Source mechanism of volcanic tremor: fluid-driven crack models and their application to the 1963 kilauea eruption

We propose a model for the mechanism of magma transport based on a fluid-filled tensile crack driven by the excess pressure of fluid. Such a transport mechanism can generate seismic waves by a succession of jerky crack extensions, if the fracture strength of rock varies in space, or if there is a difference between the dynamic and static values of the critical stress intensity factor. We also find that the opening and closing of a narrow channel connecting two fluid-filled cracks may be a source of seismic waves. Using the finite-difference method, we calculated the vibration of dry and fluid-filled cracks generated by: (1) a jerky extension at one end or at both ends and (2) a jerky opening of a narrow channel connecting two cracks. We then calculated the far-field and near-field radiation from these vibrating cracks. The spectra show peaked structures, but interestingly, most high-frequency peaks are only present in the near-field and cannot be transmitted to the far-field. The spectral features described above are often observed for volcanic tremors and in some cases for seismic signals associated with hydraulic fracturing experiments.We first consider as a model of volcanic tremor randomly occurring jerky crack extensions, and derive a formula relating the tremor amplitude to the excess pressure in the magma, the incremental area in each extension, and the frequency of extensions. These parameters are also constrained by other observations, such as the rate of magma flow.Our model was tested quantitatively against observations made in one of the best-described case histories of volcanic tremor: the October 5–6, 1963 Kilauea flank eruption. We found that a single, long crack extending from the summit to the eruptive site cannot explain the observations. The model of a steadily expanding crack ran into difficulties when quantitative comparisons were made with observations. The extension of crack area needed to explain the amplitude of volcanic tremor should accompany a large increase in tremor period which was not observed.Our second model is a chain of cracks connected by narrow channels which open and close. The length of each crack is around 1 km, the channel area connecting neighboring cracks is about 10³m², and the channel opens jerkily with the magmatic excess pressure of about 20 bars. The frequency of jerky opening of each channel is about once in 15 seconds. The channel is closed after each jerky opening, as soon as magma is moved through the channel.     

Discussion on the energy partition of volcanic eruption

Energy of volcanic eruption is divided into various ways, such as lava flows, ash production, explosion, ground vibration, air waves and so on. In order to elucidate the cruptive mechanism, energy partition of volcanic eruption in unit time is considered to be a key to solve the problem. In this short paper, partition of eruption energy was calculated for typical three basaltic volcanoes. Ratio of tremor energy to thermal energy is almost the same for both Mihara and Nyragongo in spite of their different eruptive mechanism. Tremor energy was found to be small for Kilauea Volcano compared with the above two volcanoes. This was attributed to the different source mechanism of tremor. Partition of eruption energy was calculated for Also Volcano which showed phreatic explosion in 1958. Kinetic energy is almost ten times of thermal energy. Ratio of energy converted to elastic waves to thermal energy is found to be equivalent to the ratio of energy of elastic waves to the chemical energy in case of explosion of chemical explosives.     

The influence of great earthquakes on volcanic eruption rate along the Chilean subduction zone

Seismic activity has been postulated as a trigger of volcanic eruption on a range of timescales, but demonstrating the occurrence of triggered eruptions on timescales beyond a few days has proven difficult using global datasets. Here, we use the historic earthquake and eruption records of Chile and the Andean southern volcanic zone to investigate eruption rates following large earthquakes. We show a significant increase in eruption rate following earthquakes of M_W > 8, notably in 1906 and 1960, with similar occurrences further back in the record. Eruption rates are enhanced above background levels for ~ 12 months following the 1906 and 1960 earthquakes, with the onset of 3–4 eruptions estimated to have been seismically influenced in each instance. Eruption locations suggest that these effects occur from the near-field to distances of ~ 500 km or more beyond the limits of the earthquake rupture zone. This suggests that both dynamic and static stresses associated with large earthquakes are important in eruption-triggering processes and have the potential to initiate volcanic eruption in arc settings over timescales of several months.     

