How many explosive eruptions are missing from the geologic record? Analysis of the quaternary record of large magnitude explosive eruptions in Japan
© Kiyosugi et al. 2015
Received: 6 January 2015
Accepted: 10 July 2015
Published: 24 July 2015
Large magnitude explosive eruptions in Japan were compiled for the Large Magnitude Explosive Volcanic Eruptions (LaMEVE) database. Here we use this dataset to investigate the under-recording of Japanese explosive eruptions. We identify under-recording of Volcanic Explosivity Index (VEI) 4–5 eruptions on two timescales. Model fitting and Akaike’s information criterion (AIC and AICc) model selection suggest that these trends can be represented with the double exponential decay model, reflecting geologic processes. The time series of the recording rate of larger eruptions (VEI 6 and 7) show a slowly decreasing trend in comparison to smaller eruptions. These time series can be represented with the single exponential decay model. The percentages of missing eruptions are estimated from the fitted models. Our results show an inverse correlation between VEI and degree of under-reporting suggesting that even larger VEI eruptions are under-recorded in the Quaternary. For example, 89 % of VEI 4 events, 65–66 % of VEI 5 events, 46–49 % of VEI 6 events and 36–39 % of VEI 7 events are missing from the record at 100 ka, 200 ka, 300 ka, and 500 ka, respectively. Comparison of frequencies of Japanese and global eruptions suggests that under-recording of the global database is 7.9–8.7 times larger than in the Japanese dataset. Therefore, under-recording of events must be taken into account in estimating recurrence rates of explosive eruptions using the geologic record.
KeywordsLarge Magnitude Explosive Volcanic Eruptions database Under-recording of volcanic events Recurrence rate Missing data Statistics in volcanology Natural hazard
Databases of large magnitude volcanic eruptions
Databases of large magnitude volcanic eruptions have been created to provide basic information about explosive volcanism (e.g. Machida and Arai, 2003; Committee for catalog of Quaternary volcanoes in Japan 2000; Siebert and Simkin, 2002; Siebert et al., 2010) and to facilitate assessment of hazards and risks from volcanic eruptions (e.g. Mason et al., 2004; Crosweller et al., 2012). Among these databases, the most accessible global databases of volcanic eruptions are the Smithsonian’s Global Volcanism Program database (Siebert and Simkin, 2002) and the Large Magnitude Explosive Volcanic Eruptions (LaMEVE) database (Crosweller et al., 2012). The Smithsonian’s Global Volcanism Program has compiled documentation of Holocene volcanism around the world for nearly five decades for better understanding of the full range of Earth’s eruptive activity, and to make these data available (on-line at http://www.volcano.si.edu/) to the ever-broadening community interested in volcanism (Siebert and Simkin, 2002). The database contains information about vent location, start and end dates of eruptions, dating method and Volcanic Explosivity Index (VEI; Newhall and Self 1982) of any magnitude of eruption known to have occurred during the past 10,000 years (Siebert and Simkin, 2002). The LaMEVE Quaternary database includes much older events (back to ~2.6 Ma; Crosweller et al., 2012). To support assessments of environmental and societal impacts of volcanism on global, regional and local scales and to provide basic information on global explosive volcanism, the LaMEVE database was created as a component of the Volcanic Global Risk Identification and Analysis Project (VOGRIPA) database, which is being developed as part of the Global Volcano Model (GVM) (Crosweller et al., 2012). The LaMEVE database aims to include all known explosive eruptions for which events are dated, source volcanoes are known and eruption magnitude (M = log 10 [erupted mass(kg)] - 7; Pyle 2000) and/or VEI are ≥ 4. The database contains information about the age of eruptions, deposit type, deposit volumes, VEI, eruption magnitude, intensity, basic geochemistry, source volcano location, data sources, errors and uncertainties with indices of data reliability (Crosweller et al., 2012). This database is publically available online (Crosweller et al., 2012; http://www.bgs.ac.uk/vogripa) and currently contains information on 3,107 Quaternary volcanoes and 1,887 explosive eruption records from the last 2.6 My.
