JOURNAL OF PETROLOGY
VOLUME 40
NUMBER 4
PAGES 575–599
1999
Melt Migration under Oceanic Ridges:
Inferences from Reactive Transport
Modelling of Upper Mantle Hosted Dunites
GÜNTER SUHR∗
MINERALOGISCH-GEOCHEMISCHES INSTITUT, UNIVERSITÄT ZU KÖLN, ZÜLPICHER STR. 49B, 50674 KÖLN, AND
MAX PLANCK INSTITUT FÜR CHEMIE, POSTFACH 3060, 55020 MAINZ, GERMANY
RECEIVED JULY 20, 1997; REVISED TYPESCRIPT ACCEPTED SEPTEMBER 10, 1998
Dunite bodies within the ophiolitic upper mantle are widely considered
to locate pathways for melt transport in the sub-oceanic mantle. As
such, the dunites may carry information about the primitive melts
feeding a spreading centre. Analyses by ion probe of clinopyroxene
grains from dunites in the mantle section from the Blow Me Down
(BMD) and upper Table Mountain (TM) massifs of the Bay of
Islands Ophiolite reveal that BMD dunites are highly refractory in
their trace element composition. Upper TM dunites are much less
depleted and probably reflect aggregated melts of variable compositions. A numerical reactive transport scheme was developed to
simulate replacive dunite formation from harzburgite along a melt
channel, triggered by a silica-undersaturated melt. The basic trace
element effects associated with replacive dunite formation are demonstrated for combinations of diffusive and advective transport
and varying reaction rates. They can explain relatively low NiO
concentrations observed in most dunitic olivines. To model the
incompatible trace element chemistry of the BMD dunites, extraction
of refractory melt from the depleted host harzburgite must have
dominated. Otherwise, during melt infiltration, the reactive melt
composition, assumed to be more enriched, dominates the dunite
chemistry even in the absence of local equilibrium. A preferred model
for dunite formation favours short time periods for a channel
formation by fracture and flow of melt in dykes. This event produces
an initial, centimetre-scale replacive dunite. It may be followed by
a main growth stage for dunite formation as a result of reaction of
host rock with pockets of trapped melt and porous flow-dominated
melt migration within the initial replacive dunite. The time scales
involved in the formation of metre-wide dunites are at least several
hundred, if not thousands of years. In BMD, a final event associated
with compaction of the host harzburgites, related to ceasing flow in
the porous channel, caused refractory melt migration into the dunite
by compaction of the host.
∗Present address: Max Planck Institut für Chemie, Postfach 3060,
55020 Mainz, Germany. Telephone: +49 06131 305 209. Fax: +49
6131 371 051. e-mail: [email protected]
dunite; melt migration; upper mantle; reactive transport;
Bay of Islands Ophiolite
KEY WORDS:
INTRODUCTION
There is widespread consensus that melt migration under
ocean ridges must involve some kind of channelled flow
(Kelemen et al., 1997). The need for channelling stems
mainly from geochemical arguments. Many plagioclasefree abyssal and ophiolitic mantle peridotites are highly
refractory in their composition and far from trace and
major element equilibrium with presumed primitive melts
from spatially associated oceanic spreading centres ( Johnson et al., 1990; Johnson & Dick, 1992; Kelemen et al.,
1995a; Batanova et al., 1998). Because homogeneous
porous flow would lead to equilibration between melts
and host over the time-scales for migration of melts from
their source to the oceanic crust (Iwamori, 1993a) an
efficient separation between melts derived from depth and
the refractory, shallow-level host peridotites is implied.
To produce highly refractory peridotites by partial
melting, low residual porosities (~1%) are required ( Johnson et al., 1990; Batanova et al. 1998), at least in some
part of the melting column (Kelemen et al., 1997). Equally,
for the separation of U from Th as indicated by (230Th/
238
U) data, very low residual porosities p1% are required
(McKenzie, 1985a). A mantle porosity of 1–2% is also
inferred from geophysical studies of the East Pacific Rise
(MELT Seismic Team, 1998). These low porosities are
at variance with the requirement for rapid melt transport
as derived from the (230Th/238U) and (226Ra/230Th) disequilibrium series studies (McKenzie, 1985b; Rubin &
 Oxford University Press 1999
JOURNAL OF PETROLOGY
VOLUME 40
McDougall, 1988; Richardson & McKenzie, 1994; Bourdon et al., 1996) and from massive basalt outpourings
related to deglaciation in Iceland ( Jull & McKenzie,
1996). To satisfy the need from (230Th/238U) data for
porous flow velocities of at least 1 m/yr, a minimum
porosity of ~4% is required in peridotites with a grain
diameter of 2 mm [using Darcy’s law and input parameters as given by Kelemen et al. (1997)].
Channelling of melts in the mantle is a reasonable
solution to both the problem of chemical isolation of
melts from residual peridotites and the problem of rapid
melt transport while maintaining regionally low porosities
(Nicolas, 1986; Sleep, 1988; Spiegelman & Kenyon, 1992;
Richardson & McKenzie, 1994; Kelemen et al., 1995a,
1995b; Richardson et al., 1996). Iwamori (1993b) calculated that more than 80% of all melt generated under
mid-ocean ridges must have been carried to the surface
in chemical isolation.
The physical processes involved in channel formation
are poorly understood. One model suggests hydraulic
fracturing. A hydraulic fracture in the mantle is initiated
when the tensile strength of the host rock is exceeded by
the fluid pressure (Shaw, 1980; Nicolas & Jackson, 1982;
Nicolas, 1986; Sleep, 1988). An open melt channel (vein,
dyke) is the result (e.g. Takahashi, 1992). Within a
compaction length, melt can be drained into veins if
suitable pressure gradients exist (Nicolas, 1986; Ribe,
1986; Sleep, 1988). During flow in the vein, which may
be as short as a few weeks (Lago et al., 1982; Nicolas,
1986), wall-rock reaction between melt and harzburgite
or lherzolite may produce a replacive dunite. A variant
of this model is fracturing that propagates down from
the base of the lithosphere (Fowler & Scott, 1997).
Another model involves the formation of high-porosity,
self-organized dunitic dissolution channels (Aharonov et
al., 1995, 1997; Kelemen et al., 1995b). They tend to
develop around a small physical heterogeneity during
reactive flow. As a result of a positive feedback between
regions of higher permeability and increased flow, highporosity channels may form and grow exponentially with
time, potentially traversing the entire mantle. According
to Kelemen et al. (1997), hydraulic fractures may be
initiated within such more permeable, high-porosity dunites, but not in the less permeable, low-porosity harzburgites and lherzolites.
Mantle-hosted dunite bodies are common in most
ophiolitic peridotites. They are typically thought to have
formed by opx dissolution from the host rock, i.e. they
may represent the channels required for melt transport
in the mantle. This ‘replacive dunite’ model strongly
hinges on field evidence demonstrating that many of the
dunite bodies or at least their peripheral part formed by
replacement of existing rock bodies (Boudier & Nicolas,
1972; Dick, 1977; Quick, 1981; Nicolas, 1986, 1989;
NUMBER 4
APRIL 1999
Kelemen et al., 1995a, 1995b). In this context, the generally grain-scale transition between the lithology of the
host rock into dunite could represent the site of a reaction
front involving fast reaction rates (Kelemen et al., 1995b).
Fast reaction rates are supported by laboratory experiments simulating the infiltration of a basaltic melt
into a peridotite (Daines & Kohlstedt, 1994). In a model
assuming dunite generation from harzburgite caused
solely by heat emanating from the melt channel, a more
gradual modal change of opx content in the host rocks
is expected (Kelemen et al., 1995a).
In this work mantle-hosted dunite bodies from the
ophiolitic Bay of Islands Complex (BOIC, Newfoundland)
are studied and their geochemistry is determined. The
general geochemical effects associated with replacive
dunite formation are evaluated in numerical and analytical approaches, and the modelling is extended to
likely scenarios prevailing during formation of the BOIC
dunites. Physical factors (mainly time and fluid flow
direction) involved in the formation are constrained and
a model for the BOIC dunites is presented.
FIELD RELATIONSHIPS
The BOIC is exposed in four massifs, which are, from
north to south, Table Mountain (TM), North Arm
Mountain, Blow Me Down Mountain (BMD) and the
Lewis Hills. Abundant dunites occur in two different
structural levels: in the mantle as discrete bodies of limited
size and as lenses or layers of hundreds to thousands of
metres thickness of so-called transition zone dunite below
crustal gabbros (Girardeau & Nicolas, 1981; Suhr et al.,
1998). In this paper, only mantle-hosted dunites are
discussed. The studied occurrences of dunites from the
BMD massif (Table 1) are all from the southern flank of
the massif. The morphology of the dunites in the BMD
massif is more pod shaped or irregular shaped in the
lower part and more tabular shaped, both parallel and
oblique to the foliation, in the upper part. Diffuse, centimetre-scale dunitic regions are also present but have
not been sampled. The pods reach a length of several
metres to tens of metres and their length to width ratio
tends to be below five. The tabular dunites are typically
up to a few tens of centimetres wide and tend to extend
laterally beyond typical outcrop dimensions (10 m). Both
pods and tabular dunites may contain harzburgitic
schlieren. Contacts between host and dunite are marked
by the disappearance of opx on a grain scale (<1 cm),
but locally over a width of 5 cm. Sample suite B689
derives from an exceptional occurrence of dunite. It can
be followed in the field as a perfectly straight, dyke-like
body of nearly constant width (4 m) for 600 m before it
appears to branch out 200 m below the onset of the
transition zone dunites.
576
SUHR
MANTLE HOSTED DUNITES
Table 1: Geological features of dunite bodies analysed for trace elements
Sample no.
Shape
Width
Other
% cpx
B486
elongate pod
2m
has central 0·4 m wide harzburgite
0·1
B492
discordant band
0·5 m
B496
concordant band
0·15 m
B689.1–.4
discordant band
4m
0·06
0·1
T1550
T1554
elongate pod
?
T1570
band
4 cm
600 m long
<0·01
diffuse dunite–harzburgite area
>1 + trace opx
>3
with nearby gabbro dykelet
Analyses of trace elements from dunites of the TM
massif are limited to occurrences in the uppermost mantle
section. Field data from the entire massif suggest, however, a similar morphological classification as in BMD.
In the most basal, lherzolitic part of TM, dunites are
very rare. In contrast to the occurrences from the BMD
massif, the tabular dunites of upper TM are characterized
by a typical abundance of 0·1–5% cpx whereas this phase
is <0·1% in BMD dunites. In addition, there is abundant
evidence for a melt impregnation event in the hosting
harzburgites of TM (Suhr, 1993; Suhr & Robinson, 1994;
Batanova et al., 1998), which was not obvious from
the cursory field work done in the BMD upper-mantle
section.
Preferred dissolution of opx-rich banding over harzburgite is common. Locally the contact between orthopyroxenite and harzburgite represented a plane of
weakness along which melt could penetrate and generate
dunite by reaction (Fig. 1a). Relict harzburgite within
dunite can be observed (Fig. 1b). The enclosed harzburgite may be very diffuse and opx depleted. Spinel is
locally enriched in discontinuous seams within the dunite.
