Open access

Application of the Bayesian Approach to Incorporate Helium Isotope Ratios in Long-Term Probabilistic Volcanic Hazard Assessments in Tohoku, Japan

Written By

Andrew James Martin, Koji Umeda and Tsuneari Ishimaru

Published: September 27th, 2012

DOI: 10.5772/51859

Chapter metrics overview

2,431 Chapter Downloads

View Full Metrics

1. Introduction

Geological hazard assessments based on established statistical techniques are now commonly used as a basis to make decisions that may affect society over the long-term (0.1 – 1 Ma). Volcanic risk essentially consists of:

(1) The probability of a ‘volcanic event’ occurring such as a dike intrusion or a new strato- or caldera volcano forming e.g. [1- 7]

(2) The consequences of the volcanic event e.g. [8 - 9].

A challenge with the long-term probabilistic assessment of future volcanism in relation to the siting of, for example geological repositories is that because new volcano formation is rare, uncertainties in models are inherently large [10]. Sites for nuclear facilities in particular must be located in areas of very low geologic risk [11]. Recent studies have been carried out looking at the hazard posed by volcanoes to nuclear power plants in Armenia [e.g. 9, 12] and Java, Indonesia [e.g. 13]. Here the focus was more on the consequences of an eruption at an existing volcano on the safety of an operating nuclear power plant. In the case of a geological repository for high and/or low level radioactive waste, the emphasis is on the consequences of new igneous activity such as a dike that may intrude the repository [e.g. 14] and transport the waste to the surface. In this case, the probability of a new volcano forming in the first place is very low (typically < 10-7/a) since by definition such facilities should be located away from existing Quaternary volcanoes. However the lack of volcano ‘data’ implies that addition information on the processes that control future long-term spatio-temporal distribution of volcanism are needed. This has motivated several investigators to incorporate datasets in addition to the distribution and timing of past volcanic activity in volcanic probabilistic analyses [e.g. 15]. Bayesian inference has been used to combine geophysical datasets to probability distributions constructed from known historic volcano locations in order to estimate the location of future volcanism over a regional scale [1]. More recently, [16] used Bayesian inference to merge prior information and past data to construct a probability map of vent opening at the Campi Flegrei caldera in Italy.

Here we revisit the Bayesian approach developed by [1] where seismic tomographs and geothermal gradients were incorporated into probabilistic assessments by Bayesian inference in Tohoku. We apply the same Bayesian technique in the same study area to incorporate recently acquired helium isotopes into probabilistic hazard assessments; such noble gases have been shown to be excellent natural tracers for mantle-crust interaction owing to their inert chemical properties which means they are not altered by complex chemical processes. Moreover helium isotopes provide evidence for the presence of mantle derived materials in the crust, owing to the distinct isotopic compositions between the crust and the upper mantle [e.g. 17, 18]. We examine the link between volcanism and 3He/4He ratios that may infer possible regions of magma generation and hence volcano formation. Such links between magmatism and elevated 3He/4He ratios have been proposed [e.g. 19, 20], but the link has not been examined quantitatively in probabilistic based models. Finally we discuss the Bayesian method in developed by [1] in the context of recent approaches to incorporate multiple datasets [e.g. 21, 22].


2. Japan and the Tohoku region

Japan is one of the most tectonically active regions in the world. Due to the dynamics of four plates, Quaternary volcanoes have formed along distinct volcanic fronts in east and west Japan (Figure 1).

Figure 1.

Map showing the tectonic setting of Japan (Figure modified from [1]). The four main islands that make up Japan are located on or near the boundaries of four plates. Black triangles denote Quaternary volcanoes and the red lines depict the main volcanic fronts. The thin contour lines denote the depth of the subducting Pacific Plate beneath Japan. The velocities and arrows indicate the subduction rates and directions respectively of the Pacific, Philippine Sea and Eurasian plates relative to the North American plate.

The Tohoku region (Figure 2) is arguably one of the most extensively studied volcanic arcs in the world, particularly regarding the relationship between volcanism and tectonics. Moreover there have been numerous geological and geophysical investigations yielding high-quality datasets e.g., [23 - 29].

Figure 2.

The volcanic arc in Tohoku consists of approximately 170 Quaternary edifices [28, 30] (modified from [1]). The highest density of volcanoes in Tohoku is the cluster in the Sengan region. Other notable volcanoes are the Towada volcano which has been the site of late Quaternary large-volume felsic eruptions resulting in large caldera formation [e.g., 27, 31], and the Iwaki and Chokai [32] volcanoes which are active andesitic volcanoes on the back-arc side of Tohoku. The grey line denotes the present day volcanic front.

Tohoku is a mature double volcanic arc with a back-arc marginal sea basin located on a convergent plate boundary of the subducting Pacific plate and the North American plate (Figure 1). The location and orientation of the volcanic front (grey line in Figure 2) has been linked to the opening of the Sea of Japan and subduction angle of the Pacific plate [e.g., 26, 33]. From 60 Ma up until about 10 Ma the volcanic front migrated east and west several times, however, it has been relatively static during the last 8 Ma [26].

Presently there are 15 known historically active volcanoes in the Tohoku region and a total 170 volcanoes that formed during the Quaternary [30]. Volcanism has gradually become more clustered and localized over a period from 14 Ma to present [34], thus volcano clustering is a characteristic feature in Tohoku.


3. Defining the volcanic event

What do we mean here by ‘volcano’? In developing probabilistic based models, one of the most difficult and challenging tasks is defining the ‘volcanic event’. This is because the volcanic event defined has to be simple and consistent enough for the probabilistic based models to handle. To a certain extent the degree of consistency that can be realistically included in a model is largely constrained by the size of the study area and by the amount and quality of geological, geochemical and/or geophysical data available. The volcanic event could range from a single eruption to a series of eruptions. It could be defined as the existence of a relatively young cinder cone, spatter mound, maar, tuff ring, tuff cone, pyroclastic fall, lava flow or even a large composite volcano. On the other hand older edifices may have been eroded and/or covered by sedimentary deposits such as alluvium and thus be more difficult to locate and/or are easily overlooked. Results of magnetic and gravity data have been used as evidence for locating such hidden volcanic events which in turn had an impact on resulting probabilities at given locations [e.g. 15].

If we were carrying out a hazard assessment on a single volcano we may be interested in defining the event as a series of pyroclastic flows or surges or eruptions that generate lava flows that exceed a certain volume [e.g. 9]. This is particular relevant to volcanic hazard assessments carried out at volcanoes near densely urbanized areas such as the Campi Flegrei caldera in southern Italy [16].

Several aligned edifices with the same eruption age may also be considered as a single volcanic event. Such vent alignments typically developed simultaneously as a result of magma supply from a single dike. For example the vent alignments in the Higashi-Izu monogenetic volcanic group [e.g. 35], could well be classified as a single volcanic event temporally but spatially are multiple. Where age data has been limited, some authors have implemented a condition whereby a cone or cones can only be defined as a volcanic event if they are associated with a single linear dike or a dike system with more complex geometry [e.g. 36].

Many of the advances made on modelling future spatial or spatio-temporal patterns of volcanism where carried out in monogenetic volcano fields due to the apparent relative ease of defining such volcanoes as point processes [e.g., 37, 38]. However as composite or established polygenetic volcanoes represent multiple eruptions from the same conduit occurring over several tens to hundreds of thousands of years, defining the volcanic event is not so easy if the focus is on single eruption episodes as the type of eruption can evolve significantly during the lifetime of the composite volcano. In fact the temporal definition of a monogenetic volcano appears to be not so straightforward either as this can range from several days to a few weeks or longer. For example the Ukinrek maar in Alaska formed in about eight days [39] and the 1913 eruption forming the Ambrym Volcano, Vanuatu in the south west pacific in just a few days [40]. Moreover, [41] argued that monogenetic volcanoes can be both spatially and temporarily more complex than a single eruptive event. In other words so called ‘monogenetic’ volcanoes can also be ‘polygenetic’ albeit smaller scaled than large volume complex strato or caldera volcanoes. Based on this there could be a case to look again at the volcanic event definition used in earlier probabilistic assessments carried out in monogenetic volcanic fields [e.g. 42, 43].

