JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. El2, PAGES 32,983-32,995, DECEMBER 25, 2001

Density structure of Io and the migration of magma through its lithosphere

Giovanni Leone and Lionel Wilson

Environmental Science Department, Institute of Environmental and Natural Sciences Lancaster University, Lancaster, England, United Kingdom

Abstract. We model the density structure of the outer several tens of kilometers of Io on the basis of the assumption that condensed volatiles, mainly SO2, exist at shallow depths in a mafic to ultramafic lithosphere, which has a finite porosity due to its accumulation as a mixture of pyroclastic and effusive volcanic deposits, which include condensed volatiles. The porosity decreases with increasing depth due to pressure-driven compaction and temperature-driven melting of the volatiles, and this controls the bulk density structure of the lithosphere. We also model the densities of ascending magmas as a function the types and amounts of volatiles that are available in their source regions. The relative densities of the accumulated volcanic deposits and of the magmas rising through them control whether the magmas will erupt at the surface or will stall to form intrusions which can grow into magma reservoirs. We find that the depths at which magma reservoirs may exist are strongly influenced by the void space fraction in surface deposits and only weakly controlled by the mass fraction of SO2 in the deposits and the mass fraction of SO2 in the magmas. Once nucleated, a reservoir has the potential to grow to a very large vertical extent (-15 km total height) before the magma immediately beneath its roof is again buoyant relative to the surrounding rocks. The presence of large-volume reservoirs may explain the great extent of the larger lava flow fields seen on I0 and the longevity of some eruptions. The presence of very soluble volatiles, such as water, in magmas would have virtually no effect on these findings because these volatiles would influence the densities of magmas only very near the surface (though they would, even in very small amounts, then have a dramatic effect on the explosivities of eruptions).

1. Introduction

The Galileo mission has provided abundant information on the surface morphology and composition and volcanic activity of Io [e.g., McEwen et al., 1997; McEwen et al., 1998a, 1998b; Geissler et al., 1999; Lopes-Gautier et al., 1999, 2000; McEwen et al., 2000]. Large areas are dominated by lava flow fields or pyroclastic fall deposits or both, the pyroclastic materials being in some cases silicates and in many cases condensed volatiles, chiefly SO 2 or S2 [Spencer et al., 2000]. The emerging picture is of volcanic activity dominated by the eruption of high- temperature (up to 1900 K) magmas of mafic to ultramafic composition [McEwen et al., 1998a], which commonly interact at or below the vent with layers of SO2 or sulphur deposited during earlier volcanic activity nearby [Kieffer, 1982; Davies and Wilson, 1988; Burnett et al., 1997; Kieffer et al., 2000]. In this way a range of apparent eruption temperatures can be generated as a function of the mixing ratio between juvenile magma and nonjuvenile volatiles.

This mixing ratio also determines the explosivity of the eruptions. The dynamics of eruptions producing large plumes clearly indicate that mixing is common: the -350 km height of the Pele plume [Strom et al., 1981; McEwen et al., 1998b] implies an eruption velocity of-1 km s -• [Kieffer, 1982], and speeds of this order can only be attained if the mass fraction of

Copyfight 2001 by the American Geophysical Union.

Paper number 2000JE001379. 0148-0227/01/2000JE001379509.00

volatiles in the magma is -•30%, far greater than any plausible aoun,•ance of juvenile magmatic volatiles. However, there is currently no clear picture of the distribution of nonjuvenile volatiles with depth and hence the geometric details of the magma-volatile interaction process. Nor is there any clear indication of the presence or absence of juvenile volatiles in magmas; one extreme scenario consistent with current observations is that of completely volatile-free magmas ascending from volatile-free source regions at depth and interacting only very near the surface with volatiles released from magmas in Io's distant past. These relict, near-surface volatiles would thus be recycled very many times while at the same time they were slowly being lost into space. Such a situation would require the magmas to be positively buoyant everywhere within the lithosphere. Other possible scenarios include the progressive burial to much greater depths of erupted volatiles as the crust accumulates, so that magmas ascending from the mantle can incorporate these volatiles at a much earlier stage in their ascent, thus modifying their densities over a wide range of depths. These various options lead to very different patterns of transfer of melt to the surface [Leone and Wilson, 1997, 1998; Leone et al., 2000].

Mafic eruptions on Earth are fed by elongate dikes, and eruptions commence with "curtain-of-fire" lava fountains along a fissure vent feeding lava flows as still-molten clots of magma fall back to the surface near the vent and coalesce [Wolfe et al., 1987; Bjornsson et al., 1977]. In sufficiently prolonged eruptions, activity tends to concentrate at a few locations or a single location along the original fissure [Wilson and Head, 1988; Bruce and Huppert, 1989]. The symmetry of many pyroclastic deposits

32,983

32,984 LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE

on Io is at first sight consistent with the idea that the vent feeding the eruption acts as a point source; however, when the typical radius of a deposit is many times the typical linear dimension of the vent feeding it, as is common on Io, the deposit will tend to a circular shape independent of the geometry of the source. Direct confirmation that eruptions on Io can break out from fissures was provided in late 1999 by the onset of a curtain of fire from a 25- km-long fissure in the Tvashtar Catena caldera complex [McEwen e! al., 2000; Wilson and Head, this issue]. In subsequent modeling of interactions between rising magma and volatiles present in country rocks we explicitly assume that magma rises in planar dikes.

The ability of magma to rise from the deep interior of a planet and either to intrude at shallow depth or to erupt at the surface is controlled mainly by the relative densities of the melt and the rocks through which it passes. Partial melts formed by pressure release melting in solid mantles undergoing solid-state convection are almost universally less dense than the parent rocks from which they separate. Their expulsion from the source region is driven by both buoyancy and the stress regime in the host rocks [McKenzie, 1985; Sleep, 1988], but once separated, they rise largely as a result of buoyancy forces. On Io, a second possibility exists: The heat input due to tidal deformation may be large enough that the solid lithosphere is underlain by a global magma ocean of-100 km depth [Keszthelyi et al., 1999]. If the lithosphere and the ocean are of essentially the same bulk composition, the ocean magma will be less dense than the overlying solid, and positive buoyancy will again be a major factor in magma ascent [Weertman, 1971 ], though stresses in the solid lithosphere and its rheological response to those stresses will again play an important role.

