How often does a Minoan Eruption Occur?

The c. 3600 BP eruption of Thera ejected some 30 km³ of magma. Based on present data, both historic and prehistoric, the average recurrence interval on a world-wide basis for an explosive eruption as large or larger than the Minoan eruption of Thera is approximately 300 years.

As more calderas formed by explosion and collapse are studied and their associated ejecta are carefully mapped and dated, better estimates of the average recurrence time of large explosive eruptions on both a worldwide and regional basis will be forthcoming.

INTRODUCTION

The past is a key to the future. This paper estimates how often a Minoan-size eruption of Thera occurs on a global basis, based on two historical methods: 1) the recorded eruptions of the past two hundred years; and 2) the distribution, size and geological history of large calderas associated with explosive eruptions that have occurred during the last 1,000,000 years. Method 1) indicates 200 years for an average global recurrence of eruptions as large or larger than the Minoan eruption; method 2) indicates 330 years.

Two important databases have recently been published that significantly improve the statistical basis of these estimates: McClelland et al. (1989) and Newhall and Dzurisin (1988).

It is a common observation that large volcanic eruptions occur less frequently than small ones. This is also true of many other natural phenomena such as earthquakes, landslides, and floods. To make this generality useful for forecasting, it must be quantified. This paper is a step in that direction for large explosive volcanic eruptions.

THE PAST 200 YEARS

Fig. 1 shows the graphical relationship between the number of recorded explosive eruptions during the past 200 years and past 10 years, and their magnitudes. VEI is the abbreviation for Volcanic Explosivity Index (Newhall and Self 1982) which is a measure of the size of volcanic eruptions. Each number in the VEI scale represents a 10-fold increase in the volume of pyroclastic material ejected. This logarithmic increase makes the VEI scale similar in concept to the Richter magnitude scale for earthquakes.

Fig. 1 indicates that there is a linear log-log relationship between the frequency of explosive eruptions of VEI 2 to 6 and their magnitudes with a negative slope; each increase in magnitude decreases the frequency by a factor of 5. For example, eruptions of the scale of Ruiz Volcano in Colombia in 1985 (VEI 3, 10⁷ m³ of pyroclastics) will occur on a global basis about 2 to 3 times per year. Eruptions similar to Galunggung in Indonesia in 1982 (VEI 4) will occur about once every 2 years, and those similar to Mount St. Helens in 1980 (VEI 5) about once every 10 years.

Five eruptions of VEI 6 or larger have occurred in the past 200 years. Those in the size of the 1883 Krakatau eruption (VEI 6.3, 18 km³ of pyroclastics) or larger would be expected to occur on average about once every 80 years. The Tambora eruption in 1815 is the only VEI 7 during the past 200 years. A single event does not provide useful statistics; thus it becomes important to look at the prehistoric record of explosive eruptions that were as large or larger than the Minoan eruption of Thera.

LARGE CALDERAS OF THE WORLD

Table I is a listing of large calderas of the world that have formed during the last 2,000,000 years. The 125 calderas listed in regions of subduction-related volcanoes and rift or hot-spot volcanoes in continental settings are condensed from Newhall and Dzurisin (1988). Because they were interested in 'restless calderas' - those that have had historic eruptions, seismic swarms or other signs of subsurface activity - they did not describe the 84 other known but 'non-restless' calderas in the same regions. No equivalent database exists for these other calderas.

Columns 2, 3 and 4 are condensed directly from Newhall and Dzurisin, as is much of column 5. Column 6 (Caldera volume) is estimated to the nearest 10 km³ using the formula πr²h, where r is an average radius and h= 1 km (see assumption 3 below). Column 7 is an estimate of the VEI of the eruption or eruptions that formed the caldera (see assumptions below). The numbers that follow the name of a region are first the number of calderas listed (the restless ones) and the second the number in that region not listed (the non-restless ones). For example, MEDITERRANEAN 10/2 means that 10 restless calderas in that region are listed and that there are 2 other large calderas of Quaternary age in that region not in the listing. In column 5, numbers like P80 and M16-39 mean 80 km³ of pyroclastics were deposited from the eruption of the Phlegraean Fields 35,000 years ago, and that 16 to 39 km³ of magma (4 different estimates: Heiken and McCoy 1984; Druitt 1984; Pyle 1990; Sigurdsson and Carey 1990) were erupted during the Minoan eruption of Thera.

Only about 20% of the calderas listed have been carefully mapped and studied by geologists. Therefore, to estimate the overall frequency and magnitude of large prehistoric explosive eruptions several assumptions and calculations must be made, as follows:

