Physics and chemistry of the deep earth

PHYSICS AND CHEMISTRY OF THE DEEP EARTH


Physics and Chemistry
of the Deep Earth
Edited by

Shun-ichiro Karato

Department of Geology and Geophysics
Yale University, New Haven
CT, USA

A John Wiley & Sons, Ltd., Publication


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Library of Congress Cataloging-in-Publication Data
Physics and chemistry of the deep Earth / Shun-ichiro Karato.
pages cm
Includes bibliographical references and index.
ISBN 978-0-470-65914-4 (cloth)
1. Geophysics. 2. Geochemistry. 3. Earth – Core. I. Karato, Shun-ichiro, 1949QE501.K325 2013
551.1 2 – dc23
2012045123

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Set in 9/11.5pt Trump Mediaeval by Laserwords Private Limited, Chennai, India

1 2013


Contents

Contributors, vii

Preface, ix
PART 1

Volatiles under High Pressure, 3
Hans Keppler

2

Earth’s Mantle Melting in the Presence of
C–O–H–Bearing Fluid, 38
Konstantin D. Litasov, Anton Shatskiy, and
Eiji Ohtani

3

Elasticity, Anelasticity, and Viscosity of a
Partially Molten Rock, 66
Yasuko Takei

4

Rheological Properties of Minerals and
Rocks, 94
Shun-ichiro Karato

5

Electrical Conductivity of Minerals and
Rocks, 145
Shun-ichiro Karato and Duojun Wang

6

Chemical and Physical Properties and
Thermal State of the Core, 244
Eiji Ohtani

9

Composition and Internal Dynamics of
Super-Earths, 271
Diana Valencia

MATERIALS’ PROPERTIES, 1

1

PART 2

8

PART 3 GEOPHYSICAL OBSERVATIONS
AND MODELS OF MATERIAL
CIRCULATION, 295
10 Seismic Observations of Mantle
Discontinuities and Their Mineralogical and
Dynamical Interpretation, 297
Arwen Deuss, Jennifer Andrews, and
Elizabeth Day
11 Global Imaging of the Earth’s Deep Interior:

Seismic Constraints on (An)isotropy,
Density and Attenuation, 324
Jeannot Trampert and Andreas Fichtner
12 Mantle Mixing: Processes and
Modeling, 351
Peter E. van Keken

COMPOSITIONAL MODELS, 183

Chemical Composition of the Earth’s Lower
Mantle: Constraints from Elasticity, 185
Motohiko Murakami

13 Fluid Processes in Subduction Zones and
Water Transport to the Deep Mantle, 372
Hikaru Iwamori and Tomoeki Nakakuki
Index, 393

7 Ab Initio Mineralogical Model of the Earth’s
Lower Mantle, 213
Taku Tsuchiya and Kenji Kawai

Colour plate section can be found between
pages 214–215


Contributors

J E N N I F E R A N D R E W S Bullard Laboratory, Cambridge University, Cambridge, UK
E L I Z A B E T H D A Y Bullard Laboratory, Cambridge

University, Cambridge, UK

K O N S T A N T I N L I T A S O V Department of Earth and
Planetary Materials Science, Graduate School of
Science, Tohoku University, Sendai, Japan

A R W E N D E U S S Bullard Laboratory, Cambridge
University, Cambridge, UK

M O T O H I K O M U R A K A M I Department of Earth
and Planetary Materials Science, Graduate
School of Science, Tohoku University, Sendai,
Japan

A N D R E A S F I C H T N E R Department of Earth Sciences, Utrecht University, Utrecht, The Netherland

T O M O E K I N A K A K U K I Department of Earth and
Planetary Systems Science, Hiroshima University, Hiroshima, Japan

H I K A R U I W A M O R I Department of Earth and
Planetary Sciences, Tokyo Institute of Technology, Tokyo, Japan

E I J I O H T A N I Department of Earth and Planetary
Materials Science, Graduate School of Science,
Tohoku University, Sendai, Japan

S H U N - I C H I R O K A R A T O Department of Geology
and Geophysics, Yale University, New Haven,
CT, USA

A N T O N S H A T S K I Y Department of Earth and
Planetary Materials Science, Graduate School of
Science, Tohoku University, Sendai, Japan

K E N J I K A W A I Department of Earth and Planetary Sciences, Tokyo Institute of Technology,
Tokyo, Japan

Y A S U K O T A K E I Earthquake Research Institute,
University of Tokyo, Tokyo, Japan

H A N S K E P P L E R Byerisched Geoinstitut, Univer¨ Bayreuth, Bayreuth, Germany
sitat

J E A N N O T T R A M P E R T Department of Earth Sciences, Utrecht University, Utrecht, The Netherland


viii

Contributors

T A K U T S U C H I Y A Geodynamic Research Center,
Ehime University, Matsuyama, Ehime, Japan
D I A N A V A L E N C I A Department of Earth,
Atmospheric and Planetary Sciences,
Massachusetts Institute of Technology,
Cambridge, MA, USA

P E T E R V A N K E K E N Department of Earth and
Environmental Sciences, University of Michigan,
Ann Arbor, MI, USA

D U O J U N W A N G Graduate University of Chinese
Academy of Sciences, College of Earth Sciences,
Beijing, China


