New Estimates for the Volume of the Minoan Eruption

The minimum volume of the plinian fall phase is constrained at 1.2 km³ (pumice) or 0.24 km³ dense rock equivalent (DRE). For the distal ash-fall, considered to be the co-ignimbrite ash-fall phase, the maximum volume is calculated to be 37.0 km³ ash, or 15 km³ dense rock. Using Sparks and Huang's (1980) estimate of the ignimbrite: co-ignimbrite ash ratio of 54:46 this yields a total volume of magma and lithic fragments erupted during the plinian and ignimbrite phases of 39 km³. A revised mass balance calculation for the same data gives an ignimbrite:ash ratio of 41:59 and an erupted volume of 30 km³ of dense rock. This latter figure is considered to be the better estimate, and corresponds fairly closely with the present volume of the northern part of the caldera. Making a further correction for the extent of the plinian fall contribution to the distal ash of 2-15% gives a possible range of total erupted material of 27-30 km³, and a most probable figure of 28-29 km³.

INTRODUCTION

The volume of erupted material is a notoriously difficult parameter to calculate with any precision. There have been several attempts at constraining the volume of material erupted during the Minoan eruption, with results ranging variously from 10 to 60 cubic kilometres of pumice. This paper further improves on these constraints by making use of the observation that tephra fall and co-ignimbrite ash-fall deposits behave in a simple predictable fashion, with thickness and grain-size decaying exponentially away from the source (Pyle 1989).

This paper is intended mainly to demonstrate how erupted volumes and the partitioning of vitric, crystal and lithic clasts between various eruptive phases may realistically be estimated. These estimates, of necessity, must use available physical data, but represent an improvement on previous calculations by virtue of their comprehensive nature.

VOLUME ESTIMATES

A number of attempts have been made to calculate both the volume of the caldera which collapsed as a direct result of the evacuation of the Minoan magma chamber and the volume of the erupted products.

     Volume of caldera collapse:      Estimates of this depend critically on the extent to which the present caldera formed during the Minoan eruption. Ninkovich and Heezen (1965) first evaluated the present caldera area as 83 km², and the total volume as 60 km³. Heiken and McCoy (1984) presented evidence suggesting that only the northern half of the present-day crater collapsed during the eruption, and calculated this volume to be only 19 km³. These two estimates are best considered as end-members - reflecting the likely maximum and minimum volumes of collapse respectively. Pichler and Friedrich (1980) argued that the volume was closer to 34 km³. Recently, Friedrich et al. (1988) dated several shallow marine fossils found within the Minoan deposits. These grew in the caldera which formed during the 18 ka Cape Riva eruption (Druitt 1985) and confirm the existence of a water-filled depression at some point before the Minoan eruption, but provide no constraint on how much of this had been infilled by 3.5 ka.

By using the bathymetric data from Heiken and McCoy (1984), the volume of collapse may be constrained. There is no evidence to suggest the extent to which the northern part of the caldera collapsed, but at a maximum this was 500-700 metres - being the difference between the base of the present caldera and the inferred maximum elevation of the northern shield volcanoes. Constraining the area of collapse to be the part of the caldera with a depth approaching the present maximum of 380 m gives an available area of ~43 to 55 km², and a likely volume of order 22-39 km³. However, there is still considerable uncertainty in this figure, since it does not account for the volume of the various tuff deposits which may have filled the caldera during the eruption. Druitt and Francaviglia (1990) discuss this problem at greater length, and conclude that the collapse volume was of the order of 25 km³.

     Volume of erupted products:      Bond and Sparks (1976) estimated the volume of the plinian phase to be 3-5 km³ of pumice. This was revised by Watkins et al. (1978) to 5-8 km³. Both of these were essentially qualitative estimates. Watkins et al. also calculated more precisely the volume of ash deposited within the 0.5 cm isopach to be 28 km³, or 13 km³ dense rock equivalent. On the basis of a careful grain-size study of the same deep-sea cores, Sparks and Huang (1980) concluded that less than ten percent of this 28 km³ could be plinian fall material - giving a volume for this phase of < 3 km³. Pichler and Friedrich (1980), using an over-simplistic approximation, estimated the uncompacted volumes of the tephra fall and later phases as 1.3 km³ and 8.7 km³ respectively.

METHODS

The volume of tephra deposited during the Minoan eruption was calculated using methods outlined in Pyle (1989). By plotting isopach (contours of thickness) or isopleth (contours of grain-size) data on ln (thickness or grain-size)-square root (isopach or isopleth area) diagrams it is possible to ascertain whether or not the data decay exponentially. If this is the case (which holds for a wide range of airfall deposits) the data will fall along straight lines, and the volume of the deposit may be simply calculated using

V = 13.08 T_ob_t²                 [1]

where V is the volume, T_o is the extrapolated maximum thickness and b_t² (the 'thickness half-distance') is the average distance over which the deposit becomes half as thick. A similar plot for maximum clast size data allows calculation of 'clast half distances' which relate simply to the model eruption column heights (Carey and Sparks 1986; Pyle 1989).

