Download SP-569 - GOCE, The Geoid and Oceanography

THE USE OF GOCE FOR DETECTION AND CLASSIFICATION OF MANTLE PLUMES
Gabriele Marquart
SRON and Institute of Earth Science, University of Utrecht, Post box 80021, 3508 TA Utrecht, The Netherlands
ABSTRACT
Confined hot upwelling of material in the Earth’s mantle is known as a mantle plume. Plumes are believed to origin
from the core-mantle thermal boundary layer and rise through the entire mantle driven by positive buoyancy forces. The
gravity signal caused by such a mantle plume is given by the superposition of the effect of the hot anomaly itself and the
effects of the upward deflected surface and internal phase boundaries. The strength and spectrum of the gravity signal
depends on the position of the plume in the Earth’s mantle, as well as on its temperature, size, and rise velocity, and on
the mantle viscosity. With the use of numerical fluid dynamic modeling the gravity field of a typical mantle plume is
studied for various stages of rise. The maximum gravity signal is on the order of 60 mgal and is found when the top of
the plume reaches the base of the lithosphere. The gravity anomaly spectrum of a mantle plume, while rising through
the mantle is significantly different from the gravity spectrum of an old plume, which is spreading below the lithosphere.
While the gravity field of deep mantle plumes is mainly characterized by long wavelength signals, plumes encountering
the lithosphere base and in an old stage of spreading exhibit considerable energy in a shorter wavelength band related to
the size of the plume head. Furthermore the contribution of mantle plumes to the global gravity potential field is estimated
by projecting the numerical plume on 41 known hot spot locations in the Earth’s mantle and convolving the density field
with the response function of the viscous mantle. Finally the possibility to use GOCE to classify known plumes and to
detect plumes rising through the mantle is discussed.
INTRODUCTION
Density variations within the Earth’s mantle are directly related to anomalies of the gravity field. The relation between the
global geoid height anomalies and plate subduction is well established. From the point of mass conservation, subduction
drives a major down flow of material which is compensated by both, a wide spread slow upward migration of mantle
material, and concentrated, fast material upwellings, called mantle plumes, initiated by small temperature perturbations at
the core mantle boundary. Mantle plumes have also been proposed to explain the surface observation of volcanic hot spots.
The number of hot spots varies between ˜30 to 100, depending on the authors. For this study here, I used these hot spots
which are supposed to be linked to deep rooted anomalies [1]. Mantle plumes have typical horizontal dimensions of less
than 1000 km, though in some cases a relatively narrow long swell may exist indication the relative movement between
the plate and the plume during the lifetime of the plume. Deeper in the mantle the plume stem, or the central region of
enhanced temperature is even smaller. In agreement with numerical models and seismic observations (tomography) this
zone is not wider than ˜300-400 km [2]. Numerical experiments clearly demonstrate that plume like features naturally
develop from a thermal boundary layer at the core-mantle boundary. In a viscous material, as the Earth’s mantle, any
internal density pertubations drive a creeping flow which creates a deviatoric stress field which leads to a deflection of
the surface and bottom side and any internal layers with density and viscosity changes. The effect on the gravity field
is given by the superposition of the initial (negative) density anomaly of the hot material and the effects of the deflected
boundaries. Reference [3] showed in a numerical simulation the strong effect of mantle viscosity on the size and number
of plumes and the related geoid anomalies. For this study I first examine the gravity field of a ’typical’ hot spot, both
in nature and in a numerical simulation. In a second step I use the density field of the ’typical’ hot spot, project it at 44
known plume locations and estimate the global contribution of plumes to the gravity field.
____________________________________________
Proc. Second International GOCE User Workshop “GOCE, The Geoid and Oceanography”,
ESA-ESRIN, Frascati, Italy, 8-10 March 2004 (ESA SP-569, June 2004)
Tahiti Islands Altimetry Gravity
200˚
210˚
220˚
Gravity L=2-360
200˚
210˚
Gravity L=2-100
220˚
200˚
210˚
220˚
-5˚
-5˚
-10˚
-10˚
-15˚
-15˚
-20˚
-20˚
-25˚
-25˚
-30˚
-30˚
-225-150 -75 0
75 150 225
-100-75 -50 -25 0 25 50 75 100 -50-40-30-20-10 0 10 20 30 40 50
mgal
mgal
mgal
Geoid L=10-360
Geoid L=10-100
200˚
210˚
220˚
200˚
210˚
220˚
-5˚
-10˚
-15˚
-20˚
-25˚
-30˚
-10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10
m
m
Figure 1. Gravity and geoid height anomalies for the Tahiti chain. Hot spot are marked by white circles, in the center is
Tahiti, at -29S, 140.2W is the MacDonald sea mount, and at -11S, 138W the Marquesas. In the upper row is the gravity
anomaly for different wavelengths ranges and in the lower row the geoid height anomaly.
