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Probabilistic estimation of long-term volcanic hazard with assimilation of geophysicsand tectonic data

O. Jaquet a,⁎, C. Lantuéjoul b, J. Goto c

a In2Earth Modelling Ltd, CH-4051 Basel, Switzerlandb Mines ParisTech, F-77300 Fontainebleau, Francec Nuclear Waste Management Organization of Japan, J-1080014 Tokyo, Japan

a b s t r a c ta r t i c l e i n f o

Article history:Received 24 August 2011Accepted 5 May 2012Available online 12 May 2012

Keywords:Long-term volcanic hazardProbabilistic estimationCox processGeophysics and tectonic dataIsland of Kyushu

Risk assessments in relation to the siting of potential geological repositories require the estimation of long-term volcanic hazard. Owing to their tectonic situation, many industrial regions around the world are con-cerned by such evaluation. For sites near volcanically active regions, the prevailing source of uncertainty islong-term volcanic hazard. The complexity and non-linearity of volcanic processes, the space–time variabilityin terms of distribution and intensity for volcanic events and the limited amount of information make prob-abilistic estimation of volcanic hazard ineluctable. The needs for reliable methodologies for volcanic and tec-tonic hazard assessments in Japan have stimulated the development of specific stochastic models forimproving uncertainty characterization. A conditional Cox process with a multivariate potential was devel-oped for the assimilation of geophysics and tectonic data (gravity data, GPS strain rate data and active faults).The theoretical basis and concepts of the proposed model are given and a methodological illustration is pro-vided using data from the island of Kyushu.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Quantification of long-term volcanic hazard becomes of para-mount importance when assessing risks related to the isolation of po-tential geological repository sites. Such risk evaluation concerns manyindustrial regions around the world, in particular the Japanese islandsdue to their tectonically active nature.

For sites near volcanically active regions, long-term volcanic hazardconstitute the dominant source of uncertainty as input for risk assess-ments. Uncertainty is mainly related to imperfect knowledge of non-linear volcanic processes, to space–time variability of distribution andintensity for volcanic events, and to a limited amount of information.For these reasons, the estimation of volcanic hazard based on a probabi-listic formalism is internationally getting more frequently employed(Connor et al., 2009). In addition, recent events at Fukushima highlightthe importance of using probabilistic approaches to assess tectonic haz-ards and risks to critical facilities in potentially susceptible locations(Connor, 2011). Therefore, it is of prime importance for both the Nucle-ar Waste Management Organization of Japan (NUMO) and the widergeoscientific community to have a probabilisticmethodology for the as-sessment of long-term volcanic hazard. In Japan, the siting of a geolog-ical high-level radioactivewaste (HLW) repositorywill consider regionsthat are not obviously excluded on the basis of recent and current

volcanism. At the beginning of its repository siting program in 2002,NUMO has initiated a long-running project for the development of reli-able methodologies for volcanic and tectonic hazard assessments.

The first stochastic models for the estimation of long-term volcanichazards were developed in connection with the potential high-level ra-dioactive waste (HLW) repository at the Yucca Mountain (YM) site inNevada (USA). YM is located in the vicinity of a Quaternary volcanicfield; the aim was to assess the potential for a repository disruption dueto basaltic volcanism(Perry et al., 2000). The simplest approach for the es-timation of volcanic hazard used a homogeneous Poisson model (Croweet al., 1982) under the assumption of complete spatial and temporal ran-domnesses of the events. AnonhomogeneousWeibull–Poissonmodel ap-plied by Ho (1991) at Yucca Mountain made it possible to estimate therecurrence rate of new volcanoes being formed as a function of time. Asshown by Connor and Hill (1994), the hazard estimates provided usingthis model are very sensitive to the total time under consideration. Infact, Bebbington and Lai (1996) have demonstrated that the non-homogeneous and nonstationary model of Ho (1991) was an unsatisfac-tory tool for describing the time behavior of volcanic activity. Theseauthors concluded that since datasets are small and likely incomplete, inthe absence of a simple systematic trend, a stationary model is a betterchoice as it imposes less assumptions on the volcano behavior. Ho andSmith (1998) proposed a nonhomogeneous space–time Poisson processfor the identification and quantification of volcanic phenomena distribut-ed through space and evolving in time. Using this model, they could esti-mate the probability of at least one volcanic disruption of a repository atthe YuccaMountain site during the next 10,000 years. In order to account

Journal of Volcanology and Geothermal Research 235–236 (2012) 29–36

⁎ Corresponding author.E-mail address: olivier.jaquet@in2earth.com (O. Jaquet).

0377-0273/$ – see front matter © 2012 Elsevier B.V. All rights reserved.doi:10.1016/j.jvolgeores.2012.05.003

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for the spatial distribution in basaltic volcanic fields, Connor and Hill(1995) presented nearest-neighbor nonhomogeneous Poisson modelsthat allowed the estimation of spatial intensity and the associated proba-bility of volcanic eruption occurring in the Yucca Mountain region at alocal scale. The application of these models requires using specific kernelmethods for the estimation of their parameters (Connor and Connor,2009). The nonhomogeneous Poisson models were extended by Martinet al. (2004) in a Bayesian framework to integrate additional geologicaland geophysical information. Theywere used to estimate future locationsof volcanoes for siting purposes for a nuclearwaste repository in Japan. Allthese stochastic models are of Poissonian orMarkovian type and volcaniceruptions are considered as point processes that can occur either in thetimeor in the space–timedomain. They donot describe space–time struc-tured (non-Markovian) behavior as is likely to be observed in volcanic re-gions. In addition, no uncertainty is associated with the potential ofvolcanism, as within the framework of such models it is considered tobe deterministic.