It then tends to be coarser (millimetre-sized) and is
subhedral compared with small and anhedral grains in
the harzburgites. Dunites may also occur in swarms of
cross-cutting bands (observed in upper TM) or parallel
bands (Fig. 1c) and in several generations within the
same outcrop (Fig. 1d), indicating a limited time span
for formation of dunites and showing that several duniteforming events may affect the same area. In Fig. 1a,
tabular dunites appear to include an overlapping segment
typical for crack formation (Pollard et al., 1982). It should
be noted that the low length to width ratio of many
dunite pods in the BOIC renders them unsuitable as
potential channels for melt transport over a kilometre
scale. However, in some areas several pods are aligned
>0·2
and they could conceivably be linked by smaller-scale
features if outcrop conditions allowed observation.
GEOCHEMISTRY
Regional mineral chemistry data
Mineral chemical data covering the BMD mantle dunites
and TM mantle dunites and harzburgites are reported
for TiO2 in spinel and NiO in olivine (for complete
mineral chemistry of samples selected for trace element
analysis, see Table 2). Ti and Ni represent an incompatible and a compatible element, respectively, for
which data can easily be obtained for both harzburgites
and dunites because of the ubiquitous presence of spinel
and olivine in both lithologies, even in highly serpentinized samples (typically 90% in BMD). TiO2 values
in dunite-hosted spinels from the TM massif (<0·35%)
extend to much higher values than the generally low
concentrations (mostly <0·10%) for the TM harzburgitehosted spinels (Fig. 2a). This strongly argues against a
purely residual nature of the dunites (Allan & Dick, 1996).
Both dunites and harzburgites from the uppermost part
of the mantle sequence in TM have on average higher
concentrations of TiO2 in spinel than samples from the
rest of the massif. Dunite-hosted spinels from BMD have
very low TiO2 concentrations (<0·10%), similar to those
from the lower and central harzburgites from TM. Data
for TiO2 in mid-ocean ridge basalt (MORB) have been
compiled by Dick & Bullen (1984). Virtually all MORB
samples have TiO2 in spinel values far greater than 0·1%.
BMD dunites are therefore not in equilibrium with
MORB. Such an equilibrium cannot be ruled out for
upper TM dunites but is unlikely for the deeper level
TM dunites. Rare earth elements (REE) from BMD
volcanics and mafic cumulate rocks [Suhr et al. (1998) and
577
JOURNAL OF PETROLOGY
VOLUME 40
NUMBER 4
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Fig. 1. Field relationships of upper mantle hosted dunites from the Table Mountain massif. (a) Tabular dunite cross-cutting harzburgite with
opx-banding. Opx-rich bands are selectively replaced by dunite. Dunite also penetrates along orthopyroxenite banding, possibly by delamination
of the harzburgite–orthopyroxenite interface. Overlapping dunite terminations (centre) reminiscent of crack propagation should be noted. (b)
Relic harzburgitic enclosure within tabular dunite. (c) Swarm of parallel dunite bands concordant to the foliation. (d) Drawing of field relationship
showing three cross-cutting generations of dunite (shown within dashed lines); dotted line is opx-rich banding. Du1 is dunite associated with the
layering structure of the harzburgite; it is cut by Du2. Du2 in turn is cut by an orthopyroxenite (ruled). Du3 is parallel to Du1 and reacted
preferentially with orthopyroxenite.
references therein] show MORB-like patterns, indicating
that the average melt that fed the BMD spreading centre
was akin to MORB in terms of REE.
Dunite-hosted olivines from TM have on average lower
NiO concentrations than olivines in TM harzburgites
but there is an overlap (Fig. 2b). Local dunites exist
that have very high NiO values >0·45%. Upper TM
harzburgite-hosted olivines appear not systematically
different from the rest of TM harzburgite-hosted olivines
but upper TM dunites have lower NiO in olivine than
the rest of the TM dunites. BMD dunites are systematically offset towards lower NiO values in olivine
compared with TM harzburgites.
Trace element data
Because of the low concentrations in the bulk rock, spinel,
and in olivine, a characterization in terms of incompatible
trace elements within dunite needs to be based on cpx,
the only other primary phase present. Cpx is extremely
rare in dunites from BMD (typically amounting to
<0·05% by volume) and is absent in many thin sections.
The origin of this cpx cannot be by exsolution from opx,
as opx is entirely absent. If cpx were residual, a higher
amount of cpx would be expected near dunite margins
but this was not observed. In upper TM, cpx is more
abundant. Where larger amounts of cpx are present, a
fractionation origin is likely because, as discussed by
Kelemen et al. (1995a), the alternative origin by trapped
melt crystallization must involve the coexistence with
another phase, e.g. plagioclase, to accommodate all melt
components. Some amount of cpx formed from trapped
melt (say 0·02%) is, however, likely, as complete melt
extraction is impossible.
Ion probe measurements were performed with a Cameca IMS 4F ion microprobe at the Institute for Microelectronics (Yaroslavl, Russia). An O2– primary beam was
applied instead of the more common usage of O– (Simakin
& Sobolev, 1997). Run conditions were as previously
reported (Batanova et al., 1998) except that secondary
ion voltage offset was set to –70 eV for 139La, 140Ce, 146Nd
578
579
4
3
5
4
T1550
T1554
T1570
T1571
2
4
2
7
6
6
4
B492
B496
B689†
T1550
T1554
T1570
T1571
51·09
51·80
52·51
51·77
52·18
53·60
52·88
52·31
SiO2
0·03
0·04
0·02
0·02
0·03
0·01
0·03
0·02
0·33
0·19
0·13
0·28
0·04
0·02
0·04
0·03
TiO2
0·31
0·15
0·14
0·20
0·06
0·04
0·03
0·06
TiO2
0·01
0·00
0·01
0·00
0·00
0·01
0·01
TiO2
3·80
3·69
3·55
3·95
2·91
1·51
2·76
1·80
Al2O3
30·96
33·56
29·76
36·25
29·42
24·28
32·23
20·01
Al2O3
8·90
8·88
9·04
8·59
9·20
9·22
8·98
9·04
9·54
9·83
9·74
9·93
FeO
1·13
0·99
1·24
1·16
1·09
0·50
1·00
0·95
Cr2O3
31·79
31·23
36·44
31·03
37·75
42·81
35·63
49·57
Cr2O3
50·00
49·27
50·27
49·23
50·57
51·50
50·82
50·32
50·00
49·28
49·32
48·29
MgO
2·56
2·45
2·30
2·84
1·81
1·71
1·73
2·52
FeO
19·40
18·05
17·85
16·34
15·52
17·39
15·10
17·19
FeO tot
0·14
0·16
0·15
0·17
0·13
0·14
0·14
0·13
MnO
15·32
15·78
15·91
16·85
16·55
16·88
16·12
17·88
MgO
13·99
15·25
14·22
15·45
14·63
14·07
15·66
12·70
MgO
0·05
0·09
0·17
0·18
0·07
0·13
0·15
0·06
CaO
0·06
0·06
0·07
0·09
0·06
0·03
0·06
0·10
MnO
0·15
0·13
0·15
0·13
0·14
0·13
0·11
0·18
MnO
0·40
0·36
0·35
0·37
0·39
0·40
0·37
0·42
0·33
0·33
0·33
0·34
NiO
23·62
24·28
24·22
22·31
23·98
24·99
25·02
22·52
CaO
0·19
0·19
0·12
0·15
0·12
0·12
0·11
0·06
NiO
99·75
99·47
100·61
98·58
100·37
100·40
100·36
99·87
101·24
100·84
100·00
99·15
Sum
Analyses by electron microprobe at Department of Mineralogy in Köln, unless otherwise indicated.
∗Analyses by electron microprobe at Department of Mineralogy in Bonn (analyst Dr J. Ehl).
†Sample from centre of dunite body, but different from B689.1 and B689.2.
5
B486
n
9
B689†
Cpx
5
7
B496
5
B492
SiO2
n
Spinel
B486
40·22
40·63
40·63
40·18
40·22
38·92
40·18
40·10
41·15
41·14
40·34
40·22
6
4
6
11
5
5
6
5
6
5
6
6
B486
B492
B496
B494
B689.1∗
B689.2∗
B689.3∗
B689.4∗
T1550
T1554
T1570
T1571
SiO2
n
Olivine
Table 2: Mineral chemistry of samples analysed for trace elements
0·04
0·05
0·03
0·04
0·03
0·03
0·07
0·04
NiO
96·85
98·63
98·73
99·60
97·68
98·87
98·93
99·80
Sum
90·9
90·8
90·8
91·1
90·7
90·9
91·0
90·8
90·3
89·9
90·0
89·7
mg-no.
0·45
0·35
0·41
0·34
0·42
0·20
0·11
0·27
Na2O
41
38
45
36
46
54
43
62
cr-no.
0·01
0·01
0·02
0·01
0·01
0·02
0·01
0·01
K 2O
98·42
99·63
100·38
99·64
99·08
99·48
99·80
98·43
Sum
91·4
92·0
92·5
91·4
94·2
94·6
94·3
92·7
mg-no.
SUHR
MANTLE HOSTED DUNITES
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VOLUME 40
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APRIL 1999
Fig. 2. Mineral chemistry data from mantle-hosted dunites of BMD and TM massifs. (a) Percent TiO2 in spinel; BMD dunites are of highly
depleted composition in terms of TiO2 in spinel, similar to residual harzburgites from the TM massif. TM dunites are more varied, with a
notable enrichment of TiO2 in spinels from dunites in the uppermost mantle section. (b) Percent NiO in olivine. NiO in olivine from both BMD
and TM dunites is offset towards lower concentrations compared with NiO in olivine from TM harzburgites. Upper TM dunites tend to have
lower NiO in olivine than the rest of the dunites.
and 148Sm, and to –100 eV for all other elements.
Repeated measurements of a Kilbourne Hole cpx showed
good reproducibility in comparison with previous measurements (e.g. Batanova et al., 1998). A subset of the
data, as listed in Table 3, was obtained using a laser
ablation microprobe (LAM-ICP-MS) at Memorial University (Günther et al., 1995), and one sample was analysed
by ion probe at Woods Hole Oceanographic Institution
(Shimizu & Hart, 1982).
Samples from location B689 represent a profile from
the centre of the large, dyke-like body into its immediate
host harzburgite. The harzburgitic margin was sampled
20 cm from the dunite–harzburgite contact. It shows an
REE pattern similar to that of residual cpx from high
degrees of near-fractional melting (~20%) of a MORB
source mantle as seen in the very low heavy REE (HREE)
concentrations. The very low concentrations of Dy and
Ti are, however, difficult to model with the chosen
melt mode (from Johnson et al., 1990) and distribution
coefficients (see Table 3). The REE content of the dunite
is enriched compared with the harzburgite (Fig. 3a).
