flsank collapse volcán de colima

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Flank collapse scenarios at Volcn de Colima, Mexico: A relative instability analysis

Lorenzo Borselli a,, Lucia Capra b, Damiano Sarocchi a, Servando De la Cruz-Reyna c

a Instituto de Geologia/ Fac. de Ingeniera - Universidad Autnoma de San Luis PotosUASLP, Av. Dr. Manuel Nava 5, C.P. 78240 San Luis Potos, Mexicob Centro de Geociencias, UNAM, Campus Juriquilla, 76230 Queretaro, Mexicoc Departamento de Vulcanologa, Instituto de Geofsica, Universidad Nacional Autnoma de Mxico, Coyoacn 04510, D.F., Mexico

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

Article history:

Received 31 December 2010

Accepted 23 August 2011Available online 3 September 2011

Keywords:

volcano flank collapsevolcanic hazardslope stability analysisdebris avalanche modelingstochastic numbers

Previous studies on debris avalanche deposits of Volcn de Colima suggest a cyclic process of repetitive flankcollapses triggered by major eruptions (VEIN4). The recurrence interval of major collapse events during thelast 10,000 years is calculated here using a stochastic approach, yielding a mean recurrence interval of2698 yr, with an uncertainty range of 180 yr. The analysis yields an increased probability offlank collapsein the interval between110 yr and +345 yr from the present. This generates a series of scenarios rangingfrom optimistic, considering a collapse within the next 345 years, to pessimistic, derived from the 110 yeardelay. The analysis of relative mass/volume deficit in the volcano structure, made using the new VOLCANOFIT2.0 software, and a limit equilibrium analysis on the volcano flanks point to the SW quadrant as potentiallythe most unstable sector of the edifice under a wide range of scenarios. The TITAN2D numerical model isalso used to simulate the extent of debris avalanches caused by failure of the SW flank. This approach maybe applied to any volcano with a potential for flank collapse.

2011 Elsevier B.V. All rights reserved.

1. Introduction

The 1980 sector collapse and debris avalanche at Mount St. Helenstriggered the recognition of characteristic hummocky deposits inmany similar debris avalanche deposits worldwide (Siebert, 1984;Ui and Glicken, 1986; Siebert et al., 1987; Francis and Wells, 1988;Vallance et al., 1995; Capra et al., 2002). Since then, several studieshave revealed that many volcanoes are susceptible to failure causedby exogenous or endogenous processes (McGuire, 1996), and thatthe associated deposits can completely change the topography aroundthe volcano with important secondary effects, particularly on the hy-drographic network (Swanson et al., 1986; Capra and Macas, 2002;Capra, 2007).

Instability of a volcanic edificemaybecausedbymanyfactors,eitherdirectly related to volcanic activity or to exogenous processes suchas weathering. These factors include direct magmatic intrusion intothe edifice (Bezymianny-type activity, Gorshkov, 1962) orinto the sub-volcanic crust (Day, 1996; Elsworth and Voight, 1996), deposition ofvoluminous pyroclastic deposits on steep slopes (McGuire, 1996),hydromagmatic processes (Dzurisin, 1998), and phreatomagmatic ac-tivity (Bandai-type activity, Moriya, 1980). In some cases faultingmay trigger collapse (McGuire, 1996), and the tectonic setting of thevolcano may also influence the direction of the failure (Siebert, 1984).In addition, the mass of the volcano can induce isostatic flexure,

compaction, and deformation that can lead directly to collapse (Borgia

et al., 1992; van Wyk de Vries and Borgia, 1996). Although simplegravitational failure may occur in response to progressive weakeningof an edifice, discrete triggering mechanisms are commonly indepen-dent of the processes producing edifice instability. Keefer (1984)established that numerous large landslides during historic time weretriggered by earthquakes. Other triggeringmechanisms include phreaticexplosions and precipitation. Hurricane-induced rainfall triggered aflank collapse at the Casita volcano in Nicaragua in 1998, killing 2,500people (Sheridan et al., 1999; Scott et al., 2005).

Two different approaches have been used to model volcano insta-bility; scaled analog experiments, and numerical simulation. i) Analogmodels have been widely usedto simulatesector collapses of volcanoes,mostly focusedon reproducingthe direction of the collapse with respectto the stress field affecting the volcano. Experiments of volcanic spread-ing have been performed to predict deformation, taking a volcano as afunction of its height and the brittle-ductile ratio of the substratum, inextension and strike-slip settings (e.g. Merle and Borgia, 1996; vanWyk de Vries and Merle, 1996; van Wyk de Vries et al., 2003; Acocella,2005; Norini and Lagmay, 2005). In addition, cryptodome intrusionhas also been modeled attempting to reproduce the volcano deforma-tion prior to the 1980 Mt. St. Helens collapse (Donnadieu and Merle,1998; Donnadieu et al., 2001). ii) Numerical simulations have beenused to understand how the stability of a volcano is affected by the in-crease of internal magmatic pressure (Dietrich, 1988; Russo et al.,1997), excess pore pressures due to intrusion (Voight and Elsworth,1997; Elsworth and Day, 1999; Elsworth and Voight, 2001), hydrother-mal alteration (Zimbelman et al., 2004) and even in magmatically

Journal of Volcanology and Geothermal Research 208 (2011) 5165

Corresponding author. Tel.: +52 4448171039.E-mail address: [email protected] (L. Borselli).

0377-0273/$ see front matter 2011 Elsevier B.V. All rights reserved.

doi:10.1016/j.jvolgeores.2011.08.004

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inactive volcanoes with significantmass restingover a weak substratum(Borgia, 1994; van Wyk de Vries and Matela, 1998).

The Colima volcano (3860 masl), also known as Volcn de Fuego, isan active composite cone with a maximum age of about 50,000 yr(Robin and Boudal, 1987) and is the youngest edifice of the Colima Vol-canic Complex (CVC),located in the western limitof the Trans-MexicanVolcanic Belt (Fig. 1). The older part of the edifice, Paleofuego, (theancestral Colima volcano), consists of a south-facing horseshoe-shaped

crater surrounding the present active cone. Luhr and Prestegaard(1988) describe a main debris avalanche deposit exposed south ofthe edifice, up to 70 km from the source, with an age of 4280 110 yrBP, contrasting with the age reported by Robin and Boudal (1987) of9370400 yr BP for the same deposit. Despite the difference in agedeterminations, both groups of authors agree that the deposit corre-sponds to a single event. In contrast, Komorowski et al. (1997) suggestthat collapses have occurred at least 12 times in the last 45,000 yearsand perhaps as much as 9 times at the younger edifice. Table 1 presentsthe radiocarbon ages related to these collapse events. Recently, Corteset al. (2010) have described in great detail some of the more recentcollapse events, as well as a 3600 yr BP collapse on the western flankof the edifice emplacing a 1 km3 debris avalanche deposit. Similar toolder deposits (Capra and Macas, 2002; Capra, 2007), this debris ava-lanche deposit obstructed the Armera river, forming a temporary damthat then failed, producing a voluminous debris flow. Such secondaryeffects are caused by the walls of the N-S tectonic graben in whichColima is settled, acting as topographic barriers where the voluminousdebris avalanches stop (Fig. 1).

Modern activity of the volcano has been characterized by explosivephases, including two major Plianian eruptions such that occurred in1818 and 1913 (Saucedo et al., 2010). Since the 1913 Plinian event,the volcano has had several eruptive phases. Its activity has beenmore persistent since 1998, with explosions and lava and dome extru-sions (Saucedo et al., 2005). The collapse of summit domes and lavaflow fronts has produced several block and ash flow deposits. Suchdeposits are up to several meters thick in the proximal area withfilledproximal drainages up to 6 km from the vent. The block-and-ash flowsat the Colimavolcano consistof unwelded depositwith clastsembedded

in a silty to sandy matrix. During the last 15 yr the volcano had severaleruptive episodes; in 1991, 1994, 19981999, 20012003, 2004 and2005. Despite this persistent eruptive activity, the emitted productshave not significantly affected the surrounding inhabited area. Duringheavy rains, which usually occur from June through October at thislatitude, these deposits are often remobilized, producing lahars (Capraet al., 2010).