A revised isopach map is presented in Fig. 1. This includes the data from Watkins et al. (1978), together with the more recent reports of Minoan tephra from Cape Fokas, Kos (Keller 1980), Trianda, Rhodes (Doumas and Papazoglou 1980) and Western Turkey (Sullivan 1988). These new data serve mainly to shift the probable dispersal axis towards the east. The point from Turkey, if representative, constrains (poorly) the northern side of the isopach map. This is also the most equivocal datum, but the coincidence of the age range (3100-7400 BP), the major element composition on an FeO-K₂O-CaO+MgO discriminant plot (Watkins et al. 1978) and the refractive index with known Minoan ejecta are all at least consistent with its deposition during the Bronze Age eruption. It is unlikely that the dispersal axis was much further north than drawn, because the major component of jetstream transport in these latitudes is easterly (Sparks et al. 1984).

The thickness data from Fig. 1 together with data from the best constrained isopach for the plinian phase from Bond and Sparks (1976) and Heiken and McCoy (1984) are presented in Table 1c and plotted in Fig. 1a. This plot shows a clear inflection - a feature commonly observed for eruptions where both fall-out tephra and co-ignimbrite ashes were deposited. This provides a complication, since the plinian fall component of the distal ash must be removed before the true co-ignimbrite ash volume may be calculated.

Three possible schemes for correction are shown schematically in Fig. 2b. In the first, the plinian is assumed to decay to zero thickness at the same rate as the proximal material. Such behaviour is observed elsewhere, hence this assumption can be justified. The volume calculated for the plinian fall in this fashion will be a minimum. The second and third corrections depend on the observations made on the deep sea ash cores by Sparks and Huang (1980) and Sparks et al. (1984). At distances of up to 300 km from the vent, the ash is stratified and had bimodal grain-size characteristics. The lowest few cm of the best-preserved cores tend to be coarser and richer in crystal and lithic clasts than the remainder of the core. Sparks et al. (1984) interpreted this as a distal portion of the phase 1 plinian or phase 2 phreatomagmatic fall-out, since it is known that crystal and lithic clasts are more depleted in the distal deposits of phases 3 and 4.

The most clear-cut example of this lower layer was found in core TR172-9, which had a basal thickness of 4 cm out of a total thickness of 35 cm. This is plotted and labelled in Fig. 2b, along with the correction schemes (1), (2) and (3). Correction (2) assumes that, after the point of inflection, the decay rate of the coarse mode of the distal ashes is greater than that of the fine mode, such that the plinian thickness decays with b_t = 15.6 km through the point TR172-9. This gives a realistic minimum volume for phase 1 if the coarse mode does represent plinian fall-out. (3) assumes that, at TR172-9, the coarse and fine modes are decaying at the same rate, and the inflection occurs at a thickness of about 8 cm. This will give a maximum volume for phase 1 fall-out. Since the fine and coarse modes of other ashes decay at different rates (e.g. Sparks and Huang 1980), correction (2) is likely to be more realistic.

Fig. 2c shows the first correction procedure used. Sector A represents simple plinian fall material, sufficiently close to the vent to be distinguished in the field from any co-ignimbrite ash-fall. Sector B represents the contribution to the thickness of the distal ashes of the plinian fall, and sector C represents the co-ignimbrite ash. The volumes may be calculated as below:

V(A+B), V(B+C) are calculated from equation [1], where T_o, T₁ are the respective maximum thicknesses (see Fig.2b), b_t = ln (2)/k_i.(π)^½ and k_i is the slope of the relevant part of the ln (T)-A^½ plot. The volume of sector A alone, from Pyle (1989) is given by

V(A) = T_o/k_o².exp (-k_oR) {2exp (k_oR) - k_o²R² - 2 k_oR - 2}

- T_l/k_l².exp (-k_lR) {2exp (k_lR) - k_l²R² - 2k_lR - 2}                     [2]

R is the distance in kilometres at which the break in slope occurs on the area plot. Similar calculations for corrections (2) and (3) are presented in Tables 2a and 2b. The fourth possible correction (Table 2b) is to use the estimate from Sparks and Huang that the volume proportion of the coarse mode in the cores is ≤ 10%. This gives a result very similar to correction (2).

