Dynamics of mantle flow and melting at a ridge-centered hotspot: Iceland and the Mid-Atlantic Ridge
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Earth and Planetary Science Letters 144 Ž1996. 53–74
Dynamics of mantle flow and melting at a ridge-centered hotspot:
Iceland and the Mid-Atlantic Ridge
a,) b,1 c,2
Garrett Ito , Jian Lin , Carl W. Gable
a
MIT r WHOI Joint Program, Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA 02543,
USA
b
Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
c
Earth and EnÕironmental Sciences, Los Alamos National Laboratories, Los Alamos, NM 87545, USA
Received 24 April 1996; accepted 29 July 1996
Abstract
The dynamics of mantle flow and melting of a ridge-centered plume were investigated with three-dimensional
variable-viscosity numerical models, focusing on three buoyancy sources: temperature, melt depletion, and melt retention.
The width, W, to which a plume spreads along a ridge axis, depends on plume volume flux, Q, full spreading rate, U,
buoyancy number, B, and ambientrplume viscosity contrast g . When all melting effects are considered, our numerical
results are best parameterized by W s 2.37Ž Q r U .1r2 Ž Bg . 0.04. Thermal buoyancy is first-order in controlling along-axis
plume spreading while latent heat loss due to melting, and depletion and retention buoyancy forces contribute second-order
effects. We propose two end-member models for the Iceland plume beneath the Mid-Atlantic Ridge ŽMAR.. The first has a
broad plume source with temperature anomaly DTp of 758C, radius, a, of 300 km, and Q of 1.2 = 10 7 km3rmy. The second
is of a narrower and hotter plume source with DTp of 1708C, a radius of 60 km, and Q of 2.1 = 10 6 km3rmy. The broad
plume source predicts successfully the observed seismic crustal thickness, topographic, and gravity anomalies along the
MAR, but predicts an along-axis geochemical plume width substantially broader than that suggested by the observed
87
Srr 86 Sr anomaly. The narrow plume source model predicts successfully the total excess crustal production rate along the
MAR Ž2.5 = 10 5 km3rmy. and a geochemical width consistent with that of the 87Srr 86 Sr anomaly, but it requires
substantial along-axis melt transport to explain the observed along-axis variations in crustal thickness, bathymetry, and
gravity. Calculations suggest that lateral plume dispersion may be radially symmetric rather than channelled along the ridge
axis and that the topographic swell, which is elongated along the Reykjanes Ridge, may be due to rapid off-axis subsidence
associated with lithospheric cooling superimposed on a broader hotspot swell. The two plume source models predict seismic
P-wave velocity reductions of 0.5–2% in the center of the plume, producing travel time delays of 0.2–1.2 s. Predicted
P-wave delay times for the narrow plume source model are more consistent with recent seismic observations beneath
Iceland, suggesting that this model may be more representative of the Iceland plume.
Keywords: Iceland; Mid-Atlantic Ridge; melting; hot spots; mantle plumes
)
Corresponding author. Fax: q1 508 457 2187. E-mail: gito@magellan.whoi.edu
1
Tel: q1 508 289 2576. Fax: q1 508 457 2187. E-mail: jlin@whoi.edu.
2
Tel: q1 505 665 3533. E-mail: gable@lanl.gov.
0012-821Xr96r$12.00 Copyright q 1996 Elsevier Science B.V. All rights reserved.
PII S 0 0 1 2 - 8 2 1 X Ž 9 6 . 0 0 1 5 1 - 354 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
1. Introduction and melting related buoyancy forces on along-axis
spreading of ridge-centered plumes. We used three-
Centered on the Mid-Atlantic Ridge ŽMAR., the dimensional Ž3D., variable viscosity, numerical mod-
Iceland hotspot is the largest melt anomaly through- els to simulate a buoyant plume rising beneath
out the world’s mid-ocean ridge system and is among spreading plates and systematically test the effects of
the large oceanic igneous provinces w1x. The idea that thermal, melt depletion, and melt retention buoyancy
Iceland marks a mantle convection plume rising forces. Our second objective was to constrain the
beneath the MAR has become well established since temperature anomaly, dimension, and volume flux of
its original conception in the early 1970s Že.g. w2–4x.. the Iceland plume by comparing theoretical predic-
The broad topographic swell ŽFig. 1. and correlated tions with observed variations in seismic crustal
along-spreading-axis geochemical anomalies indicate thickness, topography, gravity, and geochemistry on
that the plume rises beneath Iceland and spreads Iceland and along the Mid-Atlantic Ridge. We pro-
laterally along the ridge axis w4,5x. Such along-axis pose two end-member models for the mantle plume
spreading of a mantle plume feeding a ridge axis source beneath Iceland to explain the observations,
may also explain topographic and geochemical and discuss their implications on basalt geochem-
anomalies affected by other near ridge-axis hotspots istry, melt migration, and seismic velocity variations
Že.g. w6–8x., many of which may have contributed along the Mid-Atlantic Ridge axis.
substantially to the earth’s heat and magmatic budget
throughout geologic history.
While the original concept that plumes feed and 2. Governing equations
spread along nearby ridges was proposed two decades
ago, only recently have the fluid dynamic aspects To model mantle flow of a plume–ridge system
been investigated quantitatively. Recent numerical in the upper mantle, we treat the mantle as a fluid of
and laboratory tank experiments have shown that the zero Reynolds number and infinite Prandtl number.
width, W, over which a plume spreads along axis, The 3D stress tensor, t , is defined according to:
increases with plume volume flux, Q, and decreases
with plate full-spreading rate, U w9–11x. Such studies t s 2h Ž TR , p . e˙ y pI Ž 1.
are important in revealing the pertinent physical
where I is the identity matrix and h is viscosity,
processes governing plume–ridge interactions and in
which depends on real temperature TR and hydro-
placing theoretical constraints on properties of man-
static pressure p. The strain rate tensor e˙ depends on
tle plumes such as temperature anomaly, size and
spatial derivatives of mantle flow rate u according to
volume flux.
e˙ s 1r2Ž u i,j q u j,i .. The equilibrium equations in-
Two potentially important sources of buoyancy,
clude conservation of mass:
however, have not been considered in previous
plume–ridge studies. These are melt depletion, which = Ø us0 Ž 2.
lowers the FerMg ratio in the residual mantle and
momentum:
thus reduces its density w12x, and melt retention in
the mantle, which also reduces mantle bulk density = Ø t s yDr Ž T , X , f . gzˆ Ž 3.
Že.g. w13–15x.. It has been proposed that melt deple-
and energy:
tion may be primary in driving spreading of in-
traplate plumes beneath the lithosphere w16x. It has ET TD S
also been proposed that both melt retention buoy- s k= 2 T y u Ø = T y M˙ Ž 4.