Recently, methodologies for the assessment of the future location ofvolcanic events were developed by Marti and Felpeto (2010) for Tene-rife (Canary Islands) and Lindsay et al. (2010) for the Auckland VolcanicField in New Zealand. The former approach uses a nonhomogeneousPoisson processwith assimilation of structural lineations and past erup-tion locations for hazard estimation while the latter method appliesBayesian event trees (Newhall and Hoblitt, 2002; Marzocchi et al.,2004) for forecasting onset time and location of various eruption styles.These approaches are intended for short- tomedium time frames (yearsto decades) in relation to volcanic crises, urbanization and land-useplanning issues.

The probabilistic methodology for volcanic and tectonic hazard as-sessments developed by NUMO (Apted et al., 2004; Chapman et al.,2008, 2009b; Tsuchi et al., 2008) with an international team of geosci-entists (Japan, United Kingdom, New Zealand, USA, Switzerland andFrance), addresses time frames up to 100,000 years. As part of thismethodology, several stochastic models were developed using specificgeological conceptualizations based on various datasets and informa-tion related to past and current volcanic activity, their geophysical sig-nature and related tectonics.

The Cox process constitutes one of the stochastic models that wereapplied for the estimation of long-term volcanic hazard in Japan(Jaquet et al., 2008, 2009). This model was used previously at shortterm for the estimation of volcanic hazard at Stromboli volcano(Jaquet and Carniel, 2001). Besides describing the distribution of vol-canic events, the Cox process enables the uncertainty characterizationrelated to its intensity function, considered as random. This stochasticprocess becomes doubly stochastic and corresponds to a generaliza-tion of the nonhomogeneous Poisson process.

The concepts and theoretical basis of this model are given below;developments were undertaken in order to extend the assimilationcapabilities of the Cox process with respect to additional data types,such as rock deformation and age data. An illustration is providedusing data from Kyushu. Estimation of volcanic hazard was performedat the scale of the whole island as well as in relation to specific tecton-ic domains determined by rock deformation analysis. We emphasizethat this case study is only used as an example; no region in Japanis yet considered specifically as an HLW candidate site.

2. Conceptualization

Long-term volcanic hazard assessment requires the characterizationof distribution and occurrence of volcanic events. In order to integrategeological and tectonic information, we introduce the notion of poten-tial of volcanism which represents the propensity of a given region tobe affected by volcanic events. The potential of volcanism, being un-known, is considered as randomly structured within the context ofthe stochastic model. While the structured part represents the currentgeological and tectonic knowledge, the random part incorporates the

uncertainty, related to processes and parametrization, which is associ-ated with this information.

From a conceptual point of view, based on the current geoscientificknowledge, the following pieces of evidence and hypotheses have tobe incorporated within our modeling perspective: (i) the distributionof volcanic events presents spatial patterns describable using a randompotential of volcanism, (ii) the spatial distribution of volcanic events isexpected to be statistically correlated to the geophysical signature ofcrustal and mantle structures; to the location of active faults, as wellas to strain rates obtained from rock deformationmodeling, and (iii) fu-ture events are likely to be located in zones of past activity and their lo-cation presents some degree of statistical correlation with geophysicsand tectonic data.

3. Model development

Within the framework of the stochastic model, the volcanic eventsthat occurred during the Quaternary are considered as a particular reali-zation of a (random) point process. Likewise, the potential of volcanismduring this period is interpreted as a particular realization of a (positive)random intensity function Z. Partitioning the volcanic region of interestinto small domains (ai, i∈ I), the potential of domain ai is denoted by Zi.

In what follows, the two properties of the Cox process (Cox, 1955;Lantuéjoul, 2002) are assumed to be satisfied: (1) the number Ni ofvolcanic events that occurred in the domain ai is Poisson distributedwith random mean Zi; (2) given the potentials Zi, Zj, …, Zk of the do-mains ai, aj,…, ak the numbers of volcanic events Ni, Nj,…, Nk are mu-tually independent.

It should be emphasized that property (2) means that the num-bers of volcanic events in pairwise disjoint domains are only condi-tionally independent. They are not independent because thepotential conveys its own structure on the Cox process.

Property (1) can be expressed as:

P Ni ¼ nf g ¼ E e−ZiZni

n!

� �;n ¼ 0;1;2;… ð1Þ

which implies that Ni is not Poisson distributed unless Zi is determin-istic. However, Ni and Zi possess the same mean, and even the sameconditional mean:

E Ni Zj g ¼ Zi:f ð2Þ

In other words, given the potential of all domains of interest, themean number of events occurred in domain ai is precisely the poten-tial of that domain. The location of zones of preferential magma gen-eration is among the factors that contribute to the potential; evidencefor the location of these zones can be obtained from gravity anomalystudies and localizations of active faults.

