Downloaded from geology.gsapubs.org on 26 October 2009
Growth rates of dike-fed plutons: Are they compatible with
observations in the middle and upper crust?
Scott E. Johnson
Department of Geological Sciences, University of Maine, Orono, Maine 04469-5790, USA
Markus Albertz
Scott R. Paterson
Department of Earth Sciences, University of Southern California, Los Angeles, California 90089-0740, USA
ABSTRACT
Diapirism and dike-fed expansion are two popular models for the ascent and emplacement of large batches of granitoid magma into the middle and upper crust. Many structural and petrologic relationships in and around plutons can be cited as permissive evidence for either model, and so it has been difficult to differentiate between them on these
grounds. Here we consider wall-rock strain rates resulting from dike-fed expansion at a
constant-volume pluton-filling rate. Considering end-member pluton shapes and dike flow
rates, and dikes 1 km in plan length, the dike-fed expansion model predicts wall-rock
strain rates over the entire pluton-growth period that are up to six orders of magnitude
faster than the fastest accepted regional tectonic strain rates (10213 s21). Strain rates in
the very early stages of growth can reach values several orders of magnitude faster. Our
results suggest that evidence for or against very fast strain rates in deformation aureoles
around plutons may form a key criterion for identifying dike-fed expansion. On the other
hand, our ability to extract strain-rate information from pluton aureoles is currently extremely limited.
Keywords: deformation, diapirs, dikes, plutons, rates, strain.
INTRODUCTION
Igneous intrusions commonly make up
25%–75% of exposed rocks in eroded arcs,
yet there is no consensus regarding how large
volumes of granitoid magma ascend through
the crust and become emplaced as middle- to
upper-crustal plutons. Several papers published in the past 10 years have emphasized
the importance of granitoid magma ascent in
dikes and concluded that many large granitoid
plutons are fed by such dikes (e.g., Clemens
and Mawer, 1992; Petford et al., 1993). These
models have led to the more provocative suggestion that magmatic diapirism be discarded
as an ascent mechanism (Clemens et al., 1997;
Clemens, 1998). If magmatic diapirism is unimportant, then a profound implication is that
many or most plutons exposed in eroded arcs
must have grown virtually in situ by expansion from the blunted tips of one or more
dikes. This is perhaps one of the most important current issues in understanding magmatic
systems, because ascent by dike formation and
ascent by diapirism have very different implications for the physical and chemical evolution of Earth’s crust (Clemens, 1998; Miller
and Paterson, 1999). To avoid freezing, dikes
must have minimum widths and flow rates,
which are directly determined by factors such
as the vertical length of the dike, the density
difference between the magma and the surrounding host rocks, the far-field temperature
of the host rocks, the viscosity of the magma,
and the initial and near-solidus temperatures
of the magma. Several recent papers list critical dike widths and flow rates for granitoid
magmas (e.g., Clemens et al., 1997), in the
ranges of 2 to 20 m and 3 3 1023 to 8.0
m · s21, respectively. Given reasonable horizontal dike lengths (e.g., 1 km), these values
lead to very rapid pluton-filling rates and consequently require fast rates of host-rock deformation. One means of testing models for
the growth of dike-fed magma chambers is to
evaluate these rates and seek supporting structural and petrologic evidence.
In this paper, we evaluate pluton-filling
rates and associated wall-rock strain rates for
end-member dike widths, flow rates, and pluton shapes. Our results indicate very rapid
wall-rock strain rates over the entire growth
period of up to six orders of magnitude faster
than the fastest accepted regional tectonic
strain rates (10213 s21). We initially make a
simplifying assumption that all host-rock deformation during emplacement occurs by homogeneous, ductile strain, although we are
aware that strain is typically heterogeneously
distributed in aureoles and that host-rock deformation typically occurs by multiple mechanisms. We also explore how rates are affected
by relaxing these assumptions. The thoughtprovoking results of this analysis may provide
some clear structural and petrologic avenues
for testing the hypothesis that mid- to uppercrustal granitoid plutons expand in situ from
dikes.