Et cp
ancy and depletion buoyancy may contribute signifi-
cantly to along-axis variations in mantle flow and Žsee Table 1 for definition of variables.. Eq. Ž2.
crustal thickness beneath normal mid-ocean ridges satisfies the Boussinesq approximation and neglects
w17,18x. dilational flow due to the extraction of melt, which is
The objectives of this study were two-fold. First, likely to be small w19x. Eq. Ž3. balances viscous
we investigated numerically the effects of thermal stresses with the body force due to density varia-G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74 55
Permeability K depends on grain size b according
to K s Ž b 2f 2 .rŽ72p .. Finally, the rate of melt per-
colation is assumed to be equivalent to the rate at
which melt is generated such that:
ro z
fŽ z. vŽ z. s ˙ z
HD Md Ž 8.
rm
3. Numerical method and boundary conditions
To solve the above equations, we use a Cartesian
numerical code presented by Gable w20,21x. Time
integration is achieved by iterating through discrete
time steps, during each of which we solve for mantle
flow, mantle potential temperature, and melt deple-
tion. In solving the dimensionless forms of the flow
equations ŽEq. Ž1. Eq. Ž2. Eq. Ž3. Eq. Ž4.., horizontal
derivatives are expressed in terms of their Fourier
components while vertical derivatives are expressed
Fig. 1. Combined shipboard and Etopo5 bathymetry map Žcontour
as finite difference approximations. We then invert
interval of 0.5 km. showing Iceland Ž658N, 188W. and the Reyk- for horizontal and vertical components of velocities
janes Žsouth of Iceland. and Kolbeinsey Žnorth of Iceland. ridges. and stresses using a standard relaxation method.
Bold lines mark the ridge axes. This figure and Fig. 4, Fig. 7, Fig. The dimensionless form of Eq. Ž3. is:
8 and Fig. 10, were produced using the GMT software package
w48x.
X
r o gD 3 r o y rm
=Øt s ž a To T X q b X q f / Ž 9.
kho ro
where primes denote dimensionless variables. The
tions, which depend on potential temperature T, melt body force Žright hand side of Eq. Ž9.. is the sum of
depletion X, and mantle porosity f , according to: three terms: the first term, which scales with T X , is a
r o y rm Rayleigh number:
ž
Dr s yr o a T q b X q
ro
f / Ž 5.
Ra s
r o gD 3
a To
Eq. Ž4. balances energy transfer associated with kho
heat conduction, heat advection, and latent heat loss the second term, which scales with X, is a melt
due to melting. Melt depletion is governed by: depletion Rayleigh number:
EX r o gD 3
s yu Ø = X q M˙ Ž 6. Ra X s b
Et kho
where M is melt fraction and M˙ s Ž E M Ž p,T ..rŽ E t ..
To estimate the distribution of porosity f , we and the third term, which scales with f , is a melt
assume that melt migrates vertically through the retention Rayleigh number:
mantle at a melt–mantle velocity contrast Ž v y w . as r o gD 3 r o y rm
governed by Darcy’s flow law:
Ž r o y rm . gK
Raf s
kho ž ro /
f Ž vyw. s Ž 7. Assumed values for b and Ž r o y rm .rr o are 0.06
hm w12,16x and 0.121 w14,18x, respectively. Conse-56 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
quently, depleting the mantle by 25% yields a den- where reference viscosity ho is defined as the mantle
sity reduction equivalent to heating the mantle by viscosity for T s To and z s 0.5D; TR in Kelvin is
4408C, while a melt porosity of 3% yields a density ŽT q 0.6 z q 273., where the term 0.6 z takes into
reduction equivalent to heating the mantle by 1078C. account the adiabatic gradient; and TR o is the real
We assume that mantle viscosity varies with real temperature value of To . To approximate numerically
temperature, TR , and pressure according to: the effects of non-Newtonian rheology, we use re-
E q pV E q r o g Ž 0.5D . V duced values of activation energy E and activation
h s ho exp ½ RTR
y
RTR o 5 Ž 10 . volume V w22x ŽTable 1.. Because lateral variations
in viscosity introduce nonlinearity to the above flow
Table 1
Notation
Variable Meaning Value Units
a plume radius km
b grain size 3 = 10y4 m
B buoyancy number
cp specific heat 1000 J kgy1 8Cy1
D fluid depth 400 km
E activation energy 1.9 = 10 5 J
g acceleration of gravity 9.8 mrs
Dhc isostatic crustal topography km
Dhm mantle dynamic topography km
K mantle permeability m2
M melt fraction wt%
p pressure Pa
P plume tracer concentration
Q volumetric plume flux km3rmy
R gas constant 8.314 J Ky1 moly1
Ra thermal Rayleigh number
Ra X depletion Rayleigh number
Raf retention Rayleigh number
DS entropy change on melting 400 J kgy1 8C
T mantle potential temperature 8C
TR mantle real temperature K
DTp plume temperature anomaly 8C
uŽ u,Õ,w . mantle flow rate vector kmrmy
U ridge full spreading rate kmrmy
V activation volume 4 = 10y6 m3
W along-axis plume width km
X melt depletion wt%
a coefficient of thermal expansion 3.4 = 10y5 Ky1
b coefficient of depletion density reduction
g horhp
k thermal diffusivity 31 km2rmy
h viscosity Pa s
ho reference viscosity Pa s
hp plume viscosity at 0.5D Pa s
hm melt viscosity 1.0 Pa s
v vertical melt flow rate kmrmy
r mantle density kgrm3
rc crust density 2800–3030 kgrm3
rm melt density 2900 kgrm3
ro mantle reference density 3300 kgrm3
rw water density 1000 kgrm3G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74 57
equations, we linearized the equations by introducing determines the rate of decompression melting, com-
additional body force terms w20,23x. The nonlinear prising the source terms in Eq. Ž4. and Eq. Ž6.. The
terms and solutions were then updated upon succes- melting rate term in Eq. Ž4. is latent heat loss, which
sive iterations until solutions converged to our speci- inhibits buoyant mantle flow by increasing both
fied limit. We found that a convergence criterion of mantle density and viscosity, while the melting rate
0.1–0.5% yielded time-integrated solutions with er- term in Eq. Ž6. generates low density depleted man-
rors of - 0.5% while minimizing computing time. tle residuum. To calculate melting rate M, ˙ we incor-
This computational method was tested in 2D with porate the solidus and liquidus functions of McKen-
independent finite element solutions, while in 3D it zie and Bickle w25x, as well as their functional depen-
produced solutions within 2.6% of the best-estimated dence of M on homologous temperature for adia-
extrapolated solutions of a benchmark problem of batic batch melting.
w24x. The rate of melting also determines the volume
The final velocity field is then used in the advec- fraction of melt retained in the mantle, f , which is
tion term in Eq. Ž4. to solve for a new temperature the source of retention buoyancy. To compute poros-
field. Our energy solver uses finite differences with a ity we combine Eq. Ž7. and Eq. Ž8. and solve the
tensor diffusion scheme to reduce numerical diffu- integral in Eq. Ž8. numerically similar to w18x. The
sion, which is intrinsic to finite difference methods grain size dependent melt permeability that we incor-
w20,21x. The same tensor diffusion method is used to porate results in maximum porosities of 1–3%, which
solve Eq. Ž6. for the depletion field. Vertical flow is slightly higher than the 0.1–1% porosity range
Fig. 2. Perspective diagram illustrating steady-state flow Žsmall arrows. and potential temperature Žshaded and contoured at 1008C intervals.
fields of an example calculation that considers thermal buoyancy only and no melting effects Žmodel 5a.. Vertical plane on the right is a
depth cross-section along the ridge axis Ž x s 0., while the vertical plane to the left is a depth cross-section perpendicular to the ridge axis
Ž y s 0.. Top plot shows depth-averaged plume tracer concentration, P, along the ridge axis, which we used to define plume width W. Both
top Ž z s 0. and bottom Ž z s D . boundaries are isothermal planes with the bottom, a free slip boundary and the top, fixed at a horizontal
velocity of 0.5U Žlarge horizontal arrow.. All boundaries are closed to flow both in and out of the numerical box, thus material flows
downward at the end of the box opposite the ridge Ž x s 800 km. and recirculates toward the ridge axis along the base of the box. The effect
of this recirculation on the interaction between plume and ridge are insignificant.58
Table 2
Parameters and results of experimental sets
Model Grid size d x yd y U DTp B g Q W W Ž Qr U .y1 r2
Žkm. Žkmrmy. Ž10 6 km3 rmy.