RESULTS

The volumes of various segments calculated using the method described above are given in Table 2. These results constrain the volume of magma erupted during the plinian fall phase alone to 0.24 km³ minimum (induding 0.02 km³ of lithic fragments), and the magma volume contributing to the co-ignimbrite ash-fall to 15 km³ maximum, of which c. 0.7 km³ are lithic clasts (using component data from Sparks et al. 1984). The maximum likely plinian volume is ~1.0-1.2 km³ DRE, with this phase contributing 8-10% to the volume of the distal ashes. The influence of increasing density of the most distal ash-fall deposits is taken into account in Table 2b, where the range of DRE volumes calculated gives the extremes if (i) the whole plinian fall has a density of 500 kg/m³ and (ii) the distal ash component has a density of 800 kg/m³.

     The plinian phase:      The Minoan eruption began with a phase of plinian fall-out from a central vent. The height to which the eruptive column rose can be modelled from the grain-size and thickness parameters of the resulting deposit. The near-vent isopach and isopleths of maximum lithics and maximum pumice size are plotted in Fig. 3a and 3b.

The thickness data (Fig. 3a) have been taken from both Bond and Sparks (1976) and Heiken and McCoy (1984), and together these constrain very well the exponential decay of thickness and hence the volume. The thickness decays with a half-distance b_t of 3.3 km, and the deposit has an extrapolated maximum thickness of 8.5 m.

Measurement of lithic and pumice clast sizes (Fig. 3b) allows calculation of clast half-distance. For the pumice, b_c = 5.1, implying a total column height of 38 km. This can be regarded as an upper limit, since strong winds tend to expand pumice isopleths, leading to overestimated model-heights. The lithic data are not co-linear, possibly attributable to ballistic input of coarse clasts near to the vent. Using the 10 cm and 5 cm isopleths gives b_c = 4.4, or model column height of 36 km. These estimates agree well with the modelling of Carey and Sigurdsson (1989) who also derived a column height of 36 km. Wilson (1978) used an earlier model to calculate a column height of 29 km.

Eruption plumes are sustained only by the input of fresh material and consequently there is a simple relationship between the magma discharge rate and the plume height. For the Minoan eruption, the discharge rate is estimated to have reached a peak of between 2.1 x 10⁸ (Wilson 1978) and 2.5 x 10⁸ kg/s (Carey and Sigurdsson 1989). Since the mass of the plinian phase is now estimated to be 1.0 - 4.7 x 10¹² kg, this event would have lasted for 1-5 hours. The reverse grading of the deposit implies, however, that since the peak discharge rate was not sustained for the whole duration, these times are minima. Wilson (1978; 1980) argued on this basis that the duration was between 8 and 20-40 hours. The most probable timescale is of order 1.5-6 hours.

THE CO-IGNIMBRITE ASH-FALL

The phreatomagmatic and ignimbrite-forming phases (3 and 4) also involved ash fall-out. Glass shards elutriated during transport and deposition of these phases were dispersed by the prevailing winds. Sparks and Huang (1980) recognized the importance of this style of ash deposition, discriminating it from the plinian fall-out in distal deep-sea cores on the basis of its finer grain-size mode at any location. The isopach data plotted in Fig. 2a demonstrate clearly how widely dispersed this ash was. With a thickness half-distance b_t of 62 km and a thickness at source of only 75 cm, it would have formed a uniform ash-blanket across thousands of square kilometres, and has a volume of 37 km³. This is used in the next section to place limits on the erupted volume of the ignimbrites which generated this fine ash.

MASS-BALANCE CONSTRAINTS

Walker (1972) demonstrated that, by preferential loss of the low density glass fraction, ignimbrites tend to concentrate crystals relative to the original magma. Thus ignimbrites should be accompanied by crystal-poor ashes which may themselves account for equivalent volumes of magma. Sparks and Walker (1977) calculated ignimbrite:co-ignimbrite ash ratios by using simple mass-balance to quantify crystal partitioning in the <2 mm fraction between ignimbrites and magma. This method was applied to the Minoan eruption by Sparks and Huang (1980), who estimated the ignimbrite:ash ratio to be 54:46. Their calculation did not, however, explicitly allow for the crystal content of the co-ignimbrite ashes.