RATES AND EXAMPLE PLUTONS
To evaluate pluton-filling rates and wallrock strain rates, we must choose a horizontal
dike length and a realistic range of dike widths
and magma-flow rates. Following Clemens et
al. (1997), we consider dikes 1 km in plan
length, end-member critical dike widths of 3
and 16 m, and end-member flow rates of 3 3
1023 and 8.0 m · s21. It is instructive to evaluate two end-member pluton volumes (Fig. 1),
and for these we choose a sphere of 5 km
radius and 524 km3 volume, and a spheroid
of 5 km radius in plan and 0.915 km vertical
radius. This spheroid has a volume of 99 km3
and reflects the following power-law relationship between thickness (T) and plan length (l)
suggested by McCaffrey and Petford (1997)
for granitoid plutons:
T 5 0.29 l0.80.
(1)
We choose these two bodies because they
have very different volumes but would show
identical map-view patterns in central sections. Table 1 shows filling rates and total filling times in years for the various combinations of dike widths, flow rates, and pluton
volumes under consideration. To understand
q 2001 Geological Society of America. For permission to copy, contact Copyright Clearance Center at www.copyright.com or (978) 750-8400.
Geology; August 2001; v. 29; no. 8; p. 727–730; 5 figures; 1 table.
727
Downloaded from geology.gsapubs.org on 26 October 2009
Figure 2. Graph showing nonlinear relationship between radius and volume increase
for sphere and spheroid.
Figure 1. Three-dimensional surface plots of
(A) sphere and (B) spheroid. Both have horizontal radii of 5 km in central sections.
how such rapid filling rates
rounding wall rocks, we need
the increase in radius (R) of
thetical plutons with increase
as follows:
Rsphere 5
Rspheroid 5
affect the surexpressions for
the two hypoin volume (V),
!
!
3
3V
,
4p
(2)
3
3V
.
(0.18)(p)(4)
(3)
Figure 2 shows the nonlinear relationship between radius and volume increase, and also
the dramatic difference in volume between
these two plutons of equal final plan radius (5
km). We can represent the horizontal radii of
the two plutons in relation to time by the following two equations:
Rsphere 5
Rspheroid 5
!
!
3
(3)(t)(dV/dt)
,
4p
(4)
3
(3)(t)(dV/dt)
,
(0.18)(p)(4)
(5)
where t is time and dV/dt values are the fill
rates given in Table 1. The graphs in Figure 3
suggest that strain rates in the adjacent wall
rocks should change markedly with radius and
time, and to determine these rates we first
need to assign a strain-aureole width around
the final pluton. We select a horizontal width
of 3 km around both plutons and assume for
now that the aureole deforms homogeneously
by pure shear; we show later that partitioning
of strain in the aureole has only a secondorder effect on wall-rock strain rates. We can
define the finite stretch (S) as follows:
S5
l0 2 R
R
512 ,
l0
l0
Figure 3. Graphs showing nonlinear increase in radius with time for (A) sphere and
(B) spheroid, for four fill rates shown in Table 1. Total time 5 1 yr.
(6)
where l0 5 8 km (final pluton radius plus deformation aureole), R is the pluton radius
ranging from 0 to 5 km, and l0 2 R is the
deformed length of the aureole at any stage of
pluton growth. Because we want to determine
how strain rate changes with time and pluton
radius, we define the instantaneous strain rate
(ė) as the rate of change of the stretch (Twiss
and Moores, 1992) as follows:
[ ]
d
R
ė 5 S˙ 5
12 ,
dt
l0
cifically, Figure 4 shows the change in shortening rate in the horizontal plane passing
through the pluton centers. These graphs show
that strain rates vary by up to six orders of
magnitude during pluton filling, but the first
three orders of magnitude occur before the
pluton has a radius of 150 m. For simplicity,
we have considered dikes that are 1 km in
plan length from the smallest time step. A
more realistic model would allow a dike’s plan
length to grow with the pluton diameter until
it reached 1 km, at which time the dike would
(7)
which is equivalent to the ‘‘conventional’’
strain rate of Pfiffner and Ramsay (1982). Our
results could also be expressed as the ‘‘natural’’ strain rate, which is simply the conventional strain rate divided by the stretch. Because the stretch in this instance becomes
smaller with time, the natural strain rate would
reach values of approximately one order of
magnitude greater than the conventional strain
rate in the final stages of pluton growth. Thus,
the conventional strain rate is the more conservative of the two. Equation 7 can be solved
to obtain the change in strain rate with radius
for the sphere and spheroid (Fig. 4). More spe-
TABLE 1. STRAIN RATES AVERAGED OVER TOTAL PLUTON-FILLING TIME FOR HORIZONTAL DIKE
LENGTH OF 1 KM
Dike width (m):
Flow rate (m · s21):
3
3 3 1023
16
3 3 1023
3
8.0
16
8.0
Fill rate (km3 · yr21)
Total filling time (yr)—sphere
Total filling time (yr)—spheroid
0.28
1846.21
348.81
1.51
346.17
65.40
756.86
0.69
0.13
4036.61
0.13
0.02
728
Figure 4. Graphs showing change in strain
rate with pluton radius for (A) sphere and (B)
spheroid, for four fill rates shown in Table 1.