Enrichment is preferentially in the light REE (LREE)
and stronger in the centre of the dunite. Peculiar positive
Zr anomalies are present. NiO concentrations in olivine
are 0·42 wt % in the host harzburgite, 0·37% in the
dunite close to the contact, and 0·39 and 0·40% in the
dunite centre (Table 2) with 1r values of 0·01%. The
three other dunite bodies from BMD show similar REE
patterns to the marginal dunite sample of location B689,
with the typical low in the Nd region, but they do not
display a positive Zr anomaly (Fig. 3b). Their NiO
(olivine) concentrations range from 0·40 to 0·35%. It
580
581
cpx
host for BMD
3
7E – 06
6E – 06
0·0025
0·06
1E – 05
0·005
0·1
1E – 05
Ce
0·01
0·0055
0·0053
4·04
6E – 05
0·01
0·2
7E – 05
Nd
0·009
0·0111
0·0108
6·21
Ce
0·14
0·28
0·047
0·021
0·48
0·51
0·45
0·51
0·65
0·11
0·065
b.d.
1·49
0·21
0·24
Ce
0·07
0·024
0·123
0·004
Zr
0·01
0·0383
0·0311
8·73
Nd
0·10
0·19
0·025
0·006
0·58
0·60
0·54
0·72
0·84
0·035
0·036
b.d.
1·37
0·33
0·77
Nd
0·0006
0·02
0·3
0·0007
Sm
0·03
0·0264
0·0225
9·66
Zr
3·36
4·70
0·40
0·13
2·28
2·75
2·19
2·34
4·40
0·30
0·59
0·28
11·31
1·76
3·01
Zr
0·0008
0·03
0·37
0·001
Eu
0·05
0·214
0·0969
9·86
Sm
0·09
0·10
0·010
0·010
0·29
0·32
0·25
0·35
0·38
0·040
0·034
b.d.
0·58
0·19
0·50
Sm
0·15
0·1
0·35
0·015
Ti
0·08
0·593
0·274
10·3
Eu
0·043
0·047
0·010
0·005
0·077
0·062
0·075
0·11
0·10
b.d.
0·010
b.d.
0·24
0·091
0·24
Eu
0·0015
0·05
0·44
0·004
0·35
1·43
1
10·4
Dy
Ti
528
1043
540
141
813
831
701
414
647
237
186
286
2458
810
2058
Ti
0·003
0·07
0·43
0·009
Er
0·6
1·44
0·837
10·6
Dy
0·28
0·49
0·24
0·11
0·75
0·81
0·80
0·80
0·95
0·17
0·14
0·15
1·46
0·73
1·66
Dy
0·0045
0·09
0·41
0·014
Yb
0·9
1·69
1·1
10·6
Er
0·19
0·48
0·29
0·21
0·61
0·63
0·63
0·58
0·63
0·20
0·21
0·26
1·01
0·60
1·22
Er
1
1·8
1·26
10·6
Yb
0·24
0·48
0·36
0·24
0·75
0·73
0·66
0·63
0·67
0·28
0·36
0·17
0·87
0·64
1·12
Yb
b.d., below detection.
∗IP-YIM, ion probe, Yaroslavl Institute for Microelectronics. IP-WHOI, ion probe, Woods Hole Oceanographic Institution. LAM-MUN, laser ablation microprobe,
ICP-MS, at Memorial University, Newfoundland.
†C1-normalized, host cpx for BMD is assumed and is marginally lower than harzburgitic cpx B689.4.
‡As given by Suhr et al. (1998). LREEs for spinel were lowered to level of olivine so as not to let spinel have a special role for LREE.
10
orthopyroxene
spinel
3
12
clinopyroxene
olivine
Mineral–melt distribution coefficients‡
cpx
18% residue
La
cpx
La
Phase
melt
0·063
0·15
0·023
0·026
0·11
0·13
0·12
0·12
0·15
0·047
0·026
b.d.
0·30
0·048
0·034
La
IP-YIM
IP-YIM
IP-YIM
IP-YIM
IP-YIM
IP-YIM
IP-YIM
IP-YIM
IP-YIM
IP-WHOI
LAM-MUN
LAM-MUN
LAM-MUN
LAM-MUN
LAM-MUN
Method∗
20% residue
Ni
2
1
3
4
1
1
1
1
1
2
3
2
3
7
3
n
channel melt
Modelled input data†
B689.1
B689.2
B689.3
B689.4
T1570-1
T1570-3
T1570-6
T1570-9
T1570-11
B492
B486
B496
T1571
T1554
T1550
Sample
Table 3: Trace element data for cpx (in ppm)
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MANTLE HOSTED DUNITES
JOURNAL OF PETROLOGY
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Fig. 3. Chondrite-normalized (Sun & McDonough, 1989) cpx trace element concentrations in mantle-hosted dunites from the BMD massif and
uppermost TM. For comparison, cpx in equilibrium with N-MORB [Sun & McDonough (1989), using Kd,cpx from Table 3] and a modelled cpx
of 20% open system melting of peridotite are shown. Also shown is the cpx of an aggregated melt of 0–20% melting (linear mixing). (a) Traverse
across location B689. Dunite–harzburgite contact is at 0 m, centre of dunite at +2 m. (b) Three dunites from BMD massif. (c) Detailed, 8 cm
section across a dunite–harzburgite–gabbro sample. Gabbro is a millimetre wide dykelet. (d) Three dunites from upper TM mantle.
should be noted that all cpx grains from dunites are
extremely depleted in incompatible trace elements compared with cpx in equilibrium with N-MORB, as already
suggested by the more regional low values of TiO2 in
spinel of BMD dunites.
Concentrations in cpx grains from the upper TM
massif have generally a convex-upward shape of REE
and higher REE concentrations than the BMD dunites
(Fig. 3c, d). Sample T1570.2 represents an 8 cm wide
section across a 4 cm wide dunite that contains relict
opx grains and the adjacent harzburgitic host. The harzburgite contains a millimetre-sized gabbroic dykelet with
a 5 mm wide dunite margin. To a first order, cpx grains
from dunite, harzburgite and gabbro are very similar,
including the negative Zr and Ti anomaly and the
remarkably low Eu values (Fig. 3c). All cpx concentrations
are depleted by a factor of 2–3 compared with an average
N-MORB cpx (using distribution coefficients as given in
Table 3). For comparison, a cpx from a calculated
aggregated melt (linear mixing of 0–20% open system
melting) is shown. This aggregate melt composition will
later be used as a primary channel melt for modelling.
The other three samples from TM, all located in the
uppermost mantle section, have LaN in cpx of 0·1–1 and
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SUHR
MANTLE HOSTED DUNITES
YbN of 3–7, with negative Zr and Ti anomalies developed
in two of the three samples (Fig. 3d).
The question to be addressed in the following modelling
is whether the geochemical modification that a harzburgite undergoes when it is transformed into a replacive
dunite can explain the observed cpx trace element patterns in the dunites.
APPROACH TO MODELLING
System set-up and physical processes
considered
The basic set-up considered in the one-dimensional numerical modelling of the dunite bodies is that of a vertical
melt channel adjacent to a peridotite host (Fig. 4). The
channel carries fluid of a constant trace element Cf,ch and
m
major element concentration Cf,ch
. This fluid is in contact
with an original host rock of n solid phases i with mineral
trace element composition C0s,i and mineral major element
composition Cs,im. The original host rock further contains
a fluid volume fraction u0 (assumed to be fully connected)
with trace element composition Cf,0 and major element
m
.
composition Cf,0
For time t > 0, the channel melt components infiltrate
the host rock by advection and diffusion along a horizontal x-direction and elements exchange between fluid
and solid by diffusion (trace elements only) and solution
or precipitation (trace and major elements) [equation
(A1) in Appendix A]. Trace element compositions of
minerals and fluid in the host are modified to Cs,i and
Cf. The major element composition of the fluid is modified
to Cfm whereas the mineral major element composition
remains unchanged. Trace element equilibrium is evaluated using mineral–melt distribution coefficients Kd,i =
Cs,i/Cf. The bulk distribution coefficient KD is defined as
Fig. 4. Major physical processes included in the numerical model
simulating the interaction between a vertical melt channel (constant
composition) and a host rock containing melt and solid initially in
equilibrium with each other. Transport of components along the
horizontal direction is by advection and diffusion within the melt. Solid
and melt exchange by diffusion across the surface of the solid grain
and by solution and/or precipitation of the solid grains involving
changes in radii.
n
KD = Kd,iXi, with Xi as the modal fractions in the solid.
i=1
For the advective transport a condition v0u0 constant
is imposed for the entire profile, where v0 is the Darcy
velocity in a solid matrix with the initial porosity u0. As
a result, fluid velocities are inversely proportional to
porosities. For the diffusive transport of components in
a porous medium, the microscopic path length is dependent on the porosity u. This is accounted for by
replacing the diffusion coefficient Df with an effective
diffusion coefficient
D̄f = Df/s2
(1)
(Berner, 1980) with s being the tortuosity. For the tortuosity, the relation
s2 = 1 – ln(u2)
(2)
(Boudreau, 1996) is used. Thus, for a typical porosity of
1%, the effective diffusion coefficient is one order of
magnitude lower than Df. Diffusive equilibration between
solid and fluid occurs via the surface of the solid. Equilibrium between solid and fluid is restricted to the grain
surface, i.e. local equilibrium does not apply. The involvement of the grain surface means that the geometry
of the solid matrix is important. A spherical shape is
assumed for all phases and it is assumed that the entire
grain surface can take part in the exchange (see Vasseur
et al., 1991).
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JOURNAL OF PETROLOGY
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There is a wide range of options of how to handle the
solution–precipitation process. Ideally, a full thermodynamic data base should be incorporated. On the basis
of the major element thermodynamics, the reaction could
be determined and the trace element changes associated
with the solution–precipitation reactions are then calculated. In the case of a single reaction, this process
leads to creation of one reaction front, which moves
downstream (in the direction of the transport of the
reactive fluid) in time (e.g. Bickle & Baker, 1990). Upstream of the front, the solid is ‘reacted out’; downstream
of the front, the mode of the solid is the original mode.
The aim in this work is to simulate the following
reaction behaviour:
(1) solution–precipitation reactions should not depend
on trace element disequilibria. This is considered realistic
and allows evaluation of the source–sink effects of solution–precipitation reactions independent of any initial
trace element disequilibrium.
(2) A velocity for the reaction front should not be
imposed but should be internally controlled. This allows
the flexible simulation of the diffusion–advection controlled movement of reaction fronts.
(3) A finite reaction rate should be included, which
decreases as major element equilibrium is approached.
This can be used to impose different widths of a reaction
front.
In the present approach one major element is selected
as a ‘monitor’ element which advects and diffuses with
the liquid. It does not diffusively exchange with the solid,
so Cs,im never changes. The monitor element plays, however, a critical role in the solution–precipitation reaction
and therefore the reaction is strongly affected and presumably controlled by the fluid concentration of the
monitor element. For this monitor element, an initial
m
and an equilibrium fluid concentration is selected (Cf,ch
m
and Cf,eq, respectively) and the reaction proceeds as long
as the actual fluid Cfm concentration is different from
m
Cf,eq
. The difference between the two concentrations is
also what governs the reaction rate according to the
linear reaction rate law of Lasaga & Rye (1993),
∂Cfm
m
= Keff,i(Cf,eq
– Cfm)
∂t
AiKdiss,i
m .