Although numerous studies on the textural characteristics of the

avalanchedepositshavebeenpublished,wearenotawareofanyresultsconcerning the edifice conditionsprior to thefailureor thepossible trig-gering mechanism. Considering the present condition of the activecone, it is extremely importantto understand its stability and recognizewhich sector could be destabilized by any endogenous or exogenoustriggering process.

The aim of the present work is to evaluate the relative flank insta-bilityof the Colimavolcanousing a set of new tools; recurrence intervalsof cyclic debris avalanche events, the analysis of mass/volume deficitwith respect to a homogeneous stable reference shape, anda limit equi-librium method (LEM); and to evaluate the possible debris avalanchescenario after estimation of potential volume of the Debris AvalancheEvents (DAE).

2. Materials and methods

2.1. Recurrence time of Debris Avalanche Events (DAE)

The published average ages (BP) and associated uncertainties foreach DAE in the Colima Volcanic Complex (Komorowski et al., 1997;Cortes et al., 2005, 2010) are listed in Table 1. The number of DAE isindeed much lower than the number of explosive events. De la Cruz-Reyna (1993) established a Poissonian model for the recurrence inter-vals and occurrence frequency of explosive eruptions, and Mendoza-Rosas and De la Cruz-Reyna (2008) analyzed the distribution of eventswith VEIN4, which maybe related to large DAE,finding an 85%probabil-ity of a VEIN4 event within the next 500 yr, and an average recurrencetime for VEIN5 over 2500 yr. The fundamental problem for VEIN4events derives from the reduced number and reliability of event dating.

Fig. 1. Colima Volcan de Fuego. DEM.

52 L. Borselli et al. / Journal of Volcanology and Geothermal Research 208 (2011) 5165


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The approach used in this paper is based on a simplified statisticalapproach to assessing the recurrence time of DAE with the limitednumber of events available. We use stochastic arithmetic (Vignes,1993; Markov and Alt, 2004) adapted to the mean age of DAE and itsband of uncertainty. This technique accounts for the error propagationand uncertainty associated with the computation of successive intervalsbetween collapses. The proposed methodology resembles that pro-posed by Akiz et al. (2010) for the assessment of large earthquakerecurrence times at the San Andreas Fault (California).

Denoting the age in years before present (BP) of a DAE by Tei, andthe uncertainty band around the average age by Tei (years), weperform an analysis of the mean recurrence time between DAEs, de-fining for each DAE a stochastic number characterized by the meanand standard deviation and then use stochastic number methodology(Vignes, 1993; Alt and Markov, 2001; Markov and Alt, 2004) for thecomputation procedure. Following the definition and procedure inMarkov and Alt (2004), a stochastic number X is a Gaussian randomvariable with a known mean m and a known standard deviation sand is denotedX=(m; s). The set of stochastic numbers is denoted by

S

m; s f j

mR; sRg

:

Under these definitions, arithmetic operations between stochasticnumbers are identical to the operations between independent Gaussiandistributions (Vignes, 1993).

The application of the simple stochastic arithmetic allows the inter-val between two consecutive DAEs to be calculated as the differenceTei (years) between of the means of any given Tei and its precedingevent Tei1 as:

Tei Tei1Tei 1

We can also calculate the new width of the band of uncertainty(standard deviation) Tei (years) associated to each Tei as:

Tei ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTei1 2 Tei 2

q2

Table 1 showsthe available ages of Volcn de Colima DAEs in thelast10,000 yr BP, the VEIs, and the calculated intervals between successivecollapses and their corresponding bands of uncertainty.

WenowusethedataofTable 1, considering each DAE as a stochasticnumber, to derive the mean recurrence interval in the last 10,000 yr BPand its band of uncertainty. The mean DAE interval of recurrence in thelast 10,000 yr BP,Te

and its band of uncertaintyTe are thus:

Te

n

i1Tei

n 3a

Te

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n

i1Tei 2

n

vuuut; 3b

and their values are included in Table 1.

2.2. Digital elevation model analysis and treatment (by VOLCANOFIT 2.0)

In order to estimate possible anomalies in the Colima volcano edificestructure, we analyzed the current volcano's DEM by means of a specialprogram developed by us, VOLCANOFIT 2.0 (www.volcanofit.org). Atheoretical description of the analytical procedure is given inAppendix A.

The available DEM of the edifice was obtained from the originalLIDAR (provided by INEGI, the Mexican National Institute of Geographyand Statistics) data. It has a spatial resolution of 55 m (Fig. 1). In ouranalysis we resample the original DEM at a grid resolution of 10 10 m.The part of the edifice that could be affected by an instability (whichwe call the Upper Edifice) is shown in Fig. 2. This part of the DEM hasbeen used for the analysis carried out with VOLCANOFIT 2.0. The aimsof this analysis areto show a possible deficitorsurplusofedifice volumewith respect to an ideal 3D surface and a stable isotropic shape with-

out preferential direction of collapse due to intrinsic geometric non-homogeneities. The portion of edifice suitable for this type of analysisis the new cone built on the Paleofuego collapse caldera.

2.3. Edifice parameterization and slope stability computation

In the past, the methodologies most used to analyze volcano flankcollapses were based on slope stability computation, namely the limitequilibrium method (LEM) and the finite element method (FEM)(Duncan, 1996). Although several authors used both methodologies,the use of LEM still prevails for its relative simplicity and the limitednumber of parameters required. (Voight, 2000; Donnadieu et al.,2001; Zimbelman et al. 2004; Apuani et al., 2005a; Simmons et al.,2005; Reid et al., 2006; Hewitt, 2007; Reid et al., 2010). The basic

steps of the analysis are assumption of a basic slope geomechanicalmodel (including 2D section with strata, aquifer or piezometriclines, and geomechanical parameters assigned to each independentstratum). External forces and seismic effects can be simulated, aswell as magma intrusions orfluid pressure and overpressure (Iverson,1995; Apuani et al., 2005a; Apuani and Corazzato, 2009).

In the case of active volcanoes there are several problems, becausesampling of the internal rock bodies cannot be done with standard di-rect geotechnical methods, and thus one is limited to surface outcropsampling, or to assuming a range of possible values (Apuani et al.,2005a, 2005b).

The Colima stratovolcano structure is assumed to be composed ofthree main bodies: 1) a body composed of andesitic lava flows andpyroclastic deposits, 2) the conduit and the active andesitic dome,

and 3) a hydrothermally altered body surrounding the conduit and

Table 1

Available ages of debris avalanche in the last 10,000 years BP, VEI and calculated intervals between the successive collapses and their corresponding band of uncertainty.

Datasource

Event IDNumber()

VEI*()

Tei Debris avalanche events(DAE)(years BP)

Tei Uncertainty onDAE(years)

Tei Interval from previousDAE(years)

Tei Uncertainty on intervalfrom previous DAE(years)

1,2,3 4 5 2580 140 1020 1842,3 3 5 3600 120 3440 2002,3 2 6 7040 160 2631 1832,3 1 56 9671 88 3699 149

1,2 0 56 13370 120 n.a n.aMean interval of last four DAE (expressed as stochastic number) Te

Mean interval of last fourDAE (years)

Te Standard deviation associatedto mean DAE interval (years)

2698 180

1 Komorowski et al. (1997); 2 Cortes et al. (2005); 3 Cortes et al., 2010; *from Mendoza-Rosas and De La CruzReyna (2008).

53L. Borselli et al. / Journal of Volcanology and Geothermal Research 208 (2011) 5165
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the dome (Fig. 3). This reconstruction is based on previous knowledgeof similar volcanoes and of the Colima volcano itself, and is useful forcarrying out the relative degree of stability analysis.