Preface

Earth’s deep interior is largely inaccessible. The
deepest hole that human beings have drilled is
only to ∼11 km (Kola peninsula in Russia) which
is less than 0.2 % of the radius of Earth. Some
volcanoes carry rock samples from the deep interior, but a majority of these rocks come from
less than ∼200 km depth. Although some fragments of deep rocks (deeper than 300 km) are
discovered, the total amount of these rocks is
much less than the lunar samples collected during
the Apollo mission. Most of geological activities
that we daily face occur in the shallow portions of Earth. Devastating earthquakes occur in
the crust or in the shallow upper mantle (less
than ∼50 km depth), and the surface lithosphere
(‘‘plates’’) whose relative motion controls most
of near surface geological activities has less than
∼100 km thickness. So why do we worry about
‘‘deep Earth’’?
In a sense, the importance of deep processes
to understand the surface processes controlled by
plate tectonics is obvious. Although plate motion
appears to be nearly two-dimensional, the geometry of plate motion is in fact three-dimensional:
Plates are created at mid-ocean ridges and they
sink into the deep mantle at ocean trenches,
sometimes to the bottom of the mantle. Plate

motion that we see on the surface is part of
the three-dimensional material circulation in the
deep mantle. High-resolution seismological studies show evidence of intense interaction between
sinking plates and the deep mantle, particularly
the mid-mantle (transition zone) where minerals

undergo a series of phase transformations. Circulating materials of the mantle sometimes go
to the bottom (the core–mantle boundary) where
chemical interaction between these two distinct
materials occurs. Deep material circulation is
associated with a range of chemical processes
including partial melting and dehydration and/or
rehydration. These processes define the chemical
compositions of various regions, and the material circulation modifies the materials’ properties,
which in turn control the processes of materials
circulation.
In order to understand deep Earth, a multidisciplinary approach is essential. First, we need
to know the behavior of materials under the
extreme conditions of deep Earth (and of deep
interior of other planets). Drastic changes in properties of materials occur under the deep planetary conditions including phase transformations
(changes in crystal structures and melting). Resistance to plastic flow also changes with pressure
and temperature as well as with water content.
Secondly, we must develop methods to infer deep
Earth structures from the surface observations.
Thirdly, given some observations, we need to develop a model (or models) to interpret them in the
framework of physical/chemical models.
In this book, a collection of papers covering
these three areas is presented. The book is divided
into three parts. The first part (Keppler, Litasov
et al., Takei, Karato, Karato and Wang) includes

papers on materials properties that form the basis


x

Preface

for developing models and interpreting geophysical/geochemical observations. The second part
(Murakami, Tsuchiya and Kawai, Ohtani, Valencia) contains papers on the composition of
deep Earth and planets including the models of
the mantle and core of Earth as well as models
of super-Earths (Earth-like planets orbiting stars
other than the Sun). And finally the third part
(Deuss et al., Trampert and Fichtner, van Keken,
Iwamori) provides several papers that summarize seismological and geochemical observations
pertinent to deep mantle materials circulation
and geodynamic models of materials circulation
where geophysical/geochemical observations and

mineral physics data are integrated. All of these
papers contain reviews of the related area to
help readers understand the current status of
these areas.
I thank all the authors and reviewers and editors of Wiley-Blackwell who made it possible to
prepare this volume. I hope that this volume will
help readers to develop their own understanding
of this exciting area of research and to play a role
in the future of deep Earth and planet studies.
Shun-ichiro Karato
New Haven, Connecticut

Fabry-Perot
Interferometer
water cooling
system
scattered light
Diode laser

DAC
X-ray

X-ray CCD

CO2 laser
translation stage
for Brilouin optics
to T measurement

Spectrometer
with CCD

M ND

Temperature
measurement
system

M
CF

M

Laser heating
system

CO2 laser

BS

CCD
L

XRD
measurement
system

BS
Light

TV
monitor

ZSP
Light
M

Incident X-ray
Monochromator
SR

M

Slit
Collimator

M
L

L
M

X-ray lenses

ID

L

DAC

X-ray CCD

M
L
ID

DM

PD

ID

CCD

M
L

Collecting
assembly

M
ID

MS

ID Focusing

TV
monitor
RPF
M

M
M

Controller

Sandercock-type
tandem Fabry-Perot
interferometer

M

assembly
M

M
ID

L

VND
RP
ID
BS

CCD
Diode-pumped
laser, 532 nm
TV
monitor

Brillouin scattering measurement system

Plate 1 (Fig. 6.2) Whole view of the Brillouin scattering
measurement system combined with synchrotron X-ray
diffraction and laser heating systems at BL10XU of
SPring-8 (a), and its schematic layout (b) from
Murakami et al. (2009). Green, white and red lines
indicate the schematic optical paths for Brillouin

scattering measurements, X-ray diffraction and laser
heating system, respectively. Light green and pale red
lines indicate the scattered light and transmitted light
through the sample. SR, synchrotron radiation; M,
mirror; L, lens; BS, beam splitter; BE, beam expander;
ZSP, ZnSe plate; PD, photodiode; DM, dichroic mirror;
ID, iris diaphragm; CF, color filter; VND, variable ND
filter; RP, retardation plate; RPF, rotational polarized
filter; MS, microscope. Reproduced with permission of
Elsevier.

