Geology

doi: 10.1130/0091-7613(1993)021<0845:DTOGM>2.3.CO;2 1993;21;845-848Geology

 Nick Petford, Ross C. Kerr and John R. Lister Dike transport of granitoid magmas  

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Dike transport of granitoid magmas Nick Petford Department of Earth Sciences, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, England Ross C. Kerr Research School of Earth Sciences, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia John R. Lister Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of

Cambridge, Silver Street, Cambridge CB3 9EW, England

ABSTRACT Thermal and fluid-dynamical analyses suggest that for viscosities

and density contrasts spanning the range considered typical for many calc-alkalic granitoids, dike ascent is a viable mechanism for the trans-port of large volumes of granitoid melt through the continental crust. We present calculations showing that a granitoid melt with calculated viscosity of the order of 10® Pa • s and a density contrast between magma and crust of 200 kg/m3 can be transported 30 km through the crust in ~ 1 month, corresponding to a mean ascent velocity of 1 cm/s. Using analysis modified from numerical studies of the flow of basaltic magmas in dikes, we also present an expression that allows the cal-culation of the critical (minimum) dike or fault width required for granitic magma to ascend without freezing. For all reasonable esti-mates of Cordilleran granitoid viscosity and density contrast, the crit-ical dike width is determined to be between ~2 and 7 m. Calculated peak batholith-fìlling rates are orders of magnitude greater than mean cavity-opening rates based on estimated fault slippage, which is con-sistent with chemical evidence for intermittent supply of magma pulses.

INTRODUCTION To say that granitoids make up a significant part of the upper-

middle continental crust at active plate margins is almost a cliché. The vast Mesozoic-Cenozoic batholiths that lie along the western continental margin of North and South America contribute signifi-cantly to the total crustal volume in these regions. Many also contain a large component of mantle-derived material, implying that these rocks are instrumental in crustal growth (e.g., DePaolo, 1981; Miller and Harris, 1989). Much progress has been made in recent years in understanding the origin of these rocks on chemical and isotopie grounds (Pitcher et al., 1985; Anderson, 1990). In contrast, the phys-ical mechanisms that govern the ascent and emplacement of gran-itoid magmas are much less well understood.

Recent studies of granitoid emplacement in Cordilleran and magmatic arc settings have emphasized the important role played by regional-scale tectonics, especially strike-slip fault systems, in cre-ating space for batholithic magmas in the upper crust through the generation of tension cracks and dilational jogs (Glazner, 1991; Pet-ford and Atherton, 1992; Tikoff and Teyssier, 1992). It is implicit in these models that magmatic ascent, as well as emplacement, is fun-damentally controlled by the same fault systems, which act as con-duits by channeling large volumes of granitic magma through the crust. Because batholithic magmatism is a principal means of crustal differentiation (Silver and Chappell, 1988), reasonable estimates of the time scales over which ascent and emplacement operate are crucial to our wider understanding of the geodynamic evolution of active continental margins.

In this paper, we focus on the role of dikes in transporting granitoid magmas from their lower crustal-upper mantle source re-gions to their final level of emplacement. We take as an example a typical Cordilleran batholith from the Peruvian Andes that is rela-tively well understood in terms of field geology and general tectonic setting. Viscosity and density values for these rocks, estimated from major element data, are combined with geophysical measurements of the crustal column beneath the batholith to estimate the time

required for magmatic ascent. Motivated by the efficiency of dike transport for these magmas on both fluid-dynamical and thermal grounds, we used granitoid examples with well-determined petrol-ogy and tectonic environments to estimate the range of minimum dike widths that may be found in Cordilleran and magmatic arc settings.