For the present case, we used a LEM slope stability analysis basedon Janbu's rigorous method (Janbu, 1973) and generalized computa-tional andsearchingstrategies tofind the slidingsurfacewith minimumstability factor (Fs) (Siegel et al., 1981; Chen, 1992; Zhu et al., 2003,2005). We used a random search strategy for all possible surfaces com-patible with a potential sliding not constrained to a specific shape (e.g.circular only), which is implemented in the SSAP 4.0.6 software (onlyavailable in full freeware and non-commercial, license) (Borselli, 2011).

As input data we used the reconstructed profile of the slope and ageotechnical parametrization using the Geological Strength Index(GSI) (Hoek et al., 2002; Marinos et al., 2005; Hoek and Diederichs,

2006). This type of geomechanical parametrization provides a systemfor estimating the reduction in rock mass strength for different geo-logical conditions as identified by field observations, and derives the

local equivalent shear strength MohrCoulomb parameters for frac-tured rock masses. This methodology to characterize different partsof a stratovolcano has been previously implemented in the analysisof other volcanic edifice stabilities (Voight, 2000; Watters et al.,2000; Zimbelman et al., 2004; Apuani et al., 2005a,b; Hewitt, 2007;Gonzlez-Mellado and De la Cruz-Reyna, 2008). Table 2 shows theparameters that we assumed for each stratum in the volcanic struc-ture. The values in Table 2 are based on average values from previousstudies of stratovolcano slope stability, considering also a possible in-crease of 50% in the GSI values as the potential band of uncertainty.

Seismic effects are also considered in the analysis, adopting a pseu-dostatic method in the computation(Ashford and Sitar, 2002). To applythis method, the horizontal and vertical seismic coefficients kh and kvare considered to be a function of the maximum peak ground acceler-

ation (PGA) (Makdisi and Seed, 1978), and account for the increase inthe vertical andhorizontal inertial force components in the mass duetoseismic action. The seismic horizontal and vertical coefficients kh andkvused are respectively 0.20.25 and 0.10.125, corresponding to anequivalent PGA in the range 0.40.5 (g). Accelerations exceeding 0.4 g(40% of the acceleration of gravity) in the region of the Colima volcanowould require the occurrence of an earthquake with magnitude 7.5 orgreater at a hypocentral distance of 50 km or less. The mean recurrencetime estimated for this condition is about 1200 years (Mario Ordaz,2011; Instituto de Ingeniera UNAM Mexico, personal comm.). The seis-mic effect was considered in separate scenarios (Table 3) associatedwith the analysis using higher GSI values (Table 2).

The internalfluid pressure in a volcanic edifice has been recognizedas oneof the main triggering factors forpotential instability(Day, 1996;

Voight and Elsworth, 2000; Reid, 2004; Thomas et al., 2004). The fluid

Fig. 2. Portion of actual DEM used in VOLCANOFIT 2.0 analysis.

Fig. 3. Colima volcano structure.



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pressure produces a localreduction of shear strength along a portion orall of the potential sliding surface, producing a global reduction of thestability factor.

For the present analysis we adopt a new type offluid pressure func-tion that acts like neutral pressure reducing the effective shear strengthof rock masses. The new type of function, implemented in the SSAP4.0.6 software, is describedin Appendix B. The function is used becauseof the need to equilibrate thefluid pressure at a given depth of volcanicedifice with the lithostatic pressure, the presence of twofluid pressurephases (liquid vapor), and the possibility of progressive pressuredissipation or overpressurization in the proximity of the suface.

The SSAP software offers the possibility of excluding some por-tions of the edifice from the calculation of fluid neutral pressure.We used also this option considering the fluid pressure computationonly for the hydrothermalized and dome conduit systems. The mainbody of the stratovolcano was then excluded from the computationoffluid neutral pressure. Fig. 4 shows the pressure field inside theinner portion of the volcanic edifice. The pressure increases up to20 MPa at a depth of about 900 m from the volcano summit, andshows a non-linear decrease dueto depressurizationat the dome surfaceclose to the surface. The parameters andfluid pressure function assumedin the analysis are described in Appendix B and Fig. B.1.

The analysis divides the volcanic edifice into 12 sections (Fig. 5).These sections are drawn at angular steps of 30, in clockwise order,and centered around the summit of volcano structure. For each sec-

tion with the basic internal structure assumed in Fig. 3, the SSAP soft-ware searched for the weakest sliding surface, characterized by theminimum stability factor Fs, in a set of randomly generated samplesof 10,000 of potentially sliding surfaces.

The main objective of the relative stability analysis is to establishwhichpartofthepresentedifice is theweakestand prone toan unstablecondition. This type of analysis cannot be performed on a single user-specified surface, as many authors have done after a flank collapse(Apuani et al., 2005a) and the search for a minimum Fs must be appliedto a significant volume of the edifice structure based on its morpho-logical features that canbe directly quantified. Other possible structuralinstability factors, such as faulting or criptodome intrusion should notbe considered without clear evidence of their presence. In addition,the parameterization of geotechnical and fluid parameters within the

volcanic structure can be only relative, and not absolute, because oflimited geotechnical knowledge of the internal volcanic structure.

2.4. Debris avalanche simulation

Debris avalanches are dry, gravity-driven granularflows that followtopographic features during their emplacement. Various models havebeen proposed to explain themobility of suchflowsandhowtheenergygenerated dissipates during flowage (e.g. Hayashi and Self, 1992). Abetter way to simulate the inundation limits and thickness of this typeofflows is by computation routines that simulate the flow over realtopography. TheTITAN2D code wasdesigned to simulate a drygranularflow from an initial pointof collapse over a natural terrain (Pitman et al.,2003; Patra et al., 2005) highly suited to simulatingblock-and-ashflows

anddebris avalanches. The code is based on a model for an incompress-ible Coulomb flow adapted from the work ofSavage and Hutter (1989)using a shallow-water, depth-averaged approximation (Iverson andDenlinger, 2001). Mass and momentum conservation equations aresolved with a Coulomb friction term for the interface between the gran-ular material andbasal surfaceandfor the internal friction of theflowingmedia (Pitman et al., 2003). The resulting hyperbolic system of equa-tions is solved using a parallel adaptive mesh (Patra et al., 2005).We used the 2.0.1 version to perform the simulations. Terrain data areentered into the algorithm via GRASS GIS (Geographic ResourcesAnalysis Support System).

Themain input parameters for running simulations are: i) thevolumeof thecollapsed mass; ii) the basal friction angle (b), andiii) theinternalfrictional anglei. Initial conditions such as thecoordinates of thestarting

point, elongation and orientation of the collapsed mass, initial velocity

Table 2

Shear strength parameterization of main bodies of the stratovolcano following the Hoek and Brown strength criterion (Hoek et al., 2002).

unsaturated unitweight(kN/m3)

s saturated unitweight(kN/m3)

I uniaxial compressive strengthof intact rock element(MPa)

GSI geological strengthindex(adimensional)

mi lithological index(adimensional)

D disturbance factor(adimensional)

Strato volcano main body 24.5 25.0 50 40, (60)* 22 1.0Hydrothermal altered body 24.0 24.5 40 30, (45)* 22 1.0Dome and conduct 24.0 24.5 25 20, (30)* 22 1.0

*In parentheses the GSI value for scenario analysis Nos. 2, 3 and 4 (50% increase assumed with respect to GSI of scenario no. 1).

Table 3

Characteristics of scenario analysis adopted for limit equilibrium analysis.

Scenariono. 1

Description Notes

1 Geomechanical parameters as in Table 2 No seismic effect2 Geomechanical parameters as in Table 2 with

GSI increase of 50%No seismic effect

3 The same as scenario 2, but seismic coefficientsKh=0.2; Kv=0.1

Seismic effect by LEMpseudostatic analysis

4 The same as scenario 2, but seismic coefficientKh=0.25; Kv=0.125

Seismic effect by LEMpseudostatic analysis

Fig. 4. Fluid pressure field assumed in the relative stability analysis.