Set A: thermal buoyancy without latent heat loss
1a 12.5–12.5 20 100 1.729 2.352 0.974 512 2.322
2a 12.5–6.25 120 100 0.0522 2.352 1.059 219 2.328
3a 12.5–6.25 60 100 0.195 2.352 0.987 281 2.193
4a 12.5–6.25 40 100 0.460 2.352 1.038 362 2.251
5a 12.5–12.5 20 200 6.977 5.054 1.965 938 2.991
6a 12.5–6.25 120 200 0.244 5.054 2.478 331 2.305
7a 12.5–6.25 60 200 0.746 5.054 1.892 419 2.358
8a 12.5–12.5 50 200 1.468 5.054 2.585 662 2.914
Ice 1a 12.5–12.5 19 75 36.553 1.849 12.39 2312 2.864
Ice 2a 10.0–10.0 19 170 14.866 3.757 2.186 830 2.447
Set B: thermal buoyancy with latent heat loss
1b 12.5–12.5 20 100 1.720 2.352 0.969 488 2.215
2b 12.5–6.25 120 100 0.0463 2.352 0.939 206 2.331
3b 12.5–6.25 60 100 0.166 2.352 0.843 256 2.162
4b 12.5–12.5 40 100 0.389 2.352 0.876 312 2.111
5b 12.5–12.5 20 200 7.001 5.054 1.972 838 2.667
6b 12.5–6.25 120 200 0.203 5.054 2.059 281 2.147
7b 12.5–6.25 60 200 0.750 5.054 1.901 369 2.072
G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
8b 12.5–12.5 50 200 1.193 5.054 2.100 462 2.257
Ice 1b 12.5–12.5 19 75 34.774 1.849 11.79 2212 2.809
Ice 2b 10.0–10.0 19 170 14.857 3.757 2.185 710 2.094Set C: thermalq depletion buoyancy with latent heat loss
1c 12.5–12.5 20 100 1.427 2.352 0.804 488 2.431
2c 12.5–6.25 120 100 0.0452 2.352 0.917 206 2.360
3c 12.5–6.25 60 100 0.164 2.352 0.834 256 2.173
4c 12.5–12.5 40 100 0.385 2.352 0.868 338 2.291
5c 12.5–12.5 20 200 6.788 5.054 1.912 988 3.194
6c 12.5–6.25 120 200 0.188 5.054 1.902 281 2.234
7c 12.5–6.25 60 200 0.724 5.054 1.835 406 2.323
8c 12.5–12.5 50 200 1.159 5.054 2.040 538 2.661
Ice 1c 12.5–12.5 19 75 34.117 1.849 11.56 2288 2.932
Ice 2c 10.0–10.0 19 170 14.597 3.757 2.147 830 2.469
Set D: thermalq depletionq retention buoyancy with latent heat loss
1d 12.5–12.5 20 100 1.433 2.352 0.808 488 2.426
2d 12.5–6.25 120 100 0.0452 2.352 0.917 206 2.359
3d 12.5–6.25 60 100 0.1648 2.352 0.836 256 2.171
4d 12.5–12.5 40 100 0.358 2.352 0.868 338 2.292
5d 12.5–12.5 20 200 6.764 5.054 1.905 913 2.956
6d 12.5–6.25 120 200 0.193 5.054 1.961 281 2.200
7d 12.5–6.25 60 200 0.718 5.054 1.820 419 2.404
8d 12.5–12.5 50 200 1.139 5.054 2.005 563 2.809
Ice 1d 12.5–12.5 19 75 34.089 1.849 11.56 2288 2.933
Ice 2d 10.0–10.0 19 170 14.501 3.757 2.133 870 2.597
For all experiments vertical grid separation d z is 8 km. Models 1–8: b s 0.06, DT s13008C, ho s1=10 20 Pa s, Ras 0.915=10 6 , Ra X s1.35=10 6 , Raf s 2.75=10 6 ,
a s 70 km. Models Ice 1 and 2: b s 0.024, DT s13508C, ho s 5=10 19 Pa s, Ras1.90=10 6 , Ra X s1.12=10 6 , Raf s 5.70=10 6 . Model Ice 1: as 300 km, DTp s 758C.
Model Ice 2: as60 km, DTp s1708C.
G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
5960 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
inferred from 238 U– 230 Th– 226 Ra disequilibria in width and plume flux converged to steady-state val-
Hawaiian lavas w26x. ues. We ran four sets of experiments ŽTable 2.:
The numerical model set-up is illustrated in Fig. experimental set A includes only thermal buoyancy
2. A ridge axis Ž x s 0. is simulated by defining and omits all melting effects; set B considers only
reflecting temperature Ži.e., zero heat flux. and flow thermal buoyancy but includes latent heat loss; set C
Ži.e., zero shear stress. boundary conditions at the includes additional buoyancy from melt depletion;
vertical sides, and setting the top boundary Ž z s 0. to and set D includes additional buoyancy from melt
move at a constant half-spreading rate 0.5U. Temper- retention.
ature at the surface Ž z s 0. is maintained at 08C, Fig. 2 shows an example of steady-state velocity
which cools and thickens a high viscosity lithosphere and temperature field for a calculation in set A with
approximately with the square-root of x. A plume is a plume source temperature anomaly of 2008C Žmodel
introduced by imposing a columnar-shaped tempera- 5a.. Velocity vectors illustrate the plume rising from
ture anomaly in the lower portion of the box, cen- the conduit source and then spreading both perpen-
tered beneath the ridge axis. The plume is hottest dicular to and along the ridge axis after it impinges
ŽT s To q DTp . at its center and cools as a Gaussian on the base of the lithosphere. The combined effects
function of radial distance to To at its radius a. We of thermal buoyancy and reduced plume viscosity
exploit the symmetry in x and y by centering the result in a maximum plume upwelling rate of 244
plume column at x s y s 0, which allows a quarter kmrmy, which is ) 20 times that of the half spread-
plume in solution space to represent a fully circular ing rate of 10 kmrmy. The corresponding average
plume in virtual space. In the lower portion of the upwelling rate in the melting zone Ž z F 110 km. is
box Ž z ) 0.6 D ., we impose the potential temperature 85 kmrmy.
to be To everywhere except inside the plume source. Fig. 3a shows the steady-state velocity and mantle
Thus, the energy equation is solved only in the upper density fields for the same plume source temperature
portion of the box Ž0.6 D G z G 0.. anomaly but with the additional effects of latent heat
To ensure numerical accuracy in the flow solu- loss Žmodel 5b.. In the melting region of the plume
tions, we set a non-dimensional viscosity Žhrho . center, potential temperatures are ; 1308C cooler
upper limit of 200 and set a lower limit of 0.1. The and consequently the plume is 65% less buoyant and
upper viscosity limit is sufficient to simulate accu- 3 times more viscous than the calculation without
rately a rigid lithosphere Ži.e., u s U and Õ s w s 0 latent heat loss ŽFig. 2.. The resulting average up-
in the lithosphere., while the lower limit allows us to welling rate in the melting zone is 50 kmrmy, only
incorporate the full viscosity reduction in a plume ; 60% of the predicted average upwelling rate of
with temperature anomaly of 2008C. The depth de- the model without latent heat loss Žmodel 5a..
pendence of viscosity yields a factor of ; 4 viscos- The addition of melt depletion buoyancy in model
ity increase between top and bottom of the box for a 5c generates an additional ; 1% lateral density con-
constant mantle temperature. trast between the plume center and the mantle be-
neath normal ridge sections far from the plume ŽFig.