VfCf,eq
APRIL 1999
It is obvious that the fluid has a limited reactive capacity
before saturation is reached. The reaction also stops if
any reactant has disappeared. One way of expressing the
reaction capacity for a given system is how many units
of fluid relative to one unit of original host rock (consisting
of solid and equilibrium fluid) are required until the
reaction is completed. This volume fraction is called
ucrit. An expression for the reaction capacity is given in
Appendix B.
For example, an opx-undersaturated meltold triggers
the reaction
1 enstatite + meltold
= 1 forsterite + (1 quartz + meltold)melt,new (5)
(units are moles) which stops at a defined silica concentration of the new melt. The stoichiometric proportions in weight of the phases in the reaction are called
reaction coefficients mi, and are negative for solution
and positive for precipitation. With mi, the new modal
proportions of a phase Xi after a given extent of reaction
f can be derived from the old modal proportion Xi,old as
Xi = Xi,old + fmi
(6)
(e.g. Lichtner, 1996). For the standard input conditions
as used below for the harzburgite to dunite conversion
(see Table 4, ‘RX1’) one mass unit host is converted to
dunite by 0·46 mass units melt (or 0·51 volume units).
Given that initial porosities of a peridotite are generally
considered to be in the percent range (McKenzie, 1985a,
1985b), this reaction capacity is small in the sense that
only a small fraction of harzburgite host can be converted
to dunite with the interstitially present fluid fraction. The
value of 0·46 is within the range of 25–100% melt fraction
calculated by Kelemen et al. (1995b) for the same reaction
involving picritic to basaltic melts, respectively. Using
silica as monitor for the reaction appears therefore an
adequate representation of the reaction in equation (5).
Nomenclature and formation of cpx
(3)
with
Keff,i =
NUMBER 4
(4)
Kdiss,i is the surface dissolution rate constant of phase i in
cm/s. Ai and Vf are the surface area of phase i and the
fluid volume, respectively. The phase with the lowest net
rate coefficient Keff,i (unit–1) is used to determine Cfm.
Because of the zoned nature of the grains during the
modelling, the average concentration of any phase must
be determined by numerical integration. This composition is termed ‘instantaneous’. At the end of the
modelling, the bulk solid concentration Cbulk (excluding
the fluid fraction) is recalculated to unzoned minerals
which are in internal Kd,i equilibrium. These phases are
called ‘equilibrated’. The concentration of fully equilibrated phases is simply another way of expressing the
chemical composition of a rock of known mode and it
is also valid when the modal fraction of the chosen phase
i is zero, as follows from
584
SUHR
MANTLE HOSTED DUNITES
Table 4: Standard input conditions used for modelling
Variable
Unit
Standard input value
Initial porosity u0
0·01
Diffusion coefficient melt D f
cm2/s
Diffusion coefficient solid Di
cm2/s
10–6
10–13
Density of solid qs, of fluid qf
g/cm3
3·3, 3·0
m
Conc. of channel melt C m
f,ch, of host melt C f,eq
wt % SiO2
47, 54
Conc of olivine, cpx, opx, spinel
wt % SiO2
42·7, 55·5, 59·9; 0
Dissolution rate K diss,opx (= critical phase)
cm/s
0·15E – 07
Grain radius Ri (ol, cpx opx, sp)
cm
0·1, 0·025, 0·1, 0·025
RX1: reaction coeff. mi (ol, cpx, opx, sp)
mole
1·02, –0·04, –1·00, 0
RX2: reaction coeff. mi (ol, cpx, opx, sp)
mole
0, –0·04, –1·00, 0
Initial mode Xi (ol, cpx, opx, sp)
0·75, 0·01, 0·23, 0·01
Derived values for u0 = 0·01
RX1: critical mass/volume fraction
0·46, 0·505
Velocity of reaction front/Darcy velocity∗
0·017
Final porosity∗
0·09
RX2: critical mass/volume fraction
0·19, 0·21
Velocity of reaction front/Darcy velocity∗
0·021
Final porosity∗
0·27
Exceptions for Figs 8, 9 and 10
Initial porosity u0
0·02
Grain radius Ri (ol, cpx opx, sp)
cm
0·2, 0·05, 0·2, 0·05
∗Effect of 10% compaction in numerical program not considered.
Cs,i = CbulkKd,i/KD.
(7)
cpx is present (this is also a typical modal amount for
cpx in central TM harzburgites). Probably then, both
the cpx-out front and the opx-out front have moved with
a similar velocity, as assumed in the modelling. Overall,
the simultaneous disappearance of cpx and opx remains
a simplification, as it has no chemical basis and it must
break down if the opx/cpx modal ratio of the original
host varies significantly. In the modelling, cpx is first
completely reacted out. A small amount of cpx is reintroduced through trapped melt and, where larger
amounts of cpx are present, as in upper TM, additional
cpx is derived by open system fractionation from the
locally present melt.
Optionally, at the end of the modelling, the interstitial
melt is allowed to precipitate phases by open system
fractionation from a constant melt composition or trap
some melt, which crystallizes as a prescribed mineral
assemblage. Recalculation to a new bulk solid results
again in internally equilibrated phases designated ‘phase
i + melt’.
In the following, only two reactions will be explored:
RX1: 1 enstatite + 0·04 diopside = 1·02
forsterite + melt
RX2: 1 enstatite + 0·04 diopside = melt.
In both reactions, the presence of cpx and its disappearance in the dunite is included. Given the constraints of the program (single monitor element), initial
cpx and opx abundances are adjusted in such a way
(Table 4) that they disappear simultaneously with the
selected reaction coefficients. In the case of the harzburgitic sample B689.4, located 20 cm from the harzburgite–dunite contact, 0·5% of apparently uncorroded
POSITION AND SHAPE OF THE
REACTION FRONT
The reaction front separates dunite (upstream) from
harzburgite (downstream). Unless limited by finite
reaction rates, the reaction front progress is governed by
the flux of reactive melt through the front. For a system
where transport is by advection only and the reaction is
instantaneous, an expression for the velocity of the reaction front vfr,adv, valid for the condition that the front
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has detached from the channel wall (x > 0), is derived
in Appendix C:
vfr,adv
u0
=
.
v0
ucrit + urx
(8)
The velocity of the reaction front decreases when
abundant melt is required to convert harzburgite to
dunite (large ucrit) and when abundant fluid is created
during the reaction (large upstream porosity urx). The
latter relationship arises because a large urx means that
abundant reactive fluid is trapped between the upstream
side of the front and the channel wall. Assuming for
reaction RX1 u0 = 0·01, ucrit = 0·51, urx = 0·09, a
value vfr,adv = 0·017v0 is obtained. This compares, for
example, with a value of an imposed vfr,adv/v0 = 0·35–0·55
for a reaction to remove 15% opx and 7% cpx from a
lherzolite (Godard et al., 1995). Whether such high velocities (and implied reactivities) are realistic in terms of
mass balance constraints must be carefully evaluated for
each reaction.
Equally, if transport is by diffusion only and reaction
is instantaneous, the following relation is derived for the
velocity of the reaction front after time s (Appendix C):
vfr,diff =
( ufrD̄f,fr
ucrits
(9)
where ufr and D̄f,fr are simplified average values of the
porosity and effective diffusion coefficient of the fluid at
the reaction front as given in Appendix C. The diffusively
driven reaction front velocity decreases with time s and,
opposite to the advective case, increases with a high
upstream porosity urx [hidden in ufr; see equation (C7)].
Using the numerical approach, the effect of a finite
reaction rate and combined diffusive–advective transport,
including negative advection, on the position of the
reaction front is evaluated. The chosen dissolution rate
constant for opx in the standard input conditions is such
that the dunite–harzburgite transition occurs over <1 cm.
For the time of 100 years, cases with +5 cm/yr advection,
no advection, –2 cm/yr advection towards the channel
and a different reaction rate are shown (Fig. 5a). For this
time scale and the chosen input conditions, both advective
and diffusive transport are relevant to drive the front,
which is typically located at 10–15 cm from the channel.
A slower reaction rate is of little significance.
For very short times (1 year, Fig. 5b), the advective
flux is largely negligible compared with the strong diffusive flux because of a steep concentration gradient of the
monitor element near the channel. However, the reaction
rate comes in as a major variable. Using the standard
input values and RX1, about 1 cm half-width dunite is
586
Fig. 5. Movement of the reaction front as determined with a single
monitor element (silica) governing the reaction 1 en + 0·04 di = 1·02
fo + melt, 1% initial porosity. (For standard input conditions, see
Table 4.) Upstream of the front, lithology is opx- and cpx-free dunite,
downstream of the front it is harzburgite with 23% opx and 1% cpx.
In (a) the front position is shown depending on the presence and
direction of an advective motion, variable diffusion coefficient D(fld)
and dissolution rate constant Kdiss after simulated 100 years of reaction;
(b) for short reaction times, the effect of the presence of advection, a
small diffusion coefficient D(fld), a slow dissolution rate constant Kdiss,
and a ‘damage zone’ on the reaction progress is shown. The damage
zone is a 2 cm wide zone where the initial porosity varies linearly
between 20% at the channel and 1%. (c) The velocity of the reaction
front is shown for 0–20 years of diffusive transport. A comparison with
the analytical solution of equations (C10) and (C11) shows an initially
slower movement as a result of the assumed finite reaction rates and
extraction of excess fluid volume in the numerical approach. In (d),
the frontal position for longer times as a function of different diffusion
coefficients, with or without advective transport, is shown. A comparison
with the analytical derivation [equation (C11)] for qf = qs shows good
correspondence, but the analytical solution is somewhat ‘faster’ because
of the instantaneous reaction assumed, affecting the early movement
of the front. Location of reaction front in (c) and (d) is defined as where
the initial mode of opx has been reduced by 50%.
SUHR
MANTLE HOSTED DUNITES
produced. This is increased to 2 cm if an initial highporosity or ‘damage zone’ is postulated near the channel
(A. Nicolas, personal communication). This damage zone
might be a likely result of the channel formation itself.
In the example, it varies from 20 to 1% porosity over
2 cm width. It is initially filled by unreactive melt. Filling
it with reactive melt does not dramatically change the
result, because, to remove all opx, the fluid volume must
still be replaced by diffusion several times. It is the
increased diffusive flux made possible by the initially high
porosity that is relevant. What would further enhance
the formation of dunite is small-scale convective fluid
exchange within the high-porosity marginal zone, but
this has not been modelled. Therefore the half-width of
2 cm dunite within 1 year is probably a minimum
estimate. For a Kdiss,opx that is one order less than the
preferred value, no pure dunite is produced near the
channel and the reaction front is several centimetres
wide. It should be noted that grain size will also affect
the reaction rate [equation (4)]. Because of the importance
of the dissolution rate constant within this small scale,
the assumptions about the geometry of the grains and
the pore space become also critical input for modelling
short times. Daines & Kohlstedt (1994) arrived at reaction
front velocities of 15 cm/yr for a very short time scale
of 6–12 h. It should be noted, however, that because of
the very small grain size in their experiment (10 lm),
the reactive surface is unrealistically high compared with
natural peridotites. The analytical solution for RX1,
instantaneous reaction [equation (9)] and for t = 9 h
yields 14 cm/yr.