Rising melts generally ascend though a lithosphere that becomes less dense nearer the surface. In areas dominated by volcanic rocks on Earth, the low density at shallow depths is caused by a combination of the poor packing of pyroclastics and the vesicularity of lavas [Head and Wilson, 1992]. Compaction of pore space with increasing depth due to the increasing pressure leads to a monotonic increase in lithosphere density. As magmas that are positively buoyant in their source zones at gre•t depth rise through this density profile, they eventually reach a level at which they are neutrally buoyant, and Ryan [1987] has stressed the importance of these zones of neutral buoyancy in acting as traps at which large magma reservoirs can accumulate.

Because rising magma bodies have a finite vertical extent, the buoyancy forces acting on them have to be integrated over the whole region that they occupy. Also, rising magma bodies may have a relatively equant, diapiric shape if they rise slowly and deform the host rocks in a plastic manner, as is most likely at great depths in the lithosphere where the viscosity contrast between the magma and host is least [Rubin, 1993] but at shallow depths will take the form of elongate, blade-like dikes, which deform the host elastically. In the latter case a finite internal excess pressure commonly exists in the melt. For both of these reasons, the forces acting on rising magmas are not strictly hydrostatic, but they are commonly very nearly so [Lister, 1990]. The level at which neutral buoyancy is reached depends not only on the density structure of the lithosphere but also on the changing density of the ascending magma: Magmas on Earth contain dissolved volatiles in the source region, and these are progressively exsolved as the confining pressure decreases, thus decreasing the magma density. Commonly, the magma density decreases less rapidly than the lithosphere density at first, and so the consequence is a slight shallowing of the depth of neutral

buoyancy. However, at very shallow depths on Earth the highly soluble species H20 is released, and the magma density can become very much less than that of the surroundings. This process is responsible for the vigor of most explosive eruptions but also limits the vertical extents of magma reservoirs: If a reservoir growing upward and downward from a neutral buoyancy level extends too close the surface, H20 exsolution near its roof from batches of new magma injected from the deep source will systematically lead to eruptions rather than further reservoir growth.

The ambient atmospheric pressure on Io is extremely small, ranging from 10 -• MPa far from sites of activity to perhaps as much as 10 -9 MPa in the vicinity of eruption plumes [Spencer et al., 2000]. Thus even miniscule amounts of juvenile volatiles in magmas will become saturated on exposure at the surface and exsolve to form gas bubbles [Wilson and Head, 1981]. Equally, significant gas volumes will be generated by the incorporation into magmas in dikes of even very small amounts of volatile compounds from the dike walls. Whatever the volatile source, if the bubble volume fraction exceeds some critical value,

commonly taken to be close to 75-80 vol % [Sparks, 1978] but almost certainly a complex function of bubble size distribution, bubble number density, and magma strain rate [Mader et al., 1994; Alidibirov and Dingwell, 1996; Gardner et al., 1996], the magma is disrupted and an explosive eruption ensues, the velocity of the ejecta being an increasing function of the gas mass fraction in the explosion products [Wilson, 1980]. The adiabatic expansion of the mixture of gas and silicate droplets leads to extreme cooling and eventual freezing of most of the volatile phase so that an assemblage of cold, irregular pyroclasts forms around the vent as a loosely-packed fall deposit [Kieffer, 1982, 1984]. The random packing of irregular particles with a wide range of sizes commonly leads to porosities of order 30% [Smith, 1999]. If an explosive eruption does not take place because the mass fraction of volatiles is small enough that the bubble volume fraction in the magma nearing the surface is less than the critical value (75-80 vol %) for disruption, a vesicular lava flow could be extruded from the vent with a porosity that could lie anywhere in the range zero to 75-80%. The same is true of effusive eruptions on Earth, but empirically, the mean porosity of basaltic lava flows in Iceland and Hawaii is -25% [Head and Wilson, 1992]. We therefore feel jusnfied in assuming that volcanic deposits on Io, being mixtures of lava flows and pyroclastic falls, will on average have porosities of order 30-40 vol % and adopt 30% as a conservative estimate for use in subsequent calculations.

In this paper we use the above arguments to model the density and pressure structure of Io's lithosphere. We then examine the rise of magmas through the lithosphere, considering likely combinations of magma type and magmatic volatile composition, and explore the ways in which the lithosphere structure controls the rise of magma from deep sources, the likelihood of magma reservoirs forming within the lithosphere, and the modes of magma eruption.

2. Structure of Io's Lithosphere

It is observed that in regions on Earth where the crust is composed of successive layers of volcanic rocks, the bulk density increases with depth in a way that can be understood if the porosity decreases exponentially with increasing pressure, i.e.,

Vu = V•.o exp(-• P), (1)

where V• is the fractional void space at the depth where the

LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE 32,955

lithostatic pressure is P, Vvo is the fractional void space at the surface (0.3, based on the arguments above), and • is a constant, independent of the acceleration due to gravity, equal to -1.18 x 10 -8 Pa -• [Head and Wilson, 1992]. We assume that this same compaction process operates on lo. However, the situation is clearly complicated by the fact that the solid material at the surface is a mixture of silicate fragments and solid SO2 or sulphur. The mean bulk density of the surface materials will be controlled by the relative amounts of these components, and their proportions will vary laterally across the surface. In areas dominated by explosive activity the surface and subsurface will consist of an accumulation of pyroclasts which, as noted above, will be mixtures of silicate fragments and solid volatiles. Given that the dynamics of the plumes from the most vigorously explosive vents suggests that as much as 30 mass % of the eruption products consist of SO2 entrained into the rising magma [Kieffer, 1982], we estimate that perhaps 20 mass % of surfaces dominated by pyroclastics may be solid SO2. Areas dominated by lava flows, in contrast, will be volatile-poor for two reasons. First, any volatiles in the lavas (whether juvenile or nonjuvenile) will tend to be maintained in the vapour phase while in contact with the flow surface and only condense on surfaces at ambient temperture surrounding an active flow. Second, as a flow advances over ground which has an admixture of volatiles, the heat flow into the surface from the base and front of the flow will