Sensitivity of the dynamics of volcanic eruption columns to their shape

This paper presents a one-dimensional steady-state model to investigate the sensitivity of the dynamics of sustained eruption columns to radius variations with height due to thermal expansion of the entrained air, and decreases in atmospheric pressure with height. In contrast to a number of previous models using an equation known as the entrainment assumption, the new model is based on similarity arguments to derive an equation set equivalent to the model proposed by Woods [Bull Volcanol 50:169–193, 1988]. This approach allows investigation of the effect of gas compressibility on the entrainment rate of ambient air, which has been little examined for a system in which a decrease in pressure significantly affects the density stratification of a compressible fluid. The new model provides results that include two end members: one in which the volume change within the eruption columns affects only the radial expansion without changing the vertical motion, and the other is the converse. The Woods [Bull Volcanol 50:169–193, 1988] model can be regarded as being between those two end members. The range of uncertainty arises because the extremely high temperature of discharged materials from a volcanic vent, and the exceptional terminal height of the eruption columns, allow significant expansion of the gas component in the eruption columns, making them behave differently from common turbulent plumes. This study indicates that the maximum height of the eruption columns is affected considerably by this uncertainty, particularly when the eruption columns extend above a height of 10 km, at which the pressure is about one-fourth the pressure at the ground surface. Column collapse may also be suppressed in wider parameter ranges than previously estimated. However, the uncertainty can be reduced by measuring column radii through a vertical profile during actual volcanic eruptions. Accordingly, this paper suggests that appropriate observation of eruption column shapes is essential for improving our understanding of the dynamics of eruption columns.     

Relationship between earthquake and volcanic eruption inferred from historical records

Introduction From the records of Wudalianchi volcanic group eruption in 1720~1721 obtained from the Man ethnic group files of Heilongjiang General Yamen in Qing Dynasty (WU, 1998; CHEN, WU, 2003), we have discovered the eruption time, state, material and scale of Laoheishan and Hu-oshaoshan volcanoes, as well as numerous seismic records. These historical materials are discov-ered for the first time although the study on Wudalianchi volcanic group has a long history. These earthquakes co…     

Rhyolitic ignimbrites in the Rogerson Graben,southern Snake River Plain volcanic province: volcanic stratigraphy,eruption history and basin evolution

The 80 km long NNE-trending Rogerson Graben on the southern margin of the central Snake River Plain, Idaho, USA, hosts a rhyolitic pyroclastic succession, 200 m thick, that records a period of successive, late-Miocene, large-volume explosive eruptions from the Yellowstone–Snake River Plain volcanic province, and contemporaneous extension. The succession, here termed the Rogerson Formation, comprises seven members (defined herein) and records at least eight large explosive eruptions with numerous repose periods. Five high-grade and extremely high-grade ignimbrites are intercalated with three non-welded ignimbrites and two volcaniclastic deposits, with numerous repose periods (palaeosols) throughout. Two of the ignimbrites are dominantly rheomorphic and lava-like but contain subordinate non-welded pyroclastic layers. The ignimbrites are typical Snake River Plain high-silica rhyolites, with anhydrous crystal assemblages and high inferred magmatic temperatures (≤ 1,025°C). We tentatively infer that the Jackpot and Rabbit Springs Members may have been emplaced from the Bruneau–Jarbidge eruptive centre on the basis of: (1) flow lineation trends, (2) crystal assemblage, and (3) radiometric age. We infer that the overlying Brown’s View, Grey’s Landing, and Sand Springs Members may have been emplaced from the Twin Falls eruptive centre on the basis of: (1) kinematic indicators (from the east), and (2) crystal assemblage. Furthermore, we have established the contemporaneous evolution of the Rogerson Graben from the emplacement of the Jackpot Member onwards, and infer that it is similar to younger half-graben along the southern margin of the Snake River Plain, formed by local reactivation of Basin and Range structures by the northeastwardly migration of the Yellowstone hot-spot. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Quantitative models of the fallout and dispersal of tephra from volcanic eruption columns