Physics and Chemistry of the Deep Earth, First Edition. Edited by Shun-ichiro Karato.
 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd.


8.0
HS

Shear velocity (km/s)

7.6

HS-LS

LS

7.2
6.8
6.4

(Mg,Fe)O

6.0
XMg = 0.94 (Jackson et al., 2006)
XMg = 0.94 (Crowhurst et al., 2008)

5.6

XMg = 0.90 (Marquardt et al., 2009)
MgO (Murakami et al., 2009)

5.2
0

20

40

60
80
Pressure (GPa)

100

120

Plate 2 (Fig. 6.9) Representative high-pressure shear wave velocity profiles (Crowhurst et al., 2008; Jackson et al.,
2006; Marquardt et al., 2009) of ferropericlase together with that of MgO (Murakami et al., 2009). Shaded area
shows the possible pressure range of the spin transition. HS, high-spin state of iron; LS, low-spin state of iron.

6.0
Pyrolite
MORB
Perovskitite
PREM

Density (g/cm3)

5.5

5.0

4.5

4.0

0

50

100

150

P (GPa)

Plate 3 (Fig. 7.10) Density profiles for pyrolite (solid lines), MORB (dashed lines) and perovskitite (thin line)
calculated along the Brown and Shankland’s geotherm with the reference Earth value (black dots) (Dziewonski and
Anderson, 1981). The perovskitite’s composition was set to 100% Pv (or PPv) with XFeSiO3 = 12 mol%. Shaded areas
are out of the lower mantle range. Computational uncertainties were found comparable to the thickness of the

lines.


14
VP

Velocity (km/s)

12

10
VΦ
8

6

4

VS

0

100

50

150

P (GPa)
Plate 4 (Fig. 7.11) Seismic velocity profiles for pyrolite (solid blue line), MORB (dashed pink line), and perovskitite

(thin green line) calculated along the Brown and Shankland’s geotherm with the reference Earth value (black dots)
(Dziewonski & Anderson, 1981). Computational uncertainties were found comparable to the thickness of the lines.

Plate 5 (Fig. 8.14) An X-ray radiographic image, showing flotation of a composite marker in a Fe-10at% melt at 4.5
GPa and 1650 ◦ C. The image was taken at the beamline BL14-B2 in Photon Factory (PF). An image of the composite
marker composed of a Pt core and an alumina outer capsule is clearly shown in the radiographic image.


Ni

0.5

Fe

nte
nt,
at.
fra
c

0.5

Si

Ni
co

0.5

Ni

13.8
0.25 14.26
0.25
14.09
0.2
13.4
13.92 0.2
13.75
13.6
13.0
13.42
13.3
13.08 0.1
12.88

0.1

0
14.09
13.83 Fe

0
0

0.1

0.2

0.25 Si

Si content, at. frac.
Plate 6 (Fig. 8.22) The density of hcp-iron alloys with various compositions determined in this and previous works
at 330 GPa and 300 K. The density was calculated based on the Pt pressure scale by Fei et al. (2007). The open circles
indicate the density values for Fe0.93 Si0.07 and Fe0.83 Ni0.09 Si0.08 alloys, 13.49 g/cm3 and 13.61 g/cm3 respectively, as
determined by Asanuma et al. (2011); the solid square and a solid triangle indicate the density of pure iron and
Fe0.8 Ni0.9 , 14.09 g/cm3 , 14.37 g/cm3 are the density by Mao et al. (1990); a solid upside triangle, the density of
Fe0.84 Si0.16 alloy, 12.90 g/cm3 by Hirao et al. (2004). The densities of these alloys are recalculated using the pressure
scale by Fei et al. (2007). The estimated inner core density at 300 K, 13.3–13.6 g/cm3 (Diewonski & Anderson,
1989; Stacey & Davis, 2004; see the text in detail) locates in the blue shaded region, assuming the Ni content in the
inner core, 4 ∼ 5.4 wt%. The compositional range changes with the pressure scale. The red dashed lines are the
density isocbors (in g/cm3 ) based on the Pt pressure scale by Holmes (Holmes et al., 1989). The compositional range
explaining the inner core density by this scale is given as a red shaded area. The compositional range estimated by
Antonangeli et al. (2010) using the same pressure scale (Holmes et al., 1989) is shown as a gray shaded region.

40000

Radius [km]

30000
20000

HP-26b

500 K < Teq< 700 K
700 K < Teq< 900 K
900 K < Teq< 1100 K
1100 K < Teq< 1300 K
1300 K < Teq< 1500 K
1500 K < Teq< 1700 K
1700 K < Teq< 2200 K

K11e
K11d
GJ 1214b

K18-c

HP-11b
GJ 436b
U
K4-b
K11c N
K20c

K11f
K18-b
K11-b

55 Cnc-e
K20-b

10000

C7-b
K10-b

8000
E

6000

5000
0.4

0.7 1

2

3

5 7 10

Mass [MEarth]

20

Plate 7 (Fig. 9.3) Mass and Radius data for all transiting
exoplanets with masses below 10 ME color coded
according to the equilibrium temperature. Earth (E),
Uranus (U) and Neptune (N) are shown for reference.
Reproduced with permission of Elsevier.


