Distribution and Eruptive Volume of Aso-4 Pyroclastic Density Current and Tephra Fall Deposits, Japan: A M8 Super-Eruption

Estimations of the distribution and eruptive volume of large-scale pyroclastic density current (PDCs) and tephra fall deposits are essential for evaluation of the affected area, long-term volcanic hazards assessments, volcanic activity, and geophysical and petrological quantitative analysis at caldera volcanoes. For this study, the original distributions and eruptive volumes of large-scale PDC (up to 166 km runout distance) and tephra fall deposits derived from the last 87–89 ka caldera-forming eruption (named Aso-4) of Aso volcano in Japan were reevaluated. The original distributions and volumes of PDC deposits just after the eruption were estimated using 3,600 data from geological maps, published research papers, and borehole thickness. The original distributions and volumes of tephra falls were estimated from new isopach maps based on thickness and distribution data of submarine, lacustrine, and subaerial tephra fall deposits. The estimated original volume of the Aso-4 PDC deposits is 340–935 km3 (5.6–14.8 × 1014 kg). The estimated original volume of the Aso-4 tephra fall deposit is 590–920 km3 (6.0–9.3 × 1014 kg). The total eruptive volume of the Aso-4 eruption was 930–1,860 km3 (1.2–2.4 × 1015 kg). This estimation result is about 1.5 to 3 times larger than the previous estimation (>600 km3). Thus, the Aso-4 eruption is now defined as a M8.1–8.4 (VEI8) super-eruption. The Aso-4 results to be the largest eruption in Japan and the 2nd largest eruption in the world (after the 74 ka Toba eruption) in the last 100 ka.


INTRODUCTION
Accurate determinations of the eruptive volumes of large-scale caldera-forming eruptions provide an essential parameter for assessing long-term eruption records, eruption activity evaluations, and quantitative geophysical and petrological investigations. The eruptive volume is also used for developing reliable volume vs. time diagrams and volcanic hazard assessments. Recently, several studies to estimate the eruptive volume of tephra falls derived from large-scale volcanic eruptions were made (e.g., Costa et al., 2014;Kandlbauer and Sparks, 2014). Furthermore, a large number of studies have been published to estimate the eruptive volume of tephra fall deposits (e.g., Pyle, 1989Pyle, , 1995Fierstein and Nathenson, 1992;Legros, 2000;Bonadonna and Houghton, 2005;Sulpizio, 2005;Bonadonna and Costa, 2012;Engwell et al., 2013). However, relatively few studies have reported highresolution eruptive volume estimates of large-scale calderaforming pyroclastic density current (PDC) deposits (e.g., Cook et al., 2016).
The 87-89 ka Aso-4 eruption is the largest of the 4 major caldera-forming eruptions from Aso caldera. It is also considered to be one of the largest eruptions in Japan in the last 1 Ma (e.g., Hayakawa, 1995). Here we estimated the original distributions and eruptive volume of the large-scale Aso-4 PDC deposit, based on more than 3,600 boreholes, topography, and outcrop data with a 7 km × 5.5 km mesh interval. The eruptive volume of the co-ignimbrite ash fall deposit derived from the Aso-4 eruption was also estimated using new isopach maps based on thickness data from about 70 locations, including submarine and lacustrine sample data.