tend to drive surface volatiles ahead of the flow. Volatiles from

greater depths, which are only mobilized after the flow has completely covered them, may escape through the body of the flow as rootless vents form; depending on the details of the escape process, hundreds of meters depth of volatiles may be removed by laterally extensive flows only tens of metres thick if, as is observed in some cases, flow activity is maintained for periods of a few years [Kieffer et al., 2000]. Using the estimate based on existing global imaging of Io at varying resolutions [McEwen, 1995; Carlson et al., 1997a] that half of Io's surface may be dominated by pyroclastic deposits and half by lava flows, we adopt 10 mass % for the proportion of SO• in the solid component of Io's near-surface layers. Using this estimate, taking the surface void space fraction Vvo to be 30 vol %, and using the densities of solid SO2 (p• = 1434 kg m -3) and solid ultramafic rock (for which a value representing a compositional model suggested by R. Ghail (personal communication, 2000) averaged over several tens of kilometers of depth is p,. = 3360 kg m'3), the volume fractions of the solid SO2 and silicate rock components are Vs = 14.5% and Vr = 55.5%, respectively.

Whatever the relative proportions of silicate and volatile components at the surface, the proportions will vary with depth. As surface deposits become progressively buried by later activity, they are not only compressed but also heated as the Io geotherm migrates into them. As long as the volatile phase is solid (and its bulk modulus is not grossly different from that of silicate rocks), the compaction process proceeds as on Earth. However, if the volatile phase melts, it can potentially migrate, both horizontally and vertically (downward but not upward), leading to at least partial repacking of the silicate components. Melting of SO2 will occur at a temperature of 198 K, and sulphur will melt at about 393 K, these temperatures being essentially independent of pressure. A likely value for the geothermal gradient on Io is 39 K km '• [Keszthelyi and McEwen, 1997a; Leone and Wilson, 1999], and so with a mean surface temperature of 130 K the melting points will be reached at depths of 1.75 km for SO2 and 6.75 km for sulphur.

The pressures at these depths are dependent on the density profiles, which we calculate in section 3, showing that for a wide range of silicate/volatile mixing ratios the pressures at 1.75 and 6.75 km are -6 and -27 MPa, respectively. The critical pressures for SO2 and sulphur are 7.8 and 11.6 MPa, respectively, and so at all depths in Io's crust below the levels at which they melt, both SO2 and sulphur are near-critical or supercritical fluids with densities estimated from the van der Waals equation of state to be of order 1000 kg m -3, rather than low-density vapors. The volcanic deposits on Io, whether pyroclastic falls or lava flows, tend to be laterally extensive compared with their likely thicknesses [Lopes-Gautier et al., 1999; Kieffer et al., 2000]. The greatest barriers to fluid flow within the deposits are likely to be the massive interiors of lava flows: Gas bubbles tend to migrate away from the interiors of active flows, mainly upward, due to a combination of shear forces and buoyancy [Aubele et al., 1988]. Given these facts, we might expect that the lateral continuity of both porosity and permeability in subsurface layers will be greater than the vertical continuity, so that lateral migration of dense, supercritical fluid volatiles in "aquifers" will be easier than vertical seepage. However, unless vertical movement is suppressed by completely impermeable layers, there seems to be no constraint on the vertical distance that a liquid volatile might migrate downward through the solid lithosphere other than the closure of the pore space.

The final factor determining the distribution of volatiles in Io's crust is the total availability of the volatiles. Using compilations of planetary elemental abundances summarized by Kaula [1968] and assuming for the moment that all of the sulphur is present as SO2, if the bulk composition of Io were chondritic, SO2 would represent -5% of the mass of the body. It is likely, of course, that sulphur was lost preferentially during the accretion of Io, and we know that it is being lost now from Io's exosphere at an appreciable rate [Sandford and Allamandola, 1993]. As a result, the much smaller value corresponding to the equivalent fractional SO2 content of the Earth's crust, 0.05%, is probably a more realistic estimate. Assume that on average SO2 occupies a volume fraction V s of the outer part of Io, treated as a shell of thickness D. As long as D << R, where R is Io's radius (-1815 km), the volume of the shell is given by (4 • R 2 D) and the volume of SO• in the shell is (4 • R 2 D Vs). The mass of SO2 is (4 where Psa is the density of the SO2, say 1400 kg m '3 to average over both the solid and supercritical fluid forms, and the mass of Io is ([4/3] • R 3 p•), where the bulk density of Io is p• = 3570 kg m '3. The mass fraction of SO2 in Io is the ratio of these two masses: (4 rc R 2 D Vs psa)/([4/3] n R 3 p•) = (3 D V• Ps•)/(R P•). Equating this to the above mass fraction estimate of 0.0005 (0.05%) we find that the product (D g) is very close to 300 m. Thus, if SO• occupies a fraction Vs = 0.1446 (14.46%), as estimated above, it will do so to a total depth of D = 2075 m. On the basis of the assumed geothermal gradient, we estimated earlier that SO• would be molten at depths >1750 m. On average, therefore, there should be a volume of fluid SO• equivalent to a layer which would be 325 m deep if it continued to occupy a fraction 14.46% of the volume. If it compacted into an aquifer filling all of the available pore space (- 30% of the volume), the aquifer would be -150 m deep; alternatively, and probably much more likely, the fluid could spread vertically into an extensive convecting "hydrothermal" system in Io's crust.

If the above calculation is repeated assuming that all of the sulphur is present as the element, rather than as SO2, the mass fraction equivalent to the Earth's crustal content is approximately

32,986 LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE

halved, so that ( D V) is -150 m. A value of V• equal to 14.46 % then corresponds to a depth of--1037 m, which is much less than the 6.75 km depth at which elemental sulphur melts. Thus no fluid aquifer or hydrothermal system would be predicted in this case. Given that (1) SO2 is detected much more often than elemental sulphur in explosive eruption plumes on Io [Spencer et al., 2000] and (2) it is hard to imagine how the magma feeding a long-lived eruption can continue to mobilize and extract a solid volatile from the walls of the dike in which it rises, whereas it is

easy to imagine the liquid in an aquifer or hydrothermal system intersected by the dike flowing steadily through the dike walls, we concentrate on modeling the effects of SO2, rather than sulphur, on the crustal density structure.

