Boundary Layers:
The lithosphere + asthenosphere
Petrology, chemistry, and material
properties
Cin-Ty Lee
Rice University
Oceans and Continents
Plate Tectonics
Parsons and Sclater 1977
Stein and Stein 1992
T (oC)
1600
1400
1200
1000
800
600
400
200
0
0
2 Ma
25
Z (depth)
Ocean basins
10
50
75
L
75
100
125
150
Oceans basins are manifestations of upper
thermal boundary layer
L ~ κt
q~k
∆T k∆T
~
L
κt
buoyancy ~
ρ ∆T κt
L
ρo ∆T ~ o
2
2
Oceanic thermal boundary layers become negatively buoyant and subduct
when negative buoyancy forces > resisting forces
Oldest oceanic crust is ~200 My
ρref=STP (kg/m3)
T (oC)
25
10
Oceanic
Mantle
10
75
Z (depth)
50
75
TP =
1300 oC
TP = 1375 oC
75
100
TP = 1450 oC
Fertile
Mantle
125
A
150
B
3500
2 Ma
2 Ma
3480
3460
3440
3420
3400
3380
3360
3340
3320
1600
1400
1200
1000
800
600
400
200
0
0
Ocean basins = mobile
thermal boundary layer
=Plate tectonics
Tackley 2000
Continents underlain by thicker thermal boundary layers
Temperature (oC)
0
200
400
600
800
1000
1200
1400
1600
0
1
P (GPa)
2
Thickness of
oceanic
lithosphere
80
3
70
4
60
5
50
6
7
Mantle xenoliths
Craton
thickness
40
8
Lee et al. 2005
Continents are cold
(H. N. Pollack, S. J. Hurter, and J. R. Johnson, Reviews
of Geophysics, Vol. 31, 1993.)
Continents are old = stagnant
(Nd model ages and U-Pb crystallization ages)
Fraction of crust
in 200 Ma intervals
0.15
0.10
Age of oldest
seafloor
0.05
0.00
0
1
2
3
4
Time (Ga)
McCulloch & Bennett, 1994
Ocean
Plume
Midocean
Ridge
Mantle
Core
Continental
Crust
Base of
lithosphere
Why is the upper thermal
boundary layer
important?
• Nature of TBL controls
heat loss from planet
• Melting and
differentiation occur
(unmixing)
• Homogenization and
mixing occurs
Melting and differentiation occur at
thermal boundary layers
Mid-ocean Ridge
Hoffmann
Island and continental arcs
Cooling of Earth unmixes the Earth
CRUST is formed
Cont. crust
mafic
3.0 g/cm3
felsic
2.7 g/cm3
Melting also leaves behind a depleted mantle
residuum
(which could reside in the thermal boundary layer)
Olivine
A
94
Dunite
Melt depletion
92
Mg#
90
Lherzolite
B
88
Olivine websterite
100 95
90
85
80
75
70
65
60
55
50
Olivine mode
Orthopyroxene
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
94
Clinopyroxene
Wt. Fraction in peridotite
92
Mg#
Spinel Facies
Garnet Facies
Garnet Per.
Spinel Per.
90
C
100 95
90
85
80
75
70
65
Olivine Mode (wt. %)
Lee 2003
60
55
50
88
3.420
4.90
4.88
4.86
4.84
4.82
4.80
4.78
4.76
4.74
4.72
4.70
4.68
STP Bulk Density g/cm3
STP Vs (km/s)
STP SHEAR VELOCITIES
VS = (0.0143±0.0009)Mg#
+ (3.53±0.08)
R2 = 0.71
Garnet facies (garnet-peridotite)
Garnet facies (spinel-peridotite
(
)
ρ = -0.0144Mg# + 4.66
r2 = 0.67
3.400
3.380
3.360
3.340
3.320
A
Spinel facies
3.300
84
86
88
90
Mg#BULK
92
94
96
88
89
90
91
92
93
94
Mg#BULK
Lee 2003
Oceanic and continental lithosphere can serve as “sponges” for fluids/melts
Metasomatism
Layer of heat-production
1600
1400
Radioactive layer
Temp C
1200
1000
800
600
400
200
0
0
50
100
Depth km
150
200
Implications for estimates of Primitive Upper Mantle from Peridotites
Some peridotites could be refertilized
Peter Luffi
Na 2 O
PM
5
10
batch
aggregate
liquid
15
20
near-fractional
MgO
25
Dish Hill
East Romanche (Seyler & Bonatti, 1997)
D, L, H – MORB end-members from Elthon (1992)
mixing also occurs in the upper thermal boundary layer
Hunt & Kellogg
Pure shear
Simple shear
l ~ lo e
x
~ Gt
xo
− Gt
l
First order characteristics of the upper
thermal boundary layer?
• Compositional transition
• Rheologic transition
• Change in other physical properties (K, G)
Constitutive relationships
Brittle deformation
(fracture strength)
Plastic deformation
τ fric = τ c + µ f σ N
 E + PV 
ε& = A m exp −

d
RT 

σn
Dislocation Creep
n~3
m=0
Kohlstedt et al. 1995
Diffusion Creep
n~1
m = 1-2
As
Frost and Ashby http://engineering.dartmouth.edu/defmech/
Frost and Ashby http://engineering.dartmouth.edu/defmech/
Ductile deformation is temperature-sensitive
viscosity decreases with temperature
 E + PV 