Therefore, geophysics and active fault data are also interpreted asparticular realizations of random functions G=(Gi, i∈ I),S=(Si, i∈ I).Owing to the integration of geophysics and tectonics to the potential,the distribution of the number of volcanic events is not directly de-pendent on this information when the potential is known:

D Ni Z;G; Sj Þ ¼ D Ni Zij Þðð ð3Þ

A flexible way to model the dependence relationships betweenthe potential, the geophysical information and the active fault datais to express that their respective transforms in Gaussian space arepairwise bi-Gaussian. Z, G and S are assumed to be written as follows:

Zi ¼ φZ YZi

� �;Gi ¼ φG YG

i

� �; Si ¼ φS YS

i

� �ð4Þ

where φZ, φG and φS are monotonic increasing functions (i.e. Gaussiananamorphosis functions; Chilès and Delfiner, 1999), and where YZ, YG

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and YS are standardized Gaussian random functions. In addition, YZ,YG and YS are related by the regression formula:

YZi ¼ ρZGY

Gi þ ρZSY

Si þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ρ2

ZG � ρ2ZS

qYRi ; i∈I ð5Þ

which involves the correlation coefficients ρZG, ρZS and an additionalstandardized (residual) Gaussian random function YR independentof YG and YS. Under the assumption that the correlations with the po-tential prevail, the correlation between the geophysical informationand the active fault data is neglected since no correlation was ob-served between gravity data and active faults when comparing theirrespective maps (cf. Fig. 2).

For the estimation of volcanic hazard, the developed Cox processis characterized by a multivariate potential of volcanism, due to theassimilation of various datasets, related to geophysics and tectonics.

The estimation of volcanic hazard is performed by simulating the dis-tribution of volcanic events likely to occur during a certain period of timein the future within the region of interest. In addition, the simulation hasto deliver volcanic events that are more likely to be located in zones ofpast activity. Therefore, the simulation requires to be conditioned to allavailable data corresponding to the location of past volcanic events. Theidea is to simulate the potential of volcanism conditioned on the numberof volcanic events and on the available data known for the analyzed re-gion. The conditioning is achieved only on the numbers of past volcanicevents ni and the geophysical and active fault data gi and si known ineach domain ai. In particular, the exact location of each volcanic event isnot taken into account. The proposed algorithm for the conditional simu-lation of the potential is based on the Gibbs sampler (Geman and Geman,1984). This is an iterative algorithm that comprises the following steps:

(i) generate YiR~Gaussian(0, 1) for each i∈ I;

(ii) select an index i at random;(iii) generate y0~D(YiR|YjR=yj

R, j≠ i);(iv) compute yi

G=φG−1(gi), yiS=φS

−1(si) and

z0 ¼ φZ ρZGyGi þ ρZSy

Si þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ρ2

ZG � ρ2ZS

qy0

� �;

(v) generate n0~Ρoisson(z0);(vi) if n0=ni; then put yi

R=y0 and zi=z0;(vii) go to (ii).

Step (i) is used to initialize the Gaussian residuals YiR. This can bedone either by generating them separately, as written in the algo-rithm, or jointly, by resorting to the standard techniques used for sim-ulating Gaussian random functions such as the turning bands method(Lantuéjoul, 2002). The usual procedure for step (iii) is to sample y0from a Gaussian distribution. Its mean is the simple kriging estimate(Wackernagel, 2003) of YiR starting from all yjR except yiR. Its varianceis the corresponding kriging variance (Wackernagel, 2003). The cor-relation between the potential of volcanism and the data is intro-duced at step (iv). In its design, the algorithm runs forever. Inpractice, it is stopped when each potential zi has been effectivelyupdated more than several hundred times.

At this stage, only the potential (zi, i∈ I) of the past volcanicevents has been generated. This potential is representative only ofthe period of time tp from which all data originate. The aim is the sim-ulation of volcanic events likely to occur during the future period oftime tf, thus the future potential (zif, i∈ I) is required. Given that thepotential varies very slowly in time, past and future potentials are as-sumed proportional. This leads to the following (proportional) algo-rithm to simulate the future volcanic events nif:

(i) compute zif=zi⋅(tf/tp) for each ai;

(ii) generate nif~Ρoisson(zif) for each ai.

Since volcanic activity is characterized by periods of activity andquiescence. In general, future volcanic activity is not independent of

the recent volcanic patterns that have occurred in the past. Therefore,a correction factor Fc is applied to the previous algorithm to simulatethe future volcanic events nif:

(i) compute zfi ¼ zi⋅ tf =tp� �

⋅Fc for each ai;

(ii) generate nif~Ρoisson(zif) for each ai.

Assuming independence between time and spatial components ofvolcanic events, the estimation of the correction factor requires thesimulation of the distribution of volcanic events likely to occur duringa given interval of time in the future. The time series of interest de-scribes the occurrence of past volcanic events during a given period,e.g. the Quaternary. Therefore, along the time axis, each volcanicevent is therefore characterized by its age; taken as the age of theonset of volcanic activity. The period under study is partitioned intosmall time intervals; the analyzed variable is then the number ofevents that have occurred in these time intervals. The characteriza-tion of the past behavior of volcanic events enables to simulate thedistribution of the number of events likely to occur in a future timeinterval with a given duration, for example, of 100,000 years. Usinga Cox process in time, the future potential is simulated; its compari-son to the proportional potential delivers an estimate of the correc-tion factor.