A theoretical model of clast fallout from convective eruption columns has been developed which quantifies how the maximum clast size dispersal is determined by column height and wind strength. An eruption column consists of a buoyant convecting region which rises to a heightH _B where the column density equals that of the atmosphere. AboveH _B the column rises further to a heightH _T due to excess momentum. BetweenH _T andH _B the column is forced laterally into the atmosphere to form an upper umbrella region. Within the eruption column, the vertical and horizontal velocity fields can be calculated from exprimental and theoretical studies and consideration of mass continuity. The centreline vertical velocity falls as a nearly linear function over most of the column's height and the velocity decreases as a gaussian function radially away from the centreline. Both column height and vertical velocity are strong functions of magma discharge rate. From calculations of the velocity field and the terminal fall velocity of clasts, a series of particle support envelopes has been constructed which represents positions where the column vertical velocity and terminal velocity are equal for a clast of specific size and density. The maximum range of a clast is determined in the absence of wind by the maximum width of the clast support envelope.The trajectories of clasts leaving their relevant support envelope at its maximum width have been modelled in columns from 6 to 43 km high with no wind and in a wind field. From these calculations the shapes and areas of maximum grain size contours of the air-fall deposit have been predicted. For the no wind case the theoretical isopleths show good agreement with the Fogo A plinian deposit in the Azores. A diagram has been constructed which plots, for a particular clast size, the maximum range normal to the dispersal axis against the downward range. From the diagram the column height (and hence magma discharge rate) and wind velocity can be determined. Historic plinian eruptions of Santa Maria (1902) and Mount St. Helens (1980) give maximum heights of 34 and 19 km respectively and maximum wind speeds at the tropopause of m/s and 30 m/s respectively. Both estimates are in good agreement with observations. The model has been applied to a number of other plinian deposits, including the ultraplinian phase of theA.D. 180 Taupo eruption in New Zealand which had an estimated column height of 51 km and wind velocity of 27 m/s.     

Doppler radar sounding of volcanic eruption dynamics at Mount Etna

Besides their common use in atmospheric studies, Doppler radars are promising tools for the active remote sensing of volcanic eruptions but were little applied to this field. We present the observations made with a mid-power UHF Doppler radar (Voldorad) during a 7-h Strombolian eruption at the SE crater of Mount Etna on 11–12 October 1998. Main characteristics of radar echoes are retrieved from analysis of Doppler spectra recorded in the two range gates on either side of the jet axis. From the geometry of the sounding, the contribution of uprising and falling ejecta to each Doppler spectrum can be discriminated. The temporal evolution of total power backscattered by uprising targets is quite similar to the temporal evolution of the volcanic tremor and closely reproduces the overall evolution of the eruption before, during and after its paroxysm. Moreover, during the sharp decrease of eruptive activity following the paroxysm, detailed analysis of video (from camera recording), radar and seismic measurements reveals that radar and video signals start to decrease simultaneously, approximately 2.5 min after the tremor decline. This delay is interpreted as the ascent time through a magma conduit of large gas slugs from a shallow source roughly estimated at about 500 m beneath the SE crater. Detailed analysis of eruptive processes has been also made with Voldorad operating in a high sampling rate mode. Signature of individual outburst is clearly identified on the half part of Doppler spectra corresponding to rising ejecta: temporal variations of the backscattered power exhibit quasi periodic undulations, whereas the maximum velocity measured on each spectrum displays a sharp peak at the onset of each outburst followed by a slow decay with time. Periodicity of power variations (between 3.8 and 5.5 s) is in agreement with the occurrence of explosions visually observed at the SE vent. Maximum vertical velocities of over 160 m s^–1 were measured during the paraoxysmal stage and the renewed activity. Finally, by using a simplified model simulating the radar echoes characteristics, we show that when Voldorad is operating in high sampling rate mode, the power and maximum velocity variations are directly related to the difference in size and velocity of particles crossing the antenna beam.Editorial responsibility: A. Woods     

A new regime of volcanic eruption due to the relative motion between liquid and gas

In explosive magma eruptions, magma ascends through a conduit as a Poiseuille flow at depth, and gas exsolves gradually and expands as the pressure decreases (bubbly flow regime). When the volume fraction of gas becomes sufficiently large, liquid or solid parts of magma fragment into droplets or ashes, and the flow dynamics becomes governed by the gas phase (gas–ash flow regime). We propose a new flow regime, which we call fractured-turbulent flow regime, between the bubbly flow regime and the gas–ash flow regime. In the new regime, both liquid magma and gas are continuous phases. The high connectivity of the two phases allows the relative velocity between them to increase significantly. We present one sample calculation, which displays basically explosive characteristics, but has three features distinct from previous models. The explosive characteristics are manifested as the fragmentation of the magma and the high speed jet that issues from the vent. The first distinct feature is a nearly lithostatic pressure distribution, which results from the increase of the height of the fragmentation surface. The second one is the atmospheric pressure at the vent; the flow is not choked. The third one is that the relative velocity between the gas and the ash is large at the vent despite the large interaction force between the two phases. The large relative velocity is established in the fractured-turbulent regime, and is maintained in the subsequent gas–ash flow regime.     

