----

American Mineralogist,

Volume 81, pages 754-759,

1996

Magma transport and metasomatism in the mantle: A critical review of current
geochemical models - Discussion
ODED NAVON,l F.A. FREy,2 AND E. TAKAZAWA22Department

1
Institute of Earth Sciences, The Hebrew University, Jerusalem, Israelof Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139, U.S.A.

ABSTRACT
Nielson and Wilshire (1993) promised a review of geochemically based models formagma transport and metasomatism in the mantle. However, they focused on discrediting
the chromatographic model ofNavon and Stolper (1987). Nielson and Wilshire concluded
that the process operating during melt percolation in the mantle "resembles ion-exchange
chromatography for H20 purification, rather than the model of chromatographic species
separation proposed by Navon and Stolper (1987)." Our objective here is to show thatNielson and Wilshire (1993) did not offer any new theoretical or modeling advances. We
demonstrate that the "water-purification
model" (based on the finite-plate model of Helfferich 1962) is controlled by the same physics and mathematics as the frontal chromatography model discussed by Navon and Stolper (1987). Thus, the distinction made by Nielson and Wilshire between the two models has no basis. Moreover, we show that withappropriate boundary conditions, the model of Navon and Stolper (1987) produces an
excellent fit to the data that Nielson et al. (1993) fitted using the "water-purification
model." We emphasize that the model of Navon and Stolper can be used to model both
small- and large-scale processes and that it allows the recovery of temporal information,
which cannot be retrieved using the finite-plate model. The usefulness of these models forunderstanding the geochemistry of mantle rocks is a subject of active research and beyond
the scope of this discussion.
INTRODUCTION
To interpret properly the geochemical characteristics
of basalts, it is necessary to know the mechanisms andconsequences of melt transport from their mantle source
to the eruption site. Two end-member processes are melt
migration by percolation along grain boundaries of solid
matrix (i.e., porous flow) and melt transport in fractures
forming veins and dikes. Both processes must occur inthe mantle. Porous flow must be important, at least during the early stage of melt segregation, and field observations of lithospheric rocks clearly indicate the importance of melt transport
in fractures.
The relative
importance of these two end-member processes is a subject of active study (e.g., Bodinier et al. 1990; McKenzie
and O'Nions 1991; Hart 1993; Iwamori 1994; Stolper
and Newman 1994; Hauri et al. 1994; Kelemen et al.
1994). Nielson and Wilshire (1993) summarized experimental, theoretical, and field observations pertaining to
fluid flow in a porous medium and through fractures.
They emphasized examples of mantle xenoliths that reflect infiltration of melts from dikes into wall rocks andconcluded that the geochemical effects of porous flow are
typically limited to scale lengths of a few centimeters.
Because fracturing is a necessary condition for entrainment of xenoliths, which are typically <0.5 m in diam0003-004X/96/0506-0754$05.00

eter, it is likely that examples of large-scale porous flow
cannot be sampled by xenoliths. Large, kilometer-scale
peridotites are more suitable for evaluations of the scaleof porous flow, but they have added complexities, suchas metamorphic reactions, resulting from their transport
into the crust.
Following the pioneering work of McKenzie (1984),
Navon and Stolper (1987) examined the geochemicalconsequences of melt percolation. Their approach was
general and can be applied to any scale, as long as thepercolation distance is large relative to the grain size ofthe matrix. They concluded that when a percolating melt
is not in equilibrium with the host matrix, the interaction
between melt and matrix must lead to the developmentof chromatographic
effects. Navon and Stolper (1987)
noted that such effects are expected if a melt percolates
from a dike into the wall rock and suggested simple
chemical criteria for identifying this process, e.g., their
Figure 5. We agree with Nielson and Wilshire (1993) that
it is important to assess how well chromatographic processes explain geochemical data for mantle rocks. This is
an important objective because chromatographic
processes can create compositional effects in melts and solids, such as changes in abundance ratios of incompatible
elements that are much larger than those created by partial melting or fractional crystallization. Some aspects of754