The reaction rate affects the movement of the front
for short times because abundant reactive melt is stored
downstream of the front for slow reaction rates. Given
enough time, this reactive melt will convert harzburgite
to dunite, so that the long-term influence is small. In
addition, in the case of a system where transport of
reactive melt is controlled by diffusion, there is an immediate feedback between the reaction rate and the
diffusive flux across the reaction front. This is because
the concentration gradient of the reactive component (in
our case SiO2) is smaller for slow reaction rates.
The numerically derived velocity of the reaction front
for diffusive transport is shown in Fig. 5c. For short
distances from the channel it strongly differs from equation (9) as a result of the finite reaction rates in the
numerical approach. For longer time scales and advective–diffusive transport (Fig. 5d, 1000 years), the advective motion into the host becomes the controlling
element (see Fletcher & Hofmann, 1974; Baumgartner
& Rumble, 1988) and the expected linear relation between the position of the front and the infiltration velocity
is established.
In summary, with increasing time, the control over the
position of the front switches from the grain geometry
(surface control) to control by diffusive flux and finally
to advection control. For very short times, small-scale
convection within an initial high-porosity marginal zone
and uncertainties about the actual dissolution rate constants and grain geometry might considerably modify
the presented results. Relative to Darcy velocities in
peridotites with a porosity in the percent range, reaction
front velocities are slow.
TRACE ELEMENT BEHAVIOUR FOR
THE REACTION HARZBURGITE =
DUNITE + MELT
For the simplified case of a system controlled by advective
transport only and solid–fluid exchange by a single reaction and local equilibrium, Godard et al. (1995) have
given analytical solutions of the trace element behaviour
for instantaneous modal and porosity changes. [The last
term in equation (7) of Godard et al. (1995), (vf – vR)/(v′f
– vR), should read u′/u, and the last term in equation
(8), (v′f – vR)/(vf – vR), should read u/u′ (M. Godard,
personal communication, 1998).] They demonstrated
that the trace element behaviour can be understood by
considering the down- and upstream chemical (chromatographic) velocity of a trace element, the reaction
front velocity and the down- and upstream porosities.
Zero concentration in the fluid develops when the chemical fronts both move away relative to the reaction front
(Cf → 0). An instability arises when they both converge
towards the reaction front (Cf → x). For other scenarios
of relative movement, finite depletions or enrichments
are expected.
To develop a better understanding of the reactive
transport system, the results of the numerical program
are discussed for the case of an incompatible element, a
compatible element and an element where Cf is expected
to approach infinity. The results are compared with the
predictions of Godard et al. (1995). The case of initial
trace element equilibrium between channel and host
m
m
melt, i.e. Cf,ch
≠ Cf,eq
and Cf,ch = Cf,eq, will be emphasized,
as it isolates most clearly the processes associated with
solution–precipitation reactions.
The immediate effect of a solution–precipitation reaction can be separated into two processes. For constant
porosity, and if the KD decreases during a reaction, the
trace element balance for the fluid is such that the
concentration in the fluid is expected to increase. This
is because more of the trace element is released into the
fluid by solution than is taken out by precipitation. For
increasing KD during a reaction, the reverse is true. On
the other hand, for constant KD, incompatible elements,
and if the porosity increases during the reaction, the fluid
is diluted as a result of the addition of a trace element
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depleted component to the fluid. For compatible elements, an enrichment occurs.
Incompatible element (Nd)
For RX1, the KD decreases from 4·4 × 10–3 in harzburgite
with 1% cpx to 4·4 × 10–5 in dunite and porosity increases
from 1 to 9·2%. For the advectively controlled system
(+5 cm/yr), the analytical solution of Godard et al. (1995)
predicts a depletion factor Cf/Cf,ch of 0·87. This is also
realized in the numerical program, which in addition
considers diffusion in the fluid and solid–fluid diffusive
exchange (Fig. 6a). The reason for the good match is
because the porosity effect dominates the trace element
behaviour and the equilibration with the solid has little
influence on the mass balance. The difference between
the mainly advectively vs diffusively controlled (Fig. 6b)
system is that, because of the advective motion and high
chemical velocities of Nd, the depleted trace element
signature created at the reaction front is carried very far
into the host. This is an important criterion to discriminate between diffusive and advectively controlled
transport systems. In addition, the reaction front is
sharpened in the absence of advection. As a result of the
effect of diffusion in the fluid, the trace element depletion
in the fluid is also somewhat weakened (see Van der
Wal & Bodinier, 1996). For the modelled time span of
100 years, the instantaneous cpx is in near-equilibrium
with the fluid (note that the fluid concentration is plotted
as Cf × Kd,i) because of its small grain size (0·025 cm).
The equilibrated cpx has higher concentrations than the
instantaneous cpx because of the redistribution of Nd
from high-Nd cores in olivine and opx during equilibration. The variation of the maximum depletion factor
with time indicates a very rapid approach to an equilibrium value (Fig. 6c).
Fig. 6. Concentration changes for an incompatible element (Nd) in
cpx by solution precipitation reactions within 100 years, RX1, initial
porosity 1%, (a) with 5 cm/yr advection, (b) in the absence of advection
(note different x-scale). Channel melt and host rock are initially in Nd
equilibrium. Vertical stippled bands locate the position of reaction
fronts. (a) The great distance over which the depletion signal from the
reaction front is carried downstream into the host harzburgite should be
noted. Fluid and instantaneous cpx have virtually reached equilibrium
except near the chemical front because of the small chosen size
for cpx (0·25 mm). (c) Time-dependent maximum or minimum fluid
concentration for different elements, with or without advection, RX1.
For Ni, a different reaction, RX2, involving no olivine precipitation is
also shown. For Sc, a case involving regular input conditions is compared
with one with very small grain sizes (reflecting near-local equilibrium)
and slower diffusion. (For regular input conditions, see Table 4.) There
is no equilibrium concentration for Sc after 100 years.
Compatible element (Ni)
The same reaction, RX1, driven by diffusive and advective transport and occurring for 100 years, is shown
in Fig. 7a for Ni. The maximum depletion developed in
the fluid is weakly time dependent. The minimum occurs
at short modelling times (Fig. 6c). Even for long modelling
times, the depletion in the fluid is stronger than the
predicted factor (0·88) of Godard et al. (1995). The
predicted fluid depletion factor is, however, found in
olivine. The discrepancy from the predicted fluid depletion arises because in the Ni system, the solid fully
dominates the mass balance. In contrast to the local
equilibrium approach, where fluid and all of the solid
are always in equilibrium, in the system involving finite
solid diffusion the fluid composition is not governed
by the total solid composition but mainly by the rim
composition of the volumetrically abundant olivine. This
rim composition is depleted compared with the bulk rock
because it derives mainly from dissolved opx.
The behaviour with only diffusive transport is overall
similar but the Ni depletion in the fluid is weakened
when advective motion is absent (Fig. 7b). This can
be explained by the increased time available for the
transformation of one unit of harzburgite into dunite
compared with advection-present conditions. Within this
longer time, more Ni can diffuse from the solid phases
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MANTLE HOSTED DUNITES
Fig. 7. Concentration changes for NiO in olivine triggered by solution–
precipitation reactions within 100 years, initial porosity 1%. Channel
melt and host rock are initially in Ni equilibrium. Vertical stippled
bands locate the position of reaction fronts. (a) RX1 involving olivine
precipitation and +5 cm/yr advection; (b) RX1 but without advection;
(c) RX2 with +5 cm/yr advection. The large upstream porosity
enhances the movement of the reaction front compared with (a). It
should be noted that in the advective systems the chemical reaction
front signature is not carried downstream over any significant distance
nor is it efficiently erased upstream. (d) Concentration of Sc in fluid
and olivine for RX1 with +5 cm/yr advection. Under local equilibrium
conditions and in the absence of diffusion, the Sc signal produced is
expected to be confined to the reaction front, where it should undergo
continued growth (Godard et al., 1995). Under more realistic conditions
involving solid–fluid exchange by diffusion and presence of diffusion
in the fluid, the signal is significantly broadened relative to the reaction
front and weaker. Grain sizes for ‘small grains’ and ‘slow diffusion’
both are 1/10 of the standard values given in Table 4.
into the fluid phase. It is this strongly time-dependent
diffusion of Ni from the solid phases into the fluid that
limits the Ni depletion of the fluid.
It should be noted that the chemical velocities for Ni
are very slow. They prevent the reaction front signature
for Ni (1) being carried over any significant distance
downstream into the original host and (2) being overprinted at the upstream side by the channel composition.
Figure 7c finally shows the case of RX2, which involves
no olivine precipitation. Excess porosity in this reaction
is very high (predicted value is 26·7%). The Ni concentration in the fluid increases because the high Ni
abundances released from opx are forced to partition
back into much less mass of solid. The above-mentioned,
separable KD and porosity effects oppose: increasing KD
during the reaction depletes, whereas increasing porosity
enriches the fluid in Ni. The porosity effect dominates.
Because of the equilibration of the fluid with the enriched
Ni rim in olivine, the predicted fluid concentration from
Godard et al. (1995) of 1·08 differs from the actual
maximum enrichment of 1·21.
The long-term evolution of the maximum or minimum
fluid concentration for Ni (Fig. 6c) shows that for short
modelling times, the strong influence of diffusive transport
produces an enhanced signal compared with the longterm equilibrium enrichment or depletion. The diffusive
transport influence is strongest in the case of the reaction
involving no olivine precipitation, as a high diffusive flux
occurs because of both the effect of the high upstream
porosity and the coupling of the effective diffusion coefficient with the tortuosity.
The significance of reactive transport for highly compatible elements is that reaction front velocities tend to
be higher than chemical velocities. Therefore, for highly
compatible elements, a chemical signature is carried not
with the standard chromatographic velocity (McKenzie,
1984) but with the higher velocity of the reaction front.
For example, for u = 0·01, qs/qf = 1·0 and KD = 10,
any anomaly travels with a chemical velocity ~1/1000
of the velocity of the melt whereas the signal created
with the reaction RX1 travels with ~1/60 of that of the
melt. A very practical significance of compatible elements
lies in the potential to discriminate between different types
of reaction. For example, on the basis of mineralogical
changes along a replacive dunite–harzburgite contact in
the field, it is not possible to determine whether olivine
precipitation has taken place or not within the dunite.
On the basis of the Ni concentrations in olivine, such a
decision is possible.