JUSTIFICATION FOR DIKE-FLOW ASCENT The established idea that granitoid magmas ascend through the

continental crust as diapirs is being increasingly questioned by ig-neous and structural geologists. In particular, many of those bodies that were once considered classic diapirs, such as the Ardara, Criffel, and Chindamora plutons, have been reinterpreted as bal-looning plutons whose geometries are not controlled by ascent but by emplacement (Holder, 1979; Courrioux, 1987; Ramsay, 1989; see also Bateman, 1985). Cordilleran batholiths exposed in the Andes are typically elongate bodies found in close spatial and temporal association with large-scale faults and crustal lineaments, them-selves parallel with the continental margin and the trench. This first-order relation has led many authors to conclude that the faults them-selves are responsible not only for controlling magma emplacement but ascent as well (Pitcher, 1979; Cobbing et al., 1981; Petford and Atherton, 1992). The recent literature contains many examples of fault-controlled models of granite emplacement (e.g., Hutton, 1982, 1988; Guineberteau et al., 1987; Reavy, 1989), and many acknowl-edge implicitly the role of faults, fractures, or shear zones in magma transport, during either extension or compression (e.g., Castro, 1987; Bran et al., 1990; Schmidt et al., 1990; D'Lemos et al., 1992; Hutton, 1992). Although the possibility of diapirism as an ascent mechanism is not totally excluded (Miller et al., 1988; England, 1990), the pluton geometries, the lack of classic country-rock struc-tures such as rim synforms and symmetric high-strain zones in and around Andean batholiths, and the close proximity of the batholiths to major faults together suggest that diapiric ascent was not the transport mechanism in these instances. Because of the close asso-ciation of these rocks with major fault systems, it seems reasonable to assume that these long-lived crustal discontinuities have been periodically used by batholith magmas (Pitcher, 1979).

Most recently, Clemens and Mawer (1992) have proposed a mechanism for granitoid magma transport involving fracture prop-agation. In this model, based on earlier work by Cook and Gordon (1964) and Pollard (1977), magmas themselves generate the tensile stress conditions in the crust necessary for their ascent. Faults and shear zones are important as mechanisms for controlling the em-placement of granitoid magmas, but only if they are first intersected by a self-propagating dike. We take a slightly different and mechan-ically more simplistic view here by assuming that the deeply pene-trating faults and lineaments themselves act as feeder dikes.

CORDILLERA BLANCA BATHOLITH To estimate the effectiveness of dike-controlled magmatic as-

cent at active plate margins, we take as an example the Cordillera Blanca batholith, northwest Peru (Fig. 1). The batholith, composed mainly of leucogranodiorite (Egeler and DeBooy, 1956; Atherton and Sanderson, 1987), lies over the thickened crustal keel of the

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1.5 wt% HzO estimated from the analyses. The same data were used to calculate a mean magmatic density p of 2600 kg/m3 (Bottinga et al., 1983). Geophysical seismic and gravity surveys have been used to model a three-layered crustal structure beneath central Peru with a mean density of 2800 kg/m3 (James, 1971; Couch et al., 1981), which gives a mean density contrast between magma and country rock of 200 kg/m3. The chosen value of 30 km for the dike length that we used in this study is in keeping with the observation of Miller et al. (1988) that granitoid magmas commonly traverse most of the continental crust; the value is also consistent with recent geochem-ical evidence implying a deep crustal source for the batholith mag-mas (Atherton and Petford, 1993).

DIKE FLOW Given the above physical properties, we now consider thermal

effects during the ascent of granites. The solidification or melting of a buoyant magma during laminar flow in a dike of length H and uniform initial width w is controlled by three dimensionless param-eters (Bruce, 1989; Bruce and Huppert, 1989, 1990). The first parameter,

B=gL9w%*H, (1)

represents the ratio of advection of heat by the flow to conduction of heat into the walls, where the gravitational acceleration g = 9.8 m/s2, Ap is the difference in density between the magma and the crust, K = 8 x 10~3 cm2/s is the thermal diffusivity, and p, is the magmatic viscosity. The other two parameters are Stefan numbers:

= L/c(Tw - Tx)

Figure 1. Geologic sketch map of Andean Cordillera In northern-central Peru showing Cordillera Blanca batholith and associated fault complex (from Atherton and Petford, 1993).