The conditional simulation algorithm allows the estimation of vol-canic hazard for each domain of the region of interest during the pe-riod of time considered. A Monte Carlo approach is performed usingseveral thousand simulations in order to derive stable probability es-timates for future volcanic events:

P Nfi≥1

n o≈ 1

Ksim

XKsim

k¼1

1k nfi≥1

� �ð6Þ

where Ksim is the total number of simulations and 1k(nif≥1) equals 1when the kth simulation assigns the domain ai to one or more volca-nic events, and 0 otherwise.

The proposed model is illustrated by performing estimation of vol-canic hazard at the scale of Kyushu and regionally for two tectonicdomains.

4. Case study of Kyushu

Kyushu is the southernmost and third largest island in the Japa-nese archipelago. Since the Mesozoic, westward subduction-relatedprocesses along the eastern margin of Asia have produced most ofthe geology of Japan (Sugimura and Uyeda, 1973). The subductionof the Philippine Sea Plate beneath the Eurasian Plate at the Ryukyutrench and the Nankai trough (Fig. 1) drives the volcanism in thenorthwestern, central and southern volcanic regions of the island ofKyushu (Kamata, 1998).

For the last 2 Ma, typical arc volcanism has been predominant inKyushu island. The volcanic arc is characterized by a diversity of vol-canic manifestations such as huge and small calderas (e.g. Aso andIkeda-ko), lava dome complexes (e.g. Kuju) and polygeneticstratocones (e.g. Sakurajima). Since 2 Ma, the trend of volcanic arcformation is orientated NE–SW in the island of Kyushu.

In Kyushu, volcanism location appears to be strongly associated tolocal and regional tectonics (Chapman et al., 2009a; Mahony et al.,2011). Comparison of volcano and active fault locations displays evi-dence of some degree of correlation. These observations can beexplained by tectonic extension and thinning of the crust likely tocreate space for magma migration and potentially shape a volcanicfront development. The occurrence of faulting and the localizationof tectonic strain is also likely to be enhanced by magma ascent weak-ening the crust. Such tectonic and magmatic processes will inducepositive feedback loops, with potential improvement of correlationbetween volcanism and extensional strain in Kyushu island.

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Other evidence for zones of preferential magma generation be-neath Kyushu volcanic arc include low-velocity anomalies obtainedby seismic tomography studies (Salah and Seno, 2008; Saiga et al.,2010) as well as low-gravity anomalies. Both of these anomalies arelikely to correlate with volcano location.

The aim is the estimation of the probability for the formation ofnew volcanoes at the scale of Kyushu as well as for two tectonic do-mains (Extensional arc and Southern arc domains) over a proposedperformance period of 100,000 years. All Quaternary types of volca-noes (those active within the last 2 Ma) of Kyushu are considered asrepresenting potentially active volcanic areas for the future.

The Kyushu volcano dataset (Chapman et al., 2009a), comprising240 Quaternary volcanic events, has been created by collecting datafrom the following different sources: the AIST online Quaternary vol-cano database (AIST, 2008), various field trips, individual papers andJapanese websites. The age of volcano formation is determined bytaking the oldest available eruption data. The general location forthe 76 active faults was obtained from the database of the National

Institute of Advanced Industrial Science and Technology (AIST,2009). These faults were then more accurately localized (Chapmanet al., 2009a) using the database of Nakata and Imaizumi (2002).For the gravity data, the regional digital gravity map of Kyushu,established by the Geological Survey of Japan (AIST, 2002) was ap-plied for hazard modeling. These three datasets are displayed in Fig. 2.

The spatial variability of active faults was characterized using thedensity of faulting expressed in terms of cumulative fault length, Lc,in domain ai

Lc aið Þ ¼ ∑jlj ð7Þ

where lj is the length of fault j within domain ai.The cumulative fault length was estimated for Kyushu using a do-

main size of 5 km x5 km, which corresponds to the representativearea selected by the ITM methodology (Chapman et al., 2009b) to in-clude a geological repository.

Fig. 1. Tectonic context of Kyushu island within the Japanese archipelago (after Chapman et al., 2009a).

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For the estimation of volcanic hazard for Kyushuwith a 5 km×5 kmresolution, the potential of volcanism assimilates the following spatialdistributions: (a) Quaternary volcanic events, (b) gravity data and (c)cumulative lengths of active faults.

The statistical inference of the potential requires the following pa-rameters to be estimated: the potential and the anamorphoses φZ, φG

and φS; the correlation coefficients ρZG, ρZS; and the variogram of theGaussian random function YR.

Formally, the potential anamorphosis is defined by (Chilès andDelfiner, 1999): φZ(y)=FZ

−1° Ga(y) where FZ is the cumulative distri-

bution function of the potential, and Ga is that of a standard Gaussianvariable. The estimation of FZ is facilitated by the existence of a bijec-tive correspondence between the distributions of Ni and of Zi. A goodfit was found between the experimental distribution of the number ofvolcanic events, and a negative binomial distribution:

P Ni ¼ nf g ¼ Γ α þ nð ÞΓ αð Þn! 1−pð Þαpn; n ¼ 0;1;2;… ð8Þ

with parameter α=0.028 and proportion p=0.799. This automati-cally ensures that the potential can have its distribution modeled bya gamma distribution (Lantuéjoul, 2002):

f zð Þ ¼ bα

Γ αð Þ e−bzzα−1 ð9Þ

with the same parameter α and with the scale factor b=(1−p)/p=0.252.