An ignimbrite veneer deposit: The trail-marker of a pyroclastic flow

The term “ignimbrite veneer deposit” (IVD) is proposed for a new kind of pyroclastic deposit which is found associated with, and passes laterally into, Taupo ignimbrite of valley pond type in New Zealand. It forms a thin layer mantling the landscape over 15,000 km², and is regarded as the deposit from the trailing “tail” of a pyroclastic flow, where a relaxation of shear stress favoured the deposition of the basal part of the flow. The IVD differs little in grain-size from the associated ignimbrite, but it shows a crude internal stratification attributed to the deposition of a succession of layers, one after the passage of each pulse of the pyroclastic flow. It locally contains laterally-discontinuous lenses of coarse pumice (“lee-side lenses”) on the far-vent side of topographic obstacles. In nearvent exposures the Taupo IVD shows lensoid and cross-stratified bed-forms even where it stands on a planar surface, attributed to deposition from a flow travelling at an exceedingly high velocity.An IVD can be distinguished from a poorly sorted pyroclastic fall deposit because the beds in it show more rapid lateral variations in thickness, it may show a low-angle cross-stratification, and it contains carbonised wood from trees not in the position of growth; from the deposit of a wet base surge because it lacks vesicles and strong antidune-like structures and contains carbonised vegetation, and from a hot and dry pyroclastic surge deposit because it possesses a high content of pumice and “fines”.The significance of an IVD is that it records the passage of a pyroclastic flow, where the flow itself has moved farther on.     

An eruption of the veer cone as a volcanic event during the increase of volcanic activity in Kamchatka at the beginning of the Christian Era

Tephrochronologic studies conducted in the Levaya Avacha River valley helped determine the true age of the Veer cinder cone, which formed approximately in 470 AD (1600 ¹⁴C BP). These data refute the existing idea that it was generated in 1856. The monogenetic Veer cone should be cancelled from the catalogs of historical eruptions and active volcanoes in Kamchatka. The eruption of this cone was a reflection of the all-Kamchatkan increase in the activity of endogenous processes that occurred in 0–650 AD.     

Progressive assembly of a massive layer of ignimbrite with a normal-to-reverse compositional zoning: the Zaragoza ignimbrite of central Mexico

The Zaragoza ignimbrite and two enclosing rhyodacite pumice fall layers were emplaced during the 15 km³ (DRE), ∼0.1 Ma Zaragoza eruption from Los Humeros volcanic centre, 180 km east of Mexico City. The ignimbrite comprises several massive flow-units, the largest of which locally exceeds 20 m in thickness and is regionally traceable. It comprises massive lapilli-ash with vertical elutriation pipes, and has a fine-grained inverse-graded base and a pumice concentration zone at the top. It also exhibits an unusual gradational ‘double’ vertical compositional zonation that is widely traceable. A basal rhyodacitic (67.6–69 wt% SiO₂) zone grades up via a mixed zone into a central andesitic (58–62 wt% SiO₂) zone, which, in turn, grades up into an upper rhyodacitic (67.6–69 wt% SiO₂) zone. Zoning is also defined by vertical variations in lithic clast populations. We infer that pyroclastic fountaining fed initially rhyodacite pumice clasts to a sustained granular fluid-based pyroclastic density current. The composition of the pumice clasts supplied to the current then gradually changed, first to andesite and then back to rhyodacite. Inverse grading at the base of the massive layer may reflect initial waxing flow competence. The pumice concentration at the top of the massive layer is entirely rhyodacitic and was probably deposited during waning stages of the current, when the supply of andesitic pumice clasts had ceased. The return to rhyodacitic composition may have been the result of eruption-conduit modification during collapse of Los Potreros caldera, marked in the ignimbrite by a widespread influx of hydrothermally altered lithic blocks, and/or a decrease in draw-up depth from a compositionally stratified magma chamber as the eruptive mass flux waned. The massive layer of ignimbrite thins locally to less than 2 m, yet it still shows the double zonation. Correlation of the zoning suggests that the thin massive layer is stratigraphically condensed, and aggraded relatively slowly during the same time interval as did the much thicker (≤50 m) massive layer.Editorial responsibility: J McPhie     

Three distinct regimes of volcanic tremor associated with the eruption of Shishaldin Volcano, Alaska 1999