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and direction, duration andmassfluxrateof the initial pileof materialarealso required (Sheridan et al., 2005; Charbonnier and Gertisser, 2009;

Procter et al., 2010). After the flow starts, a criterion for determiningits stopping is crucial for an accurate assessment of the runout, sincein numerical simulations a flow never stops if its basal friction angleis higher than the slope angle. This is an unrealistic condition for realflows, where other physical parameters are involved in flow stopping(e.g. aspect ratio of the sliding pile, kinetic and potential energy of themoving flow, shape of the valley or channel for confined flows). Herewe applied the global stopping criterion proposed by Yu et al. (2009)in which a dimensionless average velocity is used to determinethe min-imum acceptable average flow velocity below which the flow stops, asalso described in Sulpizio et al. (2010).

To perform simulations, we used a DEM of 50 m in resolution(vectorial data from the INEGI). The input parameters, such as the in-ternal friction angle and basal friction angles are set as those calibrated

to reproduce the 3600 yr BP collapse event (b=8 and i=30)(Cortes et al., 2010), which represent the younger and better-studiedflank collapse episode at the Colima volcano.

3. Results

3.1. Scenario analysis from interval analysis of Debris Avalanche Events

(DAE)

Two possible scenarios of future debris avalanche occurrences dueto partial edifice collapse can be estimated using stochastic arithmetic.

Using Eq.(3a) and(3b) we obtain Te 2698 andTe=180asthe

mean DAE interval of recurrence in the last 10,000 yr BP, and its band of

uncertainty (see Table 1). The result is itself a new stochastic number.

A forecast for the time of a future collapse Tnext (year) countingfrom the present time can be calculated and expressed in terms of

the stochastic number Tnext Tnext; Tnext:

Tnext Tnext

; Tnext Te4 Te

;ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTe4 2 Te 2

q

118;F228 4

where Te4 is the time of the most recent event andTe4 is its respectiveband of uncertainty (see Table 1).

Fig. 5. Position of sections of the upper edifice, where the slope stability computation has been performed. A constant angular step of 30 has been assumed.

Fig. 6. DAE events vs. time interval from previous debris avalanche event. The projec-

tion of a possible scenario for the next DA event is included in the horizontal axis.



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Finally, considering the signs of the stochastic component inEq. (4), we have two possible scenarios.

The more optimistic scenario Top may be calculated by means ofthe following equation:

Top Tnext Tnext 345 years 5

The negative sign in Eq. (5) indicates a projection into the futureof 345 years from the present.

The more pessimistic scenario Tpe may be calculated from:

Tpe Tnext Tnext 110 years 6

The positive sign of the result of Eq. (6) indicates a projection intothe past with respect to the present time, or in other words, that thenext DAE is 110 years overdue. Fig. 6 gives a graphical and simpli-fied portrayal of the data ofTable 1 and the results of the stochasticanalysis.

3.2. DEM analysis and treatment (Volcanofit 2.0)

The application of VOLCANOFIT 2.0 to the upper edifice of the Co-lima volcano (Fig. 7a) yields a good statistical fit as indicated in

Fig. 7. a) Upper edifice of Colima volcano DEM (2005) b) fitted volcanoid 3D surface Eq. (A.5); c) Upper edifice Colima Volcan de Fuego DEM with overlaid volcanoid Eq. (A.5); d)

plot of local deficit (negative values) or surplus (positive values) calculated with Eq. (A.6).

Table 4

VOLCANOFIT 2.0 fitting parameters and statistics applied to Colima Volcan de Fuegoupper edifice 1010 Dem.

VOLCANOFIT 2.0Input grid COLIMA_UPPEREDIFICE.DATData source (INEGI)Adopted Z limit (masl) 2000Percentage random selected data used for fitting 50%Volcanoid function Negative exponential type

Fitting parametersZ1 (masl) 3860.8X0 (m local UTM grid) 645101.0Y0 (m local UTM grid) 2158131.0a 2494.9b 3334.5c 1429.0

Fitting statisticsNo. data 80146Average absolute deviation (m) 69.5R2 0.956EF 0.912



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Table 4. The volcanoid of Eq. (A.5) (Fig. 7b) fits the actual DEM well,with a high coefficient of determination (r2=0.956) and efficiencymodeling (Nash and Sutcliffe, 1970) of 0.912 over a large number ofdata points N80,000 (random selection of 50% of the total points ofthe DEM).

Fig. 7c shows the actual DEM andthe overlay of thefitted volcanoid.The f deficit-surplus analysis procedure described in Appendix A pro-duced the results shown in Fig. 7d, with a clear diffuse volume deficitintheSWflank and a significant surplus in theNEflank. The totaldeficitvolume in the SW flank is around 0.4 km3.

Fig. 8. a) Position of most critical surface in the section, azimuth 210; b) position of most critical surface in the section azimuth 240; c) position of most critical surface in thesection azimuth 60; d) position of most critical surface in the section azimuth 30.

Fig. 9. Diagrams with the corresponding safety factor and index of relative instability vs. azimuth of volcano section. a) safety factor (Fs); b) running average of Fs; c) index of rel-

ative instability; d) running average of index of relative instability. The arrows indicate the azimuth with most unstable conditions.



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3.3. Edifice slope stability

The LEM slope stability analysis performed for all sections at 30azimuthal angular steps is shown in Figs. 8 and 9. Fig. 8a, b, c and dshow theFs obtainedin four sections of thevolcano edifice at azimuthalangles of 210, 240, 60 and 30 for Scenario 1. The minimum stabilityfactor is found at azimuth 240 (Fs =0.997) and the maximum Fs atazimuth 60 (Fs=1.700). It is worth recalling that Fs b1 indicates un-

stable conditions and Fs.N

1.0 stable conditions.Fig. 9a shows the Fs values by azimuth. Fig. 9b shows the relativestability factors Rfsi for each section analyzed as defined by thefollowingequation:

Rfs i Fsi

Fs max7

where Fsmax is the maximum Fs value, and Fsi is the stability factor cor-responding to each section of the entire set of sections analyzed.

Eq. (7) enables the relative degree of stability of each section tobe expressed with respect to the most stable part of volcanic edifice. Inother words,Rfsi is a normalized stability factor Fs that helps to efficiently

display the more problematic sections in terms of global instability.Fig. 9c anddaresimilarto Fig.9a andb but they enable a comparison

betweenscenarios 1, 2, 3 and4, showing as well theinfluence of varyingmechanical parameters and seismic effects. Fig. 9a, b, c, and d indicatethat the most potential unstable area of the volcano's edifice is the SWquadrant, particularly the direction centered between azimuths 210and 270.

3.4. Debris avalanche simulation

To simulate the extentof the area that could be affected by the col-lapse of the SW sector we modified the DEM of the volcano tofind thesliding surface over which the collapsing pile is built (Fig. 10). Thesliding surface is set based on the result of the slope stability analysisdescribed above. The total mass removed from the edifice is 0.9 km3.Considering that the mass dilates during emplacement by at least 30%

in volume, thefi

nal deposit would be close to 1 km

3

. As previouslystated, the basal friction angle, one of the main parameters affectingthe simulation, was set at 8, as calibrated by Cortes et al. (2010) forthe Los Ganchos debris avalanche originating from the 3600 yr BPpartial sector collapse of the SW flank. Fig. 11 shows the distributionof the simulated flow and its thickness. The main path would be south-wards, filling the Montegrande ravine, with the greater thickness (upto 40 m) accumulating in the La Yerbabuena plain, a morphological fea-ture bounded by hummocks of older debris avalanche deposits. On theSW sector, thevillage of La Becerrerawould be completelyburied bythedeposit. Based on the simulation, part of the mass would be able to em-place towards the SE, reaching the towns of Queseria and Tonila andaffecting the main interstate road to Manzanillo, one of the main portson the Pacific coast.