40000

Radius [km]

30000
20000

HP-26b

500 K < Teq< 700 K
700 K < Teq< 900 K
900 K < Teq< 1100 K
1100 K < Teq< 1300 K
1300 K < Teq< 1500 K
1500 K < Teq< 1700 K
1700 K < Teq< 2200 K

100%
env

U N
K11d
K11c

K11f GJ 1214b

8000

K11-b

20%

HP-11b
K4-b
GJ 436b

K20c

55 Cnc-e

K18-b

50%
10000

K18-c

K11e

K20-b
C7-b
K10-b

5%
Teq = 600 K
Teq = 500 K

6000
5000

0.4 0.7 1

2

3

5 7 10

20

Mass [MEarth]
Plate 8 (Fig. 9.6) Mass–Radius relationships for warm vapor planets. Data for planets are shown color-coded by their
equilibrium temperature. The mass-radius relationships (dark blue) correspond to compositions of different
amounts – 5, 20, 50, 100% by mass – of a pure-water envelope above an Earth-like nucleus for equilibrium
temperatures of ∼500 K and 600 K, relevant to GJ 1214b, Kepler-11f and Kepler-11e. The 100% pure-water
composition is the boundary above which planets of the corresponding equilibrium temperature or above require
H-He.

Density [g/cm3]

on
10 ir

5

-like
Mercury

V

K10-b

E

C7-b

K18-b

3

-like
Earth
n
o
n -iro
K20-b

55 Cnc-e

K11-b

2

GJ 1214b

1

K11-f

0.5

N
U

K11-d

K11-e

0.3
0.7 1

2

3

5

7

10

20

Mass [MEarth]
Plate 9 (Fig. 9.8) Density vs mass of transiting super-Earths. The data for the known transiting super-Earths and
mini-Neptunes is shown, as well as the relationships for the four rocky representative compositions described in
the text. Earth, Venus, Uranus and Neptune are shown for reference.


216 224 232 240 248 256 264

210 230 250 270 290

TZ thickness (km)

TZ thickness (km)

(a)

(b)

Plate 10 (Fig. 10.7) Transition zone topography maps using (a) SS precursors (Deuss, 2009). Reproduced with
permission of Springer and (b) Pds receiver functions (Andrews & Deuss, 2008). Reproduced with permission of the
American Geophysical Union.

S40RTS at 100 km depth

−7.5

+7.5

null-space component
at 100 km depth

−1.5

+1.5

S40RTS at 500 km depth

−3.0

+3.0

null-space component
at 500 km depth

−0.6

+0.6

S40RTS at 2800 km depth

−3.0

+3.0

null-space component
at 2800 km depth

−0.6

+0.6

Plate 11 (Fig. 11.1) Top Relative S velocity variations, d ln vs , in the global model S40RTS (Ritsema et al., 2011) at
˜ null . The null-space component
100, 500 and 2800 km depth. Bottom: The corresponding null-space component m
contains short-wavelength structure that can be scaled and added to the model without changing the misfit.


dln Vs [%]

dln rho [%]

950 km (+/− 0.82)

950 km (+/− 1.1)

1500 km (+/− 0.85)

1550 km (+/− 1.0)

2600 km (+/− 0.95)

2600 km (+/− 1.0)

2891 km (+/− 1.0)

2891 km (+/− 0.99)
Plate 12 (Fig. 11.5) Left: Lateral variations in vs and ρ
at various depths in the maximum-likelihood model
of Mosca et al. 2012. The laterally averaged standard
deviations are indicated in brackets. Note the
pronounced anti-correlation of d ln vs and d ln ρ
around 2600 km depth beneath the central Pacific
and Africa. Figure modified after Mosca et al. 2012.

0

−1.8

0.0

−1.8

1.8

0.0

1.8

(b)
273

1500

(c)

3273

T (K)

(a)
Plate 13 (Fig. 12.4) Thermochemical mixing models similar to those in Brandenburg et al. (2008) with temperature
(left), MORB fraction (middle; MORB particles are white) and age since last melting in the MORB particles
(right: black/red is young, yellow/white is old). The core size is reduced in these cylindrical models to better
represent the relative surface area of the Earth’s core (van Keken, 2001). Reproduced with permission of Elsevier.


6000

4000

y (km)

−5%

3273 K

2000

−2.5%

0

−2000

+2.5%

+5%

273 K

−4000

−6000
−6000

−4000 −2000
x (km)
(a)

0

2000

4000
(b)

6000
(c)

Plate 14 (Fig. 12.6) We map temperature (left) and eclogite fraction (not shown) into shear velocity variations using
the mineralogical conversions of Cobden et al., 2008 (middle). The right frame shows the prediction how the shear
velocity variations would be recovered in S40RTS (Ritsema et al., 2011). Reproduced with permission of John Wiley
& Sons.


Recovered velocity
perturbation from
Brandenburg model

S40RTS

shear velocity variation from 1-D
−2%

+2%

Plate 15 (Fig. 12.7) Comparison of model predictions (insets) and a cross section through S40RTS across the Pacific
centered just south of Hawaii with an azimuth of 50N. The cross section goes through the Pacific super-‘blob’
structure on the left and the Farallon subduction system on the right. The left insert shows the recovery from the
dynamical model through a large thermochemical region at the base of the mantle. The right insert shows the
recover for a region dominated by a downwelling. The seismic recovery from the dynamic model represents the
tomographic model reasonably well, except for the amplitude of the thermochemical region at the base of the
mantle and the degree of separation between upper and lower mantle. The latter may indicate stronger dynamical
layering between upper and lower mantle.