Similarly, the gravity and the active fault anamorphoses are de-fined by φG(y)=FG

−1° Ga(y) and φS(y)=FS

−1° Ga(y). Their estima-

tion is simpler, because FG and FS are directly available from thedata. A dichotomic approach is used to compute the explicit valuesof φZ(y), φG(y)and φS(y) for y ranging from −5 to +5 with steps of0.01. The other values are retrieved by linear interpolation.

The next stage is the estimation of the correlation coefficients ρZGand ρZS. The starting points are the regressions E{Ni|Gi} and E{Ni|Si} ofthe number of volcanic events respectively on the gravity data and oncumulative lengths of active faults which are experimentally avail-able. Because the potential encompasses these datasets and due tothe conditional independence (cf. Eq. 3), these regressions coincidewith that of the potential on the gravity and fault data:

E Ni Gij g ¼ E Zi Gij g; E Ni Sij g ¼ E Zi Sij g:ffff ð10Þ

On the other hand, the regression of the right-hand side of thegravity Eq. (10) is analytically tractable after the estimation of the po-tential anamorphosis:

E ZijGi

¼ E φZ YZ

i

� �jYGi

¼ ∫φZ ρZGY

Gi þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−ρ2

ZG

qy

� �ga yð Þdy ð11Þ

where ga stands for the standard Gaussian probability densityfunction. Accordingly, successive guesses are made to find the ρZGvalue that best fits the empirical regression. A similar approach is per-formed for the determination of ρZS. Satisfactory agreements wereobtained for the correlation coefficients given in Table 1.

The final stage requires the characterization of the randomly struc-tured spatial patterns depicted by the potential in space. With the helpof the variogram (e.g. Chilès and Delfiner, 1999), these patterns can bequantified in terms of correlation scale. For example, if such a correla-tion exists for the number of volcanic events, then the closer the twodomains are, the more similar their numbers of volcanic events; and,vice versa, the further away they are from each other, the more inde-pendent are their number of volcanic events. For Kyushu, the determi-nation of the value for correlation scale (Table 1) was based on expertconsiderations and analog values from other regions of Japan (Jaquet etal., 2008; Jaquet et al., 2009). This procedure was dictated by theoreti-cal difficulties which have prevented the development of a generalmethod for the estimation of the correlation scale in the multivariatecase.

Past and future potentials in time were assumed proportional; i.e.zif=zi⋅(tf/tp). Using the Cox model, simulations of future volcanicevents were performed over a period of 100,000 years for Kyushu.10,000 Monte Carlo simulations were carried out to obtain stableprobability estimates. These results were displayed in form of a volca-nic hazard map for Kyushu (Fig. 3).

The complexity of Kyushu tectonics, characterized by highly dynamicand variable volcanic activity (Mahony et al., 2011), requires to better ac-count for regional particularities when performing hazard assessment.Kyushu was divided into four tectonic domains with distinct volcanicand tectonic characteristics (Chapman et al., 2009a). Such discriminationallows to improve volcanic hazard estimation, as it can be performed atthe scale of the tectonic domainwhile applying specific related data. Thetwo tectonic domains with the most Quaternary volcanic activity wereselected for hazard assessment: the Extensional arc domain and theSouthern arc domain. The datasets of these tectonic domains comprisesthe following types of data (Fig. 4):

Extensional arc domain: 87 Quaternary volcanic events, 31 activefaults and strain rates from GPS velocities.Southern arc domain: 86 Quaternary volcanic events, 28 activefaults and strain rates from GPS velocities.

Velocities of GPS sites in Japan are derived from data provided bythe Geological Survey Institute (GSI, 2009). The data were interpretedusing an elastic block model approach in order to remove from theGPS velocity field elastic strain effects due to subduction zone inter-seismic coupling (Chapman et al., 2009a; Wallace et al., 2009). Afterthe removal of the short-term elastic strain, such regional GPS veloc-ity field provides an estimation of the long-term tectonic strain rate

Fig. 2. Datasets for Kyushu with Quaternary volcanic events (black triangle), activefaults (red line) and Bouguer gravity map (colors). (For interpretation of the referencesto color in this figure legend, the reader is referred to the web version of this article.)

Table 1Parameters for Kyushu.

Case ρZGa ρZSb Variogram correlation scale Time component

I −0.18 0.40 50 km Proportional

a G: gravity data.b S: cumulative fault length.

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for the upper plate of each of the two tectonic domains studied inKyushu (cf. Fig. 4).

For the estimation of volcanic hazard for the arc domains of Kyushu,the following spatial distributions are assimilated by the potential ofvolcanism: (a) Quaternary volcanic events, (b) strain rates and (c) cu-mulative lengths of active faults. All these datasets were sampled at a5 km×5 km for the different tectonic domains. The same approach,as before (cf. Kyushu parameters), was applied for the estimation ofthe simulation parameters for the tectonic domains; their values aregiven in Table 2.

The correlation between potential and strain rate differs remark-ably when comparing Extensional and Southern arc domains. Forthe former domain, the correlation value is negative and for the latterdomain, it is positive. Such correlation means that for the Extensionalarc domain, volcanic events would tend to be more located in zoneswhere contraction occurs. This result would deserve additional anal-ysis as most of the strain rates present quite low values (i.e. below50 nanostrain/a). However, such difference in correlation values jus-tifies the estimation of volcanic hazard for each tectonic domain. Re-garding the correlation between potential and cumulative lengths ofactive faults, the Extensional and Southern tectonic domains presentsimilar values.