OBSERVED AND MODELED GRAVITY FIELD OF A MANTLE PLUME
To understand the gravity and geoid signal of a mantle plume I show in Fig. 1 the observed gravity field for three hot
spots: the Tahiti chain in the center, the MacDonald chain to the SE, and the Marquesas chain to the NE. Altimetry gravity
covers a broad spectrum of the field and shows high central values with negative side lobes close by, mainly caused by
the sea mount itself and flexure of the lithosphere. If we study the anomalies in a band for larger wavelengths, we mainly
find central anomalies with values of ˜40 mgal for gravity anomaly, 4-5 m geoid height anomaly, and a width of the whole
structure of ˜500 km.
In a first step I modeled the plume gravity field with time in a numerical simulation. The approach is based on solving
the mass and heat transport and mass conservation equations on a 3D Cartesian grid. The equations are given in nondimensionalized form by
"!#%$'&('$'&)*+-
,.0/
(1)
1
1 ('$'&
132 .54 7678 :9 $'& 31 2
(2)
;7
.</
(3)
=
is the flow pressure, ? > is the velocity vector, @ is temperature, A is viscosity, BDCFE'G denotes the density change at olivine
phase transitions in the mantle, whereby HIEJG is the percentage of material in the state of the new phase and K7E'G is the
VY_ X[Z G]\ is the Rayleigh number and MNaObPSR^cT _ G]\
latent heat change with phase transition. L is time and MNOQPSRUTW^`
R various parameters: mean mantle density C3deR O
is
Rayleigh number.l I usedhInu
themwv-following
values for the
fFg%the
h%ikj)chemical
l"m-npo , gravity
x
k
i
%
i
ikj n , scaling temperature difference B@ =1500°C,
acceleration Orq"s t
, model depth yzO<{
i€‚ƒ`… „ . The thermal expansivity † was depth dependent according to †c‡‰ˆFŠO Ž ‹ aŒ P
thermal diffusivity |}O~
R’‘”“
i%¡£¢
‘•–km
—™˜›š
¤   , and the bulk modulus ¥ Z d for a depth above 410
with Grüneisenparameter œ =1.2, specific heat 'žŸO ~%s {~

T
equal to 135e9 Pa and ¦ E =6, and below ¥ d = 200e9 Pa and ¦ E = 3.5. These values are in accordance with a PREM
Z
¦
¦
mantle.¤ For the olivine-spinel and the spinel-perovskite phase transitions in 410 and 660 km depth I used a density change
w
g
k
i
i
i
k
i
¨
o
¢
¤ The viscosity A is temperature and depth dependent using an approximation
heat of § ~
of
ƒ T \ and a latent
n
‡‰ˆFikŠ¯
‡‰°8± ²‡”³¬]´S@ŠŠ ,T with n ‡ˆ)Š is a depth function to describe a viscosity profile as shown in Fig.
as A©‡ª@¬«›ˆ)Š7O­A®d
%
i
i
2 (left) and ]´ŸOµ‰¶~
to allow additionally for a factor 1000 viscosity reduction over the scaling temperature BD@ .
The viscosity profile on Fig. 2 (left) was obtained by minimizing the misfit between the Champ hydrostatic geoid and
a synthetic geoid based on the tomography model sb4l18 [4], details are found in [5]. The numerical model box has
horizontal dimensions of 4000x4000km and a resolution of 128x128x100 grid points. A plume is forced to start by an
initial temperature pertubation at the bottom of the model with an excess temperature of 350 °C. Fig. 2 (right) shows a
typical view of the temperature field of such a 3D plume.
Figure 2. Left: Viscosity depth profile based on a global fit between the Champ geoid and a synthetic geoid deduced from
the sb4l18 [4] tomography model. Right: View of the 3D numerical plume, light color marks a temperature plane of 1650
°C.