0

1

0

C

1
T

(b)

(a)
C

1.0

0.5

0.0

(c)
Plate 16 (Fig. 12.8) Thermochemical convection models with phase transitions from (top) van Summeren (EPSL,
2009) and (bottom) Nakagawa et al. (2010). The endothermic phase transition at 670 km depth combined with
compositional variability between the MORB and harzburgite components causes localized and transient layering
at 670 and may lead to the long-term accumulation of MORB just below the transition zone. Reproduced with
permission of Elsevier.

0

2
100

200

300

6
400

8

500

600

10
H2O wt.%
700

800 depth (km)

2500

0

4

2000

us

liquid

1500

dry

s

us

26
21
15

14
% H2O)
solidus (0.2
14
sat. solidus
14

23

22
17

25

24

16
2 3

1 an
13
Jap
apan
n
tral J
apa Cen
J
9 NE
12
19
10
choke point

18

SW

5

4
6

500

lid
so

8

s

olidu

dry s

1

1
1000

Temperature (degree C)

wd–out
s
olidu
O)
dry s 0.2% H2
(
s
u
d
li

o

20

1: ol ± opx
± pl/sp/gt ± cpx
2: ol + opx + sp + amp
3: ol + opx + gt + amp
4: ol + opx + chl + amp
5: ol + opx + chl + cpx
6: ol + talc + chl + amp
7: ol + serp + chl + amp
8: ol + serp + chl + cpx
9: ol + opx + MgS + cpx
10: ol + serp + gt + cpx
11: A + serp + gt + cpx
12: A + opx + gt + cpx
13: chm + opx + gt + cpx
14: ol + ed ± opx ± gt ± cpx
15: wd ± opx/st ± gt/mj ± cpx
16: E + opx + gt + cpx
17: E + st + gt + cpx
18: E + D + gt + cpx
27 19: A + D + gt + cpx
20: br + D + gt/mj + cpx/Ca − pv
21: rg ± st/ak ± mj ± Ca − pv
22: sB + st + mj + Ca − pv
23: sB + ak + mj + Ca − pv
24: sB + D + mj + Ca − pv
25: sB + pv + gt/mj + Ca − pv

26: pv + pe + Ca − pv ± Al − phase
27: pe + D + gt + Ca − pv

0

11
5

0

10

15

20

25

Pressure (CPa)
Plate 17 (Fig. 13.1) Phase relation of H2 O-saturated peridotite and the maximum H2 O content of the solid phases
(Cmax
H O ) (modified after Iwamori, 2007). Phase assemblages of the H2 O-saturated peridotite (field no. 1 to 27) are
2

shown on the right-hand side of the diagram. The abbreviations of the phases are as follows: ol = olivine;
opx = orthopyroxene; cpx = clinopyroxene; pl = plagioclase; sp = spinel; gt = garnet; amp = amphibole;
chl = chlorite; serp = serpentine; MgS = Mg-sursassite; A = phase A; chm = clinohumite; wd = wadsleyite;
rg = ringwoodite; st = stishovite; mj = majorite; E = phase E; D = phase D; br = brucite; Ca-pv = Ca-perovskite;
ak = akimotoite; sB = superhydrous phase B; pv = perovskite; pe = periclase (or magnesiowustite);
¨

Al-phase = Al-rich phase. In the fields of no. 1, 14, 15, 21 and 26, which are above the stability fields of major
hydrous phases, Cmax
H O is not zero as H2 O is contained in the nominally anhydrous phases, although it is not fully
2

resolved by the color scale used in the diagram. In the field no. 26, the minimum estimate of 10 ppm based on
Bolfan-Casanova et al. (2000) is shown. Three thick solid lines indicate geotherms along the subducting slabs
beneath Central Japan (Pacific Plate), NE Japan (Pacific Plate), and SW Japan (Philippine Sea Plate) based on Iwamori
(2007). Reproduced with permission of Elsevier.


200

2

0
km

2

200

0

600
(b)

400

800

600
(d)

400

u0 = 2.25 cm/yr, age = 15 Ma

800

200

200

0

0
km

Distribution of maximum H2 O content (Cmax
H O ) in subduction zones associated with the subducting plates of a subduction

1000

1000

u0 = 18 cm/yr, age = 15 Ma

gradient for a given plate age and an adiabatic gradient underneath for the oceanic side boundary, with a potential temperature of 1300 ◦ C; an
error function gradient corresponding to a plate (backarc basin) age of 20 Ma for the backarc side boundary (e.g., corresponding to formation of a

backarc basin such as Japan-sea) with a potential temperature of 1300 ◦ C; zero heat flux at the bottom. The solid lines indicate the temperature
contours with the interval of 200 ◦ C. Reproduced with permission of Elsevier.

