Conceived and designed the experiments: GARG. Performed the experiments: GARG ASP MSG ATA SRS MLR. Analyzed the data: GARG ASP MSG ATA SRS. Contributed reagents/materials/analysis tools: SRS MLR MSG. Wrote the paper: GARG.
The authors have declared that no competing interests exist.
Supereruptions violently transfer huge amounts (100 s–1000 s km3) of magma to the surface in a matter of days and testify to the existence of giant pools of magma at depth. The longevity of these giant magma bodies is of significant scientific and societal interest. Radiometric data on whole rocks, glasses, feldspar and zircon crystals have been used to suggest that the Bishop Tuff giant magma body, which erupted ∼760,000 years ago and created the Long Valley caldera (California), was long-lived (>100,000 years) and evolved rather slowly. In this work, we present four lines of evidence to constrain the timescales of crystallization of the Bishop magma body: (1) quartz residence times based on diffusional relaxation of Ti profiles, (2) quartz residence times based on the kinetics of faceting of melt inclusions, (3) quartz and feldspar crystallization times derived using quartz+feldspar crystal size distributions, and (4) timescales of cooling and crystallization based on thermodynamic and heat flow modeling. All of our estimates suggest quartz crystallization on timescales of <10,000 years, more typically within 500–3,000 years before eruption. We conclude that large-volume, crystal-poor magma bodies are ephemeral features that, once established, evolve on millennial timescales. We also suggest that zircon crystals, rather than recording the timescales of crystallization of a large pool of crystal-poor magma, record the extended periods of time necessary for maturation of the crust and establishment of these giant magma bodies.
Supereruptions
The longevity of giant magma bodies has generated continued interest
In discussion here is also the potential geological significance of the various results. What are the timescales of assembly of a giant magma body? What are the timescales of crystallization of such a magma body? The challenge is that the timescales of interest are largely inaccessible to geochronology for deposits as old as the youngest supereruptions. These timescales are accessible, however, using kinetic markers of magmatic processes (i.e. geospeedometers, see
Our sample set includes 6 pumice clasts from the Chalfant Quarry in the southeastern portion of the Bishop Tuff
Studied samples encompass much of the spectrum of pumice density, porosity, crystallinity and textural variations observed in the Bishop Tuff as a whole
Samples were studied using a combination of (for details, see
Documentation of sizes and shapes of whole quartz crystals and their melt inclusions; we place whole crystals in refractive index oil (so as to emphasize the inclusions), and we make observations under a petrographic microscope; over the years, we have inspected hundreds of crystals, each one containing tens of inclusions, so we have made qualitative observations on thousands of inclusions; we have only characterized in detail a small number of inclusions;
Cathodoluminescence (CL) imaging of individual quartz crystals (∼100 in total) by electron microprobe at The University of Chicago, using methods similar to those of Peppard et al.
Trace-element analysis at low spatial resolution (∼25 µm) by laser ablation mass spectrometry (LA-ICPMS);
Trace-element analysis along traverses and 2D maps (4 crystals studied) at high spatial resolution (ca. 2–10 µm spacing) using synchrotron x-ray microfluorescence (x-ray microprobe; see
X-ray tomography of pumice chips at various resolutions (2.5 to 15 µm per voxel), performed at the GeoSoilEnviroCARS bending magnet beamline, using methods described elsewhere
Our ongoing effort to use MELTS to model the evolution of silicic systems has shown that the current calibration of MELTS
We use rhyolite-MELTS to constrain the crystallization paths, and, in particular, the heat of cooling and crystallization for compositions relevant for the Bishop Tuff. We use early- and late-erupted bulk pumice (from
Crystallization pressure is determined using rhyolite-MELTS as the pressure at which melt inclusion compositions show simultaneous crystallization of quartz+sanidine+plagioclase under fluid-saturated conditions (see
To assess the timescales of quartz crystallization and their implications for the longevity of giant rhyolitic magma bodies, we analyze three lines of evidence: (1) quartz residence times based on the diffusional relaxation of Ti zoning profiles; (2) melt inclusion faceting timescales, over which initially round melt inclusions attain partly faceted shapes; (3) quartz+feldspar crystallization times as recorded in crystal size distributions. We discuss the theory behind residence time and melt inclusion faceting timescale calculation in some detail, and highlight the connection of these results with those obtained using crystal size distributions, which are detailed elsewhere
Quartz crystals are characterized by a volumetrically predominant low-Ti (∼40 ppm Ti) interior portion (
(a–b) X-ray profiles and cathodoluminescence (CL) images of select quartz crystals with bright-CL, high-Ti cores; residence times and growth rates derived from Ti traverses (white lines) are presented. Analytical points shown by open symbols, including analytical uncertainties (bars). Best fit curve (Equation 1) is shown in gray, calculated so as to minimize the sum of the squares of the difference between calculated and observed values. Calculated residence times are also shown. (c) CL image detailing core-rim zoning of a large quartz crystal; image of whole crystal shown in inset. White line corresponds to the location of CL traverse displayed in the bottom, with contacts between different zones indicated in black. Residence times in years and derived growth rates indicated by numbers on top of arrows. Notice that innermost contact has residence time close to 3,000 years. Calculated growth rates for two interior zones are close to 10−14 m/s, while growth rate for rim is ∼10−13 m/s.