The Aso-4A PDC deposits consist of <100 m-thick, densely to partially welded and non-welded, poorly sorted, and massive ignimbrite containing relatively large amounts of pumice lapilli and blocks (Figures 2, 3a,b). The Aso-4A PDC deposits are normally massive, but flow unit boundaries are sometimes observed in a few-meters interval, suggesting that this consists of >10-20 flow units. The upper non-welded facies are sometimes eroded. The lower part of the ignimbrite consists of nonwelded grayish white to gray-colored matrix and pumice block and lapilli. The layer 2a (Sparks et al., 1973) is sometimes developed at the base of the non-welded facies. Breccia facies are sometimes developed at the bottom of the Aso-4A PDC deposit (Figures 2, 3a). The breccia facies consist of lithic-rich matrix and boulders, blocks, and lapilli-size dense rocks with a small amount of pumice lapilli. Tuff breccia blocks and boulders are sometimes included in the breccia facies. The densely welded facies consist of a dark gray matrix and black fiamme-rich block and lapilli (Figures 2, 3d). The size of the fiamme is >5 cm (sometimes >20-50 cm). A devitrification zone is developed at the lower part of the welded facies. The partially welded facies consist of gray to dark gray matrix and grayish white flattened pumice blocks and lapilli (Figure 2). The welded facies show 1-2 m wide columnar joints (Figure 3c). The non-welded facies consist of a grayish white to gray matrix and 15-40 vol. % of pumice blocks and lapilli (Figures 2, 3b). The pumice blocks and lapilli are gray to white with tube-type vesicles and are usually <20 cm in size. The matrix consists of fine glassy ash and <4 mm-size crystal fragments. The Aso-4A PDC deposits are the FIGURE 1 | Distribution of current Aso-4 PDC deposit exposures (orange-colored part) and Aso caldera (red line). Circles on the map indicate locations to measure the thickness of PDC deposits based on outcrops (blue circle), borehole (green circle), and topography (yellow circle) sites. The outcrop located at 166 km from the source is shown. The tephra fall outcrop locations at Omachi City, Nagano Prefecture, Noshiro City, Akita Prefecture, and Abashiri City, Hokkaido, are shown in the inset map (upper left corner).
Frontiers in Earth Science | www.frontiersin.org most voluminous of the Aso-4 units. The Aso-4T PDC deposits are relatively thin and distributed locally compared with the Aso-4A PDC deposits (Figure 2). The Aso-4T deposits are nonwelded and consist of orange-gray matrix and yellowish-orange to reddish-orange-colored highly vesicular pumice lapilli. The size of the pumice clasts is usually less than a few cm. A relatively small amount of <1 cm-size lithic clasts are contained. The Aso-4T unit traveled as far as 166 km from the source. The upper Aso-4B deposits are densely welded and consist of dark-gray matrix and black-colored fiamme block and lapilli (Figure 2). The thickness of the Aso-4 PDC deposits decreases in the distal facies (Figure 3e). The densely welded ca. 100-400 m-thick intracaldera Aso-4 PDC deposits are found from the borehole samples at −800 to −1000 m a.s.l. within the steep-sided low-gravity zone (Hoshizumi et al., 1997;Komazawa, 1995;NEDO, 1995).The measured densities of Aso-4 PDC welded facies are 1,690, and 1,810 (partially welded), 2,240, 2,260, and 2,270 (densely welded) kg/m 3 (mean is about 2,000 kg/m 3 ) and the non-welded facies is about 1,100 kg/m 3 . Published values for the measured densities of Aso-4 PDC welded facies range from 1,500-2,450 kg/m 3 (mean is about 2000 kg/m 3 ; Suzuki and Ono, 1963;Suzuki, 1970;Urai and Tsu, 1986;Yamaguchi et al., 2000) and the non-welded facies is about 1,100 kg/m 3 (e.g., Suzuki, 1970). The degree of welding of Aso-4 PDC deposits ranges between welded rank II (1,250-1,650 kg/m 3 ) and VI (>2,300 kg/m 3 ), according to the classification of Quane and Russell (2005).

Distribution and Thickness Estimation of Aso-4 PDC Deposits
The distribution of the current exposure of Aso-4 PDC deposits (Figures 1, 4) was compiled based on geological maps, such as 1:50,000 and 1:200,000 Geological Maps published by Geological Survey of Japan (GSJ), 1:50,000 Surface Geological Maps published by Ministry of Land, Infrastructure and Tourism (MLIT), and maps in published papers. The distribution of the current exposure of Aso-4 PDC deposits was traced using GIS software. The Aso-4 PDC distributions are not shown in areas that have been covered subsequently by thick tephra fall deposits (e.g., the eastern part of Aso caldera) and the younger Kuju volcanic area (30 km NE of Aso caldera).