3. Density Model for Io's Lithosphere

On the basis of the above arguments, the model is formulated as follows. From the surface to the depth at which SO2 melts, 1.75 km, the bulk density is calculated on the basis of the values adopted earlier for the surface volume fractions of void space, Vv0 = 30%, solid SO2, Vs = 14.46%, and solid silicates, Vr= 55.54%. The calculation is performed at each of a series of depths' 0, 3, 10, 30, and 100 m, and then at 100-m steps to 50 km. The void space decreases with increasing pressure according to (1) and the pressure P, at step i is calculated from the pressure P,_• and bulk density [3,4 at the previous step using the depth increment Ah and the acceleration due to gravity g'

P, = P,4 + [5,.• g Ah . (2)

The value of g is corrected for its variation with depth, d, by multiplying the surface value, 1.8 m s '2, by the ratio [(R-d)/R], where R is the radius of Io, 1815 km. The bulk density [3, is obtained as a function of the local pressure via

[5, = (V• p•, + Vr pr)/(V,.oexp[-•, (P, - Po)] + V• + Vr) , (3)

where P0 is the surface atmospheric pressure, -10 '• Pa. At the depth where SO2 melts, 1.75 km, it is assumed that the crust compacts by losing the volume V,. The supercritical liquid SO2 is assumed to be dispersed into the pore space of all of the crust below the melting depth. We showed above that this fluid probably represents the equivalent of a layer -150 m deep if it saturates the pore space; when spread over a depth range of several tens of kilometers, it affects the bulk density by <1%, and we therefore neglect it as regards the crustal density calculation. In order to take account of the compaction implied by the loss of the fluid SO,. we note the void space at the melting depth, found to be V .... = 27.75%, and calculate new volume fractions of silicate rock, Vrn , and void space, Vv,•, from

E• = Vr/( E + Vv,,) (4)

E•, = E,,,/( v• + E,,,), (5)

where now (Vr + V,.,•) = 1. The values found are Vr• = 66.68% and V•.,0 = 33.32%, and the density increases on compaction from 2121 to 2240 kg m '•. At depths greater than 1.75 km the density is then given by

[5, = (V r pr)/(Vv•exp[-•,(P,- P,)] + Vr) (6)

where P,,, is the lithostatic pressure at the melting depth, -6.60 MPa. Figure l a shows the density and pressure profiles resulting

from this set of parameters. We shall show in section 5 that it is important to explore the density profiles corresponding to other values of Vv0. Figure lb shows how the density profiles change if VvoiS progressively decreased from 30 mass % to 25, 20, 15, and 10%.

4. Compositions and Solubilities of Likely Magmatic Volatiles

We first explore the possibility that despite its vigorous volcanic history, Io's deep interior still retains some volatiles. The only volatiles in volcanic plumes and on the surface for which there is unambiguous evidence from spectroscopic measurements are SO2 and elemental sulphur, though there are indirect or controversial indications of very small amounts of H2S and H20 [Salama et al., 1994; Nash, 1994; Carlson et al., 1997b]. Studies of the equilibria as a function of temperature and pressure between the various gas molecules that can exist in magma-H-O- C-S systems [e.g., Gerlach, 1986; Luhr, 1990] show that sulphur is likely to be present as SO2 rather than as H2S, and so we focus almost completely on this species. Unfortunately, the way in which magmas dissolve sulphur is a very complex function of their bulk compositions [Carroll and Rutherford 1985; Luhr, 1990], and few data exist which could be used to predict the exsolution pattern of SO2 gas from an Ionian magma saturated in sulphur even if we were sure of its composition. We have used the experimental data for an albite melt described by Mysen [1977] to infer that at realistic eruption temperatures (-1700- 1800 K) this melt would have had an equivalent SO 2 solubility n ds02 (expressed as a mass fraction as a function of the pressure in Pa) given by

ndso2 = 7.5 x 10 -•2 P- 2.6 x 10 -2• p2+ 3.2 x 10 '3• p3. (7)

Compared with the commonest volatiles in basalts on Earth, this level of solubility is closer to that of CO2 than of H20. Experimental data for CO2 were approximated by Harris [1981] as

rtdco2 = 5.9 x 10 -12 P + 5 x 10 -6 . (8)

In contrast, the data summarized by Wilson and Head [1981 ] for H20 suggest

nab2, , = 6.8 x 10 '8 p07 (9)

These solubility functions are compared in Figure 2, which emphasizes the much greater solubility of water than of any other species.

Care is needed in interpreting the significance of the above solubility functions. As pointed out by Gerlach [1986], whichever species is the first to exsolve will partially control the release of other species: Once the vapor phase of one species is present, the vapor phases of others will be partitioned into it to some extent. In our case we are assuming for the moment that SO2 is the only volatile present. We therefore use equation (7) to determine the mass fraction of SO 2 exsolved at any given pressure, neso2, from the total amount of SO 2 available in the melt, n•o 2, using

neso2 = ntso2 - ndso2, ntso2 > naso2 (10a)

neso2 = 0, ntso2 < na.•o 2 . (10b)

LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE 32,987

34OO

3200

3000

2800

2600

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2200

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ß 200 •

150 5'

100

50

0

0 10 20 30 40 50

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34OO

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24OO

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,,•m• m ß ß • _ • 10 % .-'' o-ø •'

, 15 % • •

,,' 20 % •

" • 25 %

I / 30%

(b) 2000

0 10 20 30 40 50

depth in km

Figure 1. Figure 1. (a) Variation of pressure (dashed curve) and lithosphere density (solid curve) with depth in our basic model of Io's lithosphere. Void spaces occupy 30% of the volume of the surface materials, and the remaining 70% of the volume consists of 10% by mass SO2 frost (corresponding to 14.5% of the total volume) and 90% by mass silicate rock (corresponding to 55.5% of the total volume). Note the step in density and pressure at a depth of 1.75 km where solid SO2 melts and the resulting fluid is distributed over a large range of depths. (b) Variation of density with depth when the surface void space volume fraction is changed while the frost to rock ratio is kept contant. The curve labeled 30% is the same as the solid curve in Figure l a; the other curves are labeled with the relevant void space value. The abrupt density increase at 1.75 km has been smoothed slightly for clarity.