1. The ratio of bulk volume of pyroclastic deposits to the volume of magma from which it was formed is 2.5. This expansion is caused by vesiculation and the porosity between fragments.
2. The volume of a caldera formed by subsidence related to an explosive eruption is roughly equal to the volume of magma erupted. (This is not valid for the less-explosive Icelandic and Hawaiian volcanoes, so oceanic rift and hot-spot volcanoes are not included in Table I.) At 31 calderas listed in Table I, there are estimates of the volume of pyroclastic deposits or magma erupted (column 5). When these are compared to the calculated volumes in column 6, the average result is: caldera volume 388 km³; pyroclastic deposits 700 km³; and magma volume 280 km³. Thus the calculated caldera volume appears in most cases to overestimate the magma volume. Many calderas have undergone multiple eruptions and collapses which may partly explain this discrepancy.
3. The amount of caldera subsidence during a major eruption is roughly 1 km regardless of the diameter of the caldera. The caldera volumes in the 6th column of Table I are estimated to the nearest 10 km³ using this assumption.
4. The estimated VEI (column 7, Table I) is based on either the volume of pyroclastic material, if known, or on an assumed pyroclastic volume (estimated magma volume x 2.5) based on caldera diameter. Many large calderas have had 2 or more major eruptions over long spans of time. In these cases the estimated VEIs are chosen so that the sum of their pyroclastic volumes roughly equals 2 times the caldera volume.
5. To obtain the approximate ages of undated eruptions (those with no data in column 4, Table I) the distribution of their ages is assumed to be the same as the age distribution of the dated eruptions.
6. The VEIs and the ages of the 84 other large calderas are assumed to have the same distribution as the 125 calderas for which data is available in Table I.
7. There are few or no unknown calderas besides those in Table I with diameters greater than 7 km that have been formed in the last 100,000 years, and there are no unknown calderas with diameters greater than 24 km that have formed in the last million years.

The expected numbers of VEI 7 and 8 eruptions in Table II, columns (2) are obtained by using these assumptions and calculations. For example, there are 78 VEI 7 eruptions in column 7 of Table I. One of these occurred during the last 1,000 years; 11 during the interval 1,000 to 10,000 years; 33 during the interval 10,000 to 100,000 years; 20 during the interval 100,000 to 1,000,000 years; and 13 are of unknown but presumably of Quaternary age. By assumption 5, two of these undated eruptions are assigned a 1,000 to 10,000 year age; 7 a 10,000 to 100,000 year age; and 4 a 100,000 to 1,000,000 year age. By assumption 6, the other 84 'non-restless' calderas are similarly assigned to sets with various VEI ranks and ages.

The totals of these known and assigned eruptions are listed in columns (2) in Table II. Comparison of columns (1) and (2) supports the conclusion that the occurrence of one VEI 7 eruption during the past 200 years is not statistically significant, and that linear extrapolation of Fig. 1 to VEI 8 eruptions is not valid. VEI 9 eruptions (≥ 10,000 km³) probably occur only very rarely, if at all, even over long periods of geological time. This is not unexpected. There are physical limits to the size of magma chambers just as there are limits to the size of earthquake faults. Magnitude 10 earthquakes are not known and are not thought to occur.

Fig. 2 is an eruption frequency versus magnitude graph for a period of 10,000 years using data from Fig. 1 for VEI 5 and 6 eruptions and from Table II (2) for VEI 7 and 8 eruptions. Note that the slope of the logarithmic relation between frequency and magnitude steepens to -1 between VEI 6 and 7, and to -10 between VEI 7 and 8. The negative slope should become infinite beyond the physical size limit of explosive volcanic eruptions.

RECURRENCE INTERVALS

By using Fig. 1 and 2 the recurrence interval of any explosive eruption between VEI 2 and 8 can easily be estimated. For example, the volume of magma of the Minoan eruption of Thera is estimated to be 30 km³; this translates to a bulk pyroclastic volume of 75 km³ (VEI 6.9). In Fig. 1, this magnitude eruption is located at the intercept of the 200-year line with the bottom horizontal axis of the graph; thus the estimated recurrence interval for this size eruption or larger on a global basis is 200 years. In Fig. 2, a VEI 6.9 intercepts the 10,000-year line at 30 eruptions. Dividing this number into 10,000 gives an average recurrence time of approximately 330 years.

The numbers in Table II also show some interesting implications about calderas related to VEI 7 eruptions. In Table I the ratio between the number (2) of these calderas expected to form in 1,000 years and the number (22) expected in 10,000 years indicates that the rate of occurrence for eruptions of this magnitude and larger has not changed during the past 10,000 years. However, when the time period is extended to 100,000 and 1,000,000 years the number of VEI 7 and greater eruptions are much smaller than would be expected from a steady rate of occurrence. Another interpretation is that more than 50% of VEI 7 calderas are obliterated by subsequent geological processes during 100,000 years, and that only about 5 or 6% survive for 1,000,000 years. Of course, both interpretations could be partially correct. Some combination of reduced global volcanic activity prior to 10,000 years ago and obliteration by filling, re-eruption in the same site, or erosion, is a possible explanation. My subjective judgement prefers the obliteration hypothesis.

As more calderas and their associated eruption products are carefully mapped and dated, estimates of the average recurrence intervals versus VEI magnitude of large scale explosive eruptions will be refined. Based on present data, both historic and prehistoric, I think 300 years is the approximate average recurrence interval on a world-wide basis for explosive eruptions as large or larger than the Minoan eruption of Thera. Extremely large eruptions, equal to or exceeding VEI 8, occur much less often; Fig. 2 indicates their average, world-wide recurrence interval is 50,000 years. The latest known eruption of this scale occurred in Lake Toba in Sumatra, Indonesia, 75,000 years ago. It is difficult even to imagine an eruption of that size, which expelled an estimated 2800 km³ of magma, nearly 100 times the amount erupted at Thera some 3,600 years ago.

------------------------------------------------

-----------------------------------------------------