The original distribution of Aso-4 PDC deposits just after the eruption was estimated by integrating observations and data from current distributions, topographic maps, published papers, and boreholes (Figures 4-7). The distal runout distribution limit of Aso-4 PDC deposits in the sea area is assumed to be oval in shape (Machida et al., 1985;Machida and Arai, 2003), as shown in Figure 5. The maximum runout distances and apparent friction coefficient (H/L ratio) of Aso-4 PDC deposits are different from the directions, according to the topography of the source region and their pass. For example, the maximum distances of the Aso-4 PDC deposits from the source depend on direction: 166 km (NNE direction), 123 km (WNW), 84 km (SSW), 97 km (SSE), and 80 km (E). Especially, SE to SW side of the Aso caldera is high mountain areas, where the Aso-4 PDC deposits were accumulated within the basins and valleys. Therefore, we think that the oval shape is more reasonable than circular. The Aso-4 PDC deposits were considered to fill the low-land area and valleys. The Aso-4 PDC deposits were assumed to be transferred by turbidity currents and traveled further along the submarine bottom surface topography. However, we considered the Aso-4 PDC that we infer traveled on the surface of the sea, ignoring the submarine processes after entering into submarine seawater. The thin ignimbrite veneer deposits (Walker, 1981) were locally FIGURE 4 | Distribution of Aso-4 PDC deposits and thickness data. The thickness values of the deposits are shown in meters. Circles and squares on the map indicate locations to measure the thickness of PDC deposits based on outcrops (blue), borehole (green), and topography (yellow) sites. The circle marks are non-welded, and the square marks are welded points. The Geospatial Information Authority of Japan (GSI) Tile Map (English) is used as the base map. preserved, but not considered on this map because the accurate mapping of such volumetrically minor material was not possible.
The thickness of the Aso-4 PDC deposits was measured using 1:200,000 Geological Maps and 1:50,000 Geological Maps published by GSJ, 1:50,000 Surface Geological Maps published by MLIT, borehole data KuniJiban Database provided by MLIT (MLIT, 2020) and Geo Station Database provided by the National Research Institute for Earth Science and Disaster Prevention (NIED) (NIED, 2020). Location, altitude, and depth of the top and bottom of the deposits in subsurface boreholes and welded (1,070 points) and non-welded (2,541 points) data were compiled (3,611 points in total; Figures 1, 4-7). Partially welded facies are classified as non-welded in our compilation. Thickness data at outcrops obtained from published papers were used (blue circles in Figures 1, 4, 5, 7). Thickness data were measured from the top and bottom depth of the Aso-4 deposits on the KuniJiban and Geo Station Databases (green circles in Figures 1, 4-7; accuracy is about 10 cm). The thickness data were also measured from upper-limit and lower-limit altitudes on geological maps at ignimbrite plateau and measurable points (yellow circles in Figures 1, 4-7). The thickness of the deposits within the caldera (118-407 m) was also measured using borehole data (Hoshizumi et al., 1997;Komazawa, 1995;NEDO, 1995). The thickness data were compiled in an excel spreadsheet and plotted using QGIS software.