Tremor signals associated with the eruption of Shishaldin Volcano on 19 and 23 April 1999 were the strongest recorded anywhere in the Aleutian Arc by the Alaska Volcano Observatory (AVO) in its 10-year history. Reduced displacements (D_R) reached 23 cm² on 19 April and 43 cm² on 23 April. During the activity, D_R and spectral data with a frequency resolution of 0.1 Hz were computed and put on the World Wide Web every 10 min. These data are analyzed here. The general temporal patterns of seismicity of these eruption events were similar, but the eruptions and their effects quite different. The 19 April event is known to have culminated in a sub-Plinian phase, which ejected ash to an altitude of 16 km. Despite higher amplitudes and the largest hotspot from satellite data, the 23 April event produced little ash reaching only 6 km altitude. For several hours prior to the sub-Plinian phase on 19 April, tremor with a peak frequency of 1.3 Hz intensified. During the sub-Plinian phase the peak frequency increased to 4-8 Hz. However, in 15 h after the eruption, three episodes of stronger tremor occurred with a lower 1.0-Hz peak, alternating with weaker tremor with a 1.3-Hz peak. These transitions correspond to D_R=~8 cm². Although these strong tremor episodes produced higher D_R levels than the sub-Plinian phase, data from a pressure sensor show that only strong Strombolian explosions occurred. The suite of observations suggests three distinct tremor regimes that may correspond to slug flow, bubbly flow, and sustained strong eruptions, or a cyclic change in source parameters (e.g., geometry, sound speed, or ascent rate). This behavior occurred at Shishaldin only during the April 1999 sequence, and we are not aware of similar behavior at other volcanoes.     

Late Quaternary history of the Vakinankaratra volcanic field (central Madagascar): insights from luminescence dating of phreatomagmatic eruption deposits

The Quaternary Vakinankaratra volcanic field in the central Madagascar highlands consists of scoria cones, lava flows, tuff rings, and maars. These volcanic landforms are the result of processes triggered by intracontinental rifting and overlie Precambrian basement or Neogene volcanic rocks. Infrared-stimulated luminescence (IRSL) dating was applied to 13 samples taken from phreatomagmatic eruption deposits in the Antsirabe–Betafo region with the aim of constraining the chronology of the volcanic activity. Establishing such a chronology is important for evaluating volcanic hazards in this densely populated area. Stratigraphic correlations of eruption deposits and IRSL ages suggest at least five phreatomagmatic eruption events in Late Pleistocene times. In the Lake Andraikiba region, two such eruption layers can be clearly distinguished. The older one yields ages between 109?±?15 and 90?±?11 ka and is possibly related to an eruption at the Amboniloha volcanic complex to the north. The younger one gives ages between 58?±?4 and 47?±?7 ka and is clearly related to the phreatomagmatic eruption that formed Lake Andraikiba. IRSL ages of a similar eruption deposit directly overlying basement laterite in the vicinity of the Fizinana and Ampasamihaiky volcanic complexes yield coherent ages of 68?±?7 and 65?±?8 ka. These ages provide the upper age limit for the subsequently developed Iavoko, Antsifotra, and Fizinana scoria cones and their associated lava flows. Two phreatomagmatic deposits, identified near Lake Tritrivakely, yield the youngest IRSL ages in the region, with respective ages of 32?±?3 and 19?±?2 ka. The reported K-feldspar IRSL ages are the first recorded numerical ages of phreatomagmatic eruption deposits in Madagascar, and our results confirm the huge potential of this dating approach for reconstructing the volcanic activity of Late Pleistocene to Holocene volcanic provinces.     

Morphology and mechanism of eruption of postglacial shield volcanoes in Iceland

Postglacial Icelandic shield volcanoes were formed in monogenetic eruptions mainly in the early Holocene epoch. Shield volcanoes vary in their cone morphology and in the areal extent of the associated lava flows. This paper presents the results of a study of 24 olivine tholeiite and 7 picrite basaltic shield volcanoes. For the olivine tholeiitic shields the median slope is 2.7°, the median height 60 m, the median diameter 3.6 km, the median aspect ratio (height against diameter) 0.019, and the median cone volume 0.2 km³. The picritic shield volcanoes are considerably steeper and smaller. A shield-volcano cone forms from successive lava lake overflows which are of shelly-type pahoehoe. A widespread apron surrounding the cone forms from tube-fed P-type pahoehoe. The slopes of the cones have (a) a planar or slightly convex form, (b) a concave form, or (c) a convex-concave form. A successive stage of a shield volcano is determined on the basis of cone morphology and lava assemblages. A shield-producing eruption has alternating episodes of lava lake overflows and tube-fed delivery to the distal parts of the flow field. In the late stages of eruption, the cone volume increases in response to the increased amount of rootless outpouring on the cone flanks. Normally, only a small percentage of the total erupted volume of a shield volcano, sometimes as little as 1–3%, is in the shield volcano cone itself, the main volume being in the apron of the shield.     