3b.. The resulting average melting zone upwelling
rate is 67 kmrmy. As material rises more rapidly in
4. Steady-state along-axis width of a mantle plume the plume center, it spreads more rapidly along the
head base of the rigid lithosphere. This in turn inhibits
upwelling at radial distances of 100–150 km, shown
We seek here to quantify the effects of melting on as negative velocity differences in Fig. 3b.
mantle flow and thus the dependence of along-axis Finally, model 5d considers the additional buoy-
plume width, W, on plume flux, Q, and plate spread- ancy from melt retention ŽFig. 3c.. The high melting
ing rate, U. We began numerical experiments with rate in the plume center results in a maximum poros-
the steady-state temperature solution of a ridge with- ity of 2.5%, to reduce bulk density in the plume
out the plume. Then, after activating the plume, we center by an additional 0.3%. This added retention
integrated through time until both along-axis plume buoyancy further enhances the average upwellingG. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74 61 rate in the melting zone to 77 kmrmy, which is the upwelling-inhibiting effects of latent heat loss. ; 90% of that predicted by the model that neglects In all models examined we find, as did Ribe et al. all melting effects Žmodel 5a.. Thus, the added melt- w11x, that the thickening lithosphere does not channel ing-related buoyancy forces approximately balance the plume preferentially along the ridge axis. On the Fig. 3. Perspective views of depth cross-sections showing percentage density reduction in the mantle due to: Ža. thermal buoyancy with latent heat loss Ž DTp s 2008C. Žmodel 5b.; Žb. plus melt depletion buoyancy Žmodel 5c.; and Žc. plus melt retention buoyancy Žmodel 5d.. Contour interval is 0.5%. Vectors in Ža. show mantle flow. Vectors in Žb. show the differences between flows with and without melt depletion buoyancy. Vectors in Žc. show the difference between flows with and without melt retention buoyancy. Downward pointing vectors in Žb. and Žc. illustrate reduced upwelling, not downwelling.
62 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
contrary, the spreading lithosphere enhances ridge- plume flux weighted by plume temperature anomaly.
perpendicular flow by pulling plume material away With these modifications we obtain a best-fit linear
from the ridge-axis, and actually impedes along-axis regression of W s 2.80Ž QrU .1r2 B 0.05 which is in
flow by viscous shear. These effects however are good agreement with that of Ribe et al. w11x of
small — the total along-axis flux at y s 70 km is W s 2.93Ž QrU .1r2 B 0.052 . While the scaling and ex-
within a few percent of the total ridge-perpendicular ponential factors vary slightly between our results
flux at x s 70 km. Thus, the rate of spreading away and those of w9x and w11x, the general form of Eq.
from the plume center is approximately equal in all Ž11. is robust and insensitive to differences in far-
radial directions. field experimental boundary conditions.
To determine how W depends on Q and U for For calculations of thermal buoyancy with latent
each experimental set, we examine spreading rates heat loss Žset B., we obtain a best-fit linear regres-
between 20 and 120 kmrmy and we vary Q by sion function:
changing DTp between 1008C and 2008C ŽTable 2.. 1r2
Q
We track the distribution of plume material by intro- 0.02
ducing a tracer, P, in the plume and using our tensor
W s 2.21 ž /
U
Ž Bg . Ž 12 .
diffusion scheme to advect P passively with the The smaller constant and exponential coefficients
mantle. P s 1 is introduced in the plume source relative to those in Eq. Ž11. reflect the inhibiting
column to represent 100% plume material, while effects of latent heat on along-axis plume spreading.
P s 0 represents 0% plume material and 100% ambi- The average values of W Ž Q r U .y1 r2 for experi-
ent mantle. We define W as the along-axis extent to mental set B is 2.29, or ; 92% of the average in set
which the depth-integrated tracer concentration: A.
1 0.6 D
Addition of depletion buoyancy in experimental
ž 0.6 D
H0 P Ž 0, y, z . d z / set C results in a best-fit regression function:
Q 1r2
0.04
is ) 0.05 ŽFig. 2.. The volume flux of the plume is
measured at z s 0.6 D by integrating the vertical
W s 2.37 ž /
U
Ž Bg . Ž 13 .
flow of the plume source over its cross-sectional This function is essentially the same as that of Eq.
area. Ž11. for set A. The average value of W Ž Q r U .y1 r2
For calculations that include thermal buoyancy
only without latent heat loss Žset A., we find, similar
to w9,11x, that W depends primarily on the scaling
quantity Ž QrU .1r2 , and depends secondarily on the
p lu m e buoyancy num ber Ž B s
Ž Q r o a DTp .rŽ48ho U 2 .., as defined in w11x, and on
the ambientrplume viscosity ratio g s horhp , at
z s 0.5D. A modified buoyancy number which de-
pends on plume viscosity is thus Ž Bg .. The best-fit
linear regression function obtained by fitting linear
and constant coefficients to lnŽ Bg . is:
1r2
Q 0.04 Fig. 4. Numerical results Ždots. of calculations with all melting
W s 2.35 ž / U
Ž Bg . Ž 11 . effects included Žset D.. The two Iceland models are circled. The
solid black line is the best-fit linear regression shown by Eq. Ž13.,
Calculated values of W Ž Q r U .y1 r2 range from which yields a standard deviation misfit that is 7% of the median
2.2 to 2.9 ŽTable 2. with a mean value of 2.50. To value of W Ž Qr U .y1 r2 . Also shown are corresponding linear
regressions of calculations of thermal buoyancy without latent
compare our results directly with those of Ribe et al. heat loss Žset A, gray., thermal buoyancy with latent heat loss Žset
w11x, we omit the dependence on g and incorporate B, dotted., and additional buoyancy from melt depletion Žset C,
their definition of Q, which is the integrated vertical dashed..G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74 63
of 2.51 is also essentially the same as that in set A. We take the top of our model to be the isostatic
The further addition of melt retention Žset D. does depth of the seafloor for a 7 km thick model crust,
not change this relationship significantly, as shown and assume isostatic compensation of crustal thick-
by the similarity in regression lines of set C and set ness variations that deviate from this model crust.
D ŽFig. 4.. Thus, the effects of retention buoyancy Consequently, variations in crustal thickness impart
occur at wavelengths too short to affect the full no lithostatic pressure variations in the mantle. To
width W. In summary, the effects of latent heat loss prevent melting at depths shallower than the isostatic
to inhibit lateral plume spreading are approximately base of the thickened Icelandic crust we prohibit
balanced by the added buoyancy of melt depletion melting everywhere at depths - 28 km. Melting
which enhances plume spreading. may stop deeper, however, if hydrothermal cooling
is important w32x.