angle of 30 degrees and different ages of the subducting plates (15 to 130 Ma) and subduction velocities (2.25 to 9.0 cm/year). The color scale is the
same as in Figure 13.1. Two white arrows in each figure indicate the approximate location of the choke points across the subducting slab. First,
the steady state flow field and the temperature distribution have been calculated based on a standard set of conservation equations for
momentum and energy of mantle flow with temperature dependent viscosity as in Iwamori (2004). The temperature contours are shown by solid
lines with an interval of 200 degrees. An analytic corner flow solution is assumed on the backarc side boundary and a constant velocity is
assumed within the subducting plate (entire region below the diagonal interface between the mantle wedge and the subducting plate). Then,
◦
distribution of Cmax
H O has been calculated. The thermal boundary conditions are as follows: a surface temperature of 0 C; an error function

Plate 18 (Fig. 13.2)

(c)

600
400

600
600

400

400

800

200

200

1000

0

0

u0 = 12.25 cm/yr, age = 130 Ma

(a)

600
400

600
600

400

400

800

200

200

1000

0

u0 = 18 cm/yr, age = 130 Ma

0


Part 1

Materials’ Properties


1 Volatiles under High Pressure
HANS KEPPLER
¨ Bayreuth, Bayreuth, Germany
Bayerisches Geoinstitut, Universitat

Summary
Hydrogen and carbon are the two most important
volatile elements in the Earth’s interior, yet their
behavior is very different. Hydrogen is soluble in
mantle minerals as OH point defects and these
minerals constitute a water reservoir comparable
in size to the oceans. The distribution of water in
the Earth’s interior is primarily controlled by the
partitioning between minerals, melts and fluids.
Most of the water is probably concentrated in the
minerals wadsleyite and ringwoodite in the transition zone of the mantle. Carbon, on the other
hand, is nearly completely insoluble in the silicates of the mantle and therefore forms a separate

phase. Stable carbon-bearing phases are likely carbonates in the upper mantle and diamond or
carbides in the deeper mantle. Already minute
amounts of water and carbon in its oxidized form
(as carbonate or CO2 ) greatly reduce the solidus of
mantle peridotite. Melting in subduction zones is
triggered by water and both water and CO2 contribute to the melting below mid-ocean ridges and
in the seismic low-velocity zone. Redox melting may occur when oxygen fugacity increases
upon upwelling of reduced deep mantle, converting reduced carbon species to carbonate or CO2
that strongly depress solidus temperatures. The
large contrast of water storage capacity between
transition zone minerals and the mineral assemblages of the upper and lower mantle implies that

melt may form near the 440 and 660 km seismic
discontinuities. Water and carbon have been exchanged during the Earth’s history between the
surface and the mantle with typical mantle residence times in the order of billions of years.
However, the initial distribution of volatiles between these reservoirs at the beginning of the
Earth’s history is not well known. Nitrogen, noble
gases, sulfur and halogens are also continuously
exchanged between mantle, oceans and atmosphere, but the details of these element fluxes are
not well constrained.
1.1 Introduction: What Are Volatiles and Why
Are They Important?
Volatiles are chemical elements and compounds that tend to enter the gas phase in
high-temperature magmatic and metamorphic
processes. Accordingly, one can get some idea
about the types of volatiles occurring in the
Earth’s interior by looking at compositions of
volcanic gases. Table 1.1 compiles some typical
volcanic gas analyses. As is obvious from this
table, water and carbon dioxide are the two

most abundant volatiles and they are also most
important for the dynamics of the Earth’s interior
(e.g. Bercovici & Karato, 2003; Mierdel et al.,
2007; Dasgupta & Hirschmann, 2010). Other,
less abundant volatiles are sulfur and halogen

Physics and Chemistry of the Deep Earth, First Edition. Edited by Shun-ichiro Karato.
© 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd.


4

hans keppler

Table 1.1 Composition of volcanic gases (in mol%).

H2 O
H2
CO2
CO
SO2
H2 S
HCl
HF

Mt. St. Helens
1980

Kilauea
1918

Kilauea
1983

91.6
0.85
6.94
0.06
0.21
0.35

37.1
0.49
48.9
1.51
11.84
0.04
0.08

79.8
0.90
3.15
0.06
14.9
0.62
0.1
0.19

Etna
2000

92
7.3
1.0
0.1
0.07

Source: Data from Symonds et al. (1994) except for Etna (from
Allard et al., 2005).

compounds, particularly SO2 , H2 S, HCl, and HF.
Noble gases are only trace constituents of volcanic gases, but they carry important information
on the origins and history of the reservoirs they
are coming from (Graham, 2002; Hilton et al.,
2002). Nitrogen is a particular case. Volcanic
gas analyses sometimes include nitrogen, but
it is often very difficult to distinguish primary
nitrogen from contamination by air during
the sampling process. The most conclusive
evidence for the importance of nitrogen as a
volatile component in the Earth’s interior is
the occurrence of N2 -filled fluid inclusions in
eclogites and granulites (Andersen et al., 1993).
Ammonium (NH4 + ) appears to be a common
constituent in metamorphic micas, which may
therefore recycle nitrogen into the mantle in
subduction zones (Sadofsky & Bebout, 2000).
Generally, the composition of fluids trapped as
fluid inclusions in magmatic and metamorphic
rocks of the Earth’s crust is similar to volcanic
gases. Water and carbon dioxide prevail; hydrous