For such a numerical plume model I calculated the gravity anomaly B
l
using the equation
Ç Ç
Ç
Ç
Ç
Ç
Á ¼¾À¿ Á » Á Ç
l
w
g
¹
·
¸
3
º
½
»
j
~
ƒ BCËÊ dJÌ
B O
B ˆ † B @ » ƒ Í B7ˆ H E'G » ƒ BCwE'GFÎ j > ƒÐÏ'Ñ = ‡À³ > » ƒ ˆ ŠÓÒ
(4)
¼
À
¾
:
¿
Í
»
Â
Â
ƒ
Å
d
k
Ä
Æ
´
‰
È
É
´
˜
˜
˜
—
š
»
»Ã  Â
¸ is the gravitational constant and j > ƒ the complex 2D wavenumber. The summation is over all modes µ in x and modes
n in y direction and all depth layers
» i. The first term is due to the dynamic topography at top (ˆ}O i ) and bottom
=
( ˆŸOԈ ƒÕ×Ö ) determined by O
AØ Ø ž , the second term describes the effect of thermal expansion at all depth levels
Í
É
and the˜ third term gives the contribution
due
˜ Æ to phase changes in olivine; the exponential factor is due to the attenuation
with distance and wavenumber.
First I show the dynamic tomography, gravity and geoid height anomaly for the plume model with time (Fig. 3). Due
to the high viscosity in the lower mantle, plume signals are very weak and not observable as long as the plume head is
below the mantle transition zone; plume rise is also slow about 2 cm/a. Therefore the plume needs considerable time to
pass the lower mantle. This problem cannot be overcome by stronger reduction of the viscosity of the plume material,
since the slow rise is mainly caused by the viscosity of the ambient mantle. However, once the plume head has crossed
the transition zone, further rise is as rapid as 15 cm/a and clear signals for all three observables are found. When the
plume head has reached the base of the lithosphere, it starts to spread laterally; this is the point in time when the increase
in topography and gravity anomaly slows down (see Fig. 3). Finally, this stage is just reached in the model at Fig. 3, the
spreading plume head is thinning and cooling and gravity anomaly and geoid height anomaly begin to decline. The height
of the topographic swell is found to be ˜700 m, with a gravity anomaly of ˜55 mgal and a geoid height anomaly of nearly
20 m, the width of the anomaly is ˜800 km. While the gravity anomaly and also the swell height are in agreement with
observations, the geoid anomaly is too big, presumably due to the periodic boundary conditions in the numerical set up,
which lead to an increase of spectral energy for very low modes, mainly reflected in the geoid.
Figure 3. Dynamic topography, gravity anomaly and geoid height anomaly versus time for a numerical simulation of a
mantle plume.
Fig. 4 shows the plume temperature field and the topography, gravity and geoid power spectra for three characteristic
stages of plume rise. The spectra were obtained by summation over all modes Ù for each Ú ; note that mode Ú*ÛÝÜ relates
to the maximum wavelength of 4000 km. If gravity anomalies of amplitudes ˜5 mgal could accurately be measured for
wavelengths between 200 and 2000 km, plumes might be detectable while rising through the upper mantle, before a
volcanic sea mount at the surface has formed. Late stages of plumes (Fig. 4, right column) show a different spectral
energy distribution compared to earlier stages in the way that energy starts to concentrate in mode bands.
Figure 4. Top: Temperature field for a slice through the center of a 3D mantle plume for different stage of rise, time is
indicated in the title. Thick lines indicated the phase boundaries of olivine. Below: Topography, gravity and geoid spectra
for the respective times.
GLOBAL EFFECTS OF MANTLE PLUMES ON THE GRAVITY FIELD
To estimate the global effect of mantle plumes on the gravity potential field, I used the density field related to the 3D
cartesian model plume shown in the previous section, but reduced about 600 km at each side (20 grid points) to suppress
counter flow. This density field was projected in a spherical Earth at 44 hot spot location [1] using a Mercator projection.
The resulting density field at mid mantle depth is shown in Fig. 5.
-225
-200 -175
-150
-125 -100
-75
-50
density contrast kg/m^3
-25
0
Figure 5. Mid mantle density field related to mantle plumes produced by a Mercator projections of a 3D density field of a
Cartesian plume (the Cartesian grid is still weakly visible.