GEOLOGY, August 2001
Downloaded from geology.gsapubs.org on 26 October 2009
remain 1 km in length while the pluton continued to grow. Our preliminary results from
such a model also indicate that strain rates will
vary by up to six orders of magnitude, but the
first three orders of magnitude occur before
the pluton has a radius of 40 m. Thus, regardless of which model is considered, half of the
strain-rate variation occurs very early in the
inflation history, prior to the pluton radius
reaching 3% of its final dimension.
STRAIN PARTITIONING IN
AUREOLES
These calculations assume homogeneous
deformation in the 3-km-wide aureole, but
rocks exhibit both temperature- and strainrate–dependent rheology, and so strain intensity in ductile aureoles is strongly concentrated near the pluton margins, falling off
exponentially with distance (e.g., Paterson and
Fowler, 1993; Weinberg and Podladchikov,
1995). We can model nonlinear variation of
strain rate across the aureole by applying an
exponential equation of the form ė 5
ė0e2cx, where ė is strain rate (s21 ), ė0 is the
initial strain rate at distance 5 0 m and time
t, x is the distance from the contact between
pluton and host rock, and c is a constant that
determines the total variation in strain rate
through the aureole at any particular time.
This constant was chosen by assuming 95%
and 10% shortening in the inner and outer
parts, respectively, of the 3-km-wide aureole.
These are considered to be reasonable upper
and lower limits of measurable strain, and so
are reasonable for defining the deformation
aureole. We calculated inner- and outer-aureole strain rates around both plutons for each
of the four filling times. We then compared
inner- and outer-aureole strain rates at specific
times, and used the differences in these rates
as the total variation across the aureole at any
one time. The constant c was set by iteration
to a value of 0.000 90 m21 to reproduce these
results.
We combine the pluton-radius and distance
dependence of strain rate and establish the following relationship:
ė 5
[ ]
d
R
1 2 e2cx .
dt
l0
(8)
Calculations were performed for those combinations of flow rate and feeder-dike dimension corresponding to the lowest and highest
filling rates for the plutons with spherical and
spheroidal geometry, respectively. Figure 5
emphasizes that the spatial variation in strain
rate throughout the aureole (as defined) at any
one time is less than one order of magnitude,
which is consistent with the maximum difference in finite strain of less than one order of
magnitude. Thus, a simple model like the one
GEOLOGY, August 2001
Figure 5. Three-dimensional graph showing
distance versus strain rate versus pluton radius for slowest filling sphere and fastest
filling spheroid.
developed here that considers homogeneous
strain is adequate for assessing what order-ofmagnitude strain rates can be expected in the
more highly strained rocks in an aureole, given particular rates of pluton inflation.
MATERIAL TRANSFER PROCESSES
IN DEFORMATION AUREOLES
These calculations assume that all deformation in the aureole occurs by homogeneous, concentric shortening perpendicular to
the growing pluton margins. However, quantitative strain studies around plutons (e.g.,
studies summarized in Paterson and Fowler,
1993; Johnson et al., 1999) indicate that generally only 25%–40% of a pluton’s volume
can be accounted for by bulk wall-rock shortening, and so other processes must operate
(e.g., stoping, assimilation, volume loss, rigid rotation, and sill formation followed by
vertical pluton growth). The filling rates and
wall-rock strain rates determined here suggest that there would be very little time for
wall-rock volume loss or assimilation, and so
the principal combination of processes would
most likely include the brittle process of
stoping driven by thermal and/or mechanical
stress, the brittle processes of sill emplacement or fracture propagation, the ductile process of lateral wall-rock shortening, and rigid
rotation of units, presumably by a flexuralslip mechanism.