Sensitivity cases were carried out for the time component of theExtensional and Southern arc domains. For cases IIa and IIb, pastand future potentials in time were assumed proportional, and forcases IIIa and IIIb, the future potential was estimated by Cox simula-tions using a Monte Carlo approach (Fig. 5). Compared to the propor-tional case, this leads to the increase of the potential in the future toabout a correction factor of 6 for the simulated case. This result isthe consequence of integrating time correlation for the occurrenceof volcanic events. Since Kyushu has undergone numerous volcanicevents in its recent geologic history, forecasts of volcanic events forthe next 100,000 years are influenced by young volcanism.

Using the Cox model, simulations of future volcanic events wereperformed over a period of 0.1 Ma for each tectonic domain and forthe two sensitivity cases. As before, 10,000 Monte Carlo simulationswere required to obtain stable probability estimates. The hazard esti-mates are mapped at the scale of Kyushu in order to display togetherExtensional and Southern arc domains (Figs. 6 and 7).

The results of sensitivity calculations can be measured in terms ofareas presenting low probability values (Table 3); i.e. these areas in-clude only 5 km×5 km domains presenting probability values below

10−3. When comparing case I (Kyushu) and case II (with tectonic do-mains), the area with low probability values decreases from 84% (ofKyushu) to 67% (of Extensional+Southern arc domains). Regardingcase III, the higher values taken by the hazard estimates, compared tocase II, leads to a major reduction (down to 15%) for the area withlow probability values. This result highlights the importance of

Fig. 3. Volcanic hazard map for Kyushu displaying the probability of one or more vol-canic events for the next 100,000 years using a 5 km×5 km domain (case I).

Fig. 4. Datasets for the Extensional (left) and Southern arc (right) domains with Qua-ternary volcanic events (black triangle), active faults (red line) and strain rates(colors). (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this article.)

Table 2Parameters for the Extensional and Southern arc domains of Kyushu.

Case Domain ρZGa ρZSb Variogram correlation scale Time component

IIa Extensional −0.20 0.27 45 km ProportionalIIb Southern 0.26 0.31 30 km ProportionalIIIa Extensional −0.20 0.27 45 km SimulatedIIIb Southern 0.26 0.31 30 km Simulated

a G: strain rate.b S: cumulative fault length.

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gathering good and sufficient radiometric data for the age of volcanicevents as input for hazard assessments.

Therefore, such domain delineation is of importance, as it allowsfitting a model that better accounts for local characteristics of tectonicdomains and potentially avoids overestimating the area of Kyushu is-land presenting low probability values of volcanic hazard.

5. Conclusions and perspectives

By considering a Cox process with a multivariate potential of vol-canism, the assimilation of Quaternary geological information (eventsand ages), strain rates, active faults and geophysical data becomes op-erational for hazard calculations. This modeling approach constitutesa step forward with respect to the joint analysis and interpretation ofrock deformation and volcanic results for probabilistic hazard assess-ments; i.e. it enables improvement of uncertainty characterizationwhen forecasting volcanic activity on the long term. In particular,

the use of multivariate datasets will enhance hazard estimationfor non excluded regions away from recent and current volcanicactivity.

The comparison of volcanic hazard estimates relying on differentstochastic models such as the nonhomogeneous Poisson processusing kernel density methods (with a smooth deterministic potential;cf. Connor and Connor, 2009) and the Cox model (using a random po-tential) shows that the integration of the uncertainty for the potentialof volcanism causes the resulting probability estimates to have an in-creased spatial variability. Such results reveal the importance of ac-counting for the potential of volcanism uncertainty (aleatory) whenassessing long-term volcanic hazard. In addition, the application ofseveral probabilistic models is required for hazard estimation, asthey provide contribution to the perception of epistemic uncertainty;i.e. evidence in terms of its variability and possible reduction.

Additional developments are needed as to include various types ofvolcanic activity in form of selected scenarios in order to estimate

Fig. 5. Histogram of simulated number of events for a future period of 100,000 years. The (future) potential in time is estimated at 73.3 events.

Fig. 6. Volcanic hazard map for Extensional and Southern arc domains displaying theprobability of one or more volcanic events for the next 100,000 years using a5 km×5 km domain (case II).

Fig. 7. Volcanic hazard map for Extensional and Southern arc domains displaying theprobability of one or more volcanic events for the next 100,000 years using a5 km×5 km domain (case III).

35O. Jaquet et al. / Journal of Volcanology and Geothermal Research 235–236 (2012) 29–36

Author's personal copy

their specific hazards. Finally, stochastic models with non-stationarypotential are needed for complex volcanic regions, especially whendealing with time frames beyond 100,000 years.

The proposed probabilistic methodology was developed for long-term issues such as the siting of geological repositories. However, itsapplicability can be also very valuable for assessments in relation toindustrial (critical) facilities with short- to medium term consider-ations as shown by Jaquet et al. (2000).

Acknowledgments

We gratefully acknowledge the support of the Nuclear WasteManagement Organization of Japan in making this work possible.We particularly thank the contribution from LauraWallace and NicolaLitchfield (GNS Sciences, New Zealand) in terms of providing GPSstrain rate and active fault data, and also Sue Mahony (University ofBristol, UK) for enhancing the geology section. Useful discussions withH. Tsuchi, T. Miwa, H. Kawamura, K. Kiyosugi, M. Apted, N. Chapman,K. Berryman, M. Cloos, C. Connor, L. Connor, S. Sparks, M. Stirling, andP. Vilamor improved this manuscript.