4. Discussion and conclusions

The proposed new methodology for analysis of major DAE recur-rences gives a cyclic recurrence time with a relative narrow band ofuncertainty as well as the possibility of a consistent delay in genera-tion of the next DAE. This delay, of approximately 110 years, is only

Fig. 10. Titan 2D debris avalanche simulation. a) Direction of debris avalanche, b) assumed 3D sliding surface of debris avalanche, c) section of present topography and main sliding

surface.



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partiallycounter-balanced by the more optimistic scenario of the nextDAE occurring within in the next 345 years. The scarce numberof extreme DAE events (VEIN4) in the last 10,000 yr BP does not allowa reliable Poisson analysis of recurrence times. The proposed newmethod, partially based on a recently applied principle to assess thelong earthquake recurrence time at the San Andreas fault in California,

offers a new perspective that can be applied not only to the Colimavolcano but also to other similar volcanoes in Mexico and elsewhere.

The observed SW flank deficit seems to be correlated to the majorrelative instability in the same quadrant, in which steeper slopes pre-vail. It is well known that a non-homogeneous distribution of massvolume in a slope can produce either local or global instabilities.The general volcanoid surface obtained by the VOLCANOFIT programindicates the ideal surface and shape characterized by a non-prevalentunstable portion in terms of the mass volume distribution. The mass/-volume deficit analysis indicates that the SW quadrant flank has alarger difference with respect to the reference volcanoid. This differ-ence may be explained in terms of greater lahar and erosion processactivity in that quadrant (Capra et al., 2010). In fact, the SW quadrantis intensively incised and presents the most active lahar sources and

gullies. The local erosion rate may be larger than in the other quad-rants where the morphological surface is dominated by deposition.The LEM relative stability analysis and the mass deficit analysisusing VOLCANOFIT and SSAP are here proposed as an integrated pro-cedure to better support the hypothesis of differential stability in astratovolcano. The proposed analysis does not consider the possibleeffects of cryptodome intrusions, faulting, or specific seismic extremeevents. Buttheseinstability factors maybe includedif a better knowl-edge of the internal volcano structure becomes available.

Previous debris avalanche simulations made on the Colima volca-no (Cortes et al., 2010) were based on reproduction of possible vol-umes calculated from field evidence of previous DAE. In the presentcase the simulation is based on the most probable volume estimatedby LEM analysis. However, it must be kept in mind that the volume

assumption may be influenced by many non-predictable trigger

factors such as cryptodome intrusion, or highfluid circulation associ-ated with heavy rains that can modify the flow behavior (Roveratoet al., 2011).

Our results confirm and support the hypotheses from previousstudies and field evidence of cyclic DAE at the Colima volcano andprovide the possibility of forecasting a future event. The multi-sector

LEM relative instability analysis results, strongly supports previoushypotheses of a dominant SW flank instability (Cortes et al., 2010;Norini et al., 2010).

Acknowledgments

We wish to thank Roberto Bartali for his help in the revision of themanuscript. We are grateful to the Instituto de Geologia, UASLP, forthe logistic facilities. This work was partially supported by CONACyTand PROMEP (Project UASLP-PTC-241) funds. Roberto Sulpizio andan anonymous reviewer provided useful suggestions that greatly im-proved the manuscript.

Appendix A. VOLCANOFIT 2.0: Concept description and use

VOLCANOFIT 2.0 is a freeware software available for the scientificcommunity. The aim of this software is to identify departures fromthe actual DEM of a volcano in shape or volume with respect to anideal 3D surface. The authors believe that identification of theseanomalies is important to understand the evolution of the edifice;an important tool for volcanic risk scenario analysis, particularly forsector collapse events. VOLCANOFIT 2.0 performs a non-linear fittingof the actual volcano DEM to an ideal 3D surface, with some con-straints determined by the selected volcanoid surface. The non-linearfitting is obtained by minimization of the average absolute deviationbetween the actual DEM and the 3D volcanoid surface. VOLCANOFITuses the Differential Evolution Genetic Algorithm proposed by Stornand Price (1997) as an optimization engine. This algorithm performs

the optimal solution search with intrinsic properties of global

Fig. 11. Titan 2D final stopping phase with accumulated debris depth above previous topography.



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optimization (Corne et al., 1999). (the details of the software areavailable at the official site http://www.volcanofit.org).

In this appendix the theoretical basis for the development of ageneralized 3D ideal surface that we call volcanoid and the proce-dure for computing the local volume deficit/surplus of the volcanoidsurface with respect to the actual volcano edifice DEM aresummarized.

A.1. The volcanoid equation

A surface of revolution with constant negative curvature mayobtained assuming the following generatrix function Z(r):

Z a erb c A:1where r is the radius or distance with respect to the axis of rotation,and a, b, care coefficients.

The fundamental property for a surface of revolution around a Zaxis in the Cartesian system of coordinates X, Y, Z is:

X2 Y2 r Z 2 A:2

Combining Eqs. (A.1) and (A.2) we obtain a function explicitly de-scribing the surface of revolution Z(X, Y):

Z a effiffiffiffiffiffiffiffiffi

X2Y2p

b c A:3The function A.3 is the prototype of the basic shape of the sym-

metric and rotational source of revolution that appears in many stra-tovolcanoes, as well as in monogenetic cones. For simplicity we callthis function a volcanoid.

Using Cartesian coordinates, we need to specify and normalize thesurface of revolution with respect to a center positioned at X0, Y0 in-side the assumed Cartesian grid (e.g. a UTM grid) (Fig. A.1).

In this way wecan representEq.(A.3) usingtwo additionalvariables:

Z a e ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXX

0 2

YY

0 2

p b c A:4

An additional element should be inserted allowing a truncation ofthe vertices to allow for the presence of a crater at a given specific el-evation Z1.

The final shape of the volcanoid becomes:

Z a effiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

XX0 2 YY0 2p

b c if Z Z1 A:5a

Z

Z1 if Z Z1

A:5b

subject to the constraints z1Ncand z1, a, b, cN0 .

Fig. A.2 displays an example of a volcanoid obtained with Eq.(A.5a)and (A.5b).

A.2. The Mt. St. Helens 1980 pre-eruption volcanoid

An example of the use of VOLCANOFIT 2.0 is the application to thepre-eruption DEM (30 m grid) of Mt. St. Helens freely available fromUniversity of Washington, Earth and Space Science (2010).

Fig. A.3a shows the original DEM with the elevations above1200 m asl.

The VOLCANOFIT non-linear fitting output is listed in Table A.1.Fig. A.3.b displays the volcanoid fitted surface. Fig. 4a shows the vol-

canoid surface overlapped on the original DEM.

A.3. Local deficit and surplus calculation

For relative stability scenario analysis it is useful to calculate thelocal relative difference between actual DEM and the fitted volcanoidsurface. The computation of local deficit/surplus is obtained from:

Zi ZiZvi A:6

where Zi is the local volume deficit or surplus expressed as differ-ence in elevation between the local actual elevation Zi and the localelevation offitted volcanoid Zvi.

A map showing the local deficit or surplus can be produced easily.Fig. A.4b shows the deficit/surplus map of the 1980 pre-eruption Mt.

St. Helens volcano.

A.4. Other volcanoid genratrix functions

Other generatix functions can be implemented. Two examples aregiven:

Z a cosh r cb

A:7

for rbcand a, b, cN0.

Z z1a1 ercb A:8

with z1N

a and z1, a, b, cN

0.Fig. A.1. Local reference system of coordinates used for the fitting.

Fig. A.2. Example of volcanoid with constant negative curvature (Eq. (A.5)).

http://www.volcanofit.org/http://www.volcanofit.org/http://www.volcanofit.org/http://www.volcanofit.org/


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Eq. (A.7) is characterized by a constant negative curvature asEq. (A.1) and the final volcanoid equation requires only 5 parametersto be defined. Eq. (A.8) is a portion of a sigmoid function and it is suit-able for a profile with variable curvature (e.g. convexconcave pro-

file) with a flexus point indicated by the parameter c.AnexampleofprofilegivenbyEqs. (A.7) and(A.8) isshownin Fig.A.5.