To calculate isostatic topography of the seafloor,
we consider contributions from both the crust Ž D h c .
5. Models of Iceland and the Mid-Atlantic Ridge
and mantle Ž D h m .. In calculating D h c , we assume
Airy compensation of the crust with a surface den-
We next investigate models of mantle flow and sity contrast of Ž rc y r w . for the submarine portion
melting beneath Iceland, a relatively well studied of topography and rc for the subaerial portion. The
example of a ridge-centered plume. Our objective is crust along the Reykjanes and Kolbeinsey ridges is
to constrain the temperature anomaly, dimension, assumed to have a density of 2800 kgrm3 , except
and volume flux of the Iceland plume by comparing within 500 km of the plume center, where we in-
theoretical model predictions with observed along- crease it linearly to a maximum of 3030 kgrm3 at
axis variations in seismic crustal thickness, topogra- Iceland, to account for the higher MgO content of
phy, gravity, and basalt geochemistry. Previous geo- the Icelandic crust w33x. The mantle contribution to
physical studies of the Iceland–MAR system demon- topography, or dynamic topography is calculated
strated that the topographic high at Iceland coincides from vertical normal stress at the top layer of our
with a low in mantle Bouguer gravity anomaly model:
ŽMBA., and that both MBA and topographic anoma-
lies can be explained by the combined effects of tz z
anomalously thick crust and low density mantle gen- Dhm s Ž 15 .
Ž ro y rw . g
erated by the Iceland plume w27,28x. MBA are calcu-
lated by subtracting from free-air gravity the attrac- With this definition, our calculations predict
tion of seafloor topography and the crust–mantle seafloor depths to increase approximately with the
interface, assuming a uniform crustal thickness of 7 square-root of distance from the ridge-axis, which is
km Že.g., w29,30x.. Because as much as 75% of the consistent with lithospheric half space cooling mod-
along-axis topographic and MBA variations may arise els Že.g. w34x.. In addition to using D h m to predict
from thickened igneous crust w28,31x, crustal thick- topography, we also use D h m to estimate crustal
ness calculations are an important link between our thickness in a manner independent of our mantle
models and surface observations. melting calculations. This ‘isostatic crustal thick-
To predict crustal thickness from mantle melting ness’ is defined as the isostatic thickness of crust
calculations, we assume that all melt generated within required to account for the difference between the
200 km of the ridge-axis accretes perpendicularly to observed topography and D h m .
the ridge-axis and take the top of our numerical box In computing MBA we again consider both crustal
to be the isostatic depth of the seafloor for crust of and mantle contributions. The crustal contribution is
normal thickness Ž7 km.. The crustal thickness as a the gravitational signal due to undulations at the
function of along-axis coordinate y is therefore: crust–mantle interface that deviate from the constant
2 ro crustal thickness reference model originally assumed
Cr Ž y . s ž / HM˙ Ž y . d xd z Ž 14 . in generating MBA. For these calculations we em-
U rm ploy the method of w35x. The mantle contribution to64 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
gravity is calculated by integrating the contributions model Ice 1d also shows good agreement with the
from lateral density variations at each model layer observed crustal thickness profile ŽFig. 5b.. The
w29x. excess magmatic flux rate required to sustain the
anomalous Žin excess of a 7 km thick. isostatic crust
5.1. Broad plume source model along the MAR, 1000 km north and south of Iceland,
is 2.33 = 10 5 km3rmy. This value is within a few
Our first model of the Iceland–MAR system, percent of the 2.45 = 10 5 km3rmy excess crustal
much like that of Ribe et al. w11x, considers a broad production rate predicted from our melting model.
plume source with a relatively small temperature The predicted topography from the melting-model
anomaly Žmodel Ice 1, a s 300 km, and DTp s 758C. crustal profile generates 70% Ž; 2.5 km. of the total
rising beneath a model MAR with a full spreading along-axis topographic anomaly of ; 3.5 km ŽFig.
rate of 19 kmrmy w36x ŽFig. 5a.. At this spreading 5c.. We predict the remaining 30% Ž; 1 km. of
rate, To s 13508C is required to produce a ; 7 km topography to be supported by dynamic mantle uplift
thick, normal oceanic crust. The calculation that which is obtained with a b value of 0.024 w12,17x.
includes all melting effects Žmodel Ice 1d. predicts a Of mantle dynamic topography, D h m , thermal buoy-
plume volume flux of ; 1.2 = 10 7 km3rmy, gener- ancy generates ; 70% while depletion and retention
ating an along-axis plume-head width, W, of ; 2300 buoyancy generate the remaining 22% and 8%, re-
km ŽFig. 5a.. The predicted maximum upwelling rate spectively. The predicted total amplitude of D h m is
in model Ice 1d is 105 kmrmy, which is ) 10 times consistent with the 0.5–1.5 km of Eocene uplift as
that beneath the unaffected portion of the ridge far inferred from sediment core analyses w38x.
from the plume. The predicted upwelling rate aver- The mantle Bouguer anomaly along the subma-
aged through the melting zone in the plume center is rine portions of the ridge is also matched well by
20 kmrmy. Melt retention buoyancy contributes predictions of model Ice 1d using both the melting
minimal effects to this average upwelling rate and model and isostatic crust ŽFig. 5d.. Similar to
thus very little to melting rate. bathymetry, the crustal MBA accounts for most
The enhanced upwelling rate in the plume center, Ž70%. of the total predicted anomaly of ; 330
combined with an increase in total melt extent Ž23% mGal, with the mantle contributing the remaining
compared to 13% beneath the ridge far away from 30%. Of the predicted mantle gravity signal, 75% is
the plume., generates a maximum crustal thickness from thermal expansion, while 20% and 5% are
of ; 30 km, consistent with the seismic measure- generated by melt depletion and retention, respec-
ments on Iceland w37x ŽFig. 5b.. Along the length of tively. The successful predictions of both topography
the Reykjanes Ridge, the crustal thickness profiles and MBA support the hypothesis that these anoma-
predicted by melting in model Ice 1d shows striking lies are from the same sources: primarily crustal
similarity to the seismic measurements. From the thickness variations and secondarily density varia-
plume center, the predicted crust first thins to 9.5 km tions in the shallow mantle.