Andes (James, 1971), which reaches depths of nearly 70 km in this region. K-Ar and Ar-Ar analyses have given mineral cooling dates between —6 and 3.0 Ma for the central region of the intrusion (Wil-son, 1975; Petford, 1990), which would make the Cordillera Blanca one of the youngest known batholiths exposed in the Andes. The intrusion is over 150 km long and up to 20 km wide, with a vertical relief of 2 km in the most deeply eroded glacial valleys. A spectac-ular feature of the batholith is that the entire western margin abuts and is strongly deformed by the Cordillera Blanca fault complex, a major tectonic lineament believed to have been active since the Ju-rassic (Cobbing et al., 1981). Deformation fabrics in the batholith suggest that emplacement occurred over the crystallization interval, during a period of active extensional faulting with a component of right-lateral strike-slip motion (Petford and Atherton, 1992). The strongly asymmetric synmagmatic and postmagmatic deformation along the western fault-bounded flank of the batholith was taken by Petford and Atherton (1992) as evidence that the fault system also played a major role in magmatic ascent and emplacement.

PHYSICAL PROPERTIES OF MAGMA AND CRUST To model the ascent of the batholith magmas it is first necessary

to estimate two physical properties, viscosity and density, that to-gether fundamentally control magmatic ascent rates. Typical den-sities of calc-alkalic magmas range from ~2700 to 2400 kg/m3, and estimated melt viscosities are ~104-108 Pa-s (Carmichael et al., 1974; McBirney, 1984). Following the method described by Shaw (1972), we used the average of 33 whole-rock analyses covering a range in Si02 of 70-73 wt% to estimate a mean magmatic viscosity p, of ~8 x 10s Pa-s for the Cordillera Blanca leucogranodiorites. This value was calculated by assuming a crystal-free melt at 900 °C with

and (2)

Sm = L/c(Tm — Tw), where L is the latent heat of solidification, c is the specific heat, is the far-field temperature of the crust, Tm is the initial magmatic temperature, and Tw is the temperature at which magma near the dike wall is immobile and effectively frozen. Detailed analysis (Bruce, 1989) has shown that the thermal evolution of the flow can be predicted by the single parameter \ = BSlJS^. If \ is less than a critical value, then the dike will freeze before it has time to transport a significant volume of magma; if X is greater than this value, then the dike will remain open until the supply is exhausted and flow ceases. Using this result and the numerical calculations by Bruce and Huppert (1989, 1990) for basaltic magmas, it can be shown that the critical dike width wc required to transport granitic melt through the crust is estimated as follows:

wc = 1.5(S„Ab3/4(|XK///sAP)1/4. (3)

RESULTS The critical dike width is shown in Figure 2 for a range in values

of p, and Ap, based on the following: dike length H = 30 km, latent heatZ, = 300 J/g, specific heat c = 1.2J -1-°C_1 , and initial, freezing, and far-field temperatures Tm = 900 °C, 7W = 750 °C, and = 400 °C, respectively. The shaded region represents the range of Ap values likely to be found during granitoid ascent in typical crustal conditions. For granitoid magmas with a wide viscosity range of 104-108 Pa-s, the critical dike width is well constrained to a range of —2-20 m. The tightness of this constraint is due to the weak depen-dence of wc on the viscosity and density difference in equation 3. As a result, predictions of the critical dike width are robust. Figure 2 also includes data for several tonalitic to granodioritic plutons from the Cordilleran and magmatic arcs of the Andes and western United States. For comparison, a two-mica leucogranite from the Karako-

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|X (Pa-s)

Figure 2. Contours of critical dike width wc re-quired for magma ascent without freezing, calcu-lated with equation 3 and parameter values In text, as a function of the den-sity contrast Ap between magma and country rock and the magmatic vis-cosity p.. Shaded region shows range In density contrast (100-300 kg/m3) likely to be found by gra-nitic magma under ana-tectic conditions in mid-dle to lower continental crust. CBB—Cordillera Blanca batholith (Petford, 1990); PRD1, PRD2— Puscao ring dikes, Peru (Bussell, 1988); CTG— central Chilean Tertiary granitoids (Lopez-Escobar et al., 1979); WPRB— average western Peninsular Ranges batholith (Silver and Chappell, 1988; Couch and Riddihough, 1989); GTS—Great Tonalfte Sill, Alaska (Roddick, 1983); MGG—Mount Givens Granodiorite, Sierra Nevada (Bateman and Nokleburg, 1978; Dodge and Bateman, 1988); BB—Baltoro batholith (Searle et al., 1992).

ram Baltoro batholith (BB) is also included (Searle et al., 1992). Without exception, wc lies in the range 2-7 m for the Cordilleran and magmatic-arc granitoids. The Baltoro batholith, although driven by a relatively high density contrast, requires a larger width of —20 m in order to counteract its significantly higher viscosity. From the calculations we conclude that dike transport is a thermally viable process for reasonable dike widths over a range of viscosities that encompasses most granitoid magmas.