In Tohoku, new volcanoes forming at new locations typically evolve into large complex strato and/or caldera volcanoes containing multiple vents e.g. Akitakomagatake volcano [44]. Such large polygenetic volcanoes in Tohoku have been sub-grouped into unstable types where the eruptive centre has migrated more than 1.5 km within 10 ka and stable types were the vents are more concentrated around the geographic centre of the volcano [44].

The volcanic event definition requires information on both the temporal and spatial aspects; the temporal definition relates to the recurrence rate, λt(number of volcanic events per unit time), and spatial definition to the intensity or spatial recurrence rate λx,y (number of volcanic events per unit area). λtand λx,y can also be combined as a spatio-temporal recurrence rate λx,y,t (number of volcanic events per unit area per unit time) [42].

The temporal definition of a volcanic event could range from a single eruption occurring in one day or less, to an eruption cycle in which active periods of eruptions occur between dormant periods. The time scale of an active period may vary from several years to thousands of years. In previous volcanic hazard analyses carried out on complex, large-volume strato and/or caldera volcanoes, volcanologists have typically defined volcanic events as single eruptions or several eruptions within some defined time period separated by periods in which there is no activity e.g. [4]. This is because the focus at such established volcanoes is not on the probability of a new volcano forming in the vicinity of the existing volcano but rather on the probability of the next eruption or eruption phase.

3.1. Tohoku volcanic event definition

In the context of siting of a geological repository, the main concern is the formation of a new volcano in a region where volcanoes do not already exist. Thus the distinction between monogenetic (simple or complex) and polygenetic (complex strato and/or caldera) volcanism is not relevant for the definition of volcanic event here. Table 1 is a compilation of all Quaternary volcanoes in the Tohoku volcanic arc modified from the Catalog of Quaternary Volcanoes in Japan [1, 30]. Volcano complexes refer to magma systems that have evolved over the long-term (order of 0.1 Ma) which appear as regional scale clusters. In this chapter we use the same definition of volcanic event as [1] taking into account eruption volumes. This is depicted as a white triangle in Figure 3 and is the average geographic location of the vents (white dots). The eruption products released from the vents are represented by the dark grey regions in Figure 3. The lighter grey areas in Figure 3a are the eruption products of a separate volcanic event. Each volcanic event typically has a time gap of more than 10 ka, and/or is differentiated from other volcanic events according to geochemistry.