‘Unstable’ element (Sc)
Bickle & Baker (1990) and Godard et al. (1995) have shown
that if the reaction front velocity is lower than the upstream
chemical velocity but higher than the downstream chemical velocity, an instability is expected. The reason is that
the chemical signal produced within the reaction front is
forced to be confined to the reaction front vicinity, i.e.
it travels with the reaction front. As the reaction front
progresses downstream, it contains a progressively higher
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trace element abundance, reflected in a higher concentration as the width of the front remains constant.
Choosing RX1 with olivine precipitation, distribution
coefficients for Sc as given by Bédard (1994), such an unstable situation is realized. The result of the numerical
simulation predicts, however, only a moderate enrichment
of a factor of 1·6 after 100 years (Fig. 7d). At this time,
however, the system is still far from having reached an
equilibrium enrichment. Compared with the analytical
solution, two processes dramatically slow down the enrichment.
The first process is diffusion of the fluid (Van der Wal &
Bodinier, 1996), which is proportional to the concentration
gradient established in the reaction front. It tends to spread
out the sharp signal. The second process is that the effective
solid mass by which trace element exchange occurs is reduced in the absence of local equilibrium (Navon & Stolper,
1987). As a result, the theoretical chemical velocities do not
apply and part of the signal of the reaction front is carried
with a much higher velocity. This is also seen in Fig. 7d,
where the fluid signature does not remain constrained to
the reaction front vicinity. If Df and all grain sizes are reduced
by one order of magnitude, a much more rapid increase is
realized and the processed abundance of Sc is confined
closer to the reaction front (Fig. 7d, grey lines).
It should be noted that in a system with no advective
transport (not shown), the simulation predicts that there is
no effect of Df on the enrichment factor. The reason appears to be that although for small Df the chemical signal
stays more confined to the front, the front itself is also
progressing much slower and is therefore producing a
weaker signal.
The significance of an element such as Sc (called ‘unstable’) is that the long-term evolution of the system will
produce large enrichments. In this respect, this is an oreforming process. The ‘ore’ element is effectively taken out
of the host upstream of the front and the removed material
is deposited within the front zone. The reactive transport
system differs from an AFC system (dePaolo, 1981) in that
the resorbed material is not of constant composition but
that its composition is itself coupled to the reaction. This is
why theoretically instabilities can be produced. A practical
significance of an unstable element is that the strongly
time-dependent enrichment during advection controlled
reaction makes it a potential indicator for the length over
which a process has taken place in the geological past,
particularly if it can be used together with the time-dependent position of the reaction front.
APPLICATION TO THE BAY OF
ISLANDS COMPLEX
Compatible elements
If the results of Fig. 7 are applied to locality B689, the
case shown in Fig. 7a appears applicable. Specifically,
NUMBER 4
APRIL 1999
the sample located close to the rim (B689.3) has a lower
concentration than the host harzburgite B689.4 as a
result of olivine precipitation, i.e. the Ni-sink effect dominates. In the central dunite, the equilibrium Ni value
with the melt is approached. The dominant shift of
dunitic olivines in TM and presumably BMD towards
low NiO values compared with harzburgites is thus
probably the result of a reaction involving olivine precipitation. Conversely, higher NiO concentrations in
dunites than in associated host rocks could be the result
of a reaction involving no olivine precipitation or olivine
solution.
Incompatible elements
Disequilibrium fluid
For harzburgite to be converted to dunite, a reactive
melt is needed. Such a melt tends to derive from greater
depth, as reactivity may increase linearly with the pressure
difference between separation from the host and reaction
with the host (Aharonov et al., 1995; Kelemen et al.,
1995a). It is here assumed that such a melt from depth
is a linearly aggregated melt from 0 to 20% melting, i.e.
in its incompatible trace element signature it will be
considerably enriched compared with residual harzburgites in the BOIC (Batanova et al., 1998). Using Nd
as an example, Fig. 8 shows the reactive infiltration of
such a relatively enriched aggregate melt into a highly
depleted harzburgite, for different transport modes and
directions. Also shown are the fields for the Nd contents
of cpx in BMD dunites and the immediate host harzburgite, the upper TM dunites, and the upper TM
harzburgites from Batanova et al. (1998). These are plotted
here as having formed at least 2 m from any associated
dunite. The emphasis at this stage is to duplicate the
Nd concentrations and not the exact dunite thickness,
because, for wide dunites, a modified explanation is
presented in the discussion.
The Nd of upper TM dunites and the regional harzburgites is simulated using an advective infiltration model
(Fig. 8a). Overall, in this model, the infiltrating melt
characteristics dominate the cpx composition for Nd
in both harzburgite and dunite. Compared with the
concentration of the interstitial fluid × Kd,cpx, the equilibrium cpx is depleted because of the presence of residual
(depleted) olivine and opx cores. Trapped liquid effects
are strong in the dunites but weak in the harzburgites.
Given the generally high chemical velocities of the REE,
a wide area is affected by a channel melt. The interstitial
melt composition is, however, only weakly affected by the
reaction if compared with the initial difference between
channel and host melt.
In the absence of advective motion into the host, the
signature of the infiltrating melt remains largely restricted
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SUHR
MANTLE HOSTED DUNITES
to the dunite (Fig. 8c; note different x-scale from Fig. 8a).
However, within the dunite, most of the depleted signature of the initial host harzburgite is destroyed by the
combined effect of (1) reaction-related precipitation of
olivine, (2) late cpx formed from an enriched interstitial
melt and (3) the diffusive equilibration of the outer
part of the olivine grains with this enriched melt. The
dilutional effect of adding Nd-depleted opx components
to the melt is negligible compared with the original
chemical contrast between infiltrating melt and host.
This infiltration model cannot explain the highly depleted Nd signature of the BMD dunites. Instead, it is
proposed that the REE chemistry of the BMD dunites
is dominated by a melt extraction event that followed a
non-advective dunite formation (Fig. 8d, e). Two different
scenarios of extraction are distinguished, both of which
are coupled with an instantaneous compaction event
back to u0 in the replacive dunite. In Fig. 8d, the central
channel maintains the original channel concentration,
leading to a gradient in the Nd signature within the dunite.
In Fig. 8e, the central channel composition assumes the
composition of the advectively extracted melt. In both
cases, the enrichment in the surrounding host is extremely
limited, as observed in sample B689.4. It should be noted
that in both cases, because of the highly depleted fluid
sucked into the dunite, the cpx + melt signature is more
depleted than the equilibrated cpx signature. Mainly
because of the compaction (and therefore reduced diffusive flux), hardly any additional replacive dunite is formed
during the extraction stage. For the case of Fig. 8d, a
time series for the diffusion profile of olivine (located at
18 cm, i.e. 3 cm upstream of the final reaction front
position) is shown in Fig. 9. It indicates how the olivine
rim first records the passage of enriched channel melt
during the stage where replacive dunite is formed as a
result of diffusive transport of reactive melt. Shortly
before the reversal of the flow, the reaction front passes
x = 18 cm and olivine undergoes growth. During the
melt extraction event the rim rapidly adjusts to the
depleted interstitial melt but the core of the grains receives
a flux of enriched Nd diffusing in from the outer part of
the grains.
The BMD dunites could also have formed by a phase
of early advective infiltration followed by extraction
(Fig. 8b). However, much longer times of extraction than
shown are required, as a large amount of enriched melt,
derived from the infiltration period, is first sucked out
and leads to enrichment of the more inner parts of the
olivine grains. This in turn requires the extended passage
of depleted fluid to adjust the dunite to a depleted
Fig. 8. Interaction between a melt at distance x = 0 cm having a
relatively enriched composition and a depleted host harzburgite, shown
for Nd. Melt and initial host composition are fixed to values considered
realistic from regional studies in the BOIC (Table 3). Shaded fields
show ranges in B689 dunites together with immediate host harzburgite,
upper TM dunites, and three cpx harzburgites from upper TM (Batanova et al., 1998). The TM harzburgites are spatially not directly
related to any of the TM dunites shown. Legend is shown in (e).
Cpx + melt denotes formation of 0·04% cpx by open system fractionation and 0·01% cpx from trapped melt. Five cases are distinguished,
all involving RX1, 2% harzburgite porosity, different modelling times
and advective velocities as shown in the figure. Negative advection
velocities are all connected with compaction of the dunite back to the
initial porosity. The much more significant chemical effect caused by
formation of melt-derived cpx in dunite than in harzburgite should be
noted. For the upper TM occurrences, the dominance of an infiltration
event as shown in (a) is suggested. For BMD, the dominance of an
extraction event is indicated, probably following a dunite formation
stage that did not involve strong melt infiltration (d, e).
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APRIL 1999
compositions, (2) different modes of cpx formation
(trapped melt or fractionation), or (3) some mild subsequent melt extraction event following infiltration, which
carries in depleted liquids from the matrix (e.g. Fig. 8b).
For the BMD dunites with their very depleted cpx
compositions, an event involving the passage of very
refractory melt is required. The three dunites of Fig. 2b
are most easily modelled if, during this melt movement,
any potentially more enriched melt present in the channel
was fully removed during melt extraction (Fig. 10b).
Conversely, for the B689 sample set, a more enriched
central cpx REE signature might point to a residual
signal of the reactive, presumably more enriched melt
(Fig. 10c). A problem for the B689 dunites remains the
positive Zr and Ti anomalies. We have shown previously
that such anomalies can form when a more enriched
dunite is chromatographically overprinted by depleted
melt (Suhr et al., 1998), i.e. exactly the mode that is here
postulated for the BMD mantle dunites. The potential
to develop positive Zr and Ti anomalies in dunite is due
to larger Kd,ol for Zr and Ti relative to adjacent REEs.
The reason the anomalies do not develop in the present
modelling is that the percolation parameters are unsuitable to produce fractionation among the elements
over the involved distances. In other words, the intensity
of solid–fluid exchange is too low compared with the
intensity of advective transport in the present modelling.
The most likely way to produce these anomalies would
therefore be to advect the melt not at right angles towards
the channel but to let the refractory fluid move at low
velocities and for larger distances along the compacted
channel during the extraction.
Fig. 9. Sequential diffusion profiles (Dt = 50 years) in instantaneous
olivine at 18 cm from the channel for conditions as in Fig. 8d, i.e.
250 years of diffusive transport followed by 750 years with –1 cm/yr
advection. Growth of olivine (radius >2·0 mm) shortly before the flow
reversal, i.e. at time when reaction front has reached 18 cm distance,
should be noted. Upon the reversal, depleted host–harzburgite fluid
resets rim to low concentrations whereas inner part reaches higher
concentration from Nd diffusing inwards.
composition. It should be mentioned that, in the case of
Fig. 8d, compaction of the reactive dunite is essential to
generate the depleted signature. Otherwise, the high
diffusive flux of reactive and enriched melt from the
central part of the channel effectively prevents any depleted melt entering the high-porosity dunite.