at an along-axis distance of ; 300 km, then thickens
to 11 km at a distance of ; 500 km, and finally 5.2. Narrow plume source model
tapers to a thickness of 6.7 km at a distance of
; 1300 km. The predicted local minimum in crustal Our second set of models ŽIce 2. represent an-
thickness at y ; 300 km is caused by a reduced other end-member possibility — that of a narrower
mantle upwelling rate at the plume edge, caused by and hotter plume source ŽFig. 6a; a s 60 km, and
the rapid vertical flux in the plume center. Melt DTp s 1708C.. With all melting effects included,
retention does not significantly affect crustal thick- model Ice 2d predicts a plume volume flux of 2.1 =
ness because the predicted 0.5% contrast in porosity 10 6 km3rmy, which spreads plume material to a full
between the plume center and normal sub-ridge man- width, W, of 870 km along the ridge axis. The
tle is too small to appreciably enhance plume up- maximum upwelling rate of model Ice 2d is 283
welling rate in the shallowest 100 km, where melting kmrmy, which is ) 2.5 times greater than the maxi-
occurs. The isostatic crustal thickness profile of mum upwelling rate in the broad plume source ŽmodelG. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74 65 Fig. 5. Ža. Perspective diagram of model Ice 1d Žbroad plume source. shaded according to temperature. Black contours are depletion Žcontour interval is 5%. and white contours are melting rates of 0.01, 0.03, and 0.05 myy1 . Žb. Comparison between model Ice 1d melting model crust Žsolid. and isostatic crust Ždashed., and seismic crustal thickness measurements along the Reykjanes Ridge Ždots. and at older seafloor near the continental margins Žtriangles. from w37x. Žc. and Žd. Comparison between the observed bathymetry Žthick gray curve in c. and MBA Žthick gray curve in d. along the MAR and predicted profiles of model Ice 1d using the melting model crust Žbold curves in c and d. and isostatic crust Žthick dashed curved in d.. Also shown are predicted mantle components due to various mantle density sources as labeled. Bathymetry data and MBA are from w28x. We do not consider the on-land gravity of Iceland. Ice 1d., and ; 30 time faster than normal ridge that of Ice 1d, which results in melting rates an order upwelling rates. In addition, the maximum extent of of magnitude greater than those in model Ice 1d ŽFig. melting is increased to 30%. Thus, a larger volume 6a.. For the model without melt retention Žmodel Ice of mantle material is predicted to circulate more 2c., the melting-zone averaged upwelling rate is 63 rapidly through a thicker melting zone relative to kmrmy and the maximum melting model crustal
66 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
drastically exceed the observed crustal thicknesses
ŽFig. 6b.. The resulting topographic and MBA
anomalies also fail to match the observations ŽFig.
6c,d.. The isostatic crustal profile, on the other hand,
yields predictions in much better agreement with the
observed crustal thicknesses ŽFig. 6b., topography
Žby definition. ŽFig. 6c., and MBA ŽFig. 6d. along
the ridge-axis. Thus, if the Iceland plume is compa-
rable in radius and temperature to our narrow plume
source model, a substantial portion of the melt pro-
duced beneath Iceland must accrete more uniformly
along-axis than our melting-model crust, much like
our isostatic crustal profile. This condition suggests
melt migration andror lower crustal ductile flow
w40x occurs over distances of several hundreds of
kilometers away from Iceland, along the Reykjanes
and Kolbeinsey ridges.
Because the mechanisms of along-ridge-axis melt
transport are poorly understood, we do not attempt to
model this process in this study. Instead, we assume
a priori that along-axis melt redistribution does occur
and that the end result of this process leads to the
isostatic crustal profile. In arriving at our final Ice 2
models, we thus sought values of DTp and a such
that the total volume rate of melt produced by the
melting model matched that required to sustain the
isostatic crustal profile. The best solutions of DTp s
1708C and a s 60 km yield a total excess melt
production rate of 2.54 = 10 5 km3rmy Žmodel Ice
2d., which is within 1% of that required of the
Fig. 6. As Fig. 5 but for Ice 2 models Žnarrow plume source.. isostatic crustal profile.
Symbols as in Fig. 5 except melting rate contours in Ža. are 0.01,
0.03, 0.05, 0.2 and 0.4 myy1 .
In these narrower, hotter plume source models,
the mantle contribution to topography and gravity
relative to the crustal contribution becomes much
thickness is 147 km. With melt retention Žmodel Ice larger than in the broader, cooler source models. For
2d., the 2.9% porosity in the plume is sufficient to example, model Ice 2d predicts a mantle topographic
increase the predicted melting-zone-averaged up- uplift that is 51% Ž1.8 km. of the observed along-axis
welling rate to 80 kmrmy and the maximum melt- topographic anomaly ŽFig. 6c., and a mantle contri-
ing-model crustal thickness to 166 km ŽFig. 6b.. In bution to MBA that is 48% Ž158 mGal. of the
model Ice 2d, the melting-model crust thins to 3 km observed MBA variation ŽFig. 6d.. The crust there-
at an along-axis distance of 120 km, where up- fore generates only 49% and 52% of the total topo-
welling and thus melting rate is strongly reduced at graphic and MBA variations, respectively. Calcula-
the edge of the rapidly upwelling plume center ŽFig. tions also predict the importance of melt-related
6a.. buoyancy to the mantle anomalies to be significantly
The high maximum crustal thicknesses predicted greater for these hotter plume source models relative
by the narrow plume source melting model drasti- to the cooler source models. Thermal buoyancy is
cally exceed calculations of previous studies that predicted to produce 47% of D h m , and 60% of the
assumed passive mantle upwelling Že.g. w28,39x. and mantle MBA variation; melt depletion produces 39%G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74 67
of D h m and 25% of the mantle MBA; and melt between Iceland and an across-axis distance of 400
retention produces the remaining 14% of D h m and km away from the ridge-axis, and both predict the
15% of the mantle MBA variation. south-pointing swell, elongated along the Reykjanes
Ridge. As demonstrated above, the southward deep-
5.3. Reykjanes Ridge bathymetric swell ening of the ridge axis reflects crustal thinning and
mantle density increase with distance from the Ice-
Similar to along-axis topography, we predict map land plume source. But perpendicular to the ridge-
view topography by adding mantle dynamic topogra- axis, seafloor topography is dominated by the subsi-
phy ŽEq. Ž15.. and isostatic topography of the crust dence of the cooling lithosphere. Thus, contrary to
considering only along-axis variations in crustal previous notions Že.g. w5,6x., the regional bathymetric
thickness. For model Ice 1d, we use the melting- swell does not require a pipe-like flow of plume
model crust and for model Ice 2d, we use the material along the ridge axis. Instead, we predict the
isostatic crust. Fig. 7 illustrates the observed topog- plume head to spread radially and explain the gen-
raphy in map view along the Reykjanes Ridge south eral shape of the elongated Icelandic swell as the
of Iceland, and predictions of models Ice 1d and Ice superposition of radial plume spreading and across-
2d. The similarity between the predictions and obser- axis lithospheric cooling. The models presented in
vations at broad wavelengths Ž); 500 km. are this study, however, do not consider time-dependent
compelling: both models predict the ; 2.0 km variations in crustal accretion which may also con-
across-axis decrease in broad wavelength topography tribute to across-axis topographic variations.
Fig. 7. Ža. Observed topography of Iceland and the Reykjanes Ridge Žoblique Mercator projection.. Žb. Mantleq crustal topography
predicted from our broad plume source model Ice 1d using the melting model crust. Žc. Mantleq crustal topography predicted from our
narrow plume source model Ice 2d using the isostatic crust.68 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
5.4. Rare earth element and isotopic anomalies with previous inversions of melt fraction versus depth
as calculated by White et al. w33x. At the plume
A potentially useful independent constraint on center, our broad plume source model ŽIce 1d. and
melting depth and extents, which reflect mantle tem- narrow plume source model ŽIce 2d. predict melt
perature, is rare earth element ŽREE. concentrations fractions that are lower and higher, respectively, than
of axial basalts. A simple comparison can be made White et al.’s w33x inversions for Krafla volcano on
Iceland ŽFig. 8a.. The potential temperature of the
Iceland plume source, therefore, is likely to be
1425–15208C, as represented by our two end-mem-
ber models. At ; 550 km from Iceland on the
Reykjanes Ridge, model Ice 1d predicts melting
depths and extents closely matching those obtained
from the REE inversions w33x ŽFig. 8b.. Model Ice
2d, however, underpredicts the extents and depths
because plume material from our narrow plume
source did not spread to this along-axis distance.