 RT 
η = ηo exp
Viscous boundary layer can be defined to first order by a temperature isotherm
~1100-1200 o C
Ranalli and Murphy 1987
Kohlstedt et al 1995
Lithosphere & asthenosphere
Rheologic definitions
• Lithosphere = “strong” layer
from Greek lithos = “rocky”
• Asthenosphere = “weak” layer
from Greek astheno = weak
How weak is the asthenosphere and why do we care?
A low viscosity zone (LVisZ) can give rise to long wavelength convection
e.g., plate tectonics
Hoink and Lenardic 2008
See also Richards et al. 2001
ε& = A
How does one generate a low viscosity zone?
Viscosity Pas
T(C)
Viscosity Pas
140
140
120
140
120
100
120
100
80
100
80
60
80
60
40
60
40
20
40
20
0
20
0
0
E = 500 kJ/mol
V = 15 cm3 /mol
E = 400 kJ/mol
V = 60 cm3 /mol
Flow law
(wet olivine; Hirth and
Kohlstedt 1995)
Unrealistically high V
1E+25
1E+24
1E+23
1E+22
1E+21
1E+20
1E+19
1E+18
1E+17
1E+16
1E+25
1E+24
1E+23
1E+22
1E+21
1E+20
1E+19
1E+18
1E+17
1E+16
1600
1400
1200
1000
800
600
400
200
0
depth
 E + PV 
exp
−

m
d
RT


σn
Lithosphere & asthenosphere
Other “definitions” are really observables
Seismic Low Velocity Zone (LVZ) = asthenosphere?
Seismic Lid = Lithosphere?
Thermal lithosphere = lithosphere?
Tectosphere, compositional boundary layer = Lithosphere?
Fertile “convecting” mantle = asthenosphere?
Elastic lithosphere thickness = lithosphere?
Which one of these “definitions” actually = lithosphere and asthenosphere?
Be careful of confusing these terms with the rheologic definition of lithosphere
Reminder – RHEOLOGICAL LITHOSPHERE is to first order
controlled by temperature
Viscous boundary layer can be defined to first order by a temperature isotherm
~1100-1200 o C
Thermal Boundary Layer (thermal lithosphere)
Ranalli and Murphy 1987
Kohlstedt et al 1995
Seismic Lid and Low Velocity Zone (LVelZ)
seismic lithosphere
LVZ
LVZ > 5% drop in Vs
LVZ – nonexistant in shields?
Gaherty et al. 1999
LVelZ may coincide with anisotropy
Compositional boundary layers – chemical lithosphere
Continents
Lee 2005
but many others: Jordan, Hirth & Kohlstedt, Pollack
Compositional boundary layers – chemical lithosphere
Oceans
Lee et al. 2005
Motivated by Hirth and Kohlstedt 1995
Elastic Thickness
Based on flexure and loading studies with elastic plate approximation
Effective elastic thickness – always less than thermal thickness and rheological lithosphere
For oceans, roughly follows isotherms
OCEANS
Compilation from Burov
and Diament 1995
But for continents, it’s very difficult to do flexural studies (too strong so little topographic
signal)
Effective elastic thickness – much less than thermal thickness and rheological lithosphere
and often with large uncertainty
What is the nature of the lithosphere-asthenosphere
boundary (LAB)?
Identify the depth of the LAB
Identify the thickness of the asthenosphere and its viscosity
Hypotheses
1 – asthenosphere = partial melting zone
2 – asthenosphere = wet channel
3 - asthenospehre = thermal weakening (no melting)
Seismic Lid and Low Velocity Zone (LVelZ)
LVZ
LVZ > 5% drop in Vs
LVZ – nonexistant in shields?
Gaherty et al. 1999
Attenuation Q-1
Anelastic behavior
viscous effects
∆E
Q ≡
2πE
−1
Q −1
α

 E  
= A(ω )To exp −
 
 RT  

Q −1 ∝ (ωτ )
−α
∝ L−α
 Q −1 (ω , T )  E 
∂ ln VS ∂ ln VSU
=
− F (α ) 