References

AIST, 2002. Geoscientific maps of southern part of Korea, western part of Japan andtheir adjoining areas. Geological Survey of Japan, Digital Geosciences Map P-4.

AIST, 2008. Database for Quaternary Volcanoes in Japan. http://riodb02.ibase.aist.go.jp/strata/VOL_JP/EN/index.htm.

AIST, 2009. Active fault database of Japan, version 2009. Research Information DatabaseDB095, National Institute of Advanced Industrial Science and Technology. http://riodb02.ibase.aist.go.jp/activefault/index_e.html.

Apted, M., Berryman, K., Chapman, N., Cloos, M., Connor, C., Kitayama, K., Sparks, S.,Tsuchi, H., 2004. Locating a radioactive waste repository in the ring of fire. EOSTransaction of the American Geophysical Union 85 (45), 465–480.

Bebbington, M.S., Lai, C.D., 1996. On nonhomogeneous model for volcanic eruptions.Mathematical Geology 28 (No. 5), 585–600.

Chapman, N.A., Goto, J., Tsuchi, H., 2008. Likelihood of tectonic activity affecting the geo-logical stability of a repository in Japan: development of NUMO's ITM methodology.Proceedings of the Stability and Buffering Capacity of the Geosphere for Long-termIsolation of Radioactive Waste: Application to Crystalline Rock, Manchester, Novem-ber 13–15, 2007. OECD Nuclear Energy Agency, Paris, pp. 67–75.

Chapman, N., Apted, M., Beavan, J., Berryman, K., Cloos, M., Connor, C., Connor, L.,Hasenaka, T., Jaquet, O., Kiyosugi, K., Litchfield, N., Mahony, S., Miyoshi, M., Smith,W., Sparks, S., Stirling, M., Villamor, P., Wallace, L., Goto, J., Miwa, T., Tsuchi, H.,Kitayama, K., 2009a. Development of methodologies for the identification of volcanicand tectonic hazards to potential HLW repository sites in Japan — the Kyushu casestudy. Nuclear Waste Management Organisation of Japan, Tokyo. Technical Report,NUMO-TR-09-02.

Chapman, N., Apted, M., Beavan, J., Berryman, K., Cloos, M., Connor, C., Connor, L., Ellis,S., Jaquet, O., Kiyosugi, K., Litchfield, N., Mahony, S., Smith, W., Sparks, S., Stirling,M., Villamor, P., Wallace, L., Goto, J., Miwa, T., Tsuchi, H., Kitayama, K., 2009b. De-velopment of methodologies for the identification of volcanic and tectonic hazardsto potential HLW repository sites in Japan — summary report. Technical Report,NUMO-TR-09-03. Nuclear Waste Management Organisation of Japan, Tokyo.

Chilès, J.P., Delfiner, P., 1999. Geostatistics: modeling spatial uncertainty. Wiley Seriesin Probability and Mathematical Statistics. 695 pp.

Connor, C.B., Hill, B.E., 1994. Estimating the probability of volcanic disruption of thecandidate Yucca mountain repository using spatially and temporally non-homogeneous Poisson models. Focus 93: Site Characterisation and Model Valida-tion Proceedings, Las Vegas, September 26–29, 1993. American Nuclear Society,pp. 174–181.

Connor, C.B., Hill, B.E., 1995. Three nonhomogeneous Poisson models for the probabil-ity of basaltic volcanism: application to the Yucca Mountain region, Nevada. Jour-nal of Geophysical Research 100 (No. B6), 10,107–10,125.

Connor, C.B., Connor, L.J., 2009. Estimating spatial intensity with kernel methods. In:Connor, C.B., Chapman, N.A., Connor, L.J. (Eds.), Volcanic and Tectonic HazardAssessment for Nuclear Facilities. Cambridge University Press, pp. 346–368.

Volcanic and Tectonic Hazard Assessment for Nuclear Facilities. In: Connor, C.B.,Chapman, N.A., Connor, L.J. (Eds.), Cambridge University Press, Cambridge. 623 pp.

Connor, C.B., 2011. A quantitative literacy view of natural disasters and nuclear facili-ties. The Electronic Journal of the National Numeracy Network, Volume 4, Issue2, Article 2. http://services.bepress.com/numeracy.

Crowe, B.M., Johnson, M.E., Beckman, R.J., 1982. Calculation of the probability of volca-nic disruption of a high-level nuclear waste repository within southern Nevada,USA. Radioactive Waste Management and the Nuclear Fuel Cycle 3, 167–190.

Cox, D.R., 1955. Some statistical methods connected with series of events. Journal ofthe Royal Statistical Society, Series B (Methodological) XVII (No. 2), 129–164.

Geman, S., Geman, D., 1984. Stochastic relaxation, Gibbs distribution and the Bayesianrestoration of images. IEEE Transactions on Pattern Analysis and Machine Intelli-gence Vol. 6, 721–741.

GSI, 2009. Crustal Movement in Japan. Geographical Survey Institute. http://mekira.gsi.go.jp.Ho, C.H., 1991. Time trend analysis of basaltic volcanism at the Yucca Mountain site.

Journal of Volcanology and Geothermal Research 46, 61–72.Ho, C.H., Smith, E.I., 1998. A spatial–temporal/3-D model for volcanic hazard assessment:

application to the Yucca Mountain region. Mathematical Geology 30 (No. 5),497–510.