fluid inclusions often contain abundant dissolved
salts. Methane (CH4 ) containing inclusions are
also sometimes found, particularly in low-grade
metamorphic rocks of sedimentary origin and in
sediments containing organic matter (Roedder,
1984). Fluid inclusions in diamonds are an important window to fluid compositions in the mantle. Observed types include CO2 -rich inclusions,
carbonatitic compositions, water-rich inclusions

with often very high silicate content, and highly
saline brines (Navon et al., 1988; Schrauder &
Navon, 1994; Izraeli et al., 2001). Methane and
hydrocarbon-bearing inclusions have also been reported from xenoliths in kimberlites (Tomilenko
et al., 2009).
Although volatiles are only minor or trace constituents of the Earth’s interior, they control
many aspects of the evolution of our planet. This
is for several reasons: (1) Volatiles, particularly
water and carbon dioxide, strongly reduce melting temperatures; melting in subduction zones,
in the seismic low velocity zone and in deeper
parts of the mantle cannot be understood without considering the effect of water and carbon
dioxide (e.g. Tuttle & Bowen, 1958; Kushiro, 1969;
Kushiro, 1972; Tatsumi, 1989; Mierdel et al.,
2007; Hirschmann, 2010). (2) Even trace amount
of water dissolved in major mantle minerals such
as olivine can reduce their mechanical strength
and therefore the viscosity of the mantle by orders of magnitude (Mackwell et al., 1985; Karato
& Jung, 1998; Kohlstedt, 2006). Mantle convection and all associated phenomena, such as plate
movements on the Earth’s surface, are therefore intimately linked to the storage of water
in the mantle. (3) Hydrous fluids and carbonatite melts only occur in trace amounts in the
Earth’s interior. Nevertheless they are responsible for chemical transport processes on local
and on global scales (e.g. Tatsumi, 1989; Iwamori

et al., 2010). (4) The formation and evolution
of the oceans and of the atmosphere is directly
linked to the outgassing of the mantle and to
the recycling (‘‘ingassing’’) of volatiles into the
mantle (e.g. McGovern & Schubert, 1989; Rupke
¨
et al., 2006; Karato, 2011).

1.2 Earth’s Volatile Budget
The Earth very likely formed by accretion of
chondritic material that resembles the bulk
composition of the solar system. In principle,
it should therefore be possible to estimate the
Earth’s volatile budget by considering the volatile
content of chondritic meteorites (e.g. Morbidelli


Volatiles under High Pressure
`
et al., 2002; Albarede,
2009). Unfortunately,
there is a large variation in the contents of water,
carbon and other volatiles between the different
kinds of chondritic meteorites and the Earth,
likely formed by accretion of a mixture of these
different materials, the precise fractions being
poorly constrained. Moreover, during accretion,
massive loss of volatiles to space likely occurred
caused by impacts. This volatile loss has to
be accounted for, which introduces another,

considerable uncertainty.
Estimating the volatile content of the bulk
mantle or of the bulk silicate Earth (crust +
mantle) from cosmochemical arguments is even
more difficult, since the iron–nickel alloy of
the Earth’s core very likely sequestered at least
some fraction of the available volatiles. Evidence
for this comes from the occurrence of sulfides
(troilite, FeS), carbides (cohenite, Fe3 C) and nitrides (osbornite, TiN) as minerals in iron meteorites and from various experimental studies that
show that under appropriate conditions, carbon,
sulfur, nitrogen and hydrogen are quite soluble in
molten iron (Fukai, 1984; Wood, 1993; Okuchi,
1997; Adler & Williams, 2005; Terasaki et al.,
2011). Another line of evidence is the density
deficit of the Earth’s outer core (Birch, 1952),
which requires the presence of some light elements in the iron nickel melt. While most present
models suggest that Si and/or O account for most
of the density deficit, a significant contribution
from other volatiles is possible. The recent model
by Rubie et al. (2011) yields 8 wt % Si, 2 wt % S
and 0.5 wt % O as light elements in the core. The
low oxygen content appears to be consistent with
shock wave data on melts in the Fe–S–O system
(Huang et al., 2011).
The timing of volatile acquisition on the Earth
is another poorly constrained variable. One type
of models assumes that volatiles were acquired
during the main phase of accretion, while another
view holds that volatiles, in particular water were
`

delivered to the Earth very late (Albarede,
2009),
possibly during the formation of a ‘‘late veneer’’ of
chondritic materials or perhaps by comets. How14
ever, both the D/H and 15 N/ N isotope ratios of
terrestrial reservoirs are close to the chondritic

5

values, while they are much lower than those
observed in comets. This limits the cometary
contribution to the terrestrial water and nitrogen budget to a few percent at most (Marty &
Yokochi, 2006).
Recent models of the Earth’s formation (e.g.
Rubie et al., 2011) suggest that during accretion,
initially very volatile depleted chondritic material accreted, which possibly became more water
and volatile-rich towards the end of accretion,
but still before core formation. Such models are
consistent with the observed depletion of moderately volatile elements (e.g. Na, K, Zn) on the
Earth relative to CI chondrites; these elements
may have failed to condense in chondritic material that formed close to the sun. Numerical
models of early solar system evolution suggest
that at later stages of accretion, stronger radial
mixing in the solar system occurred, so that
water and volatile-rich material from the cold
outer part of the solar system entered the growing
planet (Morbidelli et al., 2002). Taking all of the
available evidence together, it is plausible that
the Earth after complete accretion contained 1–5
ocean masses of water (Jambon & Zimmermann,