Under-recording of events
Creation of databases of large magnitude explosive volcanic eruptions has clarified that under-recording of the frequency of eruptions and variable recording over time are problems (Deligne et al., 2010; Brown et al., 2014). Potential for under-recording directly impacts hazard and risk assessments (Bebbington 2013). A major challenge is to understand the degree of under-recording (Guttorp and Thompson, 1991; Deligne et al., 2010; Furlan, 2010; Brown et al., 2014).
Guttorp and Thompson (1991) studied patterns of volcanic activity during the last 500 years using the Smithsonian’s Global Volcanism Program database. Their results show that neither the global nor Japanese eruption records are significantly different from a Poisson process during this time interval. They estimated the reporting probability by smoothing the observed number of events with fitting a linear line to a locally chosen number of events, decided by cross-validation. Deligne et al. (2010) compiled a global dataset of Holocene large explosive volcanic eruptions from the Smithsonian’s Global Volcanism Program database and additional literature. They analyzed the data with the extreme value method, first applied in volcanology by Coles and Sparks (2006). In this method, under-recording of events is taken into account as a function of eruption magnitude. Their results indicate that the level of under-recording is high and fairly constant from the start of the Holocene until about 1 A.D. and then decreases dramatically over the last ~2000 years (Deligne et al., 2010). Furlan (2010) analyzed a catalogue of large eruptions that occurred during the last two millennia. To represent the temporal evolution of the censoring effect in the recording process effectively, the extreme value method was used with a change-point model. Like Coles and Sparks (2006), Furlan (2010) concluded that under-recording decreases dramatically in the most recent 400 years with increased recording of eruptions spreading throughout the South Pacific in this period. Under-reporting is significantly more pronounced during Holocene and historical time when data from small-volume eruptions (VEI 0-3) are also considered (Siebert et al., 2010). Brown et al. (2014) analyzed LaMEVE to show that under-recording is a function of magnitude and the proportion of historic and geological data in each magnitude subset. The time at which 50 % of the data are younger is a power law function of magnitude, which was attributed largely to preservation potential of deposits.
Although these analyses focused on the under−recording in different global databases, under-recording varies between regions due to variations in the length of the historic record, preservation of deposits, and number of geological investigations. For example, in the LaMEVE database, Japanese events account for about 39 % (729 out of 1,887 eruptions) of the entire set of eruptive events, whereas Japanese volcanoes only account for about 3.4 % (106 out of 3,107) of the number of volcanoes in the database (Brown et al., 2014).
In this paper we investigate under-recording of a large magnitude explosive eruption database in Japan in order to quantify under-recording of eruptions in regions where a comparatively large amount of geological data are available. We use a threshold of VEI or magnitude 4 to analyze under-reporting effects of eruptions with magnitudes large enough to have been documented both in historical and geologic records.
Data on Japanese explosive eruptions were compiled from the Smithsonian’s Global Volcanism Program database (Siebert and Simkin, 2002), additional Japanese databases and published articles. These data were used to populate LaMEVE. These additional Japanese databases are Machida and Arai (2003), Committee for Catalog of Quaternary volcanoes in Japan (2000), Geological Survey of Japan, AIST (2013) and Hayakawa (2010). Machida and Arai (2003) compiled tephra data into a catalog of tephra in and around Japan to provide basic information for identification and further investigations of regional tephra fallout deposits. As this database is focused on identification of regional tephra layers, it contains major mineral components, type and refractive index of volcanic glasses and type locality of tephra. Products of recent small eruptions are not described in detail. Committee for catalog of Quaternary volcanoes in Japan (2000) edited a Quaternary volcano catalog to understand temporal and spatial variations in magmatism in Japan. Like the database of Machida and Arai (2003), this database does not contain younger and smaller eruptions. In contrast to these databases, Geological Survey of Japan, AIST (2013) compiled published articles into an online 10,000-year eruption database of Japan. Compared to the databases of Machida and Arai (2003) and Committee for catalog of Quaternary volcanoes in Japan (2000), this database provides more details of younger and smaller eruptions, although information related to some major volcanoes is still under compilation. Moreover, Hayakawa (2010) organized online databases of 2000-year and one million-year tephra in Japan. The database contains more instances of tephra fallout deposits than other Japanese databases, but these additional units are often not described in terms of eruption age and volume.