The following is a reassessment of the mass balance equations which leads to a different result from that previously obtained:

Consider a magma mass M which fragments so that all pumices coarser than 2 mm retain the original magmatic crystal:glass ratio, and all pumices <2 mm are free of crystals. (This is the same assumption used elsewhere.) This material erupts to yield a crystal-rich ignimbrite of total mass I and crystal-depleted ash fall of total mass A (Fig. 4). The ash fall is everywhere <2 mm grain-size, while the ignimbrite has a weight fraction k finer than 2 mm. The important point here is that the free crystals can only have been derived from the magma that fragmented to a grain-size of <2 mm. This mass is denoted M_f, where

 M_f = M - (1-k)I                                                         [3]

For the <2 mm fraction the material balance gives

M_f = kI + A                                                               [4]

Dividing through by M_f, setting A/M_f to equal θ and kI/M_f to (1-θ) gives the crystal balance relation

C_m= (1-θ) C_i +  θ C_a                                                 [5]

where C_m, C_i and C_a are respectively the crystal weight fractions of the magma, lithic-free ignimbrite and lithic-free ash fall. Rearranging this yields an expression for θ

θ = {C_i - C_m} / {C_i - C_a}                                           [6]

Hence if the ash fall mass A can be independently assessed, the mass of fragmented magma is given by

M_f = A / θ                                                                  [7]

the ignimbrite mass by

I = M_f (1 - θ) / k                                                        [8]

and the ignimbrite mass as a proportion of the total magma erupted by

I% = 100 (1 - θ) / (1 + [k - 1] θ)                                 [9]

Using Sparks and Huang's (1980) data for the Minoan eruption of C_m= 0.102, C_i = 0.233 (lithic free) and C_a= 0.0335, and setting k equal to 0.75 (Sparks and Walker 1977) gives θ = 0.66, and an ignimbrite:ash ratio of 41:59. This is substantially different from the 54:46 ratio of Sparks and Huang, and is considered to be more correct since it properly accounts for the crystal partitioning between the ignimbrite and ash cloud.

The full results of the calculations are presented in Table 3, where they are compared with the results using Sparks and Huang's ratio. The masses of accidental blocks and fragments of old lava erupted at the same time are calculated from the estimated average lithic contents of the distal ash (~5 wt%, Sparks et al. 1984) ignimbrite (-30 wt%) and plinian fall (8 wt%).

The influence of uncertainty in tephra bulk volumes and magma densities are shown in 3b, where two sets of extreme results are tabulated. The columns 1a and 1b are for the favoured scenario with a magma density of 2500 kg/m³ and proximal tephra fall of 500 kg/m³. The other two columns assume a magma density of 2200 kg/m³. The results in each case are not substantially different: an improved calculation (taking account of subtle density changes with grain-size and so on) will probably deviate by only a few percent from the estimate in column a1.

For these partition calculations there are very few published comparative data. Estimates of k for several ignimbrites range from 0.6-0.8 (Sparks and Walker 1977), with unknown uncertainty. However, these calculations are fairly robust in that variations in k and C_i/C_m tend to cancel out: underestimating one parameter leads to an overestimate in the other, and the net result is only a small shift in estimate of I%. Partitioning of crystals in the distal ashes always leads to a reduction of I%: even for C_a = 0, I% for the Minoan eruption is less than 50%.

These new calculations suggest that the Minoan eruption discharged ~24 km³ of magma during the main plinian and ignimbrite phases, together with 4.8 km³ of lithic ejecta. The total likely volume for the whole eruption is ≤ 30 km³, which is 30% lower than implied by the Sparks and Huang (1980) ignimbrite:ash ratio.

A further variable that must be accounted for is the contribution of the plinian and phreatoplinian phases to the distal ash-fall. Four possible correction schemes have been outlined above, giving likely plinian fall volumes of less than 15% of the total volume of the distal ash. Fig. 5 summarizes the effects of varying amounts of phases 1 and 2 adding to the total ash fall. Simply, as the plinian contribution (P%) rises, the total volume V of the erupted products falls, since the ignimbrite + ash volume diminishes faster than the increase in plinian volume. The relation is

V = 29 - 0.14 P                                                  [10]

for V in km³ and P in percent. (Note that this does not include the <1 km² of material on the islands from phase 2 which may not have contributed to the distal ash fall.) From Fig. 5 it is clear that even in the most improbable case where the plinian accounted for 20% of the distal ash, the total volume erupted would still exceed 26 km³. The most likely scenario is that P = 8-10%, and V ~28 km³, The earlier calculation of the volume of the northern part of the caldera suggests that the volume erupted could have been accommodated by simple caldera collapse, but further discussion of this is beyond the scope of this contribution.

CONCLUSIONS

These new estimates for the volume of the Minoan eruption indicate that the total volume of collapse required is of the order of 27-30 km³, and most probably 28-29 km³. The partition or this volume between erupted magma and reworked lithics is now constrained at 5:1. The co-ignimbrite ashes generated account for 59% of the total magma erupted during the ash-flow phase. These data add further weight to the conclusion that the present day caldera was, at least in part, already extant at the time of the eruption, since these volumes can be plausibly accommodated by only partial collapse of the existing crater.

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