Volume Estimation of Aso-4 PDC Deposits
The thickness data were analyzed within a 7 km × 5.5 km mesh grid (Supplementary Table S1). The maximum (Figure 6a), minimum (Figure 6b), and average (mean; Figure 6c) of each grid cell was calculated and plotted (purple-colored numbers values in Figure 6). For example, the 3rd cell from the right in the middle of Figure 6 contains 6 thickness data of non-welded facies (48.9, 55.2, 34, 37, 9, and 50 m). Hence, the maximum, minimum, and average (mean) thickness are 55.2 m, 9 m, and ca. 39 m, respectively. The thickness was plotted for non-welded facies (Figures 6, 7b) and also welded facies (Figure 7a). The grid cells that contain no thickness data were estimated using the ordinary kriging method (geospatial interpolation; Davis, 1986;Yamamoto, 2000). When the thickness value became <0 m, the estimated thickness was assigned to be 0 m. In the sea area, the marginal thickness was set at 0 m (right-lower corner of   1 | Results of the area and volume estimation of Aso-4 PDC deposit (density of the non-welded and unclassified facies is 1,100 kg/m 3 , welded facies is 2,000 kg/m 3 , and dense rock is 2,500 kg/m 3 ).  Figure 7b), and the thickness of the PDC deposits (above the sea surface) was calculated using the ordinary kriging method. The thickness tends to decrease radially from the source toward the marginal rim in the sea area. The thickness of the deposits in the subaerial area changes according to the local topography. Local thickening of the PDC deposits is observed at the slope change or basin areas (such as the upper right of Figure 6, middle left and lower right of Figure 7a, and middle left of Figure 7b). The occupied area of the estimated original Aso-4 PDC deposit (i.e., just after the deposition; the light-pink colored area in Figures 6, 7) within each 7 km × 5.5 km grid cell was calculated using QGIS software. The maximum, minimum, and average volumes of each grid cell were calculated by multiplying the estimated thickness and area of the Aso-4 PDC deposit (volumes of non-welded and welded facies were calculated, separately). The total estimated bulk volume (km 3 ) was calculated by summing up all estimated volumes of grid cells. The DRE volume ( Table 1) was calculated from the ratio between the average non-welded density (1,100 kg/m 3 ) and dense rock density (2,500 kg/m 3 ) and also the ratio between the average welded density (2,000 kg/m 3 ) and dense rock density (2,500 kg/m 3 ).
The results of the area and volume estimations of Aso-4 PDC deposits are summarized in Table 1. The current exposure area of the Aso-4 PDC deposit is about 1,000 km 2 . The estimated original distribution area of the outflow Aso-4 PDC deposit (just after deposition) is about 34,000 km 2 . Total volumes of the current exposure of Aso-4 PDC deposits are 13-54 km 3 in bulk (8-30 km 3 in DRE). The estimated original volumes of Aso-4 PDC outflow deposits are 250-720 km 3 (170-470 km 3 in DRE). The estimated original volumes of intracaldera Aso-4 PDC deposits are 90-220 km 3 (58-120 in DRE). The total estimated original volumes of Aso-4 PDC deposit just after deposition are 335-940 km 3 (225-590 km 3 in DRE; 5.6-14.8 × 10 14 kg) ( Table 1).

Distribution Estimation of Aso-4 Tephra Fall Deposits
Thickness and location data of Aso-4 tephra fall deposits are recompiled from prior studies, which comprise data for 71 locations of outcrops, lacustrine, submarine, and on-land cores and boreholes (Supplementary Table S2). The thickness data were plotted using ArcGIS software, and isopach maps (1, 2, 4, 8, 16, 32, 64, and 128 cm) of Aso-4 tephra deposits were made (Figure 8). The thickness of the tephra fall deposit in Eastern Hokkaido is up to 15 cm (Figure 3f). This value is relatively high compared to the Honshu area (probably due to local wind effects). Hence, two types of isopach maps were made: (1) Maximum case (Figure 8a), using the thickness data of Eastern Hokkaido and assuming erosion in the Honshu area; and (2) Minimum case (Figure 8b), for which the thickness data of Eastern Hokkaido were considered to be influenced by local wind disturbance and ignored for drawing.

Volume Estimation of Aso-4 Tephra Fall Deposits
The area of each isopach contour was calculated using ArcGIS software, and the volumes of Aso-4 tephra fall deposits were estimated using the segment integration method (Takarada et al., 2001(Takarada et al., , 2016. In the maximum case, the volume was calculated by integrating 3 subdivisions (Figure 8a; subdivided at 16 and 64 cm isopachs). In each segment, the data were plotted approximately on a straight line using the least square method. The volume was calculated for the area between the caldera rim (5.3 × 10 2 km 2 ) and the distal limit, for a total area of 10 8 km 2 (0.1 mm in thickness). The thickness of the tephra fall deposit at the caldera rim was assumed at 300 cm from the extrapolation of the trend of 64 and 128 cm isopach data. The average density of the tephra fall deposit was estimated at about 1,000 kg/m 3 . The estimated results were 400 km 3 (4.0 × 10 14 kg) in the area of the distal region (<16 cm isopach data area), 470 km 3 (4.7 × 10 14 kg) in the medial region (between 16 and 64 cm data area), and 47 km 3 (4.7 × 10 13 kg) in the area of the proximal region (between 64 and 300 cm data area). The total estimated eruptive mass of the Aso-4 tephra deposit was 920 km 3 (370 km 3 in DRE; 9.2 × 10 14 kg).

