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Ongoing resurgence affects Campi Flegrei caldera (Italy) via bradyseism, i.e. a series of ground deformation episodes accompanied by increases in shallow seismicity. In this study, we perform a mathematical analysis of the GPS and seismic data in the instrumental catalogs from 2000 to 2020, and a comparison of them to the preceding data from 1983 to 1999. We clearly identify and characterize two overlying trends, i.e. a decennial-like acceleration and cyclic oscillations with various periods. In particular, we show that all the signals have been accelerating since 2005, and 90–97% of their increase has occurred since 2011, 40–80% since 2018. Nevertheless, the seismic and ground deformation signals evolved differently—the seismic count increased faster than the GPS data since 2011, and even more so since 2015, growing faster than an exponential function The ground deformation has a linearized rate slope, i.e. acceleration, of 0.6 cm/yr2 and 0.3 cm/yr2 from 2000 to 2020, respectively for the vertical (RITE GPS) and the horizontal (ACAE GPS) components. In addition, all annual rates show alternating speed-ups and slow-downs, consistent between the signals. We find seven major rate maxima since 2000, one every 2.8–3.5 years, with secondary maxima at fractions of the intervals. A cycle with longer period of 6.5–9 years is also identified. Finally, we apply the probabilistic failure forecast method, a nonlinear regression that calculates the theoretical time limit of the signals going to infinity (interpreted here as a critical state potentially reached by the volcano), conditional on the continuation of the observed nonlinear accelerations. Since 2000, we perform a retrospective analysis of the temporal evolution of these forecasts which highlight the periods of more intense acceleration. The failure forecast method applied on the seismic count from 2001 to 2020 produces upper time limits of [0, 3, 11] years (corresponding to the 5th, 50th and 95th percentiles, respectively), significantly shorter than those based on the GPS data, e.g. [0, 6, 21] years. Such estimates, only valid under the model assumption of continuation of the ongoing decennial-like acceleration, warn to keep the guard up on the future evolution of Campi Flegrei caldera.

Assessments of pyroclastic flow (PF) hazards are commonly based on mapping of PF and surge deposits and estimations of inundation limits, and/or computer models of varying degrees of sophistication. In volcanic crises a PF hazard map may be sorely needed, but limited time, exposures, or safety aspects may preclude fieldwork, and insufficient time or baseline data may be available for reliable dynamic simulations. We have developed a statistically constrained simulation model for block-and-ash type PFs to estimate potential areas of inundation by adapting methodology from Iverson et al. (Geol Soc America Bull 110:972–984, 1998) for lahars. The predictive equations for block-and-ash PFs are calibrated with data from several volcanoes and given by A = (0.05 to 0.1)V2/3, B = (35 to 40)V2/3, where A is cross-sectional area of inundation, B is planimetric area and V is deposit volume. The proportionality coefficients were obtained from regression analyses and comparison of simulations to mapped deposits. The method embeds the predictive equations in a GIS program coupled with DEM topography, using the LAHARZ program of Schilling (1998). Although the method is objective and reproducible, any PF hazard zone so computed should be considered as an approximate guide only, due to uncertainties on the coefficients applicable to individual PFs, the authenticity of DEM details, and the volume of future collapses. The statistical uncertainty of the predictive equations, which imply a factor of two or more in predicting A or B for a specified V, is superposed on the uncertainty of forecasting V for the next PF to descend a particular valley. Multiple inundation zones, produced by simulations using a selected range of volumes, partly accommodate these uncertainties. The resulting maps show graphically that PF inundation potentials are highest nearest volcano sources and along valley thalwegs, and diminish with distance from source and lateral distance from thalweg. The model does not explicitly consider dynamic behavior, which can be important. Ash-cloud surge impact limits must be extended beyond PF hazard zones and we provide several approaches to do this. The method has been used to supply PF and surge hazard maps in two crises: Merapi 2006; and Montserrat 2006–2007.

On many volcanoes, there is evidence of a relationship between dome collapse and periods of high precipitation. We propose a mechanism for this relationship and investigate the conditions that optimize failure by this process. Observations of elongate lobes that evolve through exogenous growth of lava domes reveal that they commonly develop tensile fractures perpendicular to the direction of motion. These cracks can increase in depth by localized cooling and volumetric contraction. During periods of high rainfall, water can fill these cracks, and the increase in fluid pressure on the base of the lobes and within the crack can trigger the collapse of the hot exogenous lava domes. Using limit-equilibrium analysis, it is possible to calculate the water and vapor forces acting on the rear and base of the potentially unstable part of the lobe. The model presented is rectangular in cross-section, with material properties representative of andesitic dome rocks. Vapor pressures at the base of cracks are sealed by the penetrating rainfall, which forms a saturated cap within the lobe. This leads to an increase in fluid pressurization both through the underlying gas pressure and the downslope component of the liquid water cap. Fluid pressurization increases as the penetration depth increases. This rainfall penetration depth is dependent on the thermal properties of the rocks, antecedent temperature, lobe geometry, and the intensity and duration of precipitation. Dominant parameters influencing the stability of the lobe are principally lobe thickness, duration and intensity of rainfall, and antecedent lobe temperature. Our modeling reveals that thicker lobes are intrinsically more unstable due to the amplification of downslope forces in comparison to cohesive strength. The increase in the duration and intensity of rainfall events also increases the potential for collapse, as it leads to deeper liquid penetration. Deeper penetration depths are also achieved through lower antecedent temperatures since less fluid is lost through vaporization. Thus, the potential for rain-triggered collapse increases with time from emplacement.