2 
∂T
∂T
π

 RT 
Faul and Jackson 2005
Q tomography
Dalton, Ekstrom, Dziewonski (in press)
What is the nature of the lithosphere-asthenosphere
boundary (LAB)?
Identify the depth of the LAB
Identify the thickness of the asthenosphere and its viscosity
Hypotheses
1 – asthenosphere = partial melting zone
2 – asthenosphere = wet channel
3 - asthenospehre = thermal weakening
Hypothesis 1
Asthenosphere = partial melting zone
LVZ = partial melting zone
PEPI 1970
How much melt?
Not much! < 0.2 % ?
κ (φ )
v=−
∆ρg
µ
Bulau et al. 1979
Waff and Bulau 1979
Abyssal Peridotites
Johnson et al. 1990
Hypothesis 2
LVelZ due only to thermal effects (solid state)
anelastic and anharmonic effects
Stixrude and Lithgow-Bertelloni 2005
Hypothesis 3
water or volatiles = LVZ
Hirth and Kohlstedt 1996
1.4
ORTHOPYROXENE
Cr2O3 (wt. %)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
2
4
Al2O3 (wt. %)
6
8
The effect of water on mantle viscosity
ηeff =
τ
ε
ε = Aτ f
r
H 2O
Q + PV
exp(−
)
RT
Water fugacity
1573 K
wet
dry
10-4
Strain rate (S-1 )
n
10-3
10-5
Olivine
10-6
10-7
3×101
102
4×102
Stress (Mpa)
Mei and Kohlstedt, 2000; Chopra and Paterson, 1984; Karato et al., 1986; Hirth and Kohlstedt, 1996
Li, Lee, Peslier, Lenardic, Mackwell (in press)
120o W
109o W
114o W
41o N
0
ol:
10 20 30 40 ppm
0.3 Mpa
0
10 20 30 40 ppm
ol:
100
0
10 20 30 40 ppm
ol:
TH
GC
DH
ol:
N
LVT
0
ol:
0
37o
150
10 20 30 40 ppm
10 20 30 40 ppm
SC
D
32o N
500 km
0
0
300
0
1019
1021
ηeff (Pa⋅⋅s)
600
50
100
ol:
SMORB
200
1017
SOIB
150 ppm
Hypothesis Testing (CIDER)
Is the asthenosphere a partially molten zone?
Need falsifiable predictions
Must be interesting - implications
PREDICTIONS
T
ZLAB
ZLAB
Z
Heat flow
Zbase
ZLAB - Zbase
Heat flow
Step 1. Find places with different heat flows
young ocean, old ocean, young continent, old continent
Step 2. Use magma petrology and seismology to get ZLAB and Zbase
Thermometers
Mg2SiO4 (olivine) + Fe2SiO4 (melt) = Mg2SiO4 (melt) + Fe2SiO4 (olivine)
Mg2SiO4 (olivine) = Mg2SiO4 (melt)
∆S f
 dP 
 =

 dT  2ϕ ∆V f
(Fe / Mg )ol
=
(Fe / Mg )melt
small
P
1900
1 atm = 0.1 MPa
1800
Temperature (oC)
K
Fe / Mg
D
T
1700
1600
T3
1500
T2
1400
LIQUID
“forbidden
zone”
T1
S3
L3
X3
S2
X2
S1
L2
X1
L1
1300
OLIVINE
1200
1100
Mg2SiO4
X0
Wt. % Fayalite
Fe2SiO4
Barometers (Lee et al.)
Mg2SiO4(olivine) + SiO2(melt) = Mg2Si2O6(pyroxene)
K (T , P) ~
K~
px
a Mg
2 Si 2 O 6
ol
melt
a Mg
2 SiO 4 a SiO 2
large
∆S f
 dP 
=


dT

 2ϕ ∆V f
1
a
melt
SiO 2
1 atm = 0.1 MPa
1700
T1
Liquid
+ Forsterite
T
B
LIQUID
L + Si-poly
1600
T (oC)
P
Pe
TPe
TE
E
L + En
1500
Enstatite
+ Si-polymorph
Forsterite
+ Enstatite
Xo
1400
Forsterite
Mg2SiO4
X1
Enstatite
MgSiO3
SiO2
Wt. %
of course, one needs to make sure that the magmas of interest are not plume-related!
Seismology
Levander and Miller
western Basin and Range
<1 Ma (Big Pine, CA)
<1 Ma (Coso, CA)
<1 Ma (Amboy, CA)
<1 Ma (Pisgah, CA)
Rio Grande Rift
<1 Ma (Zuni Bandera, NM)
Colorado Plateau
<1 Ma (San Francisco, AZ)
Snake
River
Plain
Basin and
Range
Colorado
Plateau
T (oC)
Levander and Miller
1300
1400
1500
1600
1700
0
TP
20
40
LABBR
60
80
LABCP
100
120
Depth (km)
P (GPa)
1200
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
140
160
180
Western North
America
200
220
Lee et al.
PREDICTIONS
ZLAB
T
ZLAB
Heat flow
Z
Zbase
ZLAB - Zbase
Heat flow
ZLAB seismology
ZLAB petrology
Step 3
Calculate reference velocity profiles
anharmonic (solid state)
anharmonic and anelastic (Q) (solid state)
anharmonic and anelastic (partial melt)
Calculate viscosity profiles
use dislocation and diffusion creep laws to calculate anhydrous viscosity profile
assess effect of grain size
assess effect of water
assess effect of melt
And finally, we head home to geodynamics
ZLAB
∆Z
Low Viscosity Channel
Zbase
Z
Basal shear will be different beneath continents and oceans
τ ∝ 2ηeff ε& ∝ 2ηeff
V
∆Z
Conrad and Lithgow-Bertelloni 2006
Why is Earth’s upper boundary layer
close to its melting point?