Number and percentage of the analyzed Japanese events for each Volcanic Explosivity Index (VEI) category
Number and percentage of the analyzed Japanese events for each eruption magnitude category
Except the category of VEI 8 due to a very small number of events (9 events), the number of missing events given the apparent change in frequency with time is estimated in three steps: (1) calculation of time dependent recording rate of events for each VEI (4 to 7) and eruption magnitude (4.0 to 7.0) category, (2) fitting a function to the time series of the observed recording rate, (3) calculation of the percentage of missing events compared to the total number of events, with both estimated from the fitted function. The modeling assumes that there are no missing events at time zero (the present day) under the present global volcano monitoring systems and the present day recurrence rate (the eruption frequency; events/ka) is calculated as the intercept of the fitted function at time zero.
Recording rate calculation
where d m+n and d m-n represent the ages of the n th older and younger events than the m th youngest event, respectively, and 2n is the number of events representing a window size, MA, of the moving average calculation. Because the smoothness of the time series of the observed recording rate depends on the window size, multiple calculations with different window sizes are necessary. Although a smaller window size (e.g. MA = 2) is suitable to detect short term recording rate changes, it often gives a zero denominator in equation 1 because some consecutive events have the same age in the database. We therefore chose the window size (MA) of 4 (n = 2), 6 (n = 3) and 8 (n = 4) in this study. This is a simpler approach than the one adopted by Sanchez and Shcherbakov (2012), in which they used logarithmically increasing bin lengths to calculate normalized recording rate.
Function fitting to the observed recording rate
represents the half-life period of recording rate R(t).
represent the half-life periods of rapid and slow decreasing processes, respectively.
The functions R e (t) and R d (t) are obtained by estimating the scale factor r after deciding the probability density functions, f e (t) and f d (t) with the decay constants, λ, λ 1 and λ 2 and the weighting factor p. The scale factor r is estimated by minimizing the square error between the probability density function and the time series of observed recording rate in logarithmic scale (Fig. 2a-k).
The critical assumption here is that the recurrence rate of explosive eruptions in Japan was constant during the last 2 Ma. This assumption is plausible because the tectonic setting of arc volcanism has not changed significantly in Japan during most of the Quaternary (e.g., Taira, 2001; Mahony et al., 2012).
Results of model fitting to the time series of recording rate. MA: window size, 2n, of the moving average calculation (equation 1). M: eruption magnitude. Model: selected model function. Rejected models are also shown when AIC or AICc difference between the accepted and the rejected models is less than 2 (Burnham and Anderson, 2002). Dexp: double exponential decay function. Exp: exponential decay function. Lr: relative likelihood. Note that the relative likelihood of the smaller AIC or AICc model is equal to 1. Values in the parentheses show the range of 95 percentile confidence interval estimated by the bootstrap method (Efron 1979) with 10,000 replicates. The recording rate of the datasets of M ≥ 4.0 (MA = 4, 6), M ≥ 4.5 (MA = 4) and M ≥ 5.0 (MA = 4) were not calculated because some of their consecutive events had the same ages and the denominator of equation 1 becomes zero
Half-life1 (×103 year)
Half-life2 (×103 year)
R0(=R1 + R2) (events/ka)
21.8 (18.4 - 31.6)
22.7 (19.9 - 34.7)
24.5 (23.0 - 39.6)
3.16 (2.72 - 5.43)
3.28 (2.91 - 6.17)
3.54 (3.27 - 7.34)
0.429 (0.343 - 0.636)
0.428 (0.351 - 0.659)
0.437 (0.379 - 0.710)
0.0582 (0.0437 - 0.101)
0.0599 (0.0464 - 0.112)
0.0627 (0.0504 - 0.127)
Half-life1 (×103 year)
Half-life2 (×103 year)
R0 (=R1 + R2) (events/ka)
26.4 (17.6 - 38.3)
5.74 (5.06 - 22.9)
0.0781 (1.15 × 10 − 6–0.120))
where k is the number of parameters in the model, N is the number of recording rate observations in the time series and lnL is the maximized value of the logarithmic likelihood function (equations 5 and 12). AICc was used for the model selection of eruption categories VEI 7 (29 events), M ≥ 6.5 (50 events) and M ≥ 7 (34 events). When the difference of the AIC or AICc values of the two models was larger than 2, the model with the smaller AIC or AICc was selected (Burnham and Anderson, 2002). For our analyses, this difference corresponds to a significance level of 4.6 % (Hudson, 1971; Zhuang et al., 2005). On the other hand, if the difference of the AIC or AICc values was less than 2, results of both models are shown in Table 3, as the models are not regarded as significantly different.