Investigation of well-exposed volcaniclastic deposits of Shiveluch volcano indicates that large-scale failures have occurred at least eight times in its history: approximately 10,000, 5700, 3700, 2600, 1600, 1000, 600 14 C BP and 1964 AD. The volcano was stable during the Late Pleistocene, when a large cone was formed (Old Shiveluch), and became unstable in the Holocene when repetitive collapses of a portion of the edifice (Young Shiveluch) generated debris avalanches. The transition in stability was connected with a change in composition of the erupting magma (increased SiO2 from ca. 55-56% to 60-62%) that resulted in an abrupt increase of viscosity and the production of lava domes. Each failure was triggered by a disturbance of the vol- canic edifice related to the ascent of a new batch of vis- cous magma. The failures occurred before magma in- truded into the upper part of the edifice, suggesting that the trigger mechanism was indirectly associated with magma and involved shaking by a moderate to large volcanic earthquake and/or enhancement of edif- ice pore pressure due to pressurised juvenile gas. The failures typically included: (a) a retrogressive landslide involving backward rotation of slide blocks; (b) frag- mentation of the leading blocks and their transforma- tion into a debris avalanche, while the trailing slide blocks decelerate and soon come to rest; and (c) long- distance runout of the avalanche as a transient wave of debris with yield strength that glides on a thin weak layer of mixed facies developed at the avalanche base. All the failures of Young Shiveluch were immediately followed by explosive eruptions that developed along a similar pattern. The slope failure was the first event, followed by a plinian eruption accompanied by partial fountain collapse and the emplacement of pumice flows. In several cases the slope failure depressurised the hydrothermal system to cause phreatic explosions that preceded the magmatic eruption. The collapse-in- duced plinian eruptions were moderate-sized and ordi- nary events in the history of the volcano. No evidence for directed blasts was found associated with any of the slope failures.

The dynamics of the shallow magma reservoir at Krafla Volcano in NE Iceland have been analyzed with three types of elastic models based on over 70 surveys of tilt and displacement made from 1975 to 1985, a period of continuous volcano-tectonic activity. Modeling results are integrated with geophysical and geological information to estimate the position, geometry, and volume change of magma reservoir domains subjected to periodic inflation and deflation. Dominating influences on magma reservoir dynamics are examined in the context of activity in Krafla's associated rift system and the deformation of its caldera from 1975–1985. Rather than the fluid-filled cavity concept of Mogi (1958) and most recent workers, our models are idealized as strained regions with spherical, double-spherical, or general ellipsoidal symmetry. The models are mathematically generalized from that of Mogi (1958) and are derived by inversion of displacements. Model results from different displacement components are remarkably consistent, although models based on vertical displacements typically have errors-of-fit much closer to expected measurement errors than those based on tilt or horizontal displacements. About one half of the double-sphere and ellipsoid models have significantly better fits than single-sphere models. Double-sphere model results are consistent with a 2 to 3 km center-to-center separation of magma storage zones from at least 2 km to 4 km depth by portions of the fissure system, as implied by S-wave attenuation patterns for 1976–1977. However, all models suggest pressurization zones of more limited extent than possible domains of storage inferred from S-wave attenuation. Ellipsoid models typically implied unrealistically shallow depths of magma storage. Caldera inflation rates decreased after January 1978 when the caldera periodically reinflated to its level prior to the initial December 1975 deflation event. From 1975–1980 the volume and duration of inflation between deflation events was strongly correlated with the volume of the previous deflation. After 1980 there was a significant increase in the duration of inflation periods and a decrease in rates of caldera inflation and fissure system widening. Consistent with these results, the magma reservoir is conceptualized as a hot rock mass containing numerous magma chambers and pressure-sensitive conduits connecting the chambers and deep magma sources. Magma is injected into the fissure system at critical pressures determined by the confining stress and rock mass strength. The duration and volume of inflation required to reach a critical pressure threshold is largely dependent on the volume of magma released in the previous deflation. Reduction of the extension rate across the Krafla fissure system after 1980 suggests that extensional forces were also reduced. A resultant rise of confining pressure on the magma reservoir and a reduced capacity of the fissure system to accommodate dike injection in combination would have increased critical stress levels for reservoir deflation and reduced the pressure gradient driving magma supply from deep sources.