Aso-4 PDC Deposit Distributions and Volume
The original distributions of Aso-4 PDC deposits just after the emplacement were made based on the current distribution of the deposits, borehole data, and topographic data (Figures 5-7). This original estimated distribution is one of the most detailed maps of the Aso-4 PDC deposit, which shows the affected areas in this region. The current exposure area of the Aso-4 PDC deposit is about 1,000 km 2 ( Table 1). The estimated original distribution area of the outflow Aso-4 PDC deposit (just after the emplacement) is about 34,000 km 2 . Therefore, the area of estimated distribution is 34 times larger than the current deposit exposure. Most of the deposits were considered to be eroded, as observed for PDC deposits after the eruption of Pinatubo in 1991 (e.g., Major et al., 1996). This new map provides essential information for considering the affected area of the Aso-4 PDC and evaluating potential future eruption scenarios at Aso caldera. We assumed an oval shape for the distal limit of the Aso-4 PDC deposit, as shown in Machida et al. (1985) and Machida and Arai (2003). The estimation of the distal limit of the large-scale PDC is relatively difficult, especially in the sea area. Numerical simulations, such as the energy cone model (Malin and Sheridan, 1982), are one of the solutions.
Maximum, minimum, and average thickness data within each 7 km × 5.5 km mesh grid were calculated based on 3,611 thickness point data (Figures 6, 7). The total estimated eruptive volume of the Aso-4 PDC deposits is 940 km 3 (590 km 3 DRE in maximum), 335 km 3 (225 km 3 DRE in minimum), and 640 km 3 (410 km 3 DRE in average) ( Table 1). This result is about 1.7-4.7 times larger than the minimum value of the previous estimation at >200 km 3 (Machida and Arai, 2003). The main reason for the larger revised value is that this study was based on a much more detailed estimation of distributions and thicknesses data, including data not exposed on the surface (borehole data). This estimation method used a 7 km × 5.5 km mesh grid, making it one of the most detailed volume estimations of large-scale PDC deposits. This method can be used to accurately estimate the volumes of other caldera-forming large-scale PDC deposits around the world.
Volume estimation method uncertainties are herein considered. Factors that may have increased the upper limit bound are as follows. (1) The upper part of Aso-4 PDC deposits are sometimes eroded due to weathering since 87-89 ka, and thus the measured thickness data from the geological maps may be underestimated. (2) The unclassified point data are included in the non-welded facies. Some of them are considered to be welded facies (increase the DRE volume and eruptive mass). (3) The distribution of the ignimbrite veneer facies in the mountain area is not included in this estimation. The distance from the source to the coast area is about 70 km on average. Therefore, the area to the coast is ca. 1.5 × 10 4 km 2 . The average thickness of the ignimbrite veneer facies is about 2 m (Watanabe, 1986;Suzuki-Kamata and Kamata, 1990). The total estimated volume of the veneer facies is estimated at about 30 km 3 . This volume is about 3.2-9 % of the estimated total volume (335-940 km 3 ) of the Aso-4 PDC deposit.
Factors that may have decreased the lower limit bound are as follows. (1) The distribution limit in the sea area is considered as oval in shape; however, the original runout distance of the Aso-4 PDC deposits may be shorter locally due to the topographical barriers in the subaerial region.
(2) The average density of the Aso-4 PDC deposits is decreasing according to the runout distance. The effect of the lower density of the distal facies tends to decrease the total DRE volume.