Volcano Complex Volcanic event Location Age (Ma) Dating Method Eruptive volume
Latitude Longitude ( km3, DRE )
Mutsuhiuchi-dake Older Mutsuhiuchi-dake 41.437 141.057 ca.0.73 K-Ar 5.9
Mutsuhiuchi-dake Younger Mutsuhiuchi-dake 41.437 141.057 0.45 0.2 Strat. 3.6
Osorezan Kamabuse-yama 41.277 141.123 ca.0.8 K-Ar 11.4
Hakkoda Hakkoda P.F.1st. 40.667 140.897 0.65 K-Ar 17.8
Hakkoda South-Hakkoda 40.600 140.850 0.65 0.4 K-Ar 52.4
Hakkoda Hakkoda P.F.2nd. 40.667 140.897 0.4 K-Ar 17.3
Hakkoda North-Hakkoda 40.650 140.883 0.16 0 K-Ar 30.4
Okiura Aoni F. Aonigawa P.F. 40.573 140.763 ca.1.7 K-Ar 17.6
Okiura Aoni F. Other P.F. 40.573 140.763 1.7 0.9 K-Ar 3.7
Okiura Okogawasawa lava 40.579 140.759 0.9 - 0.65 Strat. 0.9
Okiura Okiura dacite 40.557 140.755 0.9 - 0.7 K-Ar 2.1
Ikarigaseki Nijikai Tuff 40.500 140.625 ca.2.0 K-Ar 20.2
Ikarigaseki Ajarayama 40.490 140.600 1.91 1.89 K-Ar 2.1
Towada Herai-dake 40.450 141.000 5.1
Towada Ohanabe-yama 40.500 140.883 0.4 0.05 K-Ar 8.9
Towada Hakka 40.417 140.867 1.4
Towada Towada Okuse 40.468 140.888 0.055 14C 4.8
Towada Towada Ofudo 40.468 140.888 0.025 14C 22.1
Towada Towada Hachinohe 40.468 140.888 0.013 14C 26.9
Towada Post-caldera cones 40.457 140.913 0.013 0 Strat. 14.4
Nanashigure Nanashigure 40.068 141.112 1.06 0.72 K-Ar 55.5
Moriyoshi Moriyoshi 39.973 140.547 1.07 0.78 K-Ar 18.1
Bunamori Bunamori 39.967 140.717 1.2 K-Ar 0.1
Akita-Yakeyama Akita-Yakeyama 39.963 140.763 0.5 0 K-Ar 9.9
Nishimori/Maemori NIshimori/Maemori 39.973 140.962 0.5 0.3 K-Ar 2.6
Hachimantai/Chausu Hachimantai 39.953 140.857 1 0.7 K-Ar 5.5
Hachimantai/Chausu Chausu-dake 39.948 140.902 0.85 0.75 K-Ar 13.7
Hachimantai/Chausu Fukenoyu 39.953 140.857 ca.0.7 Strat. 0.2
Hachimantai/Chausu Gentamri 39.956 140.878 0.2
Yasemori/Magarisaki-yama Magarisaki-yama 39.878 140.803 1.9 1.52 K-Ar 0.3
Yasemori/Magarisaki-yama Yasemori 39.883 140.828 1.8 K-Ar 0.9
Kensomori/Morobidake Kensomori 39.897 140.871 ca.0.8 Strat. 0.8
Kensomori/Morobidake Morobi-dake 39.919 140.862 1 0.8 Strat. 2.5
Kensomori/Morobidake 1470m Mt. lava 39.909 140.872 0.1
Kensomori/Morobidake Mokko-dake 39.953 140.857 ca.1.0 Strat. 0.5
Tamagawa Welded Tuff Tamagawa Welded Tuffs R4 39.963 140.763 ca.2.0 K-Ar 83.2
Tamagawa Welded Tuff Tamagawa Welded Tuffs D 39.963 140.763 ca.1.0 K-Ar 32.0
Nakakura/Shimokura Obuka-dake 39.878 140.883 0.8 0.7 K-Ar 2.9
Nakakura/Shimokura Shimokura-yama 39.889 140.933 0.4
Nakakura/Shimokura Nakakura-yama 39.888 140.910 0.4
Matsukawa Matsukawa andesite 39.850 140.900 2.6 1.29 K-Ar 11.6
Iwate/Amihari Iwate 39.847 141.004 0.2 0 K-Ar 25.1
Iwate/Amihari Amihari 39.842 140.958 0.3 0.1 K-Ar 10.6
Iwate/Amihari Omatsukura-yama 39.841 140.919 0.7 0.6 K-Ar 3.3
Iwate/Amihari Kurikigahara 39.849 140.882 0.2
Iwate/Amihari Mitsuishi-yama 39.848 140.900 0.46 K-Ar 0.6
Shizukuishi/Takakura Marumori 39.775 140.877 0.4 0.3 K-Ar 2.4
Shizukuishi/Takakura Shizukuishi-Takakura-yama 39.783 140.893 0.5 0.4 Strat. 5.2
Shizukuishi/Takakura Older Kotakakura-yama 39.800 140.900 1.4 K-Ar 2.7
Shizukuishi/Takakura North Mikado-yama 39.800 140.875 0.3
Shizukuishi/Takakura Kotakakura-yama 39.797 140.907 0.6 0.5 K-Ar 1.8
Shizukuishi/Takakura Mikado-yama 39.788 140.870 ca.0.3 0.2
Shizukuishi/Takakura Tairagakura-yama 39.808 140.878 ca.0.3 0.1
Nyuto/Zarumori Tashirotai 39.812 140.827 0.3 0.2 K-Ar 0.6
Nyuto/Zarumori Sasamori-yama 39.770 140.820 0.23 0.1 K-Ar 0.4
Nyuto/Zarumori Yunomori-yama 39.772 140.827 ca.0.3 0.5
Nyuto/Zarumori Zarumori-yama 39.788 140.850 0.56 K-Ar 0.9
Nyuto/Zarumori Nyutozan 39.802 140.843 0.58 0.5 K-Ar 5.0
Nyuto/Zarumori Nyuto-kita 39.817 140.855 ca.0.4 K-Ar 0.1
Akita-Komagatake Akita-Komagatake 39.754 140.802 0.1 0 K-Ar 2.9
Kayo Kayo 39.803 140.735 2.2 1.17 K-Ar 5.9
Kayo KoJiromori 39.828 140.787 0.94 K-Ar 0.3
Kayo Akita-Ojiromori 39.839 140.788 1.7 1.7 1.7 Strat. 0.3
Innai/Takahachi Takahachi-yama 39.755 140.655 1.7 1.7 1.7 K-Ar 0.0
Innai/Takahachi Innai 39.692 140.638 2 1.6 K-Ar 0.5
Kuzumaru Aonokimori andesites 39.543 140.983 2.06 K-Ar 0.3
Yakeishi Yakeishidake 39.161 140.832 0.7 0.6 K-Ar 9.5
Yakeishi Komagatake 39.193 140.924 ca.1.0 K-Ar 7.6
Yakeishi Kyozukayama 39.178 140.892 0.6 0.4 K-Ar 5.7
Yakeishi Usagimoriyama 39.239 140.924 0.07 0.04 K-Ar 2.3
Kobinai Kobinai 39.018 140.523 1 0.57 FT, K-Ar 2.3
Takamatsu/Kabutoyama Kabutoyama Welded Tuff 39.025 140.618 1.16 TL 3.2
Takamatsu/Kabutoyama Kiji-yama Welded Tuffs 39.025 140.618 0.30 K-Ar 5.1
Takamatsu Takamatsu 38.965 140.610 0.3 0.27 K-Ar 3.8
Takamatsu Futsutsuki-dake 38.961 140.661 ca.0.3 0.8
Kurikoma Tsurugi-dake 38.963 140.792 0.1 0 K-Ar 0.2
Kurikoma Magusa-dake 38.968 140.751 0.32 0.1 K-Ar 1.5
Kurikoma Kurikoma 38.963 140.792 0.4 0.1 K-Ar 0.9
Kurikoma South volcanoes 38.852 140.875 ca.0.5 K-Ar 0.3
Kurikoma Older Higashi Kurikoma 38.934 140.779 ca.0.5 K-Ar 2.2
Kurikoma Younger Higashi Kurikoma 38.934 140.779 0.4 0.1 K-Ar 0.7
Mukaimachi Mukaimachi 38.770 140.520 ca.0.8 K-Ar 12.0
Onikobe Shimoyamasato tuff 38.830 140.695 0.21 0.21 0.21 FT 1.0
Onikobe Onikobe Centeral cones 38.805 140.727 ca.0.2 TL 1.1
Onikobe Ikezuki tuff 38.830 140.695 0.3 0.2 FT 17.3
Naruko Naruko Central cones 38.730 140.727 ca.0.045 14C 0.1
Naruko Yanagizawa tuff 38.730 140.727 ca.0.045 FT 4.8
Naruko Nizaka tuff 38.730 140.727 ca.0.073 FT 4.8
Funagata Izumigatake 38.408 140.712 1.45 1.14 K-Ar 2.3
Funagata Funagatayama 38.453 140.623 0.85 0.56 K-Ar 19.0
Yakuraisan Yakuraisan 38.563 140.717 1.65 1.04 K-Ar 0.2
Nanatsumori Nanatsumori lava 38.430 140.835 2.3 2 K-Ar 0.5
Nanatsumori Miyatoko Tuffs 38.428 140.793 ca.2.5 Strat. 6.1
Nanatsumori Akakuzure-yama lava 38.433 140.768 1.6 1.5 Strat. 1.5
Nanatsumori Kamikadajin lava 38.447 140.772 1.6 1.5 K-Ar 0.8
Shirataka Shirataka 38.220 140.177 1 0.8 K-Ar 3.8
Adachi Adachi 38.218 140.662 ca.0.08 FT 0.9
Gantosan Gantosan 38.195 140.480 0.4 0.3 K-Ar 4.6
Kamuro-dake Kamuro-dake 38.253 140.488 ca.1.67 K-Ar 5.7
Daito-dake Daito-dake 38.316 140.527 5.7
Ryuzan Ryuzan 38.181 140.397 1.1 0.9 K-Ar 4.6
Zao Central Zao 1st. 38.133 140.453 1.46 0.79 K-Ar 0.8
Zao Central Zao 2nd. 38.133 140.453 0.32 0.12 K-Ar 15.2
Zao Central Zao 3rd. 38.133 140.453 0.03 0 K-Ar 0.0
Zao Sugigamine 38.103 140.462 1 K-Ar 9.9
Zao Fubosan/byobudake 38.093 140.478 0.31 0.17 K-Ar 15.2
Aoso-yama Gairinzan 38.082 140.610 0.7 0.4 K-Ar 6.1
Aoso-yama Central Cone 38.082 140.610 0.4 0.38 K-Ar 3.0
Azuma Azuma Kitei lava 37.733 140.247 1.3 1 K-Ar 24.7
Azuma Higashi Azumasan 37.710 140.233 0.7 0 K-Ar 22.8
Azuma Nishi Azumasan 37.730 140.150 0.6 0.4 K-Ar 7.2
Azuma Naka Azumasan 37.713 140.188 0.4 0.3 K-Ar 4.6
Nishikarasugawa andesite Nishikarasugawa andesite 37.650 140.283 ca.1.5 K-Ar 1.9
Adatara Adatara Stage 1 37.625 140.280 0.55 0.44 K-Ar 0.3
Adatara Adatara Stage 2 37.625 140.280 ca.0.35 K-Ar 0.4
Adatara Adatara Stage 3a 37.625 140.280 ca.0.20 K-Ar 2.0
Adatara Adatara Stage 3b 37.625 140.280 0.12 0.0024 K-Ar 0.3
Sasamori-yama Sasamari-yama andesite 37.655 140.391 2.5 2 K-Ar 0.4
Bandai Pre-Bandai 37.598 140.075 ca.0.7 K-Ar 0.1
Bandai Bandai 37.598 140.075 0.3 0 Strat. 14.0
Nekoma Old Nekoma 37.608 140.030 1 0.7 K-Ar 11.4
Nekoma New Nekoma 37.608 140.030 0.5 0.4 K-Ar 0.9
Kasshi/Oshiromori Kasshi 37.184 139.973 0.1
Kasshi/Oshiromori Oshiromori 37.199 139.970 0.7
Kasshi/Oshiromori Matami-yama 37.292 139.886 0.3
Kasshi/Oshiromori Naka-yama 37.282 139.899 0.0
Shirakawa Kumado P.F. 37.242 140.032 1.31 K-Ar 19.2
Shirakawa Tokaichi A.F. tuffs 37.242 140.032 1.31 1.24 Strat. 12.0
Shirakawa Ashino P.F. 37.242 140.032 1.2 FT 19.2
Shirakawa Nn3 P.F. 37.242 140.032 1.2 1.17 Strat. 0.0
Shirakawa Kinshoji A.F. tuffs 37.242 140.032 1.2 1.18 Strat. 9.0
Shirakawa Nishigo P.F. 37.252 139.869 1.11 FT 28.8
Shirakawa Tenei P.F. 37.242 140.032 1.06 Strat. 7.7
Nasu Futamata-yama 37.244 139.971 0.14 K-Ar 3.2
Nasu Kasshiasahi-dake 37.177 139.963 0.6 0.4 K-Ar 12.3
Nasu Sanbonyari-dake 37.147 139.965 0.4 0.25 K-Ar 5.5
Nasu Minamigassan 37.123 139.967 0.2 0.05 K-Ar 8.7
Nasu Asahi-dake 37.134 139.971 0.2 0.05 K-Ar 4.6
Nasu Chausu-dake 37.122 139.966 0.04 0 K-Ar 0.3
Chokai Shinsan Lava flow 39.097 140.053 0.02 0 Strat.
Chokai Higashi Chokai 39.097 140.053 0.02 0.02 K-Ar 4.3
Chokai Nishi Chokai 39.097 140.020 0.09 0.02 Stra. 0.8
Chokai Nishi ChokaiII 39.097 140.020 0.13 0.01 K-Ar 21.0
Chokai Old Chokai 39.103 140.030 0.16 0.55 K-Ar 67.0
Chokai Uguisugawa Basalt 39.103 140.030 0.55 0.6 K-Ar 1.0
Chokai Tengumari volcanics 39.103 140.031 0.55 0.6 K-Ar 11.0
Gassan Ubagatake 38.533 140.005 0.400 0.300 K-Ar 3.5
Gassan Yudonosan lavas/pyroclastics 38.534 139.988 0.800 0.700 K-Ar 7.5
Gassan Gassan 38.550 140.020 0.500 0.400 K-Ar 18.0
Numazawa Sozan lava domes 37.452 139.577
Numazawa Mizunuma pyroclastic dep. 37.452 139.577 ca.0.05 FT 2.0
Numazawa Numazawa pyroclastics 37.452 139.577 0.005 0.005 14C 2.5
Numazawa Mukuresawa lava 37.452 139.577
Ryuzan Ryuzan 38.181 140.397 1.130 0.940 K-Ar 6.0
Sankichi-Hayama Sankichi-Hayama 38.137 140.315 2.400 2.300 K-Ar 2.9
Daitodake Daitodake 38.316 140.527 ca.1 Strat. 7.5
Hijiori Hijiori Pyroclastic flow 38.610 140.159 ca.0.01 Strat. 1.0
Hijiori Komatsubuchi lava dome 38.613 140.171 ca.0.01 Strat. 0.0
Tazawa Tazawa (lake) 39.723 140.667
Daibutsu Daibutsu 39.817 140.517 2.340 2.160 K-Ar 3.2
Kampu Kampu 39.928 139.877 0.030 0.000 Strat. 0.6
Toga Toga 39.950 139.718 ca.0.42 FT/K-Ar 2.0
Megata Megata 39.952 139.742 0.030 0.020 Strat. 0.1
Inaniwa Inaniwa 40.195 141.050 7.000 2.700 K-Ar 14.0
Taira-Komagatake Taira-Komagatake 40.410 140.254 0.200 0.170 Strat. 3.0
Tashiro Tashiro 40.425 140.413 0.600 0.470 K-Ar 9.0
Tashiro Hirataki nueeardente deps. 40.420 140.413 0.020 0.020 Strat. 0.7
Iwaki Iwaki 40.653 140.307 0.330 0.000 K-Ar 49.0