TESTING THE DIKE-FED MODEL
Our analysis suggests that evidence for fast
strain rates in pluton aureoles might be one of
the best tests of the dike-fed expansion model,
but what constitutes evidence for fast strain
rates? Pluton aureoles are not characterized by
steady-state thermal and dynamics conditions,
and so quantifying strain rates from microstructures in these settings is currently tenuous. In light of this limitation, we offer the
following as possible indicators of fast strain
rates.
1. If a rapidly inflating pluton grows via an
outward-migrating ‘‘shatter zone’’ or intrusive
brecciation, then it seems reasonable to assume that examples of such zones may be preserved around some plutons. One example of
such a shatter zone may be preserved around
the margins of the Cadillac Mountain intrusive
complex (e.g., Gilman and Chapman, 1988;
Wiebe, 1996) in the coastal Maine magmatic
province (Hogan and Sinha, 1989). We are investigating this possibility.
2. Other brittle features that could be caused
by fast strain rates include: (a) radiating fracture sets oriented perpendicular to the pluton
margin and the direction of minimum compressive stress; (b) local or extensive zones of
brecciation; and (c) fracturing of minerals that
were present prior to emplacement, although
later dynamic recrystallization may mask
these features as the thermal front passes outward from the pluton. These features could result from other factors (e.g., high fluid pressures), but in general we might expect their
occurrence to increase with increasing strain
rate.
3. If a rapidly-inflating pluton grows by
brittle wall-rock deformation, a large volume
of stoped wall rock may have been incorporated into the pluton at least in the early phases of emplacement. Recent work on the processes involved in stoping (e.g., stress
fracturing, partial melting, mechanical disaggregation) suggests that stoped fragments may
be reduced to a mixture of partial melts and
individual mineral grains if residence times in
the magma are long enough (e.g., Clarke et
al., 1998; Paterson and Okaya, 1999). Detailed
microstructural, isotopic, and rare-earthelement studies of ferromagnesian minerals in
plutons that show evidence for stoping may
provide important clues as to what percentage
of these grains may have originated from the
wall rocks.
4. Contact metamorphic minerals should
grow relatively late in the emplacement-related deformation, owing to conductive heat
transfer lagging behind chamber growth. An
interesting implication is that ‘‘static’’ metamorphic aureoles around plutons may in some
instances have been quite dynamic environments during pluton emplacement.
5. Wall rocks are commonly intruded by
dikes from the main pluton during its emplacement. Rapidly inflating plutons may
cause such dikes to become isoclinally folded
before cooling below their solidus. Dikes folded in the magmatic state should show magmatic, rather than solid-state, axial surface foliations. This evidence would perhaps be most
useful around middle- to upper-crustal plutons
where ambient wall-rock temperatures are
729
Downloaded from geology.gsapubs.org on 26 October 2009
well below the solidus temperatures of the
dikes.
EVIDENCE FOR HIGH WALL-ROCK
STRAIN RATES?
Tectonic strain rates are generally thought
to be in the range of 10213 to 10215 s21 (e.g.,
Pfiffner and Ramsay, 1982; Paterson and Tobisch, 1992; Dunlap et al., 1997; Foster and
Gray, 1999; Muller et al., 2000). In contrast,
theoretical analysis of dike and diapir ascent
rates suggests that faster-than-tectonic nearfield strain rates should be expected during
pluton construction (e.g., Clemens and Mawer,
1992; Weinberg and Podladchikov, 1995; Pavlis, 1996; Petford, 1996; this study). Has any
evidence for such fast rates been described?
Field studies of individual plutons have led
some workers to suggest faster-than-tectonic
strain rates during pluton emplacement. For
example, rates on the order of 10211 to 10212
s21 have been postulated in the aureoles of the
sheetlike East Piute and Old Woman plutons
in southern California (Karlstrom et al., 1993;
McCaffrey et al., 1999), accompanied by an
increase in minimum fault-displacement rates
to greater than tens of centimeters per year.