Full REE patterns
In Fig. 10a, the infiltration-dominated case, shown in
Fig. 8a for Nd only, is extended to all REEs including
Zr and Ti. It is compared with dunites and cpx-rich
harzburgites from upper TM. In keeping with the geologic evidence from upper TM, a higher fraction of cpx
derived from melt (0·5% by fractionation and 0·01%
from trapped liquid) is included. In upper TM, dunites
(grey shading) are more enriched than the peridotite
matrix (vertical ruling). Equally, in the model, dunite
(heavy continuous line) is more enriched than the host
matrix (heavy dashed lines). The advective infiltration in
this model is consistent with earlier interpretations that
the upper TM mantle rocks have been subject to a
regional melt infiltration event (Suhr, 1993; Suhr &
Robinson, 1994). The different degrees of enrichment
within the modelled matrix are due to chromatographic
fractionation of the melt. Within the infiltration-dominated model, the dunite shows virtually no fractionation
internally (not shown). The large range of dunite compositions seen in TM is then due to (1) different melt
NUMBER 4
DISCUSSION
Preliminary considerations
The following constraints for shallow-level dunite formation are available from this study:
(1) field evidence from both the BMD and upper TM
sections suggests the involvement of fractures in the
formation of at least some dunites. This includes tabular
bodies, whose shape is primary and not a result of
structural transposition, as they are at high angle to the
foliation (e.g. the 600 m × 4 m dunite B689, also Fig. 1a).
(2) The lifetime of dunites appears very limited as
indicated by mutually cross-cutting dunites (Fig. 1d),
consistent with their origin by fracture.
(3) Time constraints are imposed by the relatively slow
movement of the reaction front and are further discussed
below.
(4) The geochemistry of the BMD dunites is best
explained by assuming that locally present, depleted melt
was extracted into the replacive dunite at a late stage. In
upper TM, however, infiltration might have dominated.
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SUHR
MANTLE HOSTED DUNITES
Fig. 10. Concentrations of REE, Ti, and Zr in cpx from BMD and
upper TM dunites (shaded areas with thin grey lines indicating individual samples) and cpx harzburgites from upper TM (vertically ruled).
Modelled dunites are heavy continuous lines; modelled harzburgites in
(a) are heavy dashed lines. (a) Conditions as in Fig. 8a but cpx in dunite
from 0·5% open system fractionation and 0·01% trapped melt and
+2 cm/yr advection; (b) conditions as in Fig. 8e; (c) conditions as in
Fig. 8d.
Point (4) suggests that the ambient temperature of the
surrounding mantle was high enough so that the mantle
could contain an interstitial, depleted melt. The late
presence of a depleted melt beneath the BMD massif
was also derived from the study of the transition zone
dunites (Suhr et al., 1998). As a result, it is unlikely that
during formation of the dunites the uppermost mantle
of the BMD massif was part of the lithosphere. Whether
fracture formation is also possible at large depth inaccessible to observation has been doubted [see review
by Kelemen et al. (1997)]. In favour of its formation it is
speculated that local planes of weakness in the deep
mantle may allow the formation and propagation of
fractures on a smaller scale whereas in the shallow mantle
more important fracture formation can occur. Such local
planes of weakness might be pyroxenite–harzburgite contacts as seen in Fig. 1a. In this context, we also note the
parallelism of dunite and diffuse opx ‘layering’ common
in mantle rocks (Fig. 1d), which could be a hint for
preferred melt migration along (former) pyroxenitic banding. In addition, the anisotropic equilibrium melt distribution of a deforming and melting peridotite (Boudier
& Nicolas, 1977; Stevenson, 1989) may act as planes of
weakness.
On the basis of this work, the formation of dunites
beyond a thickness of several centimetres within weeks
is unlikely. Only a few centimetres of dunite can form
within 1 year next to an open fracture that maintains a
constant composition (Fig. 6). A 10 cm dunite would take
about 50 years to form, and a 2 m half-width dunite
20 000 years by diffusive transport only. If an advective
velocity of 10 cm/yr into the host is assumed, a time on
the order of 1200 years is required for a dunite with 2 m
half-width [assuming vfr = (1/60)v0]. However, the halo of
incompatible trace element enrichment in the peridotitic
host rocks, determined by the chemical velocities, would
be on the order of 12–60 m for host rocks with a
bulk distribution coefficient of 0·1 (Yb) to 0·01 (La),
respectively. This would preclude the preservation of
highly residual harzburgites in the vicinity of large dunite
bodies.
The times for the formation of wide dunite bodies may
be shortened if it assumed that, during the dunite growth,
reactive melt is able to advectively enter from depth
into the newly created replacive dunite. Essentially, the
constant concentration boundary condition, restricted in
the model to the centre of the replacive dunite, can then
be moved to an arbitrarily low horizontal distance from
the reaction front. The velocities of the diffusively driven
reaction front [Fig. 5c, or equations (C10) and (C11)] for
a given distance can now be applied. For a 2 cm distance
from the reaction front (to which the reactive melt
advectively advances), a velocity of 0·4 cm/yr is derived,
so a 200 cm half-width dunite would take 500 years to
form, without any significant host rock enrichment. Even
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these shorter times are, however, much longer than times
suggested by Nicolas (1986).
Alternatively, the growth of replacive dunite could be
limited by the flux of reactive melt from depth. In
other words, in contrast to Fig. 4, where the channel is
considered a condition of constant (silica-undersaturated)
melt composition, the melt composition could be affected
by the reactive exchange to a degree that limits the
progress of the reaction front. Two cases are distinguished:
(1) a finite amount of reactive melt is trapped within
an open, but stagnant channel. The largest width of the
replacive dunite wdu that can be formed from a conduit
containing reactive melt and having a width wch is
wch/wdu = ucrit.
(10)
(2) The conduit is fully closed but melt continues to
flow through the porous dunite that had been generated
adjacent to the open channel. The maximum rate at
which replacive dunite can grow is
∂wdu
v u
= wdu z,du rx
∂t
Zucrit
(11)
where Z is the assumed vertical length of constant thickness over which dunite is formed and vz,du is the Darcy
velocity in the dunite along the z-direction. By integration,
the dunite width after time t is
wdu = w0,duexp
vz,duurx
t
Zucrit
(12)
where w0,du is the initial width of the porous dunite and
the melt leaving the dunite is fully reacted out. The term
s0 = (Zucrit)/(vz,duurx) is a characteristic time over which
the original dunite width grows by a factor of e. The
biggest unknown in equation (12) is Z. If the dunite is
fed locally from a reservoir with reactive melt, then Z
may be very short and the dunite can rapidly grow in
width. If, on other hand, the replacive dunite represents
a porous melt channel supposedly reaching the source
region, Z must be very large. For example, for w0 =
2 cm, vz,du = 50 m/yr, urx = 0·09 and ucrit = 0·5, Z =
0·5 km and s0 = 56 years. For Z = 30 km and ucrit =
1, s0 = 6700 years. In general, the growth of the dunite
will start slowly but accelerate with time until it is limited
no longer by the flux of reactive melt from depth but by
the diffusive or advective flux of reactive melt across the
reaction front in the x-direction, as derived further above.
It should be noted that, for (12) to be applicable, there
must be a mechanism by which progressively more
melt is fed into the widening replacive dunite. This is
NUMBER 4
APRIL 1999
considered feasible in the model of the ‘reactive infiltration instability’ (Aharonov et al., 1995; Kelemen et
al., 1995a).
Model for dunite formation
On the basis of the observational evidence it is suggested
that dunite formation is initiated along a fracture
(Fig. 11a). The initial fracture may also be locally branching. In this way, irregular dunite widths and harzburgite
enclosures in dunite may be explained (Fig. 11e). What
is implied in this model is that the fracture can drain
melt that equilibrated at large depth in a source region
and that can therefore develop sufficient reactivity to
produce an initial replacive dunite along the wall of the
fracture (Fig. 11a). Using the time scales of several weeks
as suggested by Nicolas (1986), a replacive porous dunite
of maybe a few centimetres half-width can form along a
fracture. This estimate includes the effect of an initial,
centimetre-scale high-porosity ‘damage zone’ and the
speculative small-scale convective motion in it. This stage
is sufficient to explain the most common occurrence of
dunites in the centimetre range. However, the rarer, but
obvious presence of dunites in the decimetre and metre
range is not explained.
When the source region of the melt-filled conduit has
sufficiently compacted, flow in the open fracture ceases.
The thin replacive dunite may now grow by using reactive
melt trapped in locally present, largely stagnant melt
pockets along the closed, former conduit (Fig. 11b). A
dunite width according to equation (10) can be reached
around the pockets. For the shallow-level mantle, open
conduits are known to exist, as derived from the occurrence of chromitite deposits (Lago et al., 1982). According to Lago et al. (1982) they represent local cavities,
and it is suggested that their ubiquitous dunite rim formed
by reaction of host peridotite with interstitital melt from
the chromitite body. It is suggested that for wide tabular
dunite bodies, the time after cessation of fast flow in the
open conduit represents their main growth period but
that the main melt transfer occurred during the short
fracture event. Fracture formation and wide dunite formation are thus two subsequent, but genetically related
events. This circumvents the contradictory time constraints imposed by replacive dunite and fracture formation. At large depth, the initial fracture was less wide,
reactivities will tend to be lower, and relic melt pockets
are less likely to persist, such that the process of Fig. 11b
is expected to be less important. Large dunite widths
may not be reached at large depth and during progressive
mantle flow dunites with a width on the grain scale are
unlikely to be preserved.
After closure of the conduit, dunite growth may also
occur by porous flow within the initial replacive dunite
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MANTLE HOSTED DUNITES
Fig. 11. Model for the formation of tabular dunites in the mantle section of the BMD massif. (a) Along a fracture, a short-lived melt migration
event occurs, producing a centimetre-wide replacive dunite; (b) the initially narrow replacive dunite may grow by local, largely stagnant
accumulations of reactive melt and (c), after closure of the open conduit, by porous flow of reactive melt over a long period of time (hundreds
to thousands of years); (d) towards the final stage of dunite formation, compaction of the host rock expels refractory melt, which dominates the
signature of the dunite; (e) initial diversification of the fracture during stage (a) may lead to wider dunites and enclosure of harzburgite.
formed during the fracture–flow event (Fig. 11c), as
constrained by equation (11). It should be noted, however,
that for times <1000 years porous, reactive flow in long,
narrow channels will go largely unnoticed in terms of
dunite growth because of the large characteristic time s0.
Given that most dunites in the shallow mantle have a
thickness in the centimetre range, the dunite growth both
from melt pockets and by continued porous flow may
not be the rule.
After porous flow of melt from depth within the replacive dunite is decreasing, e.g. because of completed
compaction of the adjacent host at depth (Ribe, 1986),
the melt derived by local (that is, in our case, shallow-level)
compaction of the host becomes a dominant component
within the dunite (Fig. 11d). This explains the geochemical
signature in the BMD dunites, where the locally derived
melt is very refractory. In upper TM, this last event was
not complete as evidenced by the more abundant mineral
components derived from trapped melt present in the
host and dunite and the associated less refractory geochemistry.