Table 1.

Tohoku volcanic arc [30, 28]. Dense-rock equivalent (DRE) of eruptive volumes is the product of volume and density of the respective volcanic deposits.

Figure 3.

Two volcano types in Tohoku classified according to migration distance from eruption centre [44]: (a) an unstable type with vent (white dots) migration exceeding 1.5 km in 10 ka resulting in a summit with multiple peaks; and (b) a stable type commonly with a narrow saw-tooth or pointed appearance. For consistency in volcanic event definition over the Tohoku region, both types are treated as a single volcanic event (white triangle) in the probability analysis. However they are also optionally weighted with the corresponding eruption products (dark grey regions). (Figure modified from [1]).


4. Bayesian model

The following is a slightly shorter description of the Bayesian methodology published in [1]. A two-dimensional surface distribution is set-up showing the continuous probability of one or more volcanic event(s) forming within a region of interest, in an arbitrarily time frame of the order of 0.1 – 1 Ma. The volcanic event definition defined above means that we are estimating with known uncertainty, the probability of a new volcano forming at a given location (x, y). [1] noted that a challenge with estimating the long-term future spatial distribution of volcanism is the fact that we are trying to model something that we cannot sample directly; namely the locations of future volcanoes. In this chapter we incorporate 3He/4He ratios, as these may be indicative of conduits in the earth’s crust through which magma may rise through resulting in future volcano formation [19, 20].

Information, no matter how obtained, can be described by a probability density function (PDF) [e.g. 45, 46]. Once the dataset is expressed as a PDF, it is possible to combine with our initial PDF created based on a priori assumptions on volcanism. Bayesian inference is a powerful tool that allows us to construct an a posteriori PDF given a priori assumptions and the PDF generated by our new dataset.

Essentially, two stages are performed yielding the a posteriori PDF. The first is to make a long-term future prediction based solely on the distribution and ages of past volcanic events, creating an a priori PDF. The a priori assumption is that the past and the present provide information about the future; in other words the locations of past and present volcanism are used as an initial guide to estimating future long-term spatial patterns of volcanism. The basic logic behind the a priori assumption is that a new volcano doesn’t form far from existing volcanoes. The a priori assumption can be quite vague in the first step as it is simply the starting point. The next stage is to update or modify the a priori assumptions by incorporating information that is likely to be indicative of the locations of future volcanism and/or we have increased our understanding of the process that controls the location of volcanism. This new information and/or knowledge, obtained from chemical and/or geophysical data, is used to modify the a priori PDF to form an a posteriori PDF that is expected to better reflect the location of future volcanism. The cycle can be repeated any number of times for other datasets by treating the a posteriori PDF as the new a priori PDF in the first step above.

4.1. Bayesian inference and Bayes’ theorem

Bayes’ theorem [e.g. 47] is used to setup a model providing a joint probability distribution for the location known volcanic events (a priori PDF) and current R/RA contoured datasets recast as a PDF (likelihood function). The joint probability density function or a posteriori PDF can be written as the product of two PDFs; the a priori PDF and the sampling or likelihood PDF


where x and y represent grid point locations within the volcanic field A, θis additional dataset, P(x,y)is the a priori PDF, L(θ|x,y)the likelihood function generated by conditioning additional data on the locations of volcanic events, and P(x,y|θ) the resulting a posteriori PDF [1]. The a posteriori PDF is normalized to unity by integrating over the entire Tohoku volcanic field; hence total cumulative probability will not change but the shape of the 2-D surface distribution will be modified according to the likelihood function.

4.2. A priori PDF

We assume that past and present volcanic events can be used to estimate future locations of volcanoes over the long-term, as well as constraining upper bound recurrence rates in the volcanic field. The spatial distribution of volcanoes in volcanic arcs like Tohoku are random [48] hence by treating volcanism in Tohoku volcanic arc as a low frequency, random event, it is assumed that the underlying process could be approximated to a Poisson process [1]. Moreover, by treating the location of volcanic events as random points within some set, the spatial distribution of volcanism can be modeled as a spatial point process [1] where a spatial point process is a stochastic model that can be described as the process controlling the spatial locations of the eventss1,…,s1 in some arbitrary set S [49]. In applying point process models to volcanism, [42] eloquently defineds1,…,sn as volcanic events and S as the volcanic field.

The Poisson process is ‘homogeneous’ if the spatial distribution of point events are completely random [49]. However, as with many volcanic fields, spatial patterns of volcanism in the Tohoku volcanic arc are clustered [34, 50], hence the distribution of volcanoes are not completely random and therefore non-homogeneous (also referred to as in-homogenous). Applying the Clark-Evans nearest-neighbour test [51], [1] showed that the distribution of the volcanic events defined above is clustered with greater than 95% confidence. A non-homogeneous Poisson process is the simplest alternative for modeling such clustered events. Moreover, point process models based on non-homogeneous Poisson processes have been extensively used in modeling the spatial and spatio-temporal characteristics of several volcano fields (e.g. the Springerville volcanic fields in Arizona [38] and the Higashi-Izu monogenetic volcano group, Shizuoka Prefecture, Japan [43]. In these models the local spatial density of volcanic events λx,y is calculated using a kernel function [37, 52]. The kernel function itself is a density function used to obtain the intensity of volcanic events at a sampling pointxp,yp, calculated as a function of the distance to nearby volcanoes and a smoothing constant h (Figure 4).

Figure 4.

Local volcano intensity λx,y at each grid point (x, y) is computed using a Cauchy kernel function. λx,yis a function of volcano distance from grid point (x, y) for N = 6 volcanoes (modified from [1]).