Fernandez and Castro (1999) suggested that
strain rates of 10210 to 10211 s21 formed in
local ‘‘kink-like’’ openings during magma emplacement. John and Blundy (1993) examined
expansion of the Adamello massif, Italy, and
estimated strain rates of 10213 s21 for ductile
deformation in the aureole. Miller and Paterson (1994) described isoclinally folded tonalite to granodiorite dikes around the Mt. Stuart
batholith with magmatic axial surface foliations.
Finite difference thermal modeling suggests that
these 0.5–1.5-m-thick dikes crystallized in no
more than a few hundred thousand years and
typically record .80% shortening. Thus, a strain
rate between 5 3 10213 and 1 3 10211 s21 is
required to form these folds (Paterson and Tobisch, 1992).
All of these strain rates overlap the rates of
10210 to 10213 s21 suggested by Schmid
(1989) for some high-strain mylonite zones.
However, they do not approach the faster end
of the range of strain rates shown in Figure 4.
CONCLUSIONS
Because granitoid dikes must have minimum widths and flow rates to keep from
freezing, dike-fed plutons can grow at extremely rapid rates. Such rapid growth should
lead to rapid strain rates in the surrounding
wall rocks. Under conditions of constantvolume filling, growth can easily outpace conductive heating of the wall rocks. Thus, theoretically, dike-fed plutons could be
completely emplaced before the wall rocks
undergo contact metamorphism. These two
predictions of the dike-fed model provide pos-
730
sible structural and petrologic avenues for
testing the model. In attempting to formulate
tests, we have been reminded of how difficult
it currently is to extract strain-rate information
from pluton aureoles. Because these aureoles
are not characterized by steady-state thermal
and dynamic conditions, applying experimental rock deformation studies to microstructural
observations therein is currently tenuous. On
the bright side, this study points to an area of
research—rates of geological processes—in
which more progress is becoming essential for
modern geological studies.
ACKNOWLEDGMENTS
We thank Terence J. Hughes for commenting on
a preliminary draft, and Robert B. Miller, Mark
Handy, and Aaron S. Yoshinobu for discussions on
stoping and strain rates in pluton aureoles. Calvin
F. Miller and Nicholas G. Culshaw provided constructive and helpful reviews of the manuscript.
REFERENCES CITED
Clarke, D.B., Henry, A.S., and White, M.A., 1998,
Exploding xenoliths and the absence of ‘‘elephants’ graveyards’’ in granite batholiths:
Journal of Structural Geology, v. 20,
p. 1325–1343.
Clemens, J.D., 1998, Observations on the origins
and ascent mechanisms of granitic magmas:
Geological Society of London Journal, v. 155,
p. 843–851.
Clemens, J.D., and Mawer, C.K., 1992, Granitic
magma transport by fracture propagation: Tectonophysics, v. 204, p. 339–360.
Clemens, J.D., Petford, N., and Mawer, C.K., 1997,
Ascent mechanisms of granitic magmas:
Causes and consequences, in Holness, M.B.,
ed., Deformation-enhanced fluid transport in
the Earth’s crust and mantle: London, Chapman & Hall, p. 144–171.
Dunlap, W.J., Hirth, G., and Teyssier, C., 1997,
Thermomechanical evolution of a ductile duplex: Tectonics, v. 16, p. 983–1000.
Fernandez, C., and Castro, A., 1999, Pluton accommodation at high strain rates in the upper continental crust: The example of the central Extremadura batholith, Spain: Journal of
Structural Geology, v. 21, p. 1143–1150.
Foster, D.A., and Gray, D.R., 1999, Deformation
rates and timing of deformation in the western
Lachlan orogen, eastern Australia: Geological
Society of America Abstracts with Programs,
v. 31, no. 7, p. A-301.
Gilman, R.A., and Chapman, C.A., 1988, Bedrock
geology of Mount Desert Island: A visitor’s
guide to the geology of Acadia National Park:
Maine Geological Survey Bulletin 38, 50 p.