32,988 LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE

0.1

0.01

0.001

0.0001

10 's

mmm ß

ß ' HO ß

ß 2

ß

mmm m m mmm mmmmm m mmm mm m m mmmmmmmmmm m mm mmmm mmmm ß

.,

so

CO

0 50 100 150 200 250 300

pressure in MPa

Figure 2. Functions used in this paper for the solubilities as a function of pressure in mafic magmas of the three volatiles SO2, CO2, and H20. The solubility is shown as a mass fraction, and the functions are given as equations (7), (8), and (9).

In order to arrive at an estimate of the range of plausible values to be used for rttso2 , we first recall that we assumed earlier that SO2 formed 0.05% by mass of Io's lithosphere. If this were its content in melts from the mantle, then exsolution would begin at a pressure of--70 MPa, corresponding to depth of-16 krn. If mantle melts contained SO2 amounts more typical of those of terrestrial basalts, 0.15 mass % [Gerlach, 1986], gas release would start at a pressure of--212 MPa at a depth just >42 km. We use these values of rtts,, 2 as our starting points in section 5.

5. Bulk Densities of Magmas, Magma-Lithosphere Density Interactions, and Formation of Magma Reservoirs

Magmas rising from the deep interior of Io will do so either as relatively equant, diapiric bodies or as vertically extensive, elongate, blade-like dikes [Rubin and Pollard, 1987]. The main factor controlling the magma body morphology [Rubin, 1993] is the ratio of the apparent viscosities of the magma (which is likely to have Newtonian rheology) and the host rocks (which will

behave in a viscoelastic manner). The very high apparent viscosity of the lithosphere at shallow depths implies that however diapir-like the initial upward migration of magma, the final ascent will be as a dike. At least in the lower part of the lithosphere, the boundary between the magma and the host rocks will not be able to support large stresses, and so the pressure in the magma will be equal to the lithostatic pressure in the host material. The bulk densities of magmas rising from mantle depths

(at least several tens of kilometers) can then be found by combining the above exsolved SO 2 mass fractions as a function of lithostatic pressure with the density of the magmatic liquid, p•. A value of p• = 3050 kg m -3 is used, corresponding to the same compositional model used for the solid silicate and representing an average between values of 3000 kg m -'• at zero pressure and 3116 kg m "• at the pressure corresponding to a depth of -- 100 km (R. Ghail, personal communication, 2000). The bulk density of the magma, [•,,,, is then given by

(1/[•,,,) = [(n .... 2 Q T)/(m P)] + [(1 - neso2)/p, ] (11)

where the gas behavior is assumed to be ideal (a reasonable approximation over the pressure ranges involved), Q is the universal gas constant, 8.314 kJ kmol'l, T is the magma temperature, taken on the basis of the assumed ultrmafic

composition as 1900 K, and m is the molecular mass of SO2, taken as 64.

Using the parameter values specified so far, specifically a surface void space volume fraction of V• = 30%, a surface solid SO2 volume fraction of V, = 14.46%, and a surface solid silicate fraction of V r = 55.54%, together with the total magmatic SO2 contents of rttso2 = 0.05 and 0.15 mass %, we find the profiles of lithosphere density and magma density shown in Figure 3. The formation of gas bubbles in an ascending magma begins at ~16 km when n•o 2 = 0.05% and at ~43 km for Fttso2 ---- 0.15%. For both volatile contents the magma is less dense than the lithosphere, and therefore is positively buoyant, at all depths >-30 km (the

LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE 32,989

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lithosphere density, VvO = 0.3 ----magma density, ntso2 : 0.0015 ..... magma density, ntso2 = 0.0005

i

0 10 2o 3o 4o 5o

depth in km

Figure 3. Comparison between the density as a function of depth of the lithosphere and of a magma containing a mass fraction, ntso2, of SO 2 of either 0.0005 or 0.0015. The potential exists for the formation of a magma reservoir at the depth where the magma is neutrally buoyant, 29.6 km for rttso2 = 0.0005 and 29.3 km for rttso2 = 0.0015.

exact values are 29.6 km for ntso2 = 0.05% and 29.3 km for ntso2 = 0.15%). A neutral buoyancy level exists at this depth, and the magma is negatively buoyant for a gmat distance above it. Only at depths shallower than 200 m for the 0.05 mass % SO2 content and -800 m for the 0.15% SO 2 content does the presence of the volatile cause the magma to again become positively buoyant. In this scenario, therefore, magmas rising from the mantle under the action of no other forces than buoyancy would be likely to reach a neutral buoyancy level at a depth just <30 km. Provided that a new melt batch arrived in the immediate vicinity sufficiently often to offset the cooling of the previous batches, melt could accumulate there into a magma reservoir. This would grow, vertically and horizontally, in a way determined by a complex combination of dike and sill injection into the surrounding rocks and stoping of the roof, just as occurs on Earth.

The limit on the vertical extents of reservoirs is probably set by the ratio of the pressure- and buoyancy-driven forces acting on the magma, which are proportional to the acceleration due to gravity, and the compressive and tensile strengths of the host rocks, which are independent of gravity [Wilson and Head, 1994]. The acceleration due to gravity on Io is (9.8/1.8 =) 5.4 times less than on Earth and the summit reservoirs in basaltic

volcanoes like Kilauea, Hawaii, have vertical extents of-3 km

[Rubin and Pollard, 1987; Parfitt, 1991]; hence we expect maximum vertical extents of reservoirs on Io to be (5.4 x 3 km =)

*-16 km. Note that the top of a 16-km-high reservoir centered at *-29 km is -21 km below the surface and hence at least 20 km

deeper than the level where magma is again positively buoyant relative to the host lithosphere. Thus the rise of magma from such a reservoir to the surface must be dependent on the creation of an excess, nonhydrostatic pressure within the reservoir, as seems to be the case for many mafic magma reservoirs on Earth.

