistan (Pakistan),
exhumed oceanic island arc
Mantle - outer core boundary
Beno Gutenberg Richard Oldham
Shadow zone (103° – 143°)
Note diffracted waves at core-mantle boundary, in dashed lines
Outer-core-inner-core boundary
Inge Lehmann - 1936
Refractions of waves at outer-core-inner-core boundary (PKIKP),
appear in „shadow zone“.
Density and elastic moduli for the whole Earth
α=
K + 4 / 3µ
ρ
β = µ/ρ
However, even if we know α and β as a function of depth, we have
unknowns of K, µ and ρ.
The Adams-Williamson equation to determine density as a function of
radius:
dρ
GM r ρ (r )
GM r ρ (r )
=−
=−
2
4 2
φ
dr
r
2
2
r (α − β )
3
Starting at Earth’s surface, work inwards, and apply equation successively to
shells of uniform composition, and
a=R
G – gravitational constant
M r = M E − 4π ∫ ρ (a )a 2 da
a =r
r – radius
ME – mass of Earth
R – radius of Earth
Mr – Mass at radius r
Elastic moduli and density
with depth
Attenuation of seismic waves:
the quality factor (Q)
Q=Q=−
2π × elastic energy stored in the wave
energy lost in one cycle or wavelength
2πE
TdE / dt
2πE
dE
=−
d
QT
Perfect elastic material – Q inf
Totally dissipative material – Q=0
E – energy
t – time
T – period of the seismic wave
Through integration,
E = E0 e −2πt /( QT )
Alternatively written,
A = A0 e − wt /( 2Q )
w – angular frequency
A0 – amplitude of wave time t ago
Gravity, pressure and quality factor
with depth
361.7 GPa
Whole line Qp
Dotted line Qs
The mantle structure
Notable features
• The ”lid” above 220 km (low-velocity zone for S waves), occur
mainly beneath continents, bounded at bottom by Lehmann
discontinuity (220±30 km).
• Mantle transition zone 400 – 670 km (5-7 % increase at each
of these depths).
• Lower mantle at depth down to 2700 km, D’.
• Lowermost 150-200 km of mantle (2700-2900 km), D”.
Long-wavelength perturbations of S-wave
Cross-section from Aegean (left) to Japan (right)
P-wave mode
S-wave mode
Q-factor as function of
depth
Seismic anisotropy
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•
Directional velocity dependence in a crystal
or material
Hooke’s law in anisotropic form:
σ ij = cijkl ε kl
P-wave anisotropy
Avp = Vpmax-Vpmin/Vpmean
Shear wave splitting and anisotropy
dVs = Vsmax – Vsmin
Olivine single crystal - (Mg,Fe)2Si04
Composition of upper mantle
Ca(Mg,Fe)SiO3
(Mg,Fe)2Si04 (typical 91-94% Mg)
MgSiO3 (enstatite)
FeSiO3 (ferrosilite)
Mineral physics
High pressure, high temperature experiments to simulate
conditions and processes within the Earth.
Percy Bridgeman
Ahrens (1980: Science)
Phase transitions in the mantle transition zone
Exothermic reactions,
10 % density increase
β, γ-spinels
Pyroxene to garnet
Endothermic reaction,
10 % density increase
(Mg,Fe)SiO3 (bridgmanite)
(Mg,Fe)O
Phase transitions continued
γ-spinel to Mg-silicate perovskite
(~660 km)
γ-spinel -> ringwoodite (~520 km)
β-spinel -> wadsleyite (~400 km)
α-spinel -> olivine (upper mantle)
D”
Analogue for Earth‘s lithosphere
Very heteogeneous
Ultra-low velocity layers:
5-40 km vertical,
10% Vp, Vs reductions
Slab graveyards?
Still plenty of conjecture and
research
Composition of the inner core:
Seismic parameter as a function of density for metals
φ = K / p = α 2 − 4 / 3β 2
Shock wave experiments (i.e., Ahrens, 1980)
Anisotropic structure of the inner core
Combining lab experiments and seismic data
Shock wave experiments (generating P and T),
Measuring sound velocity and density
Up to 8 % light elements in the core
(S, O, Si, C, H)
Twice the light element content in outer core,
compared to inner core
O-rich compositions do not fit seismic constraints,
and indicate O poor core (i.e., not oxidizing
conditions)
Duffy (2011: nature); Huang et al. (2011:nature)