NAVON ET AL.: MAGMA TRANSPORT

the critical review by Nielson and Wilshire (1993), however, are confusing and erroneous, and our goal is to clarify their discussion of chromatographic processes. In particular, we discuss their conclusion that the chromatographic
model proposed by Navon and Stolper (1987) is not appropriate for the mantle.
THE

CHROMATOGRAPHIC

MODEL

Conceptually, a chromatographic
process within the
mantle is expected when melt percolates through a peridotite matrix with which it is not in equilibrium. As themelt migrates, the melt and matrix compositions change
toward equilibrium compositions'definedby solid-melt
partition coefficients (KD). Depending on the compositions of initial melt and matrix, trace element abundancesin the peridotite can increase or decrease. Chromatographic effects in the percolating melt and matrix are created during the transition to equilibrium and are a function of position and time. The treatment of Navon and
Stolper (1987) included the simplifying assumptions that
KD for each element is constant during the process andthat the chemical interaction is limited to ion exchange
without a change in mineral proportions. They recognized that the latter assumption is the major limitationin applying their model to geologic situations.
Nielson and Wilshire (1993) discussed several examples of chromatographic interaction between melt and peridotite, including the studies of Bodinier et al. (1990)
and Takazawa et al. (1992), which utilized the approachadvocated by Navon and Stolper (1987), and that ofNielson et al. (1993), which used a finite-plate model (Helfferich 1962). Nielson and Wilshire (1993) concluded that
melt-waIl-rock interactions in the mantle resemble "ionexchange chromatography
for H20 purification, rather
than the model of chromatographic
species separation
proposed by Navon and Stolper (1987)." They did notgive a quantitative description of the H20-purification
model, and the reader is referred to Helfferich (1962),
Hofmann (1972), and Fletcher and Hofmann (1974). Because all chromatographic processes are based on simple
mass-balance calculations, the basic physics and mathematics of all chromatographic models are similar. As expected, a close examination ofthe equations used by Helfferich (1962, p. 450, Eq. 9-3),(au) (az) _ ( ) _ !!!L ( ) a (1)

q axi

+

aci

u

z

Ilz

a2C;

2

az2 u

a2C;

v/V2 az2=

and Navon and Stolper (1987, p. 287, Eq. la),

aCI
at

+

+

1 - eJ>!!.!.acs
eJ> PI at

1 - eJ>~vV'c
eJ>

PI

s

s

+ vV'CI I
I
I = a- DV'2C(2)

reveal that they are identical. The interested reader need
only set the matrix velocity, V:, in Equation 2 to zero,neglect the third term in Equation 1, which is justified
when the percolation distance is large in comparison withIN THE MANTLE-DISCUSSION