The proposed model contrasts with that of Kelemen
et al. (1995b) in that the initial dunite is formed by fracture
and not by a reactive infiltration instability and that the
time of operation is limited, as evidenced by cross-cutting
relations of several dunite generations in the field. Wide
dunite bodies may include a reactive porous flow history.
The alternative is, however, growth of the dunite by
trapped, reactive melt.
It must be added that, whereas refractory melt extraction along dunites is a reasonable solution, it cannot be
ruled out with the available data that the final ‘extraction
event’ is genetically decoupled from the dunite-forming
event. It could be that there is an alternative, or additional,
event leading to large-scale migration of depleted fluids
through the harzburgite sequence, possibly related to the
compaction of the entire uppermost harzburgite during
the final stages of melting.
Other inferences
This study was originally started to derive melt compositions present under oceanic spreading centres from
the study of mantle-hosted dunites. The conclusions
concerning this aspect are that dunites must neither
record the primitive melt composition moving along the
channels nor are they likely to simply inherit the solid
composition of the harzburgite or lherzolite precursor
from which they presumably derive. Because of their low
KD for the REEs they are strongly affected by any melt
migrating through them and cpx precipitating from those
melts. In TM, we suggest that this melt is more channel
derived; in BMD, it might be host derived. In addition,
the dunite composition is strongly dependent on the
amount and mode of formation of cpx (i.e. fractionation
vs trapped melt derivation).
On the basis of the BOIC data it appears that a strong
final extraction–compaction event is marked by very
scarce cpx in the dunites. Conversely, more abundant
cpx, as in the upper TM dunites and host peridotites,
may indicate predominant infiltration or weak extraction.
The inferred extraction of depleted melt from shallowlevel harzburgites implies that the final aliquots of melt
drained out of the system could be more refractory than
the regular aggregate melt (Nicolas, 1986) as is observed
in, and may explain, some very depleted melt inclusions
from MORB (Sobolev & Shimizu, 1993).
595
JOURNAL OF PETROLOGY
VOLUME 40
CONCLUSIONS
The wide range of mantle-hosted dunite morphologies
and chemistries in the BOIC argues for their non-simple,
possibly non-unique origin. Physical factors such as compaction and direction and intensity of advective fluid
motion are likely to be of equal importance to channel
melt composition in determining the final dunite chemistry. Dunites are unique in that their incompatible
element reservoir is virtually unbuffered and likely to be
biased to late geologic events. A full understanding of
the dunite formation must include therefore the compatible and ‘unstable’ elements, the latter being specific
for each reaction. For incompatible elements, differences
in melt composition between host and channel probably
dominated over the source–sink effects associated with
the dunite-forming reaction. For compatible and unstable
elements, reaction is important to produce geochemical
signals. The suggested melt extraction model is an attempt
to reconcile the geochemical and physical constraints. Its
main point is that a short-lived fracture formation leads
to a narrow replacive dunite. Subseqently, the dunite
may grow for highly variable, but much longer times
(reflected in variable dunite widths) from trapped melt
pockets and by reactive porous flow. In a late stage of
the dunite history, the interstitial melt in the dunite is
dominated by the locally derived melt from the slowly
compacting wall rock. In the shallow mantle, this melt
may be very refractory.
ACKNOWLEDGEMENTS
Dr Sumit Chakraborty’s help and readiness to discuss
various aspects of the study were critical for progression
of the work. Sergej Simakin performed careful ion probe
analysis at the Yaroslavl Institute of Microelectronics.
Journal reviews by A. Nicolas, M. O’Hara and I. Nicholl,
informal reviews by A. Meyer and M. Godard, and
supportive editorial handling by E.-R. Neumann are
gratefully acknowledged. This work was supported by
the DFG.
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597
APPENDIX A: NUMERICAL
HANDLING
Formally, the system shown in Fig. 4 can be represented
by a one-dimensional transport equation written in terms
of the mass balance of a trace element in the fluid (e.g.
Vasseur et al., 1991) with an additional term Rchem to
handle the solution–precipitation process:
JOURNAL OF PETROLOGY
u
VOLUME 40
∂
∂Cf
∂C
∂C
=
D̄fu f −(v0u0) f
∂t
∂x
∂x
∂x
n
XiDs,iKd,i ∂Cia
q
−3(1−u) s
qf i=1
Ri
∂r
+Rchem .
NUMBER 4
APRIL 1999
APPENDIX B: CRITICAL FLUID
FRACTION
(A1)
In addition to terms already defined, r is the length scale
of the grain radius, Ri is the grain radius, Ds,i is the solid
diffusion coefficient, and ∂Cia/∂r is the concentration
gradient at the surface of the grain. The term v0u0 states
the boundary condition for the advective flux.
The terms for diffusion in the melt (first term on righthand side), advection (second term on right-hand side)
and diffusive exchange between fluid and solid (third
term on right-hand side) are solved using explicit finite
differences. For advection, a simple upwind scheme was
used. To obtain the concentration gradient at the surface
of the grain needed in the third term, a coupling with the
radial diffusion equation (e.g. Crank, 1975) is required.
Within a representative elementary volume (REV) the
fluid composition is assumed homogeneous. The solution
and precipitation processes are realized by changing
the radii of the grains, which involves interpolation of
concentration profiles to new grid points.
Numerical accuracy was tested for by comparing the
results of the program with the known analytical solution
of the advection–diffusion equation, the pure chromatographic model of Navon & Stolper (1987), and the
reaction front velocities as given in (C4) and (C10).
Convergence of the results was tested for different time
and spatial discretizations. For terms involving a closedsystem REV (solution, precipitation, and diffusive equilibration between solid and fluid) mass balance checks
are performed for selected cells. For the entire system, a
mass balance is performed using initial and final abundances of a given element and considering diffusive and
advective fluxes at system boundaries.
A major problem in the numerical handling is the high
reaction rates indicated by the sharp, sub-centimetrescale reaction fronts. For the concentration signal at the
reaction front to be smooth, the reaction front must be
spatially resolved by numerous grid points. This requires
that the REV is grain scale to even sub-grain scale.
However, the REV has here been defined using grainscale geometrical properties and so the sweeping assumption must be made that the average properties of
the medium are realized at least on a grain scale or that
actual deviations of the geometry do not critically affect
the result. Unless processes within the reaction front have
to be resolved, this assumption is probably justified.
The critical fluid fraction ucrit required to convert one
unit of reactant into product can be derived by mass
balance. The reactant consists of (1 – u0) solid. A volume
ucrit of reactive melt is added to the reactant. The reaction
proceeds by an extent ncrit until one of the phases taking
part in the reaction is exhausted. ncrit is the smallest ratio
(Xi/|mi|), where only negative reaction coefficients mi (i.e.
those indicating solution) are considered. Of interest is
the critical fluid fraction ucrit, and it can be derived using
the following mass balance for the fluid:
n
m
ucritqf−(1−u0)qsncrit
Cf,ch
(C
m)
m
s,i i
i=1
n
m
m
= Cf,eq
ucritqf−Cf,eq
(1−u0)qsncrit
m.
i
(B1)
i=1
In (B1), the left-hand side represents the abundance of
the monitor element in the disequilibrium assemblage
after reactive fluid has been added to the original host
and the right-hand side gives the abundance in the
equilibrium state. The first term on the left-hand side
represents the abundance in the added reactive fluid and
the second term gives the abundance liberated from the
solid or immobilized in the solid by the reaction. The
minus sign in front of the second term derives as solution
is attached to negative reaction coefficients. The righthand side of the equation states that the total new fluid
mass has equilibrium monitor element concentration and
it consists of the fluid mass added (first term) and any
fluid mass changes associated with the reaction (second
term). Solving for ucrit
598
n
ncritqs(1−u0)
ucrit =
n
m
(Cs,immi)−Cf,eq
i=1
m
m
qf(Cf,ch
−Cf,eq
)
m
i=1
i
(B2)
it can be seen that the reaction capacity of the fluid
increases (low ucrit) when the concentration difference
between channel and equilibrium melt is high. Any initial
equilibrium fluid fraction u0 present in the host reduces
the mass fraction of the solid such that the reaction
capacity of the incoming fluid relative to the host is
increased.
APPENDIX C: REACTION FRONT
VELOCITY
With the concentration difference between channel melt
and melt in equilibrium with the solid matrix being set
SUHR
MANTLE HOSTED DUNITES
m
m
to DC = Cf,ch
−Cf,eq
, the advective flux Jadv of the monitor
element upstream of the front is
to urx. We assume that the effective porosity can be
approximated as
Jadv = u0v0DC.
ufr = (u0 + urx)/2
(C1)
and we further simplify and set, using equations (1) and
(2)
As ucrit is exactly the porosity required to drive the
reaction front with a velocity equal to the advective
velocity, the flux at the front required to drive the front
with a velocity vfr is
Jfr,adv = ucritvfrDC.
(C2)
In a reference frame fixed with respect to the channel
at x = 0, the front is a moving boundary, so an additional
melt flux is required to satisfy the upstream porosity
urx once the front has detached from the channel. Its
magnitude is
Jadv,add = urxvfrDC.
D̄f,fr = Df/[1– ln(u2fr)].
u0v0
ucrit + urx
(C3)
∂C fm DC
≈
.
∂x
vfrt
∂(C fmuD̄f)
.
∂x
∂C fm
.
∂x
vfr,diff =
( s
Xfr =
(C6)
At the front, the upstream porosity varies from u0
( ufrD̄f,fr
ucritt
(C10)
and by integration the position of the diffusively driven
front after time s is
(C5)
We assume here that for the instantaneous reaction
front it is sufficient to define average properties ufr and
D̄f,fr for the porosity and diffusion coefficient of the fluid,
respectively, such that
Jfr,diff = ufrD̄f,fr
(C9)
By inserting (C9) into (C6) and equating with (C2), the
velocity of the front driven by diffusive transport and
instantaneous reaction is obtained as
(C4)
which is valid for x > 0, advective transport only and
instantaneous reaction.
A similar consideration is made for a diffusively driven
front. The diffusive flux at the reaction front, in the
absence of advection and for instantaneous reaction, is
Jfr,diff =
(C8)
After a time interval Dt, the reaction front has moved
a distance Dx = vfrDt and disturbs the concentration
profile of the monitor element between the channel and
the reaction front. As long as the characteristic distance
for diffusion Dx = (D̄fDt)1/2 > vfrDt (where vfr is also driven
by diffusion), the concentration profile of the monitor
element will be essentially linear. Given this condition,
m
and as the fluid concentration at the front is Cf,eq
and at
m
the channel it is Cf,ch, we can write
By equating (C1) = (C2) + (C3),
vfr,adv =
(C7)
0
ufrD̄f,fr
dt = 2
ucritt
(
ufr
D̄f,frs .
ucrit
(C11)
It should be noted that both derivations (C4) and (C10)
imply that additional porosity created by excess melt
reactions is retained in the system. For qf < qs, the system
is required to expand or an additional fluid flux is
generated. In the numerical program, the additional fluid
flux is extracted out of the system. This leads to a small
discrepancy between the numerical program and the
analytical derivation for qf≠qs (see e.g. Fig. 5d).
599