Since plumes in the Earth are different concerning their volcanic activity, geochemical composition and thus, excess
temperature, I used the mass fluxes estimated for the various plumes [1] as a weight for the densities. Based on this
density distribution and the viscosity profile from Fig. 2(left) I determined the global gravity and geoid height anomalies
using the so called kernel approach [e.g. 6]. In this appraoch Eqs. 1 and 2, but for only radial varying viscosity, are
solved for transfer functions (kernels) ÞUߔàªáIâã©àªáwäÀä , which only depend on the zonal spherical harmonics. A multiplication
of these kernels with the spectrum of the density field åæ ßÃç and integration from the core-mantle boundary ( èêéÔë is the
core radius) to the surface along the radius áIì allows to determine the global gravity (Eq. 5) and geoid height anomalies
( í”âî denote here spherical harmonics degree and order)
ÿ
í
‚
õ
ö
åDïwßÃçñð<òwóÅôrá ì í"÷ùøúüû ýÀþ ÞßÀàªáIâã©àªáwäÀä æ)ßÃçŸà‰áIä%á
(5)
In Fig. 6, I show the calculated (synthetic) gravity (top) and geoid height anomalies (bottom) using kernels up to degree
30. Geoid height anomalies are on the order of 6 to 18 m and gravity anomalies are ˜30 to 70 mgal over plume dominated
regions, which is somewhat higher than found in observations (Fig. 1). Nevertheless, the plume geoid explains well
some features up till now not properly included in global geoid modeling, namely the geoid highs in the N-Atlantic and
W-Indian Oceans. The anomalies in the E-Pacific Ocean are generally too high, indicating that already the estimated
combined density effect of the numerous plumes in this region was too large.
THE USE OF GOCE FOR DETECTION AND CLASSIFICATION OF PLUMES
How can GOCE observations help to resolve plumes in the Earth’s mantle? With GOCE it will be possible for the first
time to observe the nearly full gravity anomaly spectrum of known hot spots. This might help to determine for each plume
if vertical rise or horizontal spreading dominates the material transport in the plume, as indicated in Fig. 4. Furthermore,
since plumes have a tendency to form clusters in the Earth, a careful survey of these cluster regions may allow to detect
plumes while still rising in the upper mantle before a volcanic sea mount starts to form. Since the rise velocity of plume
between a depth of 500 km and the base of the lithosphere is high (Fig. 3), they might possibly even have a signal to be
detected in the temporal changes of the potential field.
In the past the global gravity potential field was mainly explained by subduction related density anomalies; this is also
true for densities estimated from seismic tomography, since global tomography has hardly resolution for plume like
-80
-60
-40
-20
-15
-10
-20
0
20
40
60
80
-5
0
5
10
15
20
Plume Gravity mgal
Plume Geoid m
Figure 6. Gravity and geoid height anomalies due to mantle plumes. Densities are based on the plume distribution on
Fig. 5, spherical harmonic expansion was considered up to l=30.
features. As a result the effect of plumes was generally underestimated. However, plume related geoid height anomalies
are supposed to explain about 10% of the observed field (Fig. 6) and thus are important to reduce the misfit between
observed and modeled gravity potential fields which is still on the order of 20%.
Acknowledegment. I thank Yanick Ricard for giving me access to his mantle transfer function program and Bernhard
Steinberger for providing me with his list of hot spot locations and mass fluxes.
REFERENCES
1. Steinberger B.,Plumes in a convection mantle: Models and observations for individual hotspots, J. Geophys. Res., Vol.
105, 11127-11152, 2000.
2. Montelli R., Nolet G.,Dahlen F.A., Masters G., Engdahl E.R. and Shu-Huei Hung, Finite-frequency tomography reveals
a variety of plumes in the mantle,Nature,Vol. 303, 338-342, 2004.
3. Vecsey L., Hier C., Yuen D.A. and Sevre E.R., Two dimensional wavelet analysis applied to geoid anomalies, mixing
and high Rayleigh number mantle convection, Electronic Geosciences, Vol.6, 2001.
4. Masters G., Laske G., Bolton H. and Dziewonski A.M., The relative behavior of shear velocity, bulk sound speed, and
compressional velocity in the mantle: implications for chemical and thermal structure, Vol. 117, Geophysical Monograph,
American Geophysical Union, Washington DC, 2000.
5. Marquart G.,Inferring mantle viscosity and s-wave-density conversion factor from new seismic tomography and geoid
data, J. Geophys. Int., submitted, 2003.
6. Ricard Y., Fleitout L. and Froidevaux C., Geoid height and dynamic stresses for a dynamic Earth, Ann. Geophys., Vol.
2, 267-287,1984.