Appendix B. Fluid pore pressure function

In stability computation the neutral pressure is usually obtained bythe hydrostatic pressure or seepage pressure obtained by groundwaterlevel or filtration nets. In our case, fluid pressure beneath the volcanic

edifice is an important element for magma and dome buoyancy, settinga particular fluid pressure field inside. We assume a simple hydro-static field that coincides with the land surface, and then modify thebasic field w (Eq. (B.1)) with a dissipation or overpressure modifier

factor function FD (Eq. (B.2)):

w wz B:1

where

w is the hydrostatic fluid pore pressure at a given dept (kPa)Z is the vertical distance from the surface (m)w is the fluid density (kN m

-3)

and

FD 1AekD

B:2where:

FD is the dissipation or overpressure function modifier factor(adimensional)

A is the dissipation type coefficient (adimensional) which canassume one of the three values:

A= 0 no dissipation or overpressureA =1 to produce an increase of dissipation at decreasing distance

from the surfaceA = +1 to produce increasing overpressure at decreasing distance

from the surfacek is the constant of dissipation (or overpressure) with values

in the range 0.000001 to 0.1 (m1

)

Fig. A.3. a) Mt. St. Helens 1980 pre-eruption DEM, b) fitted volcanod 3D surface Eq. (A.5).

Table A.1

Volcanofit 2.0 fitting parameters and statistics for Mt. St. Helens 1979.

VOLCANOFIT 2.0Input grid OLD_ST_HELENS. DATData source (University of Washington, Earth

and Space Science, 2010)Adopted Z limit (masl) 1200Percentage random selecteddata used for fitting

50%

Volcanoid Function Negative exponential typeFitting parameters

Z1 (masl) 2890.1X0 (m local UTM grid) 562678.0Y0 (m local UTM grid) 5116128.4a 2505.3b 2076.7c 943.9

Fitting statisticsNo. data 37808Average absolute deviat ion (m) 45.6R2 0.987EF 0.974



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D is the minimum distance from a point on the slope and thesurface (m).

The final pore fluid pressure at a given point beneath the surface isgiven by Eq. (B.3):

f wzFD U0MIN B:3

where

f is the fluid pore pressure at a given point (kPa)

U0MIN is the minimum pressure at Z=0 and D=0 to account forthe exit pressure of a fumarolic and hydrothermal system(kPa).

Fig. B.1 shows the dissipation function for A=1, w=25 (kNm3), U0MIN=65 (kpa) and k =0.005 (m

1), as used during thesimulations.

Notice that at large depths the dissipation function inFig. B.1 coin-cides asymptotically with the lithostatic equivalent pressure (equilib-rium with lithostatic pressure). Near the surface this pressuredissipates rapidly and asymptotically to U0MIN.

Fig. A.4. a) Pre-eruption 1980 DEM with overlaid volcanoid Eq. (A.5). b) Plot of local de ficit (negative values) or surplus (positive values) calculated with Eq. (A.6).

Fig. A.5. Alternative generatrix function of 3D volcanoid. Fig. B.1. Fluid pore pressure assumed in the slope stability calculation.



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References

Acocella, V., 2005. Modes of sector collapse of volcanic cones: insights from analogueexperiments. Journal of Geophysical Research 110, B02205. doi:10.1029/2004JB003166.

Akiz, S.O., Grant Ludwig, L., Arrowsmith, J.R., Zielke, O., 2010. Century-long averagetime intervals between earthquake ruptures of the San Andreas fault in the CarrizoPlain, California. Geology 38 (9), 787790. doi:10.1130/G30995.1.

Alt,R., Markov, S., 2001.On thealgebraic propertiesof stochasticarithmetic. Comparison tointerval arithmetic. In: Kraemer, W., von Gudenberg, J.W.(Eds.), Scientific Computing,

Validated Numerics, Interval Methods. Kluwer Academic, Dordrecht, pp. 331

341.Apuani, T., Corazzato, C., 2009. Numerical model of the Stromboli volcano (Italy) in-cluding the effect of magma pressure in the dyke system. Rock Mechanics andRock Engineering 42, 5372.

Apuani, T., Corazzato, C., Cancelli, A., Tibaldi, A., 2005a. Stability of a collapsing volcano(Stromboli, Italy): limit equilibrium analysis and numerical modeling. Journal ofVolcanology and Geothermal Research 144, 191210.

Apuani,T., Corazzato, C.,Cancelli,A., Tibaldi,A., 2005b. Physical andmechanical propertiesof rock masses at Stromboli: a dataset for volcano instability evaluation. Bulletin ofEngineering Geology and the Environment 64, 419431.

Ashford, S.A., Sitar, N., 2002. Simplified method for evaluating seismic stability of steepslopes. Journal of Geotechnical and Geoenvironmental Engineering ASCE 128,119128.

Borgia, A., 1994. Dynamic basis of volcanic spreading. Journal of Geophysical Research99 (B9), 1779117804.

Borgia, A., Ferrari, L., Pasquar, G., 1992. Importance of gravitational spreading in thetectonic and volcanic evolution of Mount Etna. Nature 357, 231235.

Borselli, L., 2011. Slope Stability Analysis Program (SSAP). http://www.ssap2005.it(last accessed 13-07-2011).

Capra, L., Macas, J.L., 2002. The cohesive Naranjo debris flow deposit (10 km3): a dambreakoutflow derived from the pleistocene debris-avalanche deposit of Nevado deColima volcano (Mexico). Journal of Volcanology and Geothermal Research 117,213235.

Capra, L., Macias, J.L., Scott, K.M., Abrams, M., Garduo-Monroy, V.H., 2002. Debris av-alanche and debris flow transformed from collapses in the Trans-Mexican VolcanicBelt,Mexico behavior,and implication for hazard assessment. Journalof Volcanologyand Geothermal Research 113, 81110.

Capra, L., 2007. Volcanic natural dams: identification, stability and secondary effects.Natural Hazards 43, 4561.

Capra, L., Borselli, L., Varley, N., Norini, G., Gavilanes, J.C., Sarocchi, D., Caballero, L.,2010. Rainfall-triggered laharsat Volcnde Colima, Mexico:surface hydro-repellencyas initiation process. Journal of Volcanology and Geothermal Research 189, 105117.

Charbonnier, S.J., Gertisser, R., 2009. Numerical simulations of block-and-ash flowsusing the Titan2D flow model: examples from the 2006 eruption of Merapi Volca-no, Java, Indonesia. Bulletin of Volcanology 71, 953959.

Chen, Z.Y., 1992. Random trials used in determining global minimum factors of safetyof slopes. Canadian Geotechnical Journal 29, 225233.

Corne, D., Dorigo, M., Glover, F., 1999. New Ideas in Optimization. McGrow-Hill0077095065. 450 pp.

Cortes, A., Garduno, V.H., Navarro, C., Komorowski, J.C., Saucedo, R., Macias, J.L., Gavi-lanes, J.C., 2005. Carta Geolgica del Complejo Volcnico de Colima, Con Geologadel Complejo Volcnico de Colima. CARTAS GEOLGICAS Y MINERAS 10,01854798.

Cortes, A., Macias, J.L., Capra, L., Garduo, V.H., 2010. Sector collapse of the SW flank ofVolcn de Colima, Mxico. The 3600 yr BP La Lumbre-Los Ganchos debris avalancheand associated debris flows. Journal of Volcanology and Geothermal Research 197,5266.

Day, S.J., 1996. Hydrothermal pore fluid pressure and stability of porous, permeablevolcanoes. In: McGuire, W.J., Jones, A.p., Neuberg, J. (Eds.), Volcano Instability onEarth and Other Planets: Geological Society Special Publication, 110, pp. 7793.

De la Cruz-Reyna, S., 1993. Random patterns of occurrence of explosive eruptions atColima Volcano, Mexico. Journal of Volcanology and Geothermal Research 55,5168.