Calculation of the percentage of missing events
where A s and A l are the smaller and larger AIC or AICc values, respectively (Burnham and Anderson 2002). Note that the relative likelihood of the smaller AIC or AICc model is equal to 1 in this equation (Table 3).
The recording rate of larger eruptions can be reasonably modeled with a single exponential function (Fig. 2a, b and e). For instance, the initial recording rates (recurrence rate) of VEI 6 (about 0.4 events/ka; MA = 4, 6, 8), VEI 7 (about 0.06 events/ka; MA = 4, 6, 8) and M ≥ 7 (about 0.06–0.07 events/ka; MA = 4, 6, 8) eruption categories decrease with the half-lives of 137–150 ka, 317–343 ka and 361–389 ka, respectively (Table 3). On the other hand, AIC or AICc difference between the fitted models is less than 2 in the cases of the M ≥ 6 dataset with MA = 8 and M ≥ 6.5 dataset with MA = 4 (Table 3) suggesting that these medium eruption magnitude categories might be represented by either the exponential or double exponential model (Burnham and Anderson, 2002). This transitional feature is not found in the analysis of VEI datasets but in the modeling of the eruption magnitude dataset, probably because the datasets of eruption magnitude are taken at smaller intervals (every half an order of magnitude) and also contain different magnitude eruptions, which are larger than each magnitude category. Furthermore, this transitional feature also indicates the importance of testing different window sizes in the moving average calculation in our analysis.
Under-recording of the global data
Parameters of linear relationships between logarithmic frequency and VEI or eruption magnitude categories (equation 19). MA: window size, 2n, of the moving average calculation (equation 1). M: eruption magnitude. The linear relationships were obtained for the discrete points in the VEI range and M range. The intervals of points were 1 and 0.5 for VEI and eruption magnitude, respectively. Values in the parentheses show the range of 95 percentile confidence interval estimated by the bootstrap method (Efron 1979) with 10,000 replicates
4 to 6 (3 points)
4 to 6 (3 points)
4 to 6 (3 points)
≥4.0 to ≥6.0 (5 points)
4.603 (4.228 - 5.451)
0.8202 (0.7398 - 0.9642)
0.9798 (0.9708 - 0.9989)
≥4.5 to ≥6.0 (4 points)
3.882 (3.432 - 6.009)
0.6819 (0.5838 - 1.055)
0.9880 (0.9630 - 0.9994)
The reason for many missing events
The results of our analyses suggest a large amount of under-recording of events including not only smaller (e.g. VEI 4 and 5) but also larger (e.g. VEI 6 and 7) magnitude eruptions. The under-recording of events is attributed to the absence of historical records, disappearance of tephra units from the geological record and or overlooking of events - that is, not identifying events that are preserved in the rock record. The main mechanisms of disappearance of tephra units are erosion (e.g. Lavigne 2004; Pierson et al., 2013) and alteration of tephra deposits (e.g. Pollard et al., 2003), burial of tephra deposits by younger deposits (Imura and Kobayashi, 2001) and disappearance of the source volcano itself due to burial (e.g. Kamata, 1989) or erosion (e.g. Machida et al., 1997).