1990; Hirschmann, 2006). A major depletion of
hydrogen and other light elements by loss to
space during later Earth history can be ruled out,
because the expected depletions of light isotopes
resulting from such a distillation process are not
observed on the Earth.
Evidence on the present-day volatile content of
the Earth’s mantle comes from direct studies of
mantle samples, particularly xenoliths, from measurements of water contents in basalts, which are
partial melts formed in the shallow part of the upper mantle and from remote sensing by seismic
methods and magnetotelluric studies of electrical
conductivity. While the first two methods may
provide constraints on all volatiles, remote sensing techniques are primarily sensitive to water
(Karato 2006).
Pyroxenes in mantle xenoliths that were
rapidly transported to the surface contain from
<100 to about 1000 ppm of water (Skogby, 2006);
olivines may be nearly anhydrous but sometimes contain up to 300 ppm of water (Beran &


6

hans keppler

Libowitzky, 2006). These observations show that
the upper mantle is by no means completely dry
(Bell & Rossman, 1992). However, estimating
mantle abundances of water and other volatiles
from such data is difficult, because samples often
have lost water on their way to the surface; in

some cases, this water loss is evident in diffusion
profiles that may be used to constrain ascent
rates (Demouchy et al., 2006; Peslier & Luhr,
2006; Peslier et al., 2008). Moreover, many of
these xenoliths come from alkali basalts or
kimberlites. The source region of these magmas
may be more enriched in volatiles than the
normal mantle.
Mid-ocean ridge basalts (MORB) tap a volatiledepleted reservoir that is believed to represent
most of the upper mantle. Ocean island basalts
(OIB) appear to come from a less depleted, likely
deeper source. Probably the best constraints on
volatile abundances in the mantle come from
MORB and OIB samples that have been quenched
to a glass by contact with sea water at the bottom
of the ocean (e.g. Saal et al., 2002; Dixon et al.,
2002); the fast quenching rate and the confining
pressure probably suppressed volatile loss. In principle, one can calculate from observed volatile
concentrations in quenched glasses the volatile
content in the source, if the degree of melting
and the mineral/melt partition coefficients of the
volatiles are known. Such calculations, however,
are subject to considerable uncertainties. A much
more reliable and widely used method is based
on the ratio of volatiles to certain incompatible
trace elements, such as H2 O/Ce and CO2 /Nb
(Saal et al., 2002). These ratios are nearly constant in MORB glasses over a large range of
H2 O and CO2 contents that represent different
degrees of melting and crystal fractionation. This
means that the bulk mineral/melt partition coefficient of H2 O is similar to that of Ce and the

bulk mineral/melt partition coefficient of CO2
is similar to Nb. For equal bulk partition coefficients, the H2 O/Ce ratio and the CO2 /Nb ratio
must be the same in the mantle source and in
the basalt, independent of the degree of melting.
Therefore, measured H2 O/Ce ratios and CO2 /Nb
ratios of the basalts can be used together with the

quite well-constrained Ce and Nb contents of the
mantle to estimate the water and carbon dioxide
content in the MORB and OIB sources. Using this
method, Saal et al. (2002) estimated the volatile
contents of the MORB-source upper mantle to
be 142 ± 85 ppm H2 O (by weight), 72 ± 19 ppm
CO2 , 146 ± 35 ppm S, 1 ± 0.5 ppm Cl and 250 ± 50
ppm F. In general, estimates of the water content
in the depleted MORB source using similar methods yield values of 100–250 ppm by weight for
H2 O. In particular, the work by Michael (1995)
suggests some regional variability of the MORB
source water content. Much higher volatile concentrations with up to about 1000 ppm of H2 O
have been obtained for the OIB source region (e.g.
Dixon et al., 1997; Hauri, 2002). The CO2 content
in the OIB source may range from 120 to 1830 ppm
CO2 (Hirschmann & Dasgupta, 2009). If one assumes that the MORB source is representative
for most of the mantle and the OIB source contributes a maximum of 40% to the total mantle,
these numbers would translate to a total mantle
carbon budget in the order of (1–12) . 1023 g of C
(Dasgupta & Hirschmann, 2010). A similar calculation assuming 142 ppm H2 O in the MORB
source and 1000 ppm H2 O in the OIB source
would give a bulk water reservoir in the mantle of 2 . 1024 g, i.e. about 1.4 ocean masses. The
uncertainty in this estimate is, however, quite

significant and the number given is likely to be
only an upper limit of the actual water content.
Water has a strong effect on the physical properties, particularly density, seismic velocities and
electrical conductivity of mantle minerals (Jacobsen, 2006; Karato, 2006). In addition, water may
change the depth and the width of seismic discontinuities (e.g. Frost & Dolejs, 2007), because it
stabilizes phases that can incorporate significant
amounts of water as OH point defects in their
structure. These effects may be used for a remote sensing of the water content in parts of the
mantle that are not accessible to direct sampling.
The dissolution of water as OH point defects
in minerals generally reduces their density and
both P and S wave seismic velocities (Jacobsen,
2006). This is mostly due to the formation of
cation vacancies that usually – but not always