Another possible factor in changing the upper and lower bounds is the fact that the ordinary kriging method is used for the estimation of no-measured thickness data area by the extrapolation of the surrounding measured area data. This estimation does not integrate the PDC dynamics (e.g., local deposition due to topographic changes such as slope and valley width changes). The thickness may change if the PDC dynamics are included. Future studies such as numerical simulations, including deposition processes from the bottom of the PDC, are needed.

Aso-4 Tephra Fall Distributions and Volume
The estimated volumes of Aso-4 tephra fall (590-920 km 3 ; 240-370 km 3 in DRE) became larger than the minimum value of the previous estimation (>400 km 3 ; Machida et al., 1985;Machida and Arai, 2003). The estimation result is about 56-88% volume of the estimation (1,051 km 3 ) by Suto et al. (2007). The main reasons for the calculation of a larger volume compared to the Machida et al. (1985) and Machida and Arai (2003) in this study are: (1) the isopach map area became much larger than the previous estimation due to the inclusion of more submarine tephra fall data; and (2) the calculation method is different from the previous estimation. Machida et al. (1985) and Machida and Arai (2003) estimated the eruptive volume of the Aso-4 tephra fall using the extended area (>4 × 10 6 km 2 ) multiplied by the average thickness of 10 cm. Suto et al. (2007) estimated the eruptive volume of the Aso-4 tephra fall deposits using GIS software and the isopach map published by Machida et al. (1985) and Machida and Arai (2003). However, no details of the calculation methodology were provided in the paper. The purpose of their paper was to make a tephra fall database covering the whole of Japan. The results of such volume estimations are preliminary and tend to have significant errors (e.g., Yamamoto, 2017). Uncertainties in tephra fall volume estimates originate with several factors. Factors that may have increased the upper limit bound are as follows. (1) Especially relatively thin tephra fall deposits in the distal regions are quickly eroded by wind and rainfall. The tephra deposits are preserved only in limited areas such as lakes, swamps, and peatlands. Even if the tephra was deposited in these areas, the original thickness might not be preserved (the original deposit thickness may be thicker than the current thickness). (2) The submarine tephra fall deposits are possibly diffused due to the submarine currents while settling on the bottom of the sea (other factors than the wind diffusion). (3) In this tephra fall volume estimation, up to 10 8 km 2 areas are calculated (Figure 9). Although, cryptotephras derived from the co-ignimbrite tephra falls are possibly distributed more widely as the Earth's surface area, especially for such a large-scale eruption case (e.g., Abbott and Davies, 2012;Davies, 2015). When the cryptotephra distributed to the area as large as on the Earth's surface (5.1 × 10 8 km 2 ; five times larger than the current extent), the estimated total tephra volume is 930 km 3 in maximum (extrapolated the decreasing trend of 16 cm to 1 cm isopach maps; Figure 9A). The difference is 10 km 3 , indicating that the effect of the far distal area is about 1% of the total tephra volume.
The volume ratio of tephra fall deposits in the proximal area (64-300 cm thickness segment) is relatively small compared to the total eruptive volume (45-47 km 3 ; 5-7%; Figure 9). Even if the calculation area is extended up to a vent size (e.g., 0.01 km 2 ), the result of the total volume is not changed (590-920 km 3 ). The volume ratio in the proximal area against the total volume is different from other types of eruption. For example, the volume ratio of tephra fall deposits in the proximal area (between 0.45 and 1.5 kg/m 2 ) against the total volume of the 2014 Ontake phreatic eruption is 38% (4.5 × 10 8 kg/1.18 × 10 9 kg) (Takarada et al., 2016). These differences are probably due to the different eruption mechanisms between the two types of tephra falls (largescale Plinian and small-scale phreatic eruptions).
Factors that may have decreased the lower limit bound are as follows. (1) The Aso-4 PDC deposits are subdivided into eruptive units with cooling unit hiatuses (e.g., Watanabe, 1978), suggesting the duration of the Aso-4 eruption lasted for more than a few days to months. The isopach map may consist of a combination of several isopach maps with the different wind directions. In this case, the total tephra fall volume may be decreased due to a combination of narrow isopach maps.