The absence of a historical record is a significant reason for a recording rate decrease in the past 1,000 years. For example, Furlan (2010) showed that recording of large eruptions changed considerably at AD 1900 and 1600. These changes can be explained in terms of factors such as colonization, improvements in newspaper reporting, the telegraph and more recently the internet, and development of modern scientific approaches to reporting natural events. Because of this more rapid decrease in historical data compared with geological data, Brown et al. (2014) excluded eruptions less than 1,000 years BP from their analysis to understand geological data. In our analysis, the dataset includes both historical and geological data and shows the rapid decrease process (Fig. 2c, d and h-k). On the other hand, the time scale of this process is much longer (half-life >5,000 years; Table 3) than historical time scale. Therefore, the rapid decrease observed in our analysis must be mainly caused by geological processes. For instance, erosion of tephra deposits must be a significant mechanism responsible for the under-recording of smaller eruption volume events. Especially, recording rates of smaller events show the process of the rapid decrease (Fig. 2c, d and h-k) and suggests that erosion is more dominant during this process. Conversely, older smaller events show slower decreasing process of recording rate (long tail of recording rate, Fig. 2c, d and h-k) and suggest that some of the tephra deposits are preserved from the rapid erosion process as indicated by Brown et al. (2014). Alteration of tephra deposits, burial of tephra deposits by younger deposits and disappearance of eruption source due to burial or erosion must be the mechanism of this slower decreasing process. They must also affect the long term decrease of recording rate of those large eruptions (Fig. 2a, b and e). Furthermore, overlooking events may happen if geologists are biased toward reporting younger (e.g. active volcano < 10,000 years old) and larger events. Reporting bias must affect the identification of older smaller events more than the reporting of larger and younger events.
Volcanic hazard implications
In using an eruption database, under-recording of events must be taken into account to avoid underestimation of potential hazards and spurious inferences concerning how eruption rates have varied with time. Time averaged frequency of eruptions must be calculated by averaging the number of events of each VEI or eruption magnitude category over different time scales (e.g. Simkin, 1993; Pyle, 1995). The time averaged frequency of smaller eruptions will be underestimated when considering long time periods due to their relatively quick disappearance and the time averaged frequency of larger eruptions will be less reliable when considering short time periods due to the small number of eruptions. Our method estimates the half-life of eruption records, which will help to select the calculation time scale of time averaged frequency of each VEI or eruption magnitude category. In addition to the estimation of the regional under-recording of events, under-recording of events at individual volcanoes can be evaluated by other statistical approaches (e.g. Wang and Bebbington, 2012).
We compiled data on large magnitude explosive eruptions in Japan from the LaMEVE database (Crosweller et al., 2012) and investigated the under-recording of events. Brown et al. (2014) analyzed the spatial and temporal bias of the LaMEVE database and showed that under-recording is a function of magnitude and the proportion of historic and geological data in each magnitude subset. They showed that about 40 % of all recorded eruptions have occurred in Japan. Here, we studied the under-recording of the Japanese dataset and also estimated the under-recording of the global dataset on the basis of the estimated eruption frequency and the number of volcanoes. Although the recording rate of smaller events (VEI 4, 5 and eruption magnitude 4–5.5) are basically high, it drops very rapidly to a small value and then decreases slowly back in time. The model fitting, AIC and AICc model selection suggest that the two trends of smaller eruption categories (VEI 4 and VEI 5) can be represented with the double exponential decay model. The recording rates of larger eruptions (VEI 6, 7 and M ≥ 7) show a more slowly decreasing trend, which does not have a significant initial quick drop and which can be represented by a single exponential decay model. The total number of eruptions and the percentage of missing eruptions are estimated from the fitted models. Our results suggest that even larger VEI events have significant under-recording when considering time periods of hundreds of thousands of years. For example, 89 % of VEI 4 events, 65–66 % of VEI 5 events, 46–49 % of VEI 6 events and 36–39 % of VEI 7 events are missing from the record at 100 ka, 200 ka, 300 ka, and 500 ka, respectively. Comparison of frequencies of Japanese and global eruptions suggests that under-recording of the global database is 7.9–8.7 times larger than the Japanese dataset. Therefore, under-recording of events must be taken into account in long-term volcanic hazard assessments.
Large Magnitude Explosive Volcanic Eruptions
Volcanic Explosivity Index
Double exponential decay function
Exponential decay function
This work was funded by a grant from the European Research Council (VOLDIES grant), the Natural Environment Research Council (Global Volcano Model grant), the British Geological Survey and also Munich Re in the initial stages. Support for KK was provided by the Nuclear Waste Organization of Japan (NUMO) and the Obayashi Corporation. Findings do not necessarily reflect their views. The authors benefited from conversations with R Kazahaya about the modeling of recording rate of volcanic events. We thank two anonymous reviewers and editor J. Barclay for making further improvements to the manuscript.
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