Diffusion of Ti in quartz is particularly useful for the problem of interest here, as (1) diffusion rates have been determined experimentally (i.e. DTiQtz = 8.05×10−22 m2 s−1 at 750°C; see
We use a 1D diffusion model to determine the time interval during which two zones of distinct compositions within a crystal were in contact with each other. We call this the contact residence time. We assume constant but different initial compositions in the two zones of the crystal at time t = 0. The predicted composition c(x) as a function of position x along the profile is described by
For the conditions of interest, the factor (E/RT)2 is ca. 1000, such that even though the uncertainty on L is much larger than those on E, T, and ln[D0], all terms are potentially important. Even if σT is chosen to be 2 or 3 times larger than our choice, its effect on the final uncertainty is relatively minor, and the contributions of uncertainties on E, ln[D0] and L dominate. For (σE/E) = 4.4%, (σT/T) = 1.5%, (σL/L) = 50%, and σln[D0] = 1.2, the uncertainty on t becomes (σt/t) = 215%; for (σL/L) = 5%, (σt/t) = 190%. Even if (σL/L) could be improved, (σE/E) and σln[D0] are such that the total uncertainty would not be better than ∼190%, showing that our estimates are of appropriate precision for evaluating the parameters of interest. Furthermore, even though these uncertainties are large, our knowledge of the timescales being investigated is minimal, and the estimates remain meaningful. Importantly, none of the conclusions drawn are affected by the particular choice of parameters used.
Core-interior contact residence times were estimated primarily using Ti profiles of a selected number of crystals, but also using CL images of other crystals. The most important results are shown in
CRYSTAL | CORE-INTERIOR CONTACT | ||||
|
|
|
|
|
|
|
|
|
|
||
F815-Qtz-17 | (a) | 775 [3747] | 400 | 765 | 1.5 [0.3] |
IbA1-Qtz-503 | (b) | 923 [4461] | 334 | 922 | 1.0 [0.2] |
IbA1-Qtz-518 | 512 [2477] | 260 | 506 | 1.3 [0.3] |
Quantity in brackets is the maximum residence time: t+2σt.
Interior growth time excludes the time estimated for the residence time for rim-interior contacts in crystals with bright-CL, high-Ti rims (Gualda et al., unpublished data); these times are short enough that interior growth rates would be unaltered even if they were neglected.
Quantity in brackets is the minimum growth rate obtained using t+2σt as time.
Our core-interior contact residence times are 1–2 orders of magnitude larger than – and thus consistent with – the quartz rim-interior residence times of Wark et al.
Importantly, because the growth distance is known for the interior regions, the contact residence times can be used to constrain average growth rates, an important parameter for which estimates are entirely lacking for quartz in large-volume silicic systems like the Bishop Tuff. The agreement between the interior growth rates is remarkable, with all estimates close to 10−14 m/s (
Quartz crystals from the Bishop Tuff are rich in melt inclusions (now glass), which have been extensively studied by Anderson and co-workers (e.g.
(a) Quartz crystal in refractive index oil (cross-polarized light) showing several melt inclusions. (b–d) Detailed views of the three largest inclusions; scale bar is 50 µm and applies to all 3 images; area, radius (of a circle with same area), and faceting time are indicated for each inclusion. Note that (b) is non-faceted, (c) is partly faceted, and (d) is faceted. That only (d) is faceted suggests that crystal residence times are <1,500 years. Images (a–d) are from Anderson et al.