As noted by [42] the choice of kernel function with appropriate values of h has some consequence for the parameter estimation because it controls how λx,y varies with distance from existing volcanoes. The Gaussian kernel has been used a lot in probabilistic assessments carried out in monogenetic volcanic fields, [e.g. 15, 43] since it was assumed that the next volcano to form would not be far from an existing volcanoes. In order to include extreme volcanic events further afield however, [1] modelled spatial patterns using the Cauchy kernel which has thicker tails than the Gaussian kernel. [1] also showed that the spatial distribution of volcanic events in the Tohoku volcanic arc fit a Cauchy distribution whereas monogenetic fields such as the Higashi-Izu Monogenetic Volcano Group [43] tend to be Gaussian. We therefore also use a two-dimensional Cauchy kernel here to calculate the spatial recurrence rate λx,y at grid point xp,ypwhere:

xvi,yviare Cartesian coordinates of the ith volcanic event, N the number of volcanic events used in the calculation and lvi is a factor for weighting eruption volume of the corresponding ith volcanic event. lviis set to unity when eruption volume is excluded. The calculation is repeated on a 10 km mesh in the study area 139 to 143 longitude and 37 to 41.6 latitude and the resulting PDF is normalized to unity. The 10 km grid spacing was selected taking into account the resolution of available geophysical or geochemical datasets across the entire Tohoku volcanic arc.

4.3. Estimating an optimum smoothing coefficient h for the volcanoes in Tohoku

The choice of the smoothing coefficient depends on a combination of the size of the volcanic field, size and degree of clustering and the amount of robustness and conservatism required at specific points within or nearby the volcanic fields in question. In order to estimate the most likely optimum value of smoothing coefficient, [1] plotted cumulative probability density functions with varying values of smoothing are compared with the fraction of volcanic vents and nearest-neighbour volcanic event distances in Tohoku (Figure 5).

Figure 5.

Suitable values of smoothing coefficient h are estimated by plotting cumulative distances to nearest neighbour volcanic events and cumulative probability distribution with differing values of smoothing coefficient. From this plot, suitable values of smoothing coefficient for known volcanic events in Tohoku volcanic are estimated to be 1-1.5 km for the Cauchy kernel. (Figure modified from [1]). As a comparison, the monogenetic volcanoes in the Yucca Mountain Region (YMR) and the Higashi-Izu-Oki monogenetic volcano group are also plotted.

The cumulative plots in Figure 5 suggest that the spatial distribution of volcanic events in the Tohoku volcanic arc fit a Cauchy distribution with smoothing coefficients of h = 1–1.5 km.

4.4. A priori probabilities

Probability estimates for each grid point xp,yp are computed by using a Poisson distribution where λx,y represents the intensity parameter computed using equation (2) :


where, N(t) represents the number of future volcanic vents that occur within time t and area ΔxΔy (10 km x 10 km). The parameter λx,y is normalized to unity across the Tohoku, so, equation (3) represents the probability of one or more volcanic event(s) forming in an area ΔxΔycentred on point xp,yp given the formation of a new volcanic event in Tohoku. This calculation is repeated on a grid throughout Tohoku. The resolution is such that the spatial recurrence rate λx,ydoes not vary within each cell. For the regional recurrence rateλt an average of 120 volcanic events per million years is used, effectively taking average Quaternary activity [1].

Using smoothing coefficients of 1 - 1.5 km for the Cauchy kernel, as well as weighting eruption volumes, probability plots were constructed using equation (3). A probability contour plot for one case is shown in Figure 6.

Figure 6.

Probabilities of one or more volcanic events occurring in the next 100 ka based on a priori PDF (Cauchy (h = 1.5 km). White triangles denote the volcanic events used in the calculation and black lines are active faults [35]

The highest probabilities are located in the Sengan region (10-6 - 10-5 / a) which has the highest density of volcanic events in the Tohoku volcanic arc. By testing the two volcanic event sub-definitions (weighted with and without eruption volume), [1] found that the probabilities in the vicinity of monogenetic volcanoes on the back-arc region were higher when volcanic events were not weighted with eruption volumes (1 - 4 x 10-7/a, weighted; 1 - 4 x 10-6/a, un-weighted), whereas the probabilities around established centers such as Iwaki, Towada, Sengan and Chokai were reduced slightly. This is expected as volcanoes with large eruption volumes are the sites of highest magma production. However if the focus of the assessment is on new volcano event formation, irrelevant of whether the new volcano evolves into are large complex stratovolcano and/or caldera or not, then selecting the volcanic event definition that is not weighted with eruption volume would seem more appropriate.

4.5. The likelihood function

Here the a priori PDF is conditioned 3He/4He ratios. This is done by normalizing additional data into a likelihood function according to how such information is judged by the expert and/or indicated by experimental result to relate to the distribution of volcanism [1]. Helium isotopes have been shown to provide evidence for the presence of mantle derived materials in the crust, and hence potential volcanism based on distinct 3He/4He ratios (Figure 7) [17, 18]. [1] looked at seismic tomographs and geothermal gradients. This is because P velocity perturbations (ΔV/V) in particular at 40 km depth [29] is a good estimate of the minimum depth of partial melting in the mantle for most of the volcanoes in Tohoku. Geothermal gradients on the other hand were used by [1] as an additional aid to P velocity perturbations since it is not possible to differentiate heat from P wave velocity alone.

Figure 7.

Distribution of R/RA data (Ra denotes the atmospheric 3He/4He ratio of 1.4×10-6) taken from boreholes and hot springs [20, 54, 55]

In order to compare the R/RA ratios, cumulative plots of values around all volcanic events and values of 10 km2 bins over all of Tohoku are plotted. Figure 8 shows R/RA ratios below all volcanic events (8a) and volcanic events less than 100 ka (8b). In both cases approximately 90% of all volcanic events are distributed in regions with R/RA ratios greater than 3. In other words 90% volcanoes are located in regions where 3He/4He is elevated.

The R/RA ratios are interpolated to represent a continuous, differentiable surface and then the spatial data are mapped into a likelihood function based on the percentage of recent volcanic events that lie within the binned R/RA ratios in Figure 8. For low P velocity perturbation, [1] assumed an inverse linear relationship; based on the interpretation that low P velocity perturbation corresponds to partial melting (and hence increased probability of volcanism). In this case, 10% of volcanoes less than 100 ka located in regions where ΔV/V ranged from -6% to -5% etc. For geothermal gradients [1] used a linear relationship for recasting the data values as a PDF.

Figure 8.

umulative plots of R/RA values below volcanic events and the whole of Tohoku (10km2 grid spacing).

4.6. A posteriori probabilities

Finally the a posteriori PDF is calculated from the likelihood function and the a priori PDF using equation (1). The integral across the entire field of both the a priori and the a posteriori PDFs is set to unity; however the shape of the distribution is modified by the likelihood function. The probability of a new volcanic event is calculated for each grid point using equation (3).

Figure 9.

Comparison of a priori (a) and a posteriori probability plots (b) calculated with a Cauchy kernel (h = 1.5 km) conditioned on R/RA ratios. Both PDFs a weighted by eruption volume. Black lines are active faults [53].

Using equations (1) to (3) above, two dimensional probability plots are subsequently constructed showing the probability of one or more future volcanic event(s) forming during the long-term, given that a volcanic event will occur in the Tohoku volcanic arc during 100 ka. Figure 9 shows a comparison of the a priori probability (9a) and a posteriori probability (9b) conditioned on R/RA ratios of one or more volcanic events forming in 100 ka.

The probability of new volcanic event formation in the forearc region to the east of the volcanic front is reduced slightly in the a posterior probability calculation. This is more evident when we repeat the calculation for new volcanic events forming in the next 1Ma (Figure 10).

Figure 10.

Probability of the formation of a new volcanic event over the next 1Ma; a priori (a) and a posteriori (b) probability plots calculated with a Cauchy kernel (h = 1.5 km) conditioned on R/RA ratios.

The R/RA analyses are compared with the probability calculations conditioned on P velocity perturbations (10 or 40 km) (Figure 11) and geothermal gradients (Figure 12) [1]. The a posteriori probability below Iwaki volcanic event is particularly low when conditioned on 40 km depth P velocity perturbation datasets but that there was no significant change beneath Chokai, another andesitic volcano on the back-arc side of Tohoku. With the a posteriori calculation conditioned on the R/RA analyses, no decrease is seen in the probabilities below Iwaki volcano when compared to a priori plots. Similar results can be seen when probabilities are conditioned on 10km depth P velocity perturbations (Figure 11a) or geothermal gradients (Figure 12) [1].