(2) For the tephra fall deposits in the lacustrine and submarine areas, it is possible that the thickness of the deposit is sometimes increased due to reworking by bottom currents in such settings.
Another possible factor to consider in changing the upper and lower bounds is that we used the segment integration method, which enables relatively accurate mathematical calculations (Takarada et al., 2001(Takarada et al., , 2016. Other tephra fall estimation methods such as Exponential fit (Pyle, 1989), Powerlaw fit (Bonadonna and Houghton, 2005), and Weibull fit (Bonadonna and Costa, 2012), however, are essential to check our estimation results. Such considerations will be addressed in a subsequent study.

Eruptive Volume of Aso-4 Eruption
The total eruptive volume of the Aso-4 eruption was estimated at 930-1,860 km 3 (465-962 km 3 in DRE; 1.2-2.4 × 10 15 kg). This result is about 1.5-3.1 times larger than the minimum volume of the previous estimation by Machida and Arai (2003; >600 km 3 ), 1.1-2.3 times larger than [Yamamoto (2015); 384 km 3 in DRE], and 2.2-4.5 times larger than Nakajima and Maeno (2015; 200 km 3 in DRE). The reason for the larger revised volume is mainly due to more accurate estimations of distributions and thicknesses based on detailed datasets and different estimation methods. The eruption magnitude [M = log 10 (erupted mass (kg))-7; Hayakawa, 1993;Pyle, 2000] is calculated at M8.1-8.4. The Aso-4 caldera-forming eruption is now considered to be one of the M8 (VEI8) class super-eruptions. This is the largest eruption in Japan in the last 100 ka. The eruptive volume of the 30 ka Aira eruption is estimated at 940-1,040 km 3 (380-430 km 3 in DRE; Takarada, 2019). The eruptive volume of the 106 ka Toya eruption is estimated at 230-310 km 3 (100-140 km 3 in DRE; Takarada, 2019;Tomiya and Miyagi, 2020). The Aso-4 eruption is about 0.8-2 times larger than the Aira eruption and about 3-8 times larger than the Toya eruption.
The eruptive volume of the 75 ka Youngest Toba Tuff derived from the Toba caldera is estimated at 13,200 km 3 (5,300 km 3 in DRE) (Costa et al., 2014). The eruptive volume of the 25.4 ka Oruanui eruption in the Taupo Volcanic Zone is estimated at 530 km 3 in DRE (Wilson, 2001;Vandergoes et al., 2013). Thus, the Aso-4 eruption is the 2nd largest eruption in the world in the last 100 ka. The eruptive volume of the 27.8 Ma Fish Canyon Tuff from the La Carita caldera, San Juan Volcanic Field, is estimated at 5,000 km 3 (Lipman et al., 1997;Bachmann et al., 2002). The eruptive volume of the 2.1 Ma Hukleberry Ridge Tuff derived from the Yellowstone caldera is estimated at 2,450 km 3 (Christiansen, 2001;Ellis et al., 2012). The eruptive volume of the 1.6 Ma Otowi Member of Bandelier Tuff derived from the Valles caldera is 216-550 km 3 in DRE (Cook et al., 2016). The Aso-4 eruption is one order smaller compared to the VEI 9 Youngest Toba Tuff (the largest volcanic eruption in the Quaternary), and 0.9-1.8 times larger than the Orunaui eruption in the Taupo Volcanic Zone. The Aso-4 eruption is 12-18% volume of the Fish Canyon Tuff (one of the largest ignimbrites in the world), 40-80% volume of the Hukleberry Ridge Tuff (the largest eruption from the Yellowstone), and slightly larger than the Otowi Member of Bandelier Tuff.