(a) Shape change of a melt inclusion inside a host crystal as a function of time due to faceting; initial inclusion is spherical, but with time gets transformed into a polyhedron with rounded edges; with sufficient time, inclusion may become a perfect anticrystal. (b) Evolution of shapes emphasizing the role of diffusion (green arrows) in transporting material to achieve faceting.
Importantly, many of the larger central melt inclusions are round
We note that the problem involves lateral diffusion of material from the spherical cap that is gradually dissolved into the corner region that progressively forms by reprecipitation (
The volume change ΔV can be calculated as the volume of the 12 spherical caps that stick out of the flat surfaces of a hexagonal bipyramid of side a and height h:
The flux equation simply states that material transport is by diffusion
The Thomson-Freundlich equation
Combining Equations 7 and 8, and assuming that the scaling is appropriate for non-infinitesimal changes, we can calculate the faceting time as:
Time required for faceting versus inclusion radius plot for conditions relevant for Bishop magma crystallization. Vertical lines correspond to inclusion sizes estimated from
X | σX | Unit | σX/X | Source | |
r | 100 | - | 10−6 m | ||
ΔV | 4.8 10−13 | - | m3 | ∼10% |
|
R | 8.31451 | - | J/(K·mol) | - | |
T | 750 | 15 | °C | 2% | |
C0 | 0.7 | ∼0.2 |
. | ∼30% |
|
σ | 0.02 | 0.01 | J/m2 | 50% |
|
Ω | 23.7 | 1.0 | 10−6 m3/mol | 4% |
|
H2O | 3 | - | Wt. % | ||
D0 | 25.8 | 10−9 m2/s |
|
||
ln[D0] | −17.5 | 0.70 | 4% |
|
|
E | 126.5 | 8.5 | 10+3 J/mol | 7% |
|
D | 1.28 | 1.06 | 10−14 m2/s | 83% |
|
(E/RT)2 | 132.6 | . | . | . | . |
Δt | 1,242 | 1,260 | a | 101% |
Approximate values.
Calculated using the CORBA Phase Properties applet (
Specific results for the melt inclusions shown in
Even if, for sake of argument, we assume that t values are underestimated by 250% (+2σ), our conclusions do not significantly change, as illustrated in
Crystal size distributions in rocks are typically characterized by a monotonic decrease in the number density of crystals with size, with numerous small crystals and few large crystals (see
(a) Whole-quartz crystal size distributions for pumice from Chalfant Quarry, obtained by a crushing, sieving and winnowing procedure (data from
Theoretical and observational considerations
Additional evidence for the timescales of quartz crystallization derive from crystal size distributions, given that the slope in semi-log space decreases systematically with time
Our calculations based on crystal size distributions thus suggest residence times for quartz crystals in the millennial scale, in remarkable agreement with our estimates based on diffusional relaxation and melt inclusion faceting, lending confidence to our results. Due to the simultaneous saturation in quartz and two feldspars characteristic of the Bishop magma (see below), this time frame also includes the vast majority of feldspar crystallization, leading to the conclusion that the Bishop existed as a large-volume, crystal-poor magma body for a maximum of only a few thousand years.
Different lines of evidence presented above suggest that quartz crystallization in the Bishop magma lasted only a few thousand years, and most of the crystallization occurred within the final 1,000 years before eruption. One significant question is whether such timescales are consistent with heat flow requirements, i.e. with the need to transport the heat of cooling and crystallization through the country-rocks.
It has long been argued that the Bishop magma is “eutectoid” in nature (e.g.
Using rhyolite-MELTS
Temperature (°C) versus enthalpy change (J/g; top panel) and versus abundance (wt. %; bottom panel) plot shows results of MELTS
The importance of this nearly isothermal behavior is that the amount of heat that needs to be withdrawn is essentially limited to latent heat of crystallization, which rhyolite-MELTS calculates to be only 20–30 J/g (see
Our rhyolite-MELTS simulations not only constrain the total heat of cooling and crystallization required to attain the observed compositions and crystal contents, but also confirm our expectation of nearly invariant crystallization. To contrast the behavior of invariant and non-invariant magmas, we employ well-known analytical solutions
The Bishop magma body can be reasonably approximated as a 2 km thick body
Initial thermal profile is a step-function, with hot (750 or 780°C) magma on the left side and cool (400°C) country-rock on the right side. We use three different analytical solutions: (a) Continuous source, in which crystallization is dispersed throughout the invariant magma, and the magma—country-rock interface is maintained at its original position; changes in the thermal properties of the magma as a function of crystallization are neglected. (b) Solidification front, in which crystallization of invariant magma takes place from the magma—country-rock-interface inward; as a limiting case, thermal properties of the solidified zone are taken to be the same as those of the liquid. (c) Lovering
Property | Country rock | Liquid |
|
|
|
ρ | 2.6 |
2.1 |
c | 0.21 |
0.32 |
K | 0.006 |
0.0036 |
κ = K/(ρ*c) | 0.011 | 0.0058 |
L | – | 35 |
c* = L/50+c | – | 1.02 |
Carslaw & Jaeger
Whittington et al.