Thus, in order to explain the REE composition of
basalts sampled 550 km away from Iceland, once
again our model Ice 2d seems to require plume-de-
rived melts to migrate substantially along the Reyk-
janes Ridge axis.
While REE concentrations reflect melting process
beneath Iceland, Sr isotope ratios may reflect the
concentration of the plume source material relative
to that of normal mid-ocean ridge basalts ŽMORB..
Schilling w8,41x interprets the peak in 87 Srr 86 Sr at
Iceland to mark the center of the Iceland plume,
where the plume source concentration is highest, and
interprets the decrease in 87 Srr 86 Sr north and south
of Iceland to reflect a decrease in percent of plume
material comprising the mantle melt source.
To address questions of where and how plume–
Fig. 8. Ža. and Žb. Comparison between White et al.’s w33x REE MORB mixing occurs, we calculate the fraction of
inversion of melt fraction Žgray. and our predictions from models plume tracer, P, in accumulated melts along the
Ice 1d Žsolid. and Ice 2d Ždashed. at Krafla, near the plume center model ridge-axis Žneglecting along-axis melt migra-
Ža., and at DSDP Site 409 on the Reykjanes Ridge 550 km away
from the plume center Žb.. This inversion method assumes frac-
tion. ŽFig. 8c.. At each numerical grid where new
tional melting and includes differences in partitioning coefficients melt is generated, P is weighted by melting rate. We
between the spinel and garnet stability fields. It also assumes then integrated over each ridge-perpendicular plane
complete extraction and mixing of all melts generated in the to compute a weighted mean value Ž P . for each
melting region, which makes the estimation of maximum depth of point along the ridge axis:
melting sensitive to the low-degree melt compositions w49x. An-
other assumption is the parent source composition Žprimitive
mantle beneath Krafla and a 50–50% mix of primitive and
HP Ž x , y, z . M˙ Ž x , y, z . d xd z
P Ž y. s Ž 16 .
depleted MORB source along the Reykjanes Ridge., which is HM˙ Ž x , y, z . d xd z
important in estimating the maximum extent of melting. Žc.
Comparison between observed Sr isotope concentrations w41x along This calculation thus approximates the plume con-
Iceland and the MAR and weighted mean plume tracer concentra-
tion P in the accumulated melts for models Ice 1d Žsolid. and Ice
centration of pooled melts along the ridge axis. For
2d Ždashed.. The peak in 87 Srr 86 Sr to the north of Iceland is due example, P s 1.0 indicates that all of the melt gener-
to the Jan Mayen hotspot w41x which we do not model. ated in a plane perpendicular to that point of theG. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74 69
ridge is entirely plume source derived. Likewise, km, which is more consistent with that of the
87
P s 0.0 indicates that none of the melts are plume Srr 86 Sr anomaly; however, its profile in P would
derived and 0.0 - P - 1.0 indicates plume–MORB likely be broader if along-axis melt migration were
mixing. considered. Both model Ice 1d and Ice 2d predict
Model Ice 1d predicts an along-axis geochemical that the melts are entirely plume derived Ž P s 1.0.
plume width of ) 2000 km, significantly greater over most of the plume width, and become fully
than that suggested by the 87 Srr 86 Sr anomaly. Ice ambient mantle derived Ž P s 0.0. within 200–300
2d, on the other hand, predicts a width of ; 1000 km of the edge of the plume. These results suggest
Fig. 9. Ža. Lower diagram shows predicted P-wave velocity variations with contour interval of 0.5% for model Ice 1d Žbroad plume source.
caused by the combined effects of temperature, melt depletion, and melt retention. Top panel illustrates the predicted P-wave travel-time
delays, assuming vertically passing rays, for along-axial and across-axis profiles due to successively added mantle effects as labeled. Žb.
Same as Ža. but for model Ice 2d Žnarrow plume source.. The lowest velocity region occurs at depths 50–100 km due to the predicted high
melt retention.70 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
that, within most of the plume-affected portion of the anomalies over a much narrower lateral extent. Be-
ridge, very little mixing occurs between plume and low the melting zone, the 1708C plume temperature
ambient source material in the shallow mantle. Thus, anomaly reduces calculated P-wave velocities by
if the gradients in 87 Srr 86 Sr away from Iceland more than 1%. In the melt zone, however, the P-wave
reflect plume–MORB mixing, it most likely occurs velocities are reduced to as much as 2% due to the
deeper in the mantle, possibly by ambient mantle 2.9% melt retention ŽFig. 9b.. Along the ridge-axis,
entrainment of the ascending plume Že.g. w42x.. the travel-time delay for vertically passing rays is
predicted to be q0.75 s at the plume center and to
decrease by 0.85 s within ; 80 km. Approximately
5.5. Predictions of P-waÕe seismic Õelocity anoma- half of this travel-time residual is predicted to arise
lies in the high-porosity melt zone in the shallow mantle.
Across the ridge-axis, the additional effect of litho-
Observations of compressional wave ŽP-wave. spheric cooling yields a predicted travel-time differ-
seismic travel-time variations and associated mantle ence of 1 s within ; 80 km of the plume center and
P-wave velocity variations provide critical con- a travel-time difference of 1.2 s over an across-axis
straints on mantle properties beneath Iceland. To distance of 400 km. Preliminary results of the ongo-
predict P-wave seismic velocity anomalies, we as- ing ICEMELT experiment at Iceland have revealed
sume a reference P-wave velocity of 8 kmrs, which azimuthal variations in P-wave travel times as high
decreases by 6.25 = 10y3 % for each 18C increase in as 1 s within 100 km of the ridge axis w44x, suggest-
mantle temperature, increases by 0.1% for each 1% ing that the narrow plume source model better repre-
increase in depletion, and decreases by 1.25% for sents Iceland than does the broad plume source
each 1% increase in pore volume w43x. We also model.
predict P-wave travel-time residuals by calculating
travel times of seismic rays passing vertically through
the 400 km thickness of our mantle models.
6. Discussion
The broad plume source model ŽIce 1d. predicts a
maximum decrease in P-wave velocity below the
melting region of ; 0.5% relative to the surrounding 6.1. Importance of melting effects
mantle. In the melting region, the predicted P-wave
velocity anomaly diminishes because the velocity- The importance of melting effects on mantle flow,
enhancing effects of latent heat loss and melt deple- melt production, and surface observables are summa-
tion exceed the velocity-reducing effect of melt re- rized in Fig. 10. Mantle melting generates apprecia-
tention ŽFig. 9a.. The corresponding travel-time de- ble effects on mantle properties; however, over the
lay for vertically passing rays is predicted to be range of plume viscosities considered in our models,
q0.23 s at the plume center and decrease to zero at the effect of latent heat loss on mantle flow largely
an along-axis distance of ; 1200 km. The contribu- cancels the effects of depletion and retention buoy-
tions to travel-time delay above the plume center are ancy. As a result, the combined effects of these
q0.25 s from excess mantle temperature, y0.09 s factors on mantle flow are small, as reflected in the
from melt depletion, and q0.07 s from melt reten- small changes in the predicted values of W Ž Q r
tion. Across the ridge-axis, lithospheric cooling dom- U .y1 r2 ŽFig. 4 and Fig. 10.. Similarly, when plume
inates, resulting in a predicted travel-time difference temperature anomalies are mild, as in the Ice 1
of 0.5 s between the plume center and at an across- models, the melting-related factors have only sec-
axis distance of 400 km. The broad plume source ond-order effects on upwelling rate, as reflected in
model thus predicts only a gradual decrease in small changes in the predicted crustal thickness ŽFig.