The possible size of this excess pressure depends on several factors. As noted above, the magma densities shown in Figure 3 are based on the assumption that the pressure in the magma is everywhine equal to the lithostatic pressure in the surrounding rocks, that is, that there is no appreciable stress across the boundary between the two. The presence of an excess pressure in the magma in a reservoir would imply, however, that such a stress could be supported by the elastic component of the viscoelastic rheology of the lithosphere for a timescale long enough to allow the stress to accumulate. That timescale would itself depend on the process leading to the pressure increase. We do not pursue this issue in detail here but note that at a depth of 29.6 km the lithostatic pressure is ~141 MPa (see Figure 1), and this pressure would support a static column of magma with a density of 3050 kg m -3 to a vertical height of 25.7 km. To raise the top of this column the extra 3.9 km to the surface would require an excess pressure of 21.4 MPa in the reservoir. This excess pressure is several times larger than the excess pressures inferred for the magma reservoirs beneath the summits of terrestrial basaltic volcanoes [Parfitt et al., 1993].

We now explore options for moving the neutral buoyancy level to shallower depths and hence facilitating the rise of magma to the surface. Since we have argued that supercritical SO2 fluid may be circulating in the void space down to great depths in Io's

32,990 LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE

Table 1. Values of Depth to Neutral Buoyancy Level as a Function of Fraction of Surface Volcanic Deposits Consisting of Void Space, Vv0, and Total Amount of SO 2 Dissolved in Magma at its Source Depth, rttso2, When Surface Deposits Are Assumed to Contain 10% by Mass of SO 2 Frost

Volume Fraction of Surface Consisting of Void Space

0.3 0.25 0.2 0.15 0.1

SO 2 Content Criterion tltso2 Depth tltso2 Depth tltso2 Depth tltso2 Depth tltso2 Depth

Mean Earth's crust 0.0005 29.6 0.0005 24.3 0.0005 18.7 0.0005 12.4 0.0005 1.8 Typical Earth magma 0.0015 29.3 0.0015 23.7 0.0015 17.7 0.0015 10.1 0.0015 a Initial reservoir base 0.0013 29.5 0.0012 24.0 0.0010 18.3 0.0007 12.0 0.0004 1.9

aNo neutral buoyancy level exists at any depth.

lithosphere, we might suppose that magma stored in a large reservoir centered on the original neutral buoyancy level had absorbed SO 2 to the saturation limit at the base of the reservoir and had then commenced convective overturn so that SO2 was now exsolved at shallower depths. The base of the reservoir would lie up to -8 km below the neutral buoyancy depth of 29.6 km at a depth of 37.6 km where the pressure (see Figure 1) would be about 186 MPa, so that rttso2 = rtaso2 = -0.13 mass %. A repeat of the calculations which led to Figure 3 shows that this process would move the new neutral buoyancy level to 29.5 km. Clearly, we cannot take this kind of argument much further, and the effect so far has been to raise the neutral buoyancy level by <0.5% of its original depth.vo

There is a much more efficient way of changing the neutral buoyancy depth, and that is to change the value adopted for the volume fraction of void space in the surface deposits, V•o. We have repeated the above analysis changing V•o from the initial value of 30 vol % to progressively smaller values while keeping the surface proportions of SO2 and silicate rock constant. Table 1 shows the results. For each value of V•o, values are given for the assumed amount of SO 2 in the magma and the depth of the neutral buoyancy level; these are given for each of the three criteria used above: First, that the SO2 content is equal to the mean for the Earth's crust (0.05 mass %); second, that it is equal to a typical value for terrestrial basaltic magmas (0.15%); and third, that it is equal to the maximum amount of SO2 that could be dissolved in the melt at a pressure corresponding to the base of a

16-km-high reservoir centred on the neutral buoyancy level derived from the first criterion. The result is as would be

expected: Decreasing the surface void space fraction increases the lithosphere density at all depths and thus makes the neutral buoyancy level progressively shallower. As Vvo changes from 30 vol % to 25% to 20% to 15%, the neutral buoyancy depth changes from -30 km to -24 km, -19 km, and -12 km, respectively. By the time Vvo reaches 10 vol %, magma is buoyant all the way to the surface for all r/tso2 >0.09 mass %, and there is no reason to expect magma reservoirs to exist. At smaller values of ntso2 a reservoir can exist, centered at a depth of ~ 1.8 km, but it can only grow to a vertical height of- 1000 m; beyond that point, magma at the roof of the chamber will be buoyant relative to the overlying rocks and is likely to erupt directly to the surface, preventing further upward reservoir growth.

The same kind of analysis as that illustrated in Table 1 could, of course, be carried out by varying the proportions of SO2 frost and silicate rock while keeping the surface void space constant. However, changing the SO2/rock ratio has much less effect on the lithosphere density profile than changing the void space/rock ratio. Table 2 shows the consequences of taking the SO2 content of the surface layers to be zero instead of 10 mass %: the neutral buoyancy depths change from the values in Table 1 by no more than 1%. A somewhat greater change in the neutral buoyancy depths is caused by increasing the SO2 content of the surface layers from 10 mass % to 20%, as illustrated in Table 3. Figure 4 compares all of these results and shows that by far the most

Table 2. Values of Depth to Neutral Buoyancy Level as a Function of Fraction of Surface Volcanic Deposits Consisting of Void Space, Vv0, and Total Amount of SO2 Dissolved in Magma at its Source Depth, nL•o2, When Surface Deposits Are Assumed to Contain no SO 2 Frost

Volume Fraction of Surface Consisting of Void Space

0.3 0.25 0.2 0.15 0.1

SO 2 Content Criterion tltso2 Depth titso2 Depth tltso2 Depth tltso2 Depth tltso2 Depth a

Mean Earth's crust 0.0005 29.4 0.0005 24.1 0.0005 18.5 0.0005 12.2 0.0005

Typical Earth magma 0.0015 29.1 0.0015 23.5 0.0015 17.5 0.0015 9.9 0.0015 Initial reservoir base 0.0013 29.2 0.0012 23.8 0.0010 18.1 0.0007 11.6 0.0004

aNo neutral buoyancy level exists at any depth.

LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE 32,991

m

o

m

E

35

15 -

10 -

5

0 '

0.05

ß

ß

ß

ß

ß

ß

ß ß

oø 0.1 ß

0.1 0.15 0.2 0.25 0.3

volume fraction of void space at surface

Figure 4. Variation in depth to magma neutral buoyancy level as a function of volume fraction of surface deposits that consists of void space and of mass fraction of the surface deposits that consists of SO2 frost (curves labeled by mass fraction). Note that neutral buoyancy zones exist for all surface void space fractions >-0.1 for SO2 frost fractions of 0.2 (short dashed curves) and 0.1 (long dashed curves), but do not exist at surface void space fractions <-0.15 when the SO2 frost fraction is zero (solid curve almost coincident with long-dashed curve).

important control on the locations of neutral buoyancy zones where magma reservoirs may form is the volume fraction of the surface rocks that consists of void space.

6. Consequences of Presence of Other Volatiles

So far we have assumed that SO2 is the only volatile exsolved from magmas rising through the lithosphere on Io, the justification being the lack of hard evidence for significant amounts of other magmatic volatiles. Locally, gaseous S2 has

been detected in the Pele plume [Spencer et al., 2000] but is likely to have been produced by a reequilibration between S, S 2, SO, and SO2 at pressures <10 MPa [Zolotov and Fegley, 1999]. Only if S2 became dominant at much higher pressures would this affect our conclusions. We now consider the possibility that other volatile species are present but have somehow evaded detection.

If CO2 were present in amounts similar to those common in mafic magmas on Earth, -0.7 mass % [Gerlach, 1986], (8) shows that it would begin to exsolve at a pressure of-1.2 GPa, corresponding to a depth of -200 km. Thus free CO2 fluid would

Table 3. Values of Depth to Neutral Buoyancy Level as a Function of Fraction of Surface Volcanic Deposits Consisting of Void Space, Vv0, and Total Amount of SO 2 Dissolved in Magma at its Source Depth, tltso2 , When Surface Deposits Are Assumed to Contain 20% by Mass of SO2 Frost

Volume Fraction of Surface Consisting of Void Space

0.3 0.25 0.2 0.15 0.1

SO 2 Content Criterion rltso2 Depth rltso2 Depth rltso2 Depth rltso2 Depth rltso2 Depth

Mean Earth's crust 0.0005 35.0 0.0005 29.3 0.0005 23.3 0.0005 16.8 0.0005 8.4 Typical Earth magma 0.0015 34.8 0.0015 28.9 0.0015 22.7 0.0015 15.5 0.0015 1.1 Initial reservoir base 0.0013 34.8 0.0012 29.1 0.0010 23.1 0.0007 16.4 0.0004 8.0

32,992 LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE

3500

3000

2500

2000

0 10 20 30 40 50

depth in km

Figure 5. Consequences which would ensue if magmas on Io contained from 0.0025 to 0.04 mass fraction of H20 in addition to 0.0015 mass fraction of SO2. The long-dashed curve for 0.0025 water is effectively the magma density profile with SO• alone. It crosses the bold solid curve showing the lithosphere density profile at a neutral buoyancy depth close to 29 km. Progressively larger amounts of H20 cause the onset of a dramatic decrease in magma density to occur at progressively greater depths until, for 0.04 mass fraction H•O, the magma is buoyant at all depths and no neutral buoyancy level exists. The points where the magma density profiles again cross the lithosphere density profile mark the maximum upper extent of any magma reservoir centered on the neutral buoyancy depth. See text for discussion.

be present in partial melts from a solid mantle and would presumably have been rapidly lost from a magma ocean very soon after its inception until the saturation limit at the top of the ocean was reached, perhaps 0.3 mass % at a pressure of-500 MPa at 100 km depth below the surface. A magma ascending from this depth containing a CO2 fraction of 0.3 mass % would reach neutral buoyancy in our standard model crust at a depth of 27.3 km, to be compared with 29.3 km for a magma containing 0.15 mass % of SO2. Even if both species were present together in these amounts the neutral buoyancy depth would still only decrease to 26.3 km. Indeed, because of the similar (low)

solubilities of CO• and SO2, adding CO2 has almost the same effect as increasing the SO2 proportion by the same amount.

More interesting are the results of assuming that significant amounts of some much more soluble species are present in magmas. Figure 5 shows the consequences if a magma containing 0.15 mass % of SO2 also contains from 0.25 to 4 mass % of H20. Adding 0.25 mass % of H20 has little effect on the density even after the water exsolves, and so the curve for 0.25 % H 20 (long- dashed curve) is effectively the magma density profile with SO2 alone. It crosses the bold solid curve marking the lithosphere density profile at a neutral buoyancy depth close to 29 km, as before. Progressively larger amounts of H•O cause the onset of a dramatic decrease in magma density to occur at progressively greater depths until, for 0.04 mass fraction H20, the magma is buoyant at all depths and no neutral buoyancy level exists.

Interpolating between the curves shown suggests that magma reservoirs would be absent for all H20 contents >~3.5 mass %. The points where the magma density profiles for 0.5, 1 and 2 mass % H•O again cross the lithosphere density profile above the neutral buoyancy level mark the maximum upper extent of any magma reservoir, since they indicate the depths at which the magma would again become positively buoyant. However, we argued earlier that no magma reservoir on Io would be likely to extend more than 8 km above and below the neutral buoyancy depth, and so the presence of H20 would not have any effect on limiting the vertical extents of reservoirs unless it formed >-2.5 mass % of the magma.

7. Discussion

Because large numbers of high-temperature volcanic vents have been detected on Io, we have concentrated in this paper on modeling the rise of mafic melts through a mafic lithosphere. However, Keszthelyi and McEwen [1997b] suggested that a possible alternative is the extreme differentiation of Io's crust. If we accept that a wide range of magma compositions could be produced on Io, some of the variations in observed eruption temperature could be the consequences of varying magma chemistry rather than varying amounts of mixing with surface volatiles. The lithosphere could be vertically and horizontally heterogeneous, and we would need to consider the implications

LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE 32,993

of permutating a wider range of melt and lithosphere density profiles. Fortunately, the effects of varying the densities of the bubble-free magmatic liquid and the void-free solid lithosphere are easy to predict from the trends of the models already considered: For the same magmatic volatile contents, intermediate to silicic magmas rising through more mafic lithospheric rocks would form magma reservoirs at systematically shallower depths than mafic magmas. Conversely, mafic magma rising through silicic lithosphere would form deeper reservoirs. The exact changes in reservoir depth would depend, of course, on the specific volatile contents and compositions, but the relative effects of high- and low-solubility volatiles would be the same as those already illustrated.