755

the grain size, and make the necessary transformations
between the parameters used in the two references: Xi =CIPleJ> + C;Ps(1 - eJ», U = qeJ>(Vlt- z), VI = VjeJ>,D =DiV2, and Ci = CJPj,where q is the column cross section;z is the distance from the bottom of the column; IlZ =1.64a is the thickness of a layer of close-packed sphericalgrains of radius a; Xi is amount of species i (in the melt
and the matrix) per unit volume of column; U is melt
volume that passed through distance z during time t, since
operation started; VI is the melt volume per unit crosssection per unit time; C; and CI are the concentration of
the species of interest in the melt in weight per unit volume and weight per unit weight of melt, respectively; Cs
is the concentration in the matrix (weight species ilweightof matrix); t is time; eJ>
is porosity; PI and Psare the densities of the melt and matrix, respectively; Vj and v: aretheir respective velocities; and DI is the diffusivity of thespecies in the melt.
As shown by Navon and Stolper, the effect of diffusionin the melt can be neglected in columns that are on theorder of 100 m or longer. Then, if local equilibrium between melt and matrix is assumed (i.e., Cs = KDCI at any
point, and diffusion in the solid is not an important constraint), a mass balance for a trace element in the porous
matrix (Eq. 4 ofNavon and Stolper 1987) leads to a simple analytical solution for the position of the concentration fronts of the various elements (see Eq. 5 of Navonand Stolper 1987). These equations are valid for any initial matrix concentration, C~. In the simple case whereq = 0, Equation 4 of Navon and Stolper (1987) reduces
to(3)
where z and Z are the locations of the concentration frontof the element of interest and of the melt, respectively,
and q is the concentration of this element in the input
melt. In Equation 3 the right side represents the total
mass of the trace element that was introduced into thecolumn by the input melt, and the left side describes the
distribution of this element between the melt and equilibrated matrix behind the concentration front at z. Between z and Z in the column, the melt concentration, CI,
was reduced to zero as the input melt equilibrated withthe matrix in the interval from the base of the column toz. The mass-balance equation is the basis for all chromatographic models and is responsible for the well-known
effect of incompatible elements migrating through thecolumn faster than more compatible elements. The effects of diffusion in the melt are to broaden concentration
fronts, but their relative positions are not changed.
Iflocal equilibrium is not attained because of slow solid-state diffusion in the grains, the only difference between the Helfferich (1962) and Navon and Stolper (1987)
approaches is in the mathematical method used for solving the mass-balance equations; the same input parameters, diffusion coefficients, porosity, and melt velocities
are required by Equations 1 and 2. Helfferich (1962) estimated the time it takes to approach equilibrium and the
distance, I, traveled by the melt during that time. He then

756

NAVON ET AL.: MAGMA TRANSPORT

used the approximation that a chromatographic column
can be considered as a series of segments or discrete plateswith thickness I where complete equilibrium is achieved.
After equilibration the melt is transferred to the next plateand so on until it reaches the top of the column. This
simple scheme was used by Farmer and DePaolo (1987)
and by Nielson et al. (1993). Navon and Stolper (1987)
demonstrated that the major impediment to achieving
local equilibrium is the slowness of volume diffusion insolids. They used a numerical model and formulated ananalytical approximation(Appendix A of Navon and
Stolper 1987) to evaluate the effects of solid-state diffusion on concentration gradients in the melt and matrix.
We emphasize that the solutions of Helfferich (1962) andNavon and Stolper are identical when local equilibriumis achieved. If slow diffusion in the solid prevents such
equilibrium, the only difference is in the method used tosolve the differential equation. Nielson and Wilshire(1993) used the simplified approximation given in Helfferich (1962), but this approximation and the solutions
given by Navon and Stolper lead to similar results.
In summary, there are no fundamental physical ormathematical differences between the chromatographic
models discussed by Navon and Stolper (1987) and thatfavored by Nielson and Wilshire (1993). Their assertion
that the chromatographic process in the mantle "resembles ion-exchange chromatography for H20 purification,rather than the model of chromatographic species separation proposed by Navon and Stolper (1987)" has nobasis.
In the following discussion we answer the questions put
forward by Nielson and Wilshire (1993, p. 1123) as "Important questions. . . unanswered by Navon and Stolper(1987)."(1) "What region of the mantle constitutes the top of areacting column?" Chromatographic reaction ceases whenmelt stops migrating by porous flow. Therefore, a simple
answer is that the top may be defined by the level atwhich melt migration is dominantly in veins and dikes,
but this transition may be gradational (Hart 1993). In thecase of melt migrating away from a dike, the top of thecolumn may be placed at the melt front. In mathematicalterms, the real answer is that there are no boundary conditions pertaining to the top of the column, and so thelocation of the top is not important. The only constraint
is that the whole column must be uniform on a scale thatis large in comparison with the grain size.
(2) "Why does the migrating melt react in this region
if the matrix is the same as that within the column?"
Because this question directly follows Question 1, we infer that by "this region" Nielson and Wilshire are referring to the top of the reacting column. Our answer is thatthe melt reacts with the matrix as long as they are not in
equilibrium. The very first melt emerging from the column has equilibrated with the column matrix (it is aheadof all the concentration fronts and does not react with thematrix). Later, concentration fronts of the various elements reach the column top, and the matrix there reacts