Jaquet, O., Löw, S., Martinelli, B., Dietrich, V., Gilby, D., 2000. Estimation of volcanichazards based on Cox stochastic processes. Physics and Chemistry of the Earth(A) 25 (6–7), 571–579.

Jaquet, O., Carniel, R., 2001. Stochastic modelling at Stromboli: a volcano with remark-able memory. Journal of Volcanology and Geothermal Research 105, 249–262.

Jaquet, O., Connor, C., Connor, L., 2008. Probabilistic methodology for long-term assess-ment of volcanic hazards. Journal of Nuclear Technology 163, 180–189.

Jaquet, O., Lantuéjoul, C., Goto, J., 2009. Cox process models for the estimation of long-term volcanic hazard, in volcanic and tectonic hazard assessment for nuclear facil-ities. In: Connor, C.B., Chapman, N.A., Connor, L.J. (Eds.), Cambridge UniversityPress, pp. 369–384.

Kamata, H., 1998. Quaternary volcanic front at the junction of the South-west Japan Arcand the Ryukyu Arc. Journal of Asian Earth Sciences 16, 67–75.

Lantuéjoul, C., 2002. Geostatistical Simulation: Models and Algorithms. Springer, Berlin.256 pp.

Lindsay, J., Marzocchi, W., Jolly, G., Constantinescu, R., Selva, J., Sandri, L., 2010. Towardsreal-time eruption forecasting in the Auckland Volcanic Field: application ofBET_EF during the New Zealand National Disaster Exercise “Ruaumoko”. Bulletinof Volcanology 72, 185–204.

Mahony, S.H., Wallace, L.M., Miyoshi, M., Villamor, P., Sparks, R.S.J., Hasenaka, T., 2011.Volcano-tectonic interactions during rapid plate boundary evolution in the Kyushuregion, SW Japan. Bulletin of Geological Society of America 123 (11–12), 2201–2223.

Marti, J., Felpeto, A., 2010. Methodology for the computation of volcanic susceptibility.An example for mafic and felsic eruptions on Tenerife (Canary Islands). Journal ofVolcanology and Geothermal Research 195, 69–77.

Martin, A.J., Umeda, K., Connor, C.B., Weller, J.N., Zhao, D., Takahashi, M., 2004. Model-ing long-term volcanic hazard through Bayesian inference: an example from theTohoku volcanic arc, Japan. Journal of Geophysical Research 109, B10208, http://dx.doi.org/10.1029/2004JB003201.

Marzocchi, W., Sandri, L., Gasparini, P., Newhall, C., Boschi, E., 2004. Quantifying prob-abilities of volcanic events: the example of volcanic hazard at Mt. Vesuvius. Journalof Geophysical Research 109, B11201, http://dx.doi.org/10.1029/2004JB003155.

Digital Active Fault Map of Japan. In: Nakata, T., Imaizumi, T. (Eds.), University of TokyoPress. 68 pp., 1 sheet and 2 DVDs.

Newhall, C.G., Hoblitt, R.P., 2002. Constructing event trees for volcanic crisis. Bulletin ofVolcanology 64, 3–20.

Perry, F.V., Crowe, B.M., Valentine, G.A., 2000. Analyzing volcanic hazards at YuccaMountain. Los Alamos Science Number 26, 492–493.

Tsuchi, H., Goto, J., Chapman, N.A., Kawamura, H., 2008. Tectonic hazard and the siting ofJapan's HLWRepository: preliminary results of the Tohoku case study in the ITM pro-ject. Proceedings of the 12th International High-Level Radioactive Waste Manage-ment Conference (IHLRWM), 7–11 September 2008, Las Vegas, Nevada, pp. 134–141.

Saiga, A., Matsumuto, S., Uehira, K., Matsushima, T., Shimizu, H., 2010. Velocity struc-ture in the crust beneath the Kyushu area. Earth Planets Space 62, 1–14.

Salah, M.K., Seno, T., 2008. Imaging of Vp, Vs and Poisson's ratio anomalies beneathKyushu, southwest Japan: implications for volcanism and forearc mantle wedgeserpentinization. Journal of Asian Earth Sciences 31, 404–428.

Sugimura, A., Uyeda, S., 1973. Island Arc — Japan and Its Environs. Elsevier, Amsterdam.247 pp.

Wackernagel, H., 2003. Multivariate Geostatistics, third edition. Springer-Verlag, Berlin.387 p.

Wallace, L.M., Ellis, S., Miyao, K., Miura, S., Beavan, J., Goto, J., 2009. Enigmatic, highlyactive left-lateral shear zone in southwest Japan explained by aseismic ridge colli-sion. Geology 37 (2), 143–146, http://dx.doi.org/10.1130/G25221A.

Table 3Percentiles and areas with low probability values at 100,000 year scale.

Case P5 P15 P33 P50 P67 P84 P95 Area(km2) with probability value below 10−3

I NA NA NA 10−4 3·10−4 10−3 2·10−2 33,432IIa 10−4 2·10−4 4·10−4 6·10−4 10−3 5·10−3 4·10−2 14,020IIIa 8·10−4 10−3 2·10−3 3·10−3 7·10−3 3·10−2 2·10−1 3139

a Extensional and Southern arc domains cover about 53% of Kyushu island.

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