The total eruptive mass is estimated at 1.2-2.4 × 10 15 kg. The Aso-4 PDC deposits consist of 8 eruptive units, which sometimes show discontinuities of welding degree and cooling unit hiatuses between them (e.g., Watanabe, 1978); thus, the volume of 1 flow unit (1 event) is on the order of 10 13 -10 14 kg. For example, if an event occurred within a period of 10-60 min, the average mass flow rate (MFR) is calculated at 10 9 -10 11 kg/s. The numerical 3D simulation suggests that the expected eruption column height of co-ignimbrite tephra fall would be as high as 40-60 km at this MFR (Costa et al., 2018). A significant global climate and environmental impact would occur from such a large eruption column due to the release of a large amount of volcanic gas (SO 2 , HCl, and HF) (e.g., Rampino and Self, 1982;Trenberth and Dai, 2007;Kravitz and Robock, 2011). Long-term catastrophic effects on vegetation and ecosystem would be expected (e.g., Costa et al., 2014). Interaction with rainfall would cause the tephra fall deposits covering Japan to produce abundant lahars over large areas for more than 10 years (e.g., a large number of lahars occurred due to the ca. 10 km 3 1991 Pinatubo eruption for more than 10 years; Major et al., 1996). Therefore, a M8 class supereruption would cause long-term severe volcanic hazards. Further studies on climate and volcanic hazard assessments are necessary.
The estimated distributions and eruptive volume of the Aso-4 PDC and tephra fall deposits are considered to become an essential dataset for volcanological, geophysical, and petrological investigations, and volcanic hazard assessments for large-scale super-eruptions. This volume data is also useful to establish a more precise volume vs. time diagram of Aso volcano. The distribution and thickness data are useful for future studies on volcanic hazards. Research efforts on the estimation of the eruptive volume of other large-scale eruptions in Japan, such as Aira, Toya, Kutcharo, and Towada calderas, were made recently (e.g., Takarada et al., 2017Takarada et al., , 2018Takarada, 2019). Reevaluation of the eruptive volumes of major caldera-forming eruptions in other countries is also crucial. The estimation methods outlined in this contribution are applicable to any other large-scale calderaforming eruptions and will enable the progression of similar volcanological research worldwide.

CONCLUSION
Detailed distributions of 87-89 ka Aso-4 PDC deposits were made based on published papers, geological maps, and borehole data (Figures 5-7). Thickness data were compiled from a total of 3,611 outcrops, geological maps, and borehole locations. The volume was calculated using thickness data and area of PDC deposit within each 7 km × 5.5 km mesh grid. The ordinary kriging method was used when no thickness data existed in the mesh grid. The maximum, minimum, and average volumes were calculated. The total eruptive volume of the Aso-4 PDC deposit was estimated at 340-940 km 3 (225-590 km 3 in DRE). The volume of co-ignimbrite Aso-4 tephra fall was estimated using two new isopach maps based on 71 submarine, lacustrine, and subaerial tephra deposits. The estimated volume of the Aso-4 tephra fall was 590-920 km 3 (240-370 km 3 in DRE), using the segment integration method (Takarada et al., 2001(Takarada et al., , 2016. The total estimated eruptive volume of the Aso-4 eruption was 930-1,860 km 3 (465-960 km 3 in DRE; 1.2-2.4 × 10 15 kg). Therefore, the Aso-4 eruption is now considered to have been a M8.1-8.4 (VEI 8) super-eruption. The Aso-4 eruption is the largest volcanic eruption in Japan and considered to be the 2nd largest eruption in the world in the last 100 ka. It is expected that these estimation results will provide essential parameters for long-term eruption forecasting, evaluation of volcanic activities, quantitative geophysical and petrological research work, and future volcanic hazards assessment. The proposed estimation method can be applied to any large-scale caldera-forming eruptions in the world for the reevaluation of eruptive volumes of PDC and tephra fall deposits.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article are available in the Supplementary Material. We include the data on location, area, measured thickness, estimated thickness (using ordinary kriging method), and original and current exposure volume in each mesh of the Aso-4 PDC deposits (Supplementary  Table S1). Location, thickness, and references of the Aso-4 tephra fall deposits are also provided (Supplementary Table S2).

AUTHOR CONTRIBUTIONS
ST and HH conducted the fieldwork, compiled the data, determined the distribution of the Aso-4 PDC and tephra fall deposits, and undertook data interpretation as well as the refinement of this article.

FUNDING
This study was partly supported by the Secretariat of the Nuclear Regulation Authority, Japan.