Finally, we have discussed the effects of the presence of H20 and CO 2 in magmas on Io, despite the fact that the significant presence of these species is in doubt. We note that even if these volatiles are completely absent now, they were probably present in some proportions in Io's past. Provided that major changes in the composition of the lithosphere did not occur at the same time, the progressive loss of CO 2 (like that of SO2) over Io' geologic history would have caused the average depths of magma reservoirs to have increased with time; see trends in Table 1.

Also, if magmas contained large amounts of H20 in the past, reservoirs would have been less vertically extensive and so on average would have had smaller volumes. The implication is that eruptions on Io may have become somewhat more voluminous with time due to the larger reservoir volumes and more infrequent due to the larger excess pressures needed to drive magma to the surface.

8. Summary

We have explored the ways in which variations in the void space fraction and the proportion of SO 2 frost in surface volcanic deposits on Io influence the density structure of the lithosphere. Account was taken of the melting and downward migration of SO 2 fluid as surface deposits are progressively buried, compressed, and heated. We have also modeled the bulk densities of magmas rising from melt sources at great depth on the assumption that they contain various amounts of dissolved SO 2 which exsolves in response to the decreasing pressure as the magmas rise. Our main findings are as follows:

1. The variation with depth of the bulk density of the lithosphere (Figures. 1 a and 1 b) is mainly controlled by the void space fraction in the surface materials and depends much less strongly on the relative proportions of silicate rock and SO2 frost (or any other solid volatile with a comparable density) (Figure 4).

2. The bulk density of a rising magma depends mainly on the amount of any low-solubility volatile which it contains. Such volatiles begin to exsolve early in the rise of the magma (Figure 2) and so exert an influence on its density over a wide range of depths. The most likely candidate volatile on Io, whether present as juvenile material in the mantle (or a magma ocean), or as a fluid circulating in deep "hydrothermal" systems, is SO 2, and SO 2 is just such a low-solubility volatile. High-solubility volatiles (such as water if it were present) only influence magma densities at depths less than a very few kilometers unless they are present in very large amounts.

3. For our initial estimate of the surface void space volume fraction on Io (30 vol %), mafic magmas rising from deep sources are likely to be positively buoyant in a mafic lithosphere until they reach depths of-30 km (Figure 3). At these neutral buoyancy depths, magma reservoirs are likely to form. Significant excess pressures (-20 MPa) need to develop in such

deep reservoirs before magmas can be expelled upward from them far enough to reach the surface.

4. The depths to neutral buoyancy zones, and hence the depths at which magma reservoirs would be centered, decrease rapidly if the void space volume fraction is assumed to be <30 % (Figure 4). The optimum conditions to favor eruption of magmas to the surface involve combining the largest possible reservoir vertical extent (-8 km) with a shallow depth of reservoir roof (-1 km); these conditions would require a neutral buoyancy depth of-9 km which would require a surface void space volume fraction of --14 %.

5. If a very soluble volatile (such as H20) were present in Io's magmas in amounts exceeding -0.25 mass %, it would have an influence on the variation of magma bulk density with depth (Figure 5). By reducing the density of magma at shallow depths it would enhance the ability of magmas to erupt and would limit how close to the surface the roofs of magma reservoirs would be expected to be found.

6. If more silicic magmas were produced on Io, they would have a greater buoyancy in a mafic lithosphere than mafic magmas and would tend to form shallower magma reservoirs than those indicated above. Conversely, mafic magma rising through parts of the lithosphere dominated by silicic rocks would form deeper reservoirs.

7. If the deep interior of Io had contained significant amounts of CO2 in the past, and also, as seems likely, more SO 2 than at present, this would have allowed magma reservoirs to form at shallower depths than those present now. If significant amounts of H20 were present in the deep interior in the past, magma reservoirs would have had smaller vertical extents and hence

smaller volumes, leading to more frequent, and smaller volume, eruptions.

Notation

D thickness of a shell of Io's lithosphere, m. P lithostatic pressure inside Io, Pa. P,, lithostatic pressure at depth where SO 2 melts, Pa. P0 surface atmospheric pressure on Io, equal to -10 '•, Pa. Q universal gas constant, equal to 8.314, kJ kmol -•. R radius of Io, equal to 1815, km. T magma temperature, equal to 1900, K. Vs lithospheric volume fraction of solid SO2, equal to 0.1446. Vr lithospheric volume fraction of solid silicate rock, equal to

0.5554.

V m volume fraction of silicate rock after SO 2 melts. Vv fractional void space. V,, fractional void space at depth where SO 2 melts. V•o volume fraction of void space after SO2 melts. V•o fractional void space at the surface. d depth below Io's surface, m. g acceleration due to gravity, equal to 1.8, m s -2. m molecular mass of SO 2, equal to 64. rtdco2 solubility of CO 2 in magma, (mass fraction). rtdh2o solubility of H20 in magma, (mass fraction). rtdso2 solubility of SO 2 in magma, (mass fraction). neso2 amount of SO2 exsolved from melt, (mass fraction). rtm2 amount of SO2 available in the melt, (mass fraction).

bulk density of Io's lithosphere, kg m -3. bulk density of vesiculating magma, kg m '3. constant controlling compaction, equal to 1.18 x 10 '8, Pa '•. bulk density of Io, equal to 3570, kg m '3. density of magmatic liquid, equal to 3050, kg m -3. density of solid lithospheric rock, equal to 3360, kg m -3.

32,994 LEONE AND WILSON: DENSITY STRUCTURE OF IO'S LITHOSPHERE

Ps density of solid SO2, equal to 1434, kg m '3. Psa average density of SO2 in Io's lithosphere, equal to 1400,

kg m '3.

Acknowledgments. We thank Laszlo Keszthelyi, Rosaly Lopes- Gautier, Ashley G. Davies, John Spencer, James W. Head, and Vincenzo Cataldo for useful discussions on various aspects of this work and an anonymous reviewer for valuable comments which helped clarify parts of the text.

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(Received September 11, 2000; revised January 31, 2001; accepted February 19, 2001.)