IN THE MANTLE-DISCUSSION

and equilibrates with the original melt composition, firstwith the incompatible elements and then with the morecompatible elements.
(3) "Why does the matrix pattern so accurately reproduce that in the melt if K~ values remain constant?" In
this context, matrix pattern refers to relative abundancesof elements such as the REE. If equilibrium is achieved,
then the concentration in the solid matrix is C, = KoCj,
and the matrix pattern reflects the melt through the partition-coefficient operator. In general, because Ko
1 andvalues of Ko are not similar for all trace elements, themelt and matrix never have the same relative abundanceof trace elements. If equilibrium is not achieved, becauseof slow solid-state diffusion, it is also evident that relative
abundances of trace elements are very different in themelt and solid, as is clearly illustrated in Figure 4 of Navon and Stolper (1987). It is not clear to us why such aquestion would be asked. A possible motivation is thesuperficial similarity of chondrite-normalized
REE patterns (on a logarithmic scale) in an amphibole selvage andthe adjacent amphibole-peridotite
wall rock in a Dish
Hill xenolith (Figs. 3 and 5 of Nielson et al. 1993). Thissimilarity may reflect trapped melt in the peridotite or
the assumption that amphibole in the selvage represents
the REE abundances in a metasomatic agent rather than
REE abundances of amphibole crystallized from a melt
(Nielson et al. 1993, p. 111).
(4) "What is the likely proportion of melt relative tomatrix that can percolate far enough to produce the transient fractionation
patterns?" Transient fractionation
patterns or, in other words, large variations in the abundance ratios of two elements, i and}, with different compatibility, e.g., Kb < Ki" occur in the volume between
the concentration fronts of these elements (e.g., Fig. la,of Navon and Stolper 1987). The melt-matrix ratio required to generate this region can be determined from
Equation 5 of Navon and Stolper (1987). The mass ofmelt between the concentration fronts for i and} is=1=(4)
where q is the column cross section and Xi = z,lZ = rjJpJ[rjJPj + (1 - rjJ)p,Kb]. The mass of the matrix that interacted with the melt is the matrix
front. That is,qZ(1Therefore, the melt-matrix

-

mass

rjJ)p,.

behindthe melt(5)

ratio is(6)

Alternatively, we can consider only the matrix behindthe front of the more incompatible element i. In this casethe melt-matrix ratio is(7)
In both cases the melt-matrix ratio depends only on
the melt fraction, rjJ,the densities, P'fand p" and the partition coefficient of the two elements, Kb and J(io. The