Dietrich, J.H., 1988. Growth and persistence of Hawaiian volcanic rift zones. Journal ofGeophysical Research 93, 42584270.

Donnadieu,F., Merle,O., 1998.Experiments on the indentation process during cryptodome

intrusions : new insights into Mount St. Helens deformation. Geology 26, 79

82.Donnadieu, F., Merle, O., Besson, J.C., 2001. Volcanic edifice stability during cryptodomeintrusion. Bulletin of Volcanology 63, 6173.

Duncan, J.M., 1996. State of the art: limit equilibrium and finite element analysis ofslopes. Journal of Geotechnical Engineering, American Society of Civil Engineers122, 577597.

Dzurisin, D., 1998. Geodetic detection of inflating stratovolcanoes: a potential break-through for mitigating volcanic hazards in the 21st century. Eos 79 973 pp.

Elsworth, D., Day, S.J., 1999. Flank collapse triggered by intrusion: the Canarian andCape Verde Archipelagoes. Journal of Volcanology and Geothermal Research 94,323340.

Elsworth, D., Voight, B., 1996. Dike intrusion as a trigger for large earthquakes and thefailure of volcano flanks. Journal of Geophysical Research 100, 60056024.

Elsworth,D., Voight, B., 2001. The mechanics of harmonic gas pressurization and failureof lava domes. Geophysical Journal International, Royal Astronomical Society 145,187198.

Francis, P.W., Wells,G.L., 1988. Landsat thematic mapper observation of debris avalanchedeposits in Central Andes. Bulletin of Volcanology 50, 258278.

Gonzlez-Mellado, A.O., De la Cruz-Reyna, S., 2008. A simplified equation of state forthe density of silicate hydrous magmas: an application to the Popocatpetl buoy-ancy-driven dome growth process. Journal of Volcanology and Geothermal Re-search 171, 287300.

Gorshkov, G.S., 1962. On the classification and terminology of Pele and Katmai typeeruption. Bulletin of Volcanology 24, 155165.

Hayashi, J.N., Self, S., 1992. A comparison of pyroclastic flow and debris avalanche mo-bility. Journal of Geophysical Research 97 (B6), 90639071.

Hewitt D., 2007. Risk analysis associated with flank failure from Putauaki, Bay of Plenty,New Zealand. Master Sc. Thesis. University of Waikato. http://researchcommons.waikato.ac.nz/handle/10289/2337 (last accessed 21-12-2010).

Hoek, E., Diederichs, M.S., 2006. Empirical estimation of rock mass modulus. Interna-tional Journal of Rock Mechanics and Mining Sciences 43, 203215.Hoek, E., Carranza-Torres, C., Corkum, B., 2002. HoekBrown criterion 2002 edition.

Proc. NARMS-TAC Conference, Toronto 1, pp. 267273.Iverson, R.M., 1995. Can magma injection and groundwater forces cause massive land-

slides on Hawaiian volcanoes? Journal of Volcanology and Geothermal Research66, 295308.

Iverson, R.M., Denlinger, R.P., 2001. Flow of variably fluidized granular material acrossthree-dimensional terrain: 1. Coulomb mixture theory. Journal of Geophysical Re-search 106, 537552.

Janbu, N., 1973. Slope stability computations. The Embankment Dam Engineering Casa-grande Volume. John Willey & Sons. 4786 pp.

Keefer, D.K., 1984. Landslides caused by earthquakes. Geological Society of AmericaBulletin 95, 406421.

Komorowski, J.C., Navarro, C., Cortes, A., Saucedo, R., Gavilanes, J.C., Siebe, C., Espndola,J.M., Rodriguez-Elizarrars, S.R., 1997. The Colima Volcanic Complex. Field Guide#3, IAVCEI, General Assembly, Puerto Vallarta, Mexico.

Luhr, J.F., Prestegaard, K.L., 1988. Caldera formation at Volcn de Colima, Mexico, bylarge Holocene volcanic debris avalanche. Journal of Volcanology and Geothermal

Research 35, 335348.Makdisi, F.I., Seed, H.B., 1978. Simplified procedure for estimating dam and embank-

ment earthquake-induced deformations. Journal of Geotechnical Engineering,American Society of Civil Engineers 104, 849867.

Marinos, V., Marinos, P., Hoek,E., 2005.The GeologicalStrength Index:applications andlimitations. Bulletin of Engineering Geology and the Environment 64, 5565.

Markov, S., Alt, R., 2004. Stochastic arithmetic: addition and multiplication by scalars.Applied Numerical Mathematics 50, 475488.

McGuire, W.J., 1996. Volcano instability: a review of contemporary themes. In:McGuire, W.J., Jones, A.P., Neuberg, J. (Eds.), Volcano Instability on the Earth andOther Planets: Geological Society Special Publication, 110, pp. 123.

Mendoza-Rosas, A.T., De la Cruz-Reyna, S., 2008. A statistical method linking geologicaland historical eruption time series for volcanic hazard estimations: applications toactive polygenetic volcanoes. Journal of Volcanology and Geothermal Research176, 277290.

Merle, O., Borgia, A., 1996. Scaled experiments of volcanic spreading. Journal of Geo-physical Research 101 (B6), 1380513817.

Moriya, I., 1980. Bandaian eruption and landforms associated with it. Collection of Ar-ticles in Memory of Retirement of Prof K Nishimura from Tohoku University. . 214219 pp.

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I a discussion of principles. Journal of Hydrology 10, 282290.

Norini, G., Lagmay, A.M.F., 2005. Deformed symmetrical volcanoes. Geology 33,605608.

Norini, G., Capra, L., Groppelli, G., Agliardi, F., Pola, A., Cortes, A., 2010. Structural archi-tecture of the Colima Volcanic Complex. Journal of Geophysical Research 115,B12209. doi:10.1029/2010JB007649.

Ordaz, M., 2011. (Mario Ordaz, Instituto de Ingeniera UNAM., Mexico City, Mexico,personal comm.).

Patra, A., Bauer, A., Nichita, C.C., Pitman, E.B., Sheridan, M.F., Bursik, M.I., Rupp, B., Web-ber, A., Stinton, A.J., Namikawa, L., Renschler, C., 2005. Parallel adaptive numericalsimulation of dry avalanches over natural terrain. Journal of Volcanology and Geo-thermal Research 139, 121.

Pitman, E.B., Patra, A., Bauer, A., Sheridan, M.F., Bursik, M.I., 2003. Computing debrisflow and landslides. Physics of Fluids 15, 36383646.

Procter, J.N., Cronin, S.J., Platz, S.J., Patra, A., Dalbey, K., Sheridan, M.F., Neall, V.E., 2010.Mapping block-and-ash flow hazards based on Titan2D simulations a case study

from Mt Taranaki NZ. Natural Hazards 53 (3), 483

501 doi:10.1007/s11069-009-9440-x.Reid, M.E., 2004. Massive collapse of volcano edifice triggered by hydrothermal pres-

surization. Geology 32, 373376.Reid, M.E., Brien, D.L., Waythomas, C.F., 2006. Preliminary slope-stability analysis of

Augustine Volcano. In: Power, J.A., Coombs, M.L., Freymueller, J.T. (Eds.), The2006 Eruption of Augustine Volcano, Alaska: U.S. Geological Survey ProfessionalPaper, 1769.

Reid, M.E., Keith, T.E.C., Kayen, R.E., Iverson, N.R., Iverson, R.M., Brien, D.L., 2010. Volcanocollapse promoted by progressive strength reduction: new data from Mount St.Helens. Bulletin of Volcanology 72, 761766.

Robin, C.,Boudal,C., 1987. A giganticBezymianni-typeevent at thebeginning of mod-ern volcano Popocatpetl. Journal of Volcanology and Geothermal Research 31,115130.