Rhyolite-MELTS simulations.
Only for Lovering-type simulation.
Interestingly, solutions (1) and (2) are two end-members of invariant crystallization. In (1), crystallization is dispersed within the melt, with no gradient in crystallinity within the magma, while in (2), melt is always crystal-free and crystallization takes place along the walls. Crystallization of an invariant magma is likely to be intermediate in character between these two models.
Application of the analytical solutions discussed above (
Notice the dramatic differences in behavior between the solutions for invariant magmas (Continuous Source and Solidification Front) and for non-invariant magmas (Lovering). Curves for Lovering-type crystallization are for the center and the bottom of the 1 km column. In particular, notice that significant crystallization (e.g. 25 vol. %) is attained in <1 ka for invariant magmas, in accordance with geospeedometry estimates presented in the text. Much longer timescales are required to cause significant crystallization of the interior of non-invariant magma bodies.
The contrast in timescales between invariant and non-invariant magmas can be understood based on the differences between the two kinds of heat flow problems. For invariant magmas, all heat loss promotes crystallization, given that there is no sensible heat generation within the magma. Further, with magma temperatures buffered at the invariant temperature, thermal gradients at the magma-rock contact are steeper in the invariant case than the thermal gradients within the magma in the non-invariant case. It results that crystallization proceeds a lot more quickly in the invariant case. That invariant magmas can crystallize as much as 25 vol. % in ca. 1,000 years lends significant support to the timescales of crystallization estimated based on quartz geospeedometry.
Geospeedometry results suggest quartz crystallization on millennial timescales, and heat flow considerations suggest that these are the expected timescales for the problem of interest. These timescales contrast drastically with radiometric results (e.g.
Ion probe U-Pb dating suggest zircon crystallization spanned over >100,000 years
Crystallization timescales on the order of millions of years have been recently suggested based on MELTS calculations and simple heat balance considerations
Our interpretation has fundamental implications. The Bishop magma is characteristically zoned in many respects
We use four lines of evidence to infer the timescales of crystallization of the Bishop Tuff magma body:
Timescales of relaxation of Ti profiles in quartz suggest quartz residence times of ∼500–3,000 years; crystal size distributions suggest that >99 wt. % of crystals present would have crystallized within this timeframe;
The coexistence of round and partly faceted (negative crystal shape) melt inclusions in quartz suggest that quartz residence times are similar to the timescale for melt inclusion faceting; calculated faceting times suggest quartz residence times of ∼500–1,500 years;
Using growth rates constrained by Ti relaxation times and known crystal sizes, we calculate crystallization times based on crystal size distributions of ∼500–2,500 years;
Thermodynamic considerations suggest crystallization of nearly invariant magma under essentially isothermal conditions; crystallization of such magma would be particularly efficient due to the absence of sensible heat contributions and steep thermal gradients, resulting in crystallization times of <1,000 years.
The agreement between these various estimates strongly supports crystallization of a giant magma body from a nearly crystal-free initial state over millennial timescales. We thus argue that giant magma bodies are ephemeral.
Animation showing 3D view of crystals in pumice chip (sample AB-6203F). Euhedral quartz and feldspar grains shown in green, magnetite in blue, and pyroxene±biotite in white. Note the overall trend of decreasing numbers of crystals with increasing size. Sample is approximately cylindrical, field of view ∼9 mm in diameter.
(MPG)
We thank Ian Steele and Matthew Newville for assistance with analytical work, Bruce Buffet and David Furbish for discussions on diffusion and numerical problems, and Calvin Miller and other MESSY members for suggestions on the manuscript. Reviews by Victoria Smith, Jacob Lowenstern, Jon Blundy and Christian Huber, and suggestions by Olivier Bachmann are greatly appreciated.