In Figure 3, the critical dike width is shown for a range of values of the superheat Tm - Tw and undercooling Tw - Tm based on the values of 106 Pa-s for magmatic viscosity and 200 kg/m3 for mean crustal density difference, which maybe considered typical for most Cordilleran granitoids. We see again that critical dike widths are in the range 2-20 m.

SPECIFIC CASE For the Cordillera Blanca batholith we take the mean crustal Ap

to be 200 kg/m3, the magmatic viscosity p, to be 8 X 10s Pa-s, and the fault length H to be 30 km. We find from Figure 2 that the critical dike width is ~6 m. This width corresponds to a horizontally aver-aged velocity (Vav = gApw|/12 p,) of 1 cm/s, an ascent time for the magma of about 41 days, and a time to fill the batholith (minimum estimated volume Q = 6000 km3) by a dike of lateral extent I = 10 km,

Ai = Q/V^wJ, (4)

of 350 yr. Clearly, this time of active flow is likely to be divided into a number of smaller events interspersed by periods of source re-charge. These simple calculations show that the transport of large volumes of granitoid magmas by dikes can be surprisingly fast (see also Clemens and Mawer, 1992).

DISCUSSION These calculated values of wc are typically larger than the 1-4

m widths of felsic dikes reported by Cony (1988). However, as pointed out by Bedard and Sawyer (1991) and Clemens and Mawer (1992), any final dike thickness observed in the field may well be much smaller than the original width during active flow. This is because the process of emplacing a finite amount of magma at some crustal level will also act to progressively drain the dike of magma as flow wanes. For example, the 6 m dike proposed for the Cordillera Blanca batholith would drain to a width of about 2 m if the dike

Figure 3. Contours of critical dike width (in me-tres) as function of mag-matic superheat Tm - Tw and undercooling T„ -

for magmatic viscos-ity of 106 Pa-s and Ap of 200 kg/m3. CBB de-notes Cordillera Blanca batholith.

continued to feed the batholith for —6 months after supply had ceased and before it finally solidified.

It is worth emphasizing here that dikes, once they begin to form, cannot close completely from the bottom upward because it is impossible to expel viscous magma completely from a narrow gap (Lister and Kerr, 1991). Thus, the mechanism for the formation of magma pulses suggested by Weertman (1971,1980), Takada (1990), and Clemens and Mawer (1992) will not operate during magma trans-port because it is essentially based on an inviscid theory. However, it is evident that many granitoids including the Cordillera Blanca batholith do show a fine chemical structure that may reflect the incomplete mixing at the emplacement level of discrete magma batches or pulses. We propose that a more likely explanation for the pulsed nature of some granitoid intrusions is a decrease in the vol-ume of granitoid melt available for extraction from the source rocks. A progressive draining of the magma at the source will lead to a steady decrease in the dike width until its thickness becomes small enough for the magma to freeze. Melt may then accumulate in the source until a new dike begins to form, either directly (Clemens and Mawer, 1992) or by large-scale tectonic motions. The volume of such pulses will thus be governed by the dynamics of the source supply rather than by the elastostatic theory of Weertman.

As a final point, we note that our calculated batholith filling times of a few hundred years are many orders of magnitude less than total emplacement time scales based on the estimated slip rates (0.7 cm/yr) believed to be applicable to some faults during granitoid em-placement (Tikoff and Teyssier, 1992), consistent with the evidence for a pulsed supply.

ACKNOWLEDGMENTS Supported by a grant from the British Council (to Kerr) and by Royal

Society Research Fellowships (to Petford and Lister). We thank J. Clemens and A. Glazner for helpful and constructive comments in reviews of the manuscript.

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Manuscript received January 8, 1993 Revised manuscript received May 17, 1993 Manuscript accepted May 24, 1993

Reviewer's comment

The paradigm of granite emplacement is rapidly shifting, and this paper will help to push it over the edge.

Allen Glazner

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