Roverato, M., Capra, L., Sulpizio, R., Norini, G., 2011. Stratigraphic reconstruction of twodebris avalanche deposits at Colima Volcano (Mexico): insights into pre-failureconditions and climate influence. Journal of Volcanology and Geothermal Research207 (12), 3346.

http://dx.doi.org/10.1029/2004JB003166http://dx.doi.org/10.1029/2004JB003166http://dx.doi.org/10.1130/G30995.1http://www.ssap2005.it/http://dx.doi.org/10.1029/2010JB007649http://dx.doi.org/10.1029/2010JB007649http://www.ssap2005.it/http://dx.doi.org/10.1130/G30995.1http://dx.doi.org/10.1029/2004JB003166http://dx.doi.org/10.1029/2004JB003166


15/15

Russo, G., Giberti, G., Sartoris, G., 1997. Numerical modeling of surface deformation andmechanical stability of Vesuvius Volcano, Italy. Journal of Geophysical Research102, 2478524800.

Saucedo, R., Macas, J.L., Sheridan, M.F., Bursik, M.I.,Komorowski, J.C.,2005. Modeling ofpyroclastic flows of Colima Volcano, Mexico: implications for hazard assessment.

Journal of Volcanology and Geothermal Research 139, 103115.Saucedo, R., Macias, J.L., Gavilanes, J.C., Arce, J.L., Komorowski, J.C., Gardner, J.E., Valdez-

Moreno, G., 2010. Eyewitness, stratigraphy, chemistry, and eruptive dynamics ofthe 1913 Plinian eruption of Volcn de Colima, Mxico. Journal of Volcanologyand Geothermal Research 191, 149166.

Savage, S.B., Hutter, K., 1989. The motion of a finite mass of granular material down a

rough incline. Journal of Fluid Mechanics. 199, 177

215.Scott, K.M., Vallance, J.V., Kerle, N., Macias, J.L., Strauch, W., Devoli, G., 2005. Cata-strophic precipitation-triggered lahars at Casita Volcano, Nicaragua: occurrence,bulking and transformation. Earth Surface Processes and Landforms 30, 5979.

Sheridan,M.F., Bonnard,C., Carreno,C., Siebe, C.,Strauch,W.,Navarro, M.,Calero, J.C.,Trujilo,N.B.,1999.Report onthe 30 October 1998 rock fall/ avalanche andbreakout flowofCa-sita Volcano, Nicaragua, triggered by Hurricane Mitch. Lanslide News 12, 24.

Sheridan, M.F., Stinton, A.J., Patra, A., Pitman, E.B., Bauer, A., Nichita, C.C., 2005. Evalu-ating Titan2D mass-flow model using the 1963 Little Tahoma Peak avalanches,Mount Rainier, Washington. Journal of Volcanology and Geothermal Research139, 89102.

Siebert, L., 1984. Large volcanic debris avalanches: characteristics of source areas, de-posits and associated eruptions. Journal of Volcanology and Geothermal Research22, 163197.

Siebert, L., Glicken, H., Ui, T., 1987. Volcanic hazards from Bezymianny- and Bandai-type eruptions. Bulletin of Volcanology 49, 435459.

Siegel, R.A., Kovacs, W.D., Lovell, C.W., 1981. Random surface generation in stabilityanalysis. Journal of Geotechnical Engineering 107 (7), 9961002.

Simmons, J., Elsworth, D., Barry, Voight B., 2005. Classification and idealized limit-

equilibrium analysesof dome collapses at Soufrire Hills volcano, Montserrat, duringgrowth of the first lava dome: November 1995March 1998. Journal of Volcanologyand Geothermal Research 139 (34), 241258.

Storn, R., Price, K., 1997. Differential evolutiona simple and efficient heuristic for globaloptimization over continuous spaces. Journal of Global Optimization 11, 341359.

Sulpizio, R., Capra, L., Sarocchi, D., Saucedo, R., Gavilanes, J.C., Varley, N., 2010. Predict-ing the block-and-ash flow inundation areas at Volcn de Colima (Colima, Mexico)based on the present day (February 2010) status. Journal of Volcanology and Geo-thermal Research 193, 4966.

Swanson, F.J., Norio, O., Masaki, T., 1986. Landslide dams in Japan. In: Schuster, R.L.(Ed.), Landslide Dams Processes, Risk and Mitigation: American Society of CivilEngineers Geotechnical Special Publication, pp. 131145.

Thomas, M.E., Petford, N., Bromhead, E.N., 2004. The effect of internal gas pressuriza-tion on volcanic edifice stability: evolution towards a critical state. Terra Nova16, 312317.

Ui, T., Glicken, H., 1986. Internal structural variations in a debris-avalanche depositfrom ancestral Mount Shasta, California, USA. Bulletin of Volcanology 48,189194.

Universityof Washington,Earthand Spacescience,2010. http://rocky.ess.washington.edu/data/raster/thirtymeter/mtsthelens/OldMtStHelens.zip(last accessed : july 2010).

Vallance, J.V., Siebert, L., Rose, W.I., Girn, J.R., Banks, N.G.,1995. Edifice collapse and re-lated hazard in Guatemala. Journal of Volcanology and Geothermal Research 66,337355.

van Wyk de Vries, B., Borgia, A., 1996. The role of basement in volcano deformation. In:McGuire, M.J., Jones, A.P., Neuberg, J. (Eds.), Volcano Instability on the Earth andOther Planets: Geological Society Special Publication, 110, pp. 95110.

van Wyk de Vries, B., Matela, R., 1998. Styles of volcano-induced deformation: numericalmodels of substratum flexure, spreading and extrusion. Journal of Volcanology andGeothermal Research 81, 118.

vanWyk de Vries, B.,Merle,O., 1996. Theeffectof volcanicconstructs onrift fault patterns.Geology 24, 643646.

vanWyk de Vries,B., Wooller,L., Cecchi, E.,Murray, J.B., 2003. Theimportance of strike-slip faulting in spreading volcanoes. EGS-AGU-EUG Meeting, Nice, France.

Vignes, J., 1993. A stochastic arithmetic for reliable scientific computation. Mathemat-ics and Computers in Simulation 35, 233261.

Voight, B., 2000. Structural stability of andesite volcanoes and lava domes. PhilosophicalTransactions of the Royal Society of London 358, 16631703.

Voight, B., Elsworth, D., 1997. Failure of volcano slopes. Geotechnique 47, 131.Voight, B., Elsworth, D., 2000. Stability of gas-pressurised lava-domes. Geophysical Re-

search Letters 27, 14.Watters, R.J., Zimbelman, D.R., Bowman, S.D., Crowley, J.K., 2000. Rock mass strength

assessment and significance to edifice stabilityMount Rainier and Mount Hood,

Cascade Range volcanoes. Pure and Applied Geophysics 157, 957976.Yu, B., Dalbey, K., Webb, A., Bursik, M.I., Patra, A., Pitman, E.B., Nichita, C., 2009. Numer-

ical issues in computing inundation areas over natural terrains using Savage-Hut-ter theory. Natural Hazards 50, 249267.

Zhu, D.Y., Lee, C.F., Jiang, H.D., 2003. Generalised framework of limit equilibriummethods for slope stability analysis. Geotechnique 53 (4), 377395.

Zhu, D.Y., Lee, C.F., Quian, Q.H., Chen, G.R., 2005. A concise algorithm for computing thefactor of safety using the MorgensternPrice method. Candadian Geotechnical

Journal 42, 272278.Zimbelman, D.R., Watters, R.J., Firth, I.R., Breit, G.N., Carrasco-Nuez, G., 2004. Strato-

volcano stability assessment methods and results from Citlaltpetl, Mexico. Bulletinof Volcanology 66 (1), 6679.

http://rocky.ess.washington.edu/data/raster/thirtymeter/mtsthelens/OldMtStHelens.ziphttp://rocky.ess.washington.edu/data/raster/thirtymeter/mtsthelens/OldMtStHelens.ziphttp://rocky.ess.washington.edu/data/raster/thirtymeter/mtsthelens/OldMtStHelens.ziphttp://rocky.ess.washington.edu/data/raster/thirtymeter/mtsthelens/OldMtStHelens.zip

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