NAVON ET AL.: MAGMA TRANSPORT

calculation is more complex for the nonequilibrium case,but all the required information is in Appendix A ofNavon and Stolper (1987).
These questions of Nielson and Wilshire (1993) lead
us to infer that they did not have a thorough understanding of the chromatographic process modeled by Navonand Stolper (1987). This inference is reinforced by theirrepeated statement that the Navon and Stolper approachis based on the supposition oflarge-scale percolative processes (see Abstract and p. 1129 of Nielson and Wilshire1993). Navon and Stolper emphasized applications of themodel to problems oflarge scale, but the model is equallyapplicable to small-scale problems when the concentrations in matrix and melt vary on a length scale that islarge in comparison with the matrix grain size. Anothersignificant erroneous statement by Nielson and Wilshireis that in their discussion of the Dish Hill xenolith theystate (p. 1130) ". . . contrary to Navon and Stolper (1987),
the most elevated LREEcn contents and fractionated patterns of LREEcn vs. HREEcn occur within 2 cm of the dike
contact." As discussed below these observations are exactly those predicted by the Navon and Stolper model.
THE DISH HILL XENOLITH
The compositional variations in a xenolith from DishHill, California (Nielson et al. 1993), are the basis for thewater-purification model that Nielson and Wilshire (1993)
proposed as appropriate for describing chromatographic
processes in the mantle. The xenolith is a lherzolite (17x 16 x 9.5 cm) with a selvage of amphibolite at one end.
On the basis of modes inferred from mineral and wholerock compositions, Nielson and Wilshire found that theamphibole mode in the peridotite decreases from 1.9 to
0.6% with increasing distance from the amphibolite. Major and trace element concentrations and isotopic ratios
also vary systematically as a function of distance fromthe amphibolite selvage; the concentration profiles resemble those produced by chromatographic processes.
Nielson and Wilshire (1993) stated that the reaction
gradients in the Dish Hill xenolith can be modeled fairly
well by simple finite-plate calculations (Helft'erich 1962;
Farmer and DePaolo 1987) that are a simplification ofNavon and Stolper's (1987) approach. Nevertheless, theyclaim that the water-purification model can explain observations that cannot be explained by the model ofNavon and Stolper (e.g., in the Abstract and p. 1127 and1130 of Nielson and Wilshire 1993).
How can one model do what the other cannot when
they are almost mathematically identical? In particular,
Nielson and Wilshire (1993) emphasized that abundancesof incompatible elements, such as light REE, are highest
in the peridotite wall rocks closest to the amphibolite,
and they inferred (p. 1130) that this observation is contrary to the model of Navon and Stolper (1987). In response, we note that when a melt enriched in incompatible elements reacts with a peridotite depleted in suchelements, addition of incompatible elements to the peri-

757

IN THE MANTLE-DISCUSSION4

0.5 135
0.5134

3'"
Z

0.5133

E0.

28
'"
z

--- ~0.5132'"
Z'":! 0.5131
0.5 1300.5129

0
o

2

4

6
8
Distance

10
(em)

12

14

16

FIGURE 1. Comparison of measured Nd content and '43Nd/'44Nd vs. distance from amphibolite selvage in Dish Hill xenolith (Ba-2-1) with theoretical profiles, dashed and solid lines,
based on Equations 5 and 10, respectively, ofNavon and Stolper(1987). Nd isotopic compositions (open symbols, left scale), Nd
concentrations (solid symbols, right scale) and estimated uncertainties are from Nielson et al. (1993). Initial matrix values arethose for WR-4, the peridotite with the highest 143Nd/144Nd,
0.513443, and an Nd content of 0.38 ppm. The more distantwhole-rock (WR-5) has a lower isotope ratio, possibly because
there was another amphibolite selvage, now dislodged, on thisside of the xenolith. Initial melt concentration is 40 ppm Nd,
the value for the amphibolite selvage. The amphibole in theselvage and WR-I, the peridotite at the amphibolite-peridotite
contact, are not in equilibrium; consequently, two alternativevalues were chosen for the isotopic ratio of the initial melt:
0.512965, the measured ratio in the amphibolite; and 0.513055,
the value for the whole-rock closest to the amphibolite. If theinitial melt has an isotopic ratio of 0.513055, the model provides
a good fit to the data when the porosity is I %, the percolation
distance, Z, is 14 em, the percolation velocity is 21 cm/yr, theNd partition coefficient is 0.09, and a diffusion coefficient of 10-7
cm2/s is assumed. This choice of partition coefficient and diffusion coefficient constrains the time required to create the profile
to a few months.

dotite is an expected consequence of the Navon and Stolper (1987) model. Because the length scale is centimetersin the Dish Hill sample, diffusion in the melt should be
important (Navon and Stolper 1987, p. 293). Under theseboundary conditions, the simple chromatographic modelof Navon and Stolper may be used to model trace element profiles and to constrain time-scale and other physical parameters of the process. For example, by using theNavon and Stolper equations with the KD values (~ =0.06 and IG;d = 0.09) proposed by Nielson and Wilshire(1993), a pore volume of 1%, densities of 2. 7 and 3.3 gm/
cm' for melt and matrix, respectively, and a melt percolation distance of 14 cm, we find that the observed Ndabundances and isotopic variations with distance fromthe contact can be matched by the theoretical profiles(Fig. I). The observed dispersion of the concentrationand isotopic fronts could have been caused by several
processes (Navon and Stolper 1987). If this dispersion
reflects control by diffusion in the melt and a diffusion