Under the surface: Pressure-induced planetary-scale waves,volcanic lightning,and gaseous clouds caused by the submarine eruption of Hunga Tonga-Hunga Ha'apai volcano

We present a narrative of the eruptive events culminating in the cataclysmic January 15, 2022 eruption of Hunga Tonga-Hunga Ha'apai Volcano by synthesizing diverse preliminary seismic, volcanological, sound wave, and lightning data available within the first few weeks after the eruption occurred. The first hour of eruptive activity produced fast-propagating tsunami waves, long-period seismic waves, loud audible sound waves, infrasonic waves, exceptionally intense volcanic lightning and an unsteady volcanic plume that transiently reached—at 58 ?km—the Earth's mesosphere. Energetic seismic signals were recorded worldwide and the globally stacked seismogram showed episodic seismic events within the most intense periods of phreatoplinian activity, and they correlated well with the infrasound pressure waveform recorded in Fiji. Gravity wave signals were strong enough to be observed over the entire planet in just the first few hours, with some circling the Earth multiple times subsequently. These large-amplitude, long-wavelength atmospheric disturbances come from the Earth's atmosphere being forced by the magmatic mixture of tephra, melt and gasses emitted by the unsteady but quasi-continuous eruption from 0402±1–1800 UTC on January 15, 2022. Atmospheric forcing lasted much longer than rupturing from large earthquakes recorded on modern instruments, producing a type of shock wave that originated from the interaction between compressed air and ambient (wavy) sea surface. This scenario differs from conventional ideas of earthquake slip, landslides, or caldera collapse-generated tsunami waves because of the enormous (～1000x) volumetric change due to the supercritical nature of volatiles associated with the hot, volatile-rich phreatoplinian plume. The time series of plume altitude can be translated to volumetric discharge and mass flow rate. For an eruption duration of ～12 ?h, the eruptive volume and mass are estimated at 1.9 ?km³ and ～2 900 ?Tg, respectively, corresponding to a VEI of 5–6 for this event. The high frequency and intensity of lightning was enhanced by the production of fine ash due to magma—seawater interaction with concomitant high charge per unit mass and the high pre-eruptive concentration of dissolved volatiles. Analysis of lightning flash frequencies provides a rapid metric for plume activity and eruption magnitude. Many aspects of this eruption await further investigation by multidisciplinary teams. It represents a unique opportunity for fundamental research regarding the complex, non-linear behavior of high energetic volcanic eruptions and attendant phenomena, with critical implications for hazard mitigation, volcano forecasting, and first-response efforts in future disasters.     

A statistical method linking geological and historical eruption time series for volcanic hazard estimations: Applications to active polygenetic volcanoes

The probabilistic analysis of volcanic eruption time series is an essential step for the assessment of volcanic hazard and risk. Such series describe complex processes involving different types of eruptions over different time scales. A statistical method linking geological and historical eruption time series is proposed for calculating the probabilities of future eruptions. The first step of the analysis is to characterize the eruptions by their magnitudes. As is the case in most natural phenomena, lower magnitude events are more frequent, and the behavior of the eruption series may be biased by such events. On the other hand, eruptive series are commonly studied using conventional statistics and treated as homogeneous Poisson processes. However, time-dependent series, or sequences including rare or extreme events, represented by very few data of large eruptions require special methods of analysis, such as the extreme-value theory applied to non-homogeneous Poisson processes. Here we propose a general methodology for analyzing such processes attempting to obtain better estimates of the volcanic hazard. This is done in three steps: Firstly, the historical eruptive series is complemented with the available geological eruption data. The linking of these series is done assuming an inverse relationship between the eruption magnitudes and the occurrence rate of each magnitude class. Secondly, we perform a Weibull analysis of the distribution of repose time between successive eruptions. Thirdly, the linked eruption series are analyzed as a non-homogeneous Poisson process with a generalized Pareto distribution as intensity function. As an application, the method is tested on the eruption series of five active polygenetic Mexican volcanoes: Colima, Citlaltépetl, Nevado de Toluca, Popocatépetl and El Chichón, to obtain hazard estimates.