[1] found that a posteriori probabilities are not reduced when compared to a priori probabilities in the northern regions when conditioning on shallower (10 km) P velocity perturbations or on geothermal gradients. This seems reasonable as seismic velocity structure [57] and the depth of Curie isotherms [58] in this part of Tohoku reveal high-temperature-like geophysical anomalies at depths of up to 10 km below Iwaki volcano which may be indicative of the shallower depths (ca. 10km) of magma chambers.

Figure 11.

A posteriori probability plots calculated with: (a) Cauchy kernel (h = 1.5 km) conditioned on ΔV/V at 10 km depth; (b) Cauchy kernel (h = 1.5 km) conditioned on ΔV/V at 40 km depth (modified from [1]).

Figure 12.

A posteriori probability plots calculated with Cauchy kernel (h = 1.5 km) conditioned on geothermal gradients (modified from [1])


5. Discussion

The main advantage of probabilistic based models over deterministic models is that the probability of new volcano event formation is never zero. [1] showed that Bayesian inference is well-suited for formally combining observations relevant to the imaging of the magma source region (e.g. seismic tomography) with quantitative methods for estimation of volcano intensity. Moreover, the strength of Bayesian inference is that probabilistic assessments can be improved with increased understanding of the physical processes governing magmatism and/or data that may be indicative of future volcanism such as the helium isotope ratios presented here. Nevertheless it is worth examining the logic behind what we perceive to be ‘data’ and what we mean by a priori information and knowledge.

5.1. Which datasets are a priori information?

[1] used the volcano geographical datasets themselves as a starting point in their analysis. The same approach was applied in this chapter. In the first step a Cauchy kernel was used to calculateλx,y. This means that the probability new volcanic event formation decreases with increasing distance from existing volcanic events. In the case of selecting a location for a geological repository, there may be a need to have a conservative estimate and accept that extreme events may occur. In this case, selection of the Cauchy as the a priori PDF would be most appropriate due to the thickness of the tails. This is especially the case if we have to make probability calculations for periods for 1Ma where the tectonic setting can change, and we may have a shift in the location of the volcanic front. The probabilities in distal regions would only be reduced in the a posterior probability calculation if newly obtained evidence in such regions shows that volcano formation is zero or close to zero. Since R/RA ratios vary due to the heterogeneous release of mantle helium and elevated ratios and are likely to indicate the presence of partial melting [e.g. 20] datasets may give some indication on the future location of volcanism even in non-volcanic regions. Seismic tomography on the other hand offers a direct view of the mantle that can be interpreted in terms of degree of partial melting [e.g. 58, 59].

It could be equally argued, however that the logic of [1] should be reversed in that the models based on seismic tomography or elevated helium isotope ratios are in fact a priori information or knowledge, and the location of volcanic events the ‘data’. The philosophy here is that we assume new volcanic events will form in regions where partial melting is likely to be occurring now and that the distribution of known volcanic events are the datasets updating our model and/or knowledge. However, this may be true for the very recent volcanism up to about 1,000 years say, but how relevant are volcanic events that formed over 100,000 years ago or more to the present day geophysical snap-shot of the Earth’s crust or upper mantle? This question is difficult to answer as there is very little information on the temporal behaviour of partial melting in the mantle. This is also evident when we try to evaluate our forecasts below. A problem here is that we are always trying to predict the formation of future volcanic events which may or may not be related to historic volcanic events. Our closest ‘data’ to such future events are thus present day geophysical snap shots of the current conditions in the crust or upper mantle and/or newly formed or forming volcanic events. This has been the motivation for [1] to use such geophysical data or models as the basis of the likelihood function.

On the other hand there are also practical aspects to be considered particularly when starting a hazard analysis in a region where there have not been many studies. In such a case, the only data available to begin with might be just the geographical location of volcanoes. Information from more complicated and expensive surface based investigations might not come until later.

5.2. Model evaluation

Since it is not possible to infer directly the location of future volcanic events that will form in the next 0.1 to 1 Ma from now, models can instead by evaluated by calculating the probability of the new volcanic events that formed after some time in the past, using all volcanic events that formed before that time [1, 38]. Since we calculate the probability of future volcanism in the next 100 ka in most of the analyses described here, 100 ka is selected as the timeframe in the verification calculations. In Tohoku, as there are a large number of dated volcanic events it is possible to verify the Bayesian models developed to a certain extent by using all volcanic events that formed before 100 ka to predict the location of volcanic events that formed between 100 ka and the present day. Since the ‘new’ volcanic events are still in the past, it is possible to compare probability plots with the locations of volcanic events we are attempting to forecast. Figure 13 shows probability plots for the Cauchy PDF (h=1.5 km) and the a posterior probability conditioned on R/RA ratios. All volcanic events that formed before 100 ka (white triangles) during the Quaternary were used to make a forecast for the period from 100 ka ago to the present day. All subsequent volcanic events that formed during the forecast period are shown in red. Probability calculations are then compared with the locations of volcanoes that formed during the forecast period.

Figure 13.

Verification probability plots calculated using all volcanic events before 100 ka (white triangles) in order to predict the subsequent distribution of volcanic events that formed from 100 ka to present (red triangles) for (a) the a priori probability (Cauchy, h=1.5km, eruption volume weighting included) and the a posteriori probability (b) conditioned on R/RA ratios.

In both cases, all subsequent volcanoes formed in regions where the probability was at least 10%. Approximately 50% of newly formed volcanic events formed in regions where the probability was at least 25%. There was approximately 10% increase in probabilities in the locations were volcanoes formed in the a posteriori probability calculations.

Probability calculations above were made using single inferences on one set of data. However, Bayes’ theorem allows beliefs to be updated as additional information becomes available. [1] attempted this by combining geothermal and seismic tomography datasets (Figure 14).

Figure 14.

Verification probability plots calculated using all volcanic events before 100 ka (white triangles) in order to predict the subsequent distribution of volcanic events that formed from 100 ka to present (red triangles): (a) Cauchy kernel (h = 1.5 km) conditioned on ΔV/V at 40 km depth, (b) Cauchy kernel (h = 1.5 km) conditioned on geothermal gradient and ΔV/V at 10 and 40 km depths. (Figure modified from [1]).

By conditioning on P velocity perturbations at 40 km depth, the model assigned a low probability for the Iwaki volcano which formed in region where probability was calculated to be low (< 10-9/a). This could be improved upon by including both P velocity perturbations at 10 km depth and geothermal gradients [1].

5.3. Varying the temporal recurrence rate

The temporal recurrence rates in Tohoku have been steady state from 0.5 Ma to present [28]. This implies that recurrence rates are likely to remain steady state for at least the next 0.1 Ma. However if we need to assess volcanism over a much longer time frame such as 1.0 Ma more care is needed. In addition to temporal recurrence rates, the type of volcanism can also change over extended timeframes. For example, [28] used eruptive volumes of volcanic products along the volcanic front in Tohoku to identify three sub-stages with distinct types of volcanism and volumetric changes in the last 2.0 Ma. From 2.0 to 1.2 Ma large-scale felsic eruptions were predominant; during 1.2 to 0.5 Ma, the crustal stress changed to compression yielding the formation of strato-volcanoes all along the Tohoku volcanic arc. Finally, from 0.5 Ma to the present day, volcanically active areas became localized [34]. The volcanic front also shifted over a 2.0 Ma period [60] (Figure 15)

Figure 15.

Shift in the volcanic front in Tohoku (compiled from [60])

It can thus be argued that for periods beyond 0.1Ma, it is unreasonable to treat λtin equation (3) as constant or steady state. One option might be to assign say a Weibull function where recurrence rates can increase or decrease with time [61] if there is sufficient age data to indicate temporal trends statistically. Alternatively one could assume that the temporal recurrence rates are entirely random with a tendency to cluster temporally [e.g. 22, 62]. Moreover, [22] showed that time clustering can have an impact on the spatial intensity of volcanoes.