Hogan, J.P., and Sinha, A.K., 1989, Compositional
variation of plutonism in the coastal Maine
magmatic province: Mode of origin and tectonic setting in Tucker, R.D., and Marvinney,
R.G., eds., Studies in Maine Geology, Volume 4: Augusta, Maine Geological Survey,
p. 1–33.
John, B.E., and Blundy, J.D., 1993, Emplacementrelated deformation of granitoid magmas,
southern Adamello massif, Italy: Geological
Society of America Bulletin, v. 105,
p. 1517–1541.
Johnson, S.E., Paterson, S.R., and Tate, M.C., 1999,
Structure and emplacement history of a multiple-center, cone-sheet-bearing ring complex:
The Zarza Intrusive Complex, Baja California,
Mexico: Geological Society of America Bulletin, v. 111, p. 607–619.
Karlstrom, K.E., Miller, C.F., Kingsbury, J.A., and
Wooden, J.L., 1993, Pluton emplacement
along an active ductile thrust zone, Piute
Mountains, southeastern California: Interaction between deformational and solidification
processes: Geological Society of America Bulletin, v. 105, p. 213–230.
McCaffrey, K.J.W., and Petford, N., 1997, Are granitic intrusions scale invariant?: Geological
Society of London Journal, v. 154, p. 1–4.
McCaffrey, K.J.W., Miller, C.F., Karlstrom, K.E.,
and Simpson, C., 1999, Synmagmatic deformation patterns in the Old Women Mountains,
SE California: Journal of Structural Geology,
v. 21, p. 335–349.
Miller, R.B., and Paterson, S.R., 1994, The transition from magmatic to high-temperature solid
state deformation: Implications from the
Mount Stuart batholith, Washington: Journal
of Structural Geology, v. 16, p. 853–865.
Miller, R.B., and Paterson, S.R., 1999, In defense
of magmatic diapirs: Journal of Structural Geology, v. 16, p. 853–865.
Muller, W., Aerden, D., and Halliday, A.N., 2000,
Isotopic dating of strain fringe increments:
Duration and rates of deformation in shear
zones: Science, v. 288, p. 2195–2198.
Paterson, S.R., and Fowler, T.K., Jr., 1993, Reexamining pluton emplacement processes:
Journal of Structural Geology, v. 15,
p. 191–206.
Paterson, S.R., and Okaya, D., 1999, Why don’t we
see more stoped blocks in plutons? Results
from thermal-mechanical modeling: Eos
(Transactions, American Geophysical Union),
v. 80, p. F983.
Paterson, S.R., and Tobisch, O.T., 1992, Rates of
processes in magmatic arcs: Implications for
the timing and nature of pluton emplacement
and wall rock deformation: Journal of Structural Geology, v. 14, p. 291–300.
Pavlis, T.L., 1996, Fabric development in syntectonic intrusive sheets as a consequence of
melt-dominated flow and thermal softening of
the crust: Tectonophysics, v. 253, p. 1–31.
Petford, N., 1996, Dykes or diapirs?: Royal Society
of Edinburgh Transactions, Earth Sciences,
v. 87, p. 105–114.
Petford, N., Kerr, R.C., and Lister, J.R., 1993, Dike
transport of granitoid magmas: Geology,
v. 21, p. 845–848.
Pfiffner, O.A., and Ramsay, J.G., 1982, Constraints
on geological strain rates: Arguments from finite strain states of naturally deformed rocks:
Journal of Geophysical Research, v. 87,
p. 311–321.
Schmid, S.M., 1989, Episodes in Alpine orogeny:
Geological Society of America Abstracts with
Programs, v. 21, no. 6, p. A28.
Twiss, R.J., and Moores, E.M., 1992, Structural geology: San Francisco, W.H. Freeman, 532 p.
Weinberg, R.F., and Podladchikov, Y.Y., 1995, The
rise of solid-state diapirs: Journal of Structural
Geology, v. 17, p. 1183–1195.
Wiebe, R.A., 1996, Mafic-silicic layered intrusions:
The role of basaltic injections on magmatic
processes and the evolution of silicic magma
chambers: Royal Society of Edinburgh Transactions, Earth Sciences, v. 87, p. 233–242.
Manuscript received October 23, 2000
Revised manuscript received April 5, 2001
Manuscript accepted May 3, 2001
Printed in USA
GEOLOGY, August 2001