---

758

NAVON ET AL.: MAGMA TRANSPORT

coefficient of I x 10-7 cm2/s is assumed (Magaritz and
Hofmann 1978), the best fit to the data requires a timescale of about eight months, corresponding to a percolation rate of 21 cm/yr.
The preferred KD values for Nd and Sr used by Nielson
and Wilshire (1993) are higher than expected from recent
measurements of clinopyroxene/melt
KD (e.g., Hart andDunn 1993). These high KD values may reflect amphibole
formation during the melt-wall-rockreactions. Navonand Stolper (1987) cautioned that their model assumed
major element equilibrium between migrating melt andmatrix; hence, modal mineralogy and KD are constant intheir model. However, if the H20 content of the metasomatic melt (or fluid) were higher than -5%, then, because the rock now contains <0.2% H20, the effective
partition coefficient for H20 would be <0.04. If so, theH20 front preceded the Sr and Nd concentration fronts,
and the Sr and Nd fronts migrated through an amphibole
peridotite. Because the amphibole grain size is small, it
is logical, in this case, to assume local equilibrium. Bulk
solid-melt partition coefficients are functions of mineral
KD and mass fraction of the mineral in the solid. Because
clinopyroxene forms 10-20% of the Dish Hill peridotite,clinopyroxene was the major contributor to the bulk solid
KD for Sr and Nd. However, amphibole typically has KD
values higher than clinopyroxene (e.g., Green et al. 1992),
and it is possible that during the chromatographic process
the creation of amphibole was in part responsible for incorporation of Sr and Nd into the peridotite wall rocksof the amphibolite.
Undoubtedly, the actual process was more complex than
this simple model. For example, formation of additional
pore volume, the rates of amphibole formation, and theretention of some melt, along with its trace element content, may also have been important. The model preferredby Nielson and Wilshire (1993), however, does not address any of these additional complexities, and it is a lessaccurate solution that adds nothing to the model proposed by Navon and Stolper (1987).

-

CONCLUSION
Since the early recognition of relative light REE enrichments in dunite and harzburgite (e.g., Varne and Graham 1971; Frey and Green 1974), there have been many
proposed explanations for that phenomenon (see review
by McDonough and Frey 1989). There is now consensus
that chromatographic processes, such as proposed by Navon and Stolper (1987), are important in creating incompatible element enrichments in mantle rocks. An unresolved question is the scale of such a process. We agreewith Nielson and Wilshire (1993) that study of well-exposed samples collected from xenoliths and massive peridotites on scales ranging from centimeters to hundredsof meters is the best way to evaluate the scales of porous
flow in the mantle.
As for the models used to simulate the geochemicalconsequences of porous flow, we stress that the model

IN THE MANTLE-DISCUSSION

preferred by Nielson and Wilshire (1993) offers no advantage in comparison with the model of Navon and
Stolper (1987). The physics of both models are identical,
but the preferred approach of Nielson and Wilshire uses
a cruder mathematical
approximation,
disregards the
temporal information in the concentration profiles, anddoes not describe accurately the position of the concentration fronts when slow diffusion into the crystals of thematrix prevents local equilibration of melt and rock.
ACKNOWLEDGMENTS
Preparation of this paper was supported by the Basic Research Foundation administered by the Israeli Academy of Sciences and Humanities,
the Foundation for Scientific Cooperation Austria-Israel, and NSF grantEAR-9406105. We thank W. McDonough and E. Stolper for their comments.
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MANUSCRIPT RECEIVED DECEMBER 23, 1994
MANUSCRIPT ACCEPTED JANUARY 15, 1996