A challenge though with utilizing temporal data are the quantity and quality of the age datasets and being consistent enough with the temporal definitions since eruptions may last for several days, weeks, months, years even longer. Having a consistent temporal definition is especially challenging when handling volcanic datasets on the regional scale described in this chapter. As highlighted in section 3, even for monogenetic volcanoes, the temporal definition is not so straightforward [41]. It was for this reason [42] argued that a drawback with nearest-neighbour models which are a function of both spatial and temporal parameters is that they require the ages of every single volcanic event within the volcanic field in question. Nevertheless in certain cases such as tectonically controlled basaltic fields, eruptions can be time predictable, [63] hence there is potential to improve on the Bayesian model presented here by taking into account time clustering in the temporal rate parameter.


6. Conclusions

Bayes’ thereom is a powerful statistical tool for incorporating additional datasets. In this chapter R/RA ratios were used in probabilistic volcanic hazard assessments applying the methodology developed by [1]. These were compared with earlier assessments in Tohoku incorporating low P perturbations at 10km and 40km depth and geothermal gradients. Probabilities of one or more volcanic event(s) forming in Tohoku for both analyses were found to be similar ranging from 10-10 – 10-9 /a between clusters and 10-5 /a within clusters. The Cauchy kernel, combined with multiple datasets successfully captures all subsequent volcanic events, including extreme events. This is particularly important when making calculations over 1Ma when the tectonic setting is likely to change resulting in a potential shift of the volcanic front. Although the Cauchy kernel appears to be over conservative for regions east of the volcanic front, where probabilities are expected to be negligible, values are reduced when R/RA ratios are included.



Diagrams of the probability plots were made using Generic Mapping Tools (GMT) [64]. The authors thank the constructive comments made by two anonymous reviewers which improved the manuscript.