travel-time delay across the ridge axis and even 10.. When plume temperature anomalies are larger,
smaller variations along the ridge-axis. however, as in the Ice 2 models, melt retention may
In contrast, the narrow plume source of model Ice enhance the predicted crustal thickness by 20% rela-
2d predicts significantly larger amplitudes of P-wave tive to calculations that do not include retention.G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74 71
6.2. Model uncertainties
Because melting-related factors do not affect sig-
nificantly large-scale mantle flow, uncertainties asso-
ciated with our melt calculations, such as the as-
sumed batch melting w25x, our choice of b values,
and the melt porosity calculations, are likely to have
only secondary effect on our estimates of plume
source radius and temperature. By far the most im-
portant uncertainty in this regard is mantle rheology.
The reference mantle viscosity ho controls directly
the rate of mantle upwelling in response to density
variations ŽEq. Ž9... But, unfortunately, viscosity be-
neath ridges is not known to within one or even two
orders of magnitude Že.g. w45x.. One mechanism that
may yield a substantially higher viscosity than that
which we have assumed is dehydration at the onset
of melting w45x. A higher melting zone viscosity, for
example, would most likely require a greater temper-
ature anomaly of the broad plume source model to
explain the geophysical observations, or require a
greater source radius and less along-axis melt redis-
Fig. 10. Characteristic variables predicted by models with melting
normalized by those predicted by models without melting. We
tribution of our narrow plume source model to ex-
choose the mean value of W Ž Qr U .y1 r2 for each experimental plain the observations. Thus, because of the uncer-
set and maximum value of along-axis variations for each of the tainty of viscosity, our Iceland plume models are not
other variables. Crustal thickness anomalies are normalized by unique. However, they do provide reasonable bounds
calculations with thermal buoyancy and latent heat loss. on the plume source radius and temperature given
the similarities between model predictions and the
variety of geophysical and geochemical observations
Contrasting with their mild influence on mantle considered.
flow, the melting-related factors have substantial ef-
fects on the predicted geophysical observables and 6.3. Plume Õolume flux estimates
these effects increase with increasing plume tempera-
ture ŽFig. 10.. For mantle contributions to topogra- It may still be possible to constraint plume vol-
phy and MBA, latent heat loss reduces the ampli- ume flux independent of ambient viscosity based on
tudes of predicted anomalies by 20–40% relative to the observed MBA and bathymetric anomaly widths
calculations without latent heat loss. Depletion buoy- and the theoretical relationship between flux and W
ancy increases predicted mantle topographic anoma- Ži.e. Eq. Ž13... The use of Eq. Ž13. to infer plume
lies and MBA by 10–65% relative to calculations volume flux is valid if the surface anomaly widths
without depletion, while retention buoyancy in- directly reflect the along-axis plume width in the
creases predicted anomalies by 5–25% relative to mantle, which would be the case if along-axis melt
calculations without retention. Melting effects on migration is negligible, as assumed in the Ice 1
P-wave delay-time are also important: latent heat models. The flux required to match the along-axis
loss decreases predicted delay-time by ; 13%, melt MBA and bathymetric anomaly widths as predicted
depletion decreases delay-time by 20–30%, but melt from model Ice 1d is 1.2 = 10 7 km3rmy. This flux,
retention increases delay-time by 20–60%. It is thus however, is several times larger than previous esti-
important to consider melting effects on mantle mates of the Iceland plume of 2 = 10 6 kmrmy w46x,
properties when predicting geophysical observables. 1.43 = 10 6 kmrmy w8x, and 2.2 = 10 6 kmrmy w28x.72 G. Ito et al.r Earth and Planetary Science Letters 144 (1996) 53–74
If, on the other hand, along-axis melt migration is melt migration andror lower crustal ductile flow to
important, as suggested for the Ice 2 models, we occur over hundreds of kilometers along the MAR in
cannot use Eq. Ž13. to constrain the Iceland plume order to explain the geophysical and geochemical
volume flux independent of ho . We must therefore observations. Our calculations predict that plume
rely on the fact that our melt production rate esti- spreading away from the plume center is radially
mates are consistent with the total volume of ob- symmetric rather than channelled preferentially along
served excess crust as we did for the Ice 2 models. the ridge axis. The elongated bathymetric swell along
Indeed, model Ice 2d predicts a plume volume flux the Reykjanes Ridge can be explained by rapid
of 2.1 = 10 6 km3rmy which is more consistent with off-axis subsidence due to lithospheric cooling super-
the above estimates of the previous studies. An imposed on a broader hotspot swell. Both the broad
intriguing new question arising from this narrow and narrow plume source models predict very little
plume source model is, what specific mechanisms mixing between the plume and MORB sources in the
may allow melt generated beneath Iceland to migrate shallow mantle; hence, we suggest that mixing may
hundreds of kilometers along-axis? Possible evi- occur deeper in the mantle, possibly due to entrain-
dence for such melt transport may include the V- ment of the isotopically depleted portion of the
shaped axial bathymetric highs propagating away mantle by the rising mantle plume. Our narrow
from Iceland along the Reykjanes Ridge as first plume source model predicts seismic P-wave veloc-
noted by Vogt w47x in 1971. ity variations more consistent with recent seismic
observations beneath Iceland, suggesting that this
model may better represent the Iceland plume.
7. Conclusions
We have investigated the dynamics of mantle Acknowledgements
flow and melting of a ridge-centered plume using
three-dimensional, variable-viscosity models with fo- We gratefully acknowledge N. Ribe, D. Sparks,
cus on three buoyancy sources: temperature, melt and C. Wolfe for their constructive and timely re-
depletion, and melt retention. When all melting ef- views. We thank Y. Shen and P. van Keken for
fects are considered, the relationship between along- supplying independent finite element solutions used
axis plume width, W, plume volume flux, Q, full to test our variable viscosity flow solver. This paper
spreading rate, U, buoyancy number, B, and ambi- also benefited from discussions with R. Detrick, J.G.
entrplume viscosity ratio, g , is best parameterized Schilling, and M. Spiegelman. This work was sup-
by W s 2.37Ž Q r U .1r2 Ž Bg . 0.04 . Calculations that ported by NSF grant OCE-9302915 and benefited
include melting yield a similar relationship to those from collaborations facilitated through a NSF-sup-
that do not include melting because of the competing ported Mantle Convection Workshop at the Los
effects of latent heat loss and depletion buoyancy. Alamos National Laboratories and additional funds
We propose two end-member models for the Iceland granted through the WHOI Education Office. Contri-
plume beneath the MAR. The broad plume source of bution 9217 of the Woods Hole Oceanographic Insti-
radius s 300 km represents a low temperature Ž DTp tution. [CL]
s 758C. and high flux Ž Q s 1.2 = 10 7 km3rmy.
end-member, while the narrow plume source of ra-
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