  1. 1. Martin, A. J., Umeda, K., Connor, C. B., Weller, J. N., Zhao, D. and Takahashi, M. (2004), Modeling long-term volcanic hazards through Bayesian inference: An example from the Tohoku volcanic arc, Japan. J. Geophys. Res., 109, B10208, doi:10.1029/2004JB003201.
  2. 2. Wickman, F. E. (1966), Repose period patterns of volcanoes, Ark. Mineral. Geol., 4, 291-301.
  3. 3. Wadge, G. (1982), Steady state volcanism: Evidence from eruption histories of polygenetic volcanoes, J. Geophys. Res. 87, 4035-4049.
  4. 4. Klein, F. W. (1984), Eruption forecasting at Kilauea Volcano, Hawaii, J. Geophys. Res., 89, 3059-3073.
  5. 5. Sornette, A., J. Dubois, J. L. Cheminee, and D. Sornette (1991), Are sequences of volcanic eruptions deterministically chaotic? J. Geophys. Res., 96, 11,931-11,945.
  6. 6. Dubois, J., and J. L. Cheminee (1991), Fractal analysis of eruptive activity of some basaltic volcanoes, J. Volcanol. Geotherm. Res., 45, 197-208.
  7. 7. Pyle, D. M. (1998), Forecasting sizes and repose times of future extreme volcanic events, Geology, 26, 367-370.
  8. 8. Wadge, G., P. A. V. Young, and I. J. McKendrick (1994), Mapping lava flow hazards using computer simulation. J. Geophys. Res. 99, 489-504.
  9. 9. Connor L. J., C. B. Connor, K. Meliksetian and I. Savov (2012). Probabistic approach to modeling lava flow inundation: a lava flow hazard assessment for a nuclear facility in Armenia. J. App. Volc. 1, 3-19.
  10. 10. Crowe, B. M., M. E. Johnson, and R. J. Beckman (1982), Calculation of the probability of volcanic disruption of a high-level radioactive waste repository within southern Nevada, USA. Radioact. Waste Manage. Nucl, Fuel Cycle, 3, 167-190.
  11. 11. International Atomic Energy Agency (1997), Volcanoes and associated topics in relation to nuclear power plant siting, a safety guide, Provisional Safety Stand. Ser. 1, 49 pp., Vienna, Austria.
  12. 12. Weller, J. N., A. J. Martin, C. B. Connor, and L. Connor (2006), Modelling the spatial distribution of volcanoes: An example from Armenia, in Statistics in Volcanology, edited by Mader, H. M., Coles, S. G., Connor, C. B. and Connor, L. J, pp. 296, Geol. Soc. Lon. on behalf of IAVCEI.
  13. 13. McBirney, A., L. Serva, M. Guerra and C. B. Connor (2003), Volcanic and seismic hazards at a proposed nuclear power site in central Java, J. Volcanol. Geotherm. Res., 126, 11-30.
  14. 14. Woods A. W., Sparks S., Bokhove, O., LeJeune A. M., Connor C. B. and Hill B. E. (2002), Modeling magma-drift interaction at the proposed high-level radioactive waste repository at Yucca Mountain, Nevada, USA. Geophys. Res. Lett. 29 (13), 1641, doi:10.1029/2002GL014665
  15. 15. Connor, C. B., J. A. Stamatakos, D. A. Ferrill, B. E. Hill, I. Goodluck,, F. Ofoegbu, M. Conway, S. Budhi, and J. Trapp (2000), Geologic factors controlling patterns of small-volume basaltic volcanism: Application to a volcanic hazards assessment at Yucca Mountain, Nevada, J. Geophys. Res., 105, 417-432.
  16. 16. Selva J., Orsi G., Di Vito M. A., Marzocchi W., Sandri L. (2012) Probability hazard map for future vent opening at the Campi Flegrei caldera, Italy. Bull. Volc. 74: 497-510
  17. 17. Ozima, M., and F. A. Podosek (2002), Noble Gas Geochemistry, 2nd ed., 286 pp., Cambridge Univ. Press, New York.
  18. 18. Hilton, D. R. (2007), Geochemistry - The leaking mantle, Science, 318, 1389-1390.
  19. 19. Sano, Y., and H. Wakita, (1985), Geographical distribution of 3He/4He ratios in Japan: Implications for arc tectonics and incipient magmatism, J. Geophys. Res., 90, 8729-8741.
  20. 20. Umeda, K., K. Asamori, A. Ninomiya, S. Kanazawa, and T. Oikawa (2007), Multiple lines of evidence for crustal magma storage beneath the Mesozoic crystalline Iide Mountains, northeast Japan. J. Geophys. Res., 112, B05207, doi:10.1029/2006JB004590.
  21. 21. Marti J., and Felpeto A. (2010), Methodology for the computation of volcanic susceptibility An example for mafic and felsic eruptions on Tenerife (Canary Islands). J. Volcanol. Geotherm. Res., 195, 69-77.
  22. 22. Jaquet, O, C. Lantuejoul, and J. Goto (2012), Probabilistic estimation of long-term volcanic hazard with assimilation of geophysics and tectonic data. J. Volcanol. Geotherm. Res. 235-236: 29-36, doi:10.1016/j.jvolgeores.2012.05.003.
  23. 23. Hasegawa, A., N. Umino, and A. Takagi (1978), Double-planed structure of the deep seismic zone in the northeastern Japan arc, Tectonophysics, 47, 43-58.
  24. 24. Nakagawa, M., H. Shimotori, and T. Yoshida (1986), Aoso-Osore volcanic zone- The volcanic front of the northeast Honshu arc, Japan, Journal of the Japan Association of Mineralogy and Economic Geology, 81, 471-478.
  25. 25. Hasegawa, A., S. Horiuchi, and N. Umino (1994), Seismic structure of the northeastern Japan convergent margin: A synthesis, J. Geophys. Res., 99, 22,295-22,311.
  26. 26. Yoshida, T., T. Oguchi, and T. Abe (1995), Structure and evolution of source area of the Cenozoic volcanic rocks in Northeast Honshu arc, Japan, Memoirs of the Geological Society of Japan, 44, 263-308.
  27. 27. Takahashi, M. (1995), Large-volume felsic volcanism and crustal strain rate, Bulletin of the Volcanological Society of Japan, 40, 33-42.
  28. 28. Umeda, K., S. Hayashi, M. Ban, M. Sasaki, T. Oba, and K. Akaishi (1999), Sequence of volcanism and tectonics during the last 2.0 million years along the volcanic front in Tohoku district, NE Japan, Bulletin of the Volcanological Society of Japan, 44, 233-249.
  29. 29. Zhao, D., F. Ochi, A. Hasegawa, and A. Yamamoto (2000), Evidence for the location and cause of large crustal earthquakes in Japan, J. Geophys. Res., 105, 13,579-13,594.
  30. 30. Committee for Catalog of Quaternary Volcanoes in Japan (1999), eds. Catalog of Quaternary volcanoes in Japan [CD-ROM], The Volcanological Society of Japan.
  31. 31. Hayakawa, Y. (1985), Pyroclastic geology of Towada volcano, Bulletin of the Earthquake Research Institute, University of Tokyo, 60, 507-592.
  32. 32. Ban, M., S. Hayashi and N. Takaoka, K-Ar dating of the Chokai volcano, northeast Japan arc: A compound volcano composed of continuously established three stratovolcanoes, 46, 317 – 333.
  33. 33. Oki, J., N. Watanabe, K. Shuto, and T. Itaya (1993), Shifting of the volcanic fronts during Early to Late Miocene age in the Northeast Japan arc, The Island Arc, 2, 87-93.
  34. 34. Kondo, H., K. Kaneko, and K. Tanaka (1998), Characterization of spatial and temporal distribution of volcanoes since 14 Ma in the northeast Japan arc, Bulletin of the Volcanological Society of Japan, 43, 173-180.
  35. 35. Koyama, M., Y. Hayakawa, and F. Arai (1995), Eruptive history of the Higashi-Izu Monogenetic Volcano field 2: Mainly on volcanoes older than 32,000 years ago, Kazan, 40, 191-209.
  36. 36. Sheridan, M. F. (1992), A Monte Carlo technique to estimate the probability of volcanic dikes, paper presented at Third International Conference on High-Level Radioactive Waste Management, Am. Nucl. Soc., La Grange Park, Ill., 2033-2038.
  37. 37. Lutz, T. M., and J. T. Gutmann (1995), An improved method for determining and characterizing alignments of point like features and its implications for the Pinacate volcanic field, Sonora, Mexico, J. Geophys. Res. 100, 17,659-17,670.
  38. 38. Condit, C. D., and C. B. Connor (1996), Recurrence rates of volcanism in basaltic volcanic fields: An example from the Springerville volcanic field, Arizona, Geol. Soc. Am. Bull., 108, 1225-1241.
  39. 39. Kienle J., P. R. Kyle, S. Self, R. J. Motyka and V. Lorenz, (1980), Ukinrek Maars, Alaska: I, April 1977 eruption sequence, petrology and tectonic setting: J. Volcanol. Geotherm. Res., 7, 11-37.
  40. 40. Nemeth K. and S. J. Cronin (2011), Drivers of explosivity and elevated hazard in basaltic fissure eruptions: The 1913 eruption of Ambrym Volcano, Vanuatu (SW-Pacific). Jour. Volcanol. Geoth. Res., 201, 194-209, doi: 10.1016/j.jvolgeores.2010.12.007.
  41. 41. Kereszturi, G., K. Nemeth, G. Csillag, K. Balogh and J. Kovacs (2011). The role of external environmental factors in changing eruption styles of monogenetic volcanoes in a Mio/Pleistocene continental volcanic field in western Hungary J. Volcanol. Geotherm. Res., 201, 227-240. doi: 10.1016/j.jvolgeores.2010.08.018.
  42. 42. Connor, C. B., and B. E. Hill (1995), Three nonhomogenous Poission models for the probability of basaltic volcanism: Application to the Yucca Mountain region, Nevada. J. Geophys. Res., 100, 10,107-10,125.
  43. 43. Martin, A. J., M. Takahashi, K. Umeda, and Y. Yusa (2003), Probabilistic methods for estimating the long-term spatial characteristics of monogenetic volcanoes in Japan, Acta. Geophys., Pol.,51, 271-291.
  44. 44. Takahashi, M. (1994), Structure of polygenetic volcano and its relation to crustal stress field: 1. Stable and unstable vent types, Bulletin of the Volcanological Society of Japan, 39, 191-206.
  45. 45. Tarantola, A. (1990), Probabilistic Foundations of Inverse Theory, in Oceanographic and Geophysical Tomography, edited by Y. Desaubies, A. Tarantola and J. Zinn-Justin, pp. 1-27, Elsivier Science Publishers B. V.
  46. 46. Debski, W. (2004), Application of Monte Carlo techniques for solving selected seismological inverse problems, Publications of the Institute of Geophysics, Polish Academy of Sciences, B-34 (367), 207 pp., Warszawa, Poland.
  47. 47. Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin (1995), Bayesian Data Analysis, 526 pp., Chapman and Hall/CRC, Boca Raton.
  48. 48. de Bremond d’Ars, J., C. Jaupart, and R. S. J. Sparks (1995), Distribution of volcanoes in active margins, J. Geophys. Res., 100, 20,421-20,432.
  49. 49. Cressie, N. A. C. (1991), Statistics for Spatial Data, 900 pp., John Wiley, New York.
  50. 50. Hayashi, S., K. Umeda, M. Ban, M. Sasaki, M. Yamamoto, T. Oba, K. Akaishi, and T. Oguchi (1996), Temporal and spatial distribution of Quaternary volcanoes in northeastern Japan (1) - Spreading of volcanic area toward back-arc side – Program and Abstract, Volcanological Society of Japan, no. 2, 71-71.
  51. 51. Clark, P. J., and F. C. Evans (1954), Distance to nearest neighbour as a measure of spatial relationships in populations. Ecology, 35, 445-453.
  52. 52. Diggle, P. J. (1985), A kernel method for smoothing point process data, Appl. Statist., 34, 138-147.
  53. 53. AIST (2009), Active fault database of Japan, version 2009. Research Information Database DB095, National Institute of Advanced Industrial Science and Technology.
  54. 54. Wakita, H., and Y. Sano (1983), 3He/4He ratios in CH4-rich natural gases suggest magmatic origin, Nature, 305, 792-794.
  55. 55. Sano, Y., Y. Nakamura, and H. Wakita (1985), Areal distribution of 3He/4He ratios in the Tohoku district, Northeastern Japan, Chem. Geol., 52, 1-8.
  56. 56. Nakajima, J., T. Matsuzawa, A. Hasegawa and D. Zhao (2001), Three-dimensional structure of Vp, Vs and Vp/Vs beneath northeastern Japan: Implications for arc magmatism and fluids, J. Geophys. Res., 106, 21,843 – 21,857, doi:10.1029/2000JB000008
  57. 57. Tamanyu S., K. Sakaguchi, T. Sato and M. Kato (2008), Integration of geological and geophysical data for extraction of subsurface thermal and hydrothermal anomaly areas – Examples in Tohoku and Chugoku/Shikoku districts, Japan, Bulletin of the Geological Survey of Japan, 59, 7-26.
  58. 58. Zhao, D., A. Hasegawa, and S. Horiuchi (1992), Tomographic imaging of P and S wave velocity structure beneath northeastern Japan, J. Geophys. Res., 97, 19,909-19,928.
  59. 59. Zhao, D. (2001), Seismological structure of subduction zones and its implications for arc magmatism and dynamics, Phys. Earth Planet. Int., 127, 197-214.
  60. 60. Umeda. K., H. Osawa, T. Nohara, E. Sasao, O. Fujiwara, K. Asamori, and N. Nakatsuka (2005), Current status of the geoscientific research for long-term stability of the geological environment in JNC’s R& D programme, Journal of Nuclear Fuel Cycle and Environment, 11, 97-112.
  61. 61. Ho, C-H. (1991), Nonhomogenous Poisson model for volcanic eruptions, Mathematical Geology, 23, 167-173.
  62. 62. Jaquet, O., S. Low, B. Martinelli, V. Dietrich, and D. Gilby (2000), Estimation of volcanic hazards based on Cox stochastic processes, Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, 25, 571-579.
  63. 63. Valentine, G. A. and F. Perry (2007). Tectonically controlled, time-predictable basaltic volcanism from a lithospheric mantle source (central Basin and Range Province, USA). Earth Planet. Sci. Lett., 261, 201-216, doi: 10.1016/j.epsl.2007.06.029.
  64. 64. Wessel, G. P. L., and W. H. F. Smith (1998), New improved version of the generic mapping tools released, Eos, 79, 579.

Written By

Andrew James Martin, Koji Umeda and Tsuneari Ishimaru

Published: September 27th, 2012