THE 'materials science' method for eruption prediction1–3 arises from the application of a general law governing the failure of materials: Ω⊙−α Ω¨ − A = 0, where A and α are empirical constants, and Ω is an observable quantity such as ground deformation, seismicity or gas emission. This law leads to the idea of the 'inverse-rate' plot, in which the time of failure can be estimated by extrapolation of the curve of Ω−1 versus time to a pre-deter-mined intercept. Here we suggest that this method can be combined with real-time seismic amplitude monitoring to provide a tool for near-real-time eruption prediction, and we demonstrate how it might have been used to predict two dome-growth episodes at Mount St Helens volcano in 1985 and 1986, and two explosive eruptions at Redoubt volcano in 1989–90.

We compare eruptive dynamics, effects and deposits of the Bezymianny 1956 (BZ), Mount St Helens 1980 (MSH), and Soufriere Hills volcano, Montserrat 1997 (SHV) eruptions, the key events of which included powerful directed blasts. Each blast subsequently generated a high-energy stratified pyroclastic density current (PDC) with a high speed at onset. The blasts were triggered by rapid unloading of an extruding or intruding shallow magma body (lava dome and/or cryptodome) of andesitic or dacitic composition. The unloading was caused by sector failures of the volcanic edifices, with respective volumes for BZ, MSH, and SHV c. 0.5, 2.5, and 0.05 km3. The blasts devastated approximately elliptical areas, axial directions of which coincided with the directions of sector failures. We separate the transient directed blast phenomenon into three main parts, the burst phase, the collapse phase, and the PDC phase. In the burst phase the pressurized mixture is driven by initial kinetic energy and expands rapidly into the atmosphere, with much of the expansion having an initially lateral component. The erupted material fails to mix with sufficient air to form a buoyant column, but in the collapse phase, falls beyond the source as an inclined fountain, and thereafter generates a PDC moving parallel to the ground surface. It is possible for the burst phase to comprise an overpressured jet, which requires injection of momentum from an orifice; however some exploding sources may have different geometry and a jet is not necessarily formed. A major unresolved question is whether the preponderance of strong damage observed in the volcanic blasts should be attributed to shock waves within an overpressured jet, or alternatively to dynamic pressures and shocks within the energetic collapse and PDC phases. Internal shock structures related to unsteady flow and compressibility effects can occur in each phase. We withhold judgment about published shock models as a primary explanation for the damage sustained at MSH until modern 3D numerical modeling is accomplished, but argue that much of the damage observed in directed blasts can be reasonably interpreted to have been caused by high dynamic pressures and clast impact loading by an inclined collapsing fountain and stratified PDC. This view is reinforced by recent modeling cited for SHV. In distal and peripheral regions, solids concentration, maximum particle size, current speed, and dynamic pressure are diminished, resulting in lesser damage and enhanced influence by local topography on the PDC. Despite the different scales of the blasts (devastated areas were respectively 500, 600, and >10 km2 for BZ, MSH, and SHV), and some complexity involving retrogressive slide blocks and clusters of explosions, their pyroclastic deposits demonstrate strong similarity. Juvenile material composes >50% of the deposits, implying for the blasts a dominantly magmatic mechanism although hydrothermal explosions also occurred. The character of the magma fragmented by explosions (highly viscous, phenocryst-rich, variable microlite content) determined the bimodal distributions of juvenile clast density and vesicularity. Thickness of the deposits fluctuates in proximal areas but in general decreases with distance from the crater, and laterally from the axial region. The proximal stratigraphy of the blast deposits comprises four layers named A, B, C, D from bottom to top. Layer A is represented by very poorly sorted debris with admixtures of vegetation and soil, with a strongly erosive ground contact; its appearance varies at different sites due to different ground conditions at the time of the blasts. The layer reflects intense turbulent boundary shear between the basal part of the energetic head of the PDC and the substrate. Layer B exhibits relatively well-sorted fines-depleted debris with some charred plant fragments; its deposition occurred by rapid suspension sedimentation in rapidly waning, high-concentration conditions. Layer C is mainly a poorly sorted massive layer enriched by fines with its uppermost part laminated, created by rapid sedimentation under moderate-concentration, weakly tractive conditions, with the uppermost laminated part reflecting a dilute depositional regime with grain-by-grain traction deposition. By analogy to laboratory experiments, mixing at the flow head of the PDC created a turbulent dilute wake above the body of a gravity current, with layer B deposited by the flow body and layer C by the wake. The uppermost layer D of fines and accretionary lapilli is an ash fallout deposit of the finest particles from the high-rising buoyant thermal plume derived from the sediment-depleted pyroclastic density current. The strong similarity among these eruptions and their deposits suggests that these cases represent similar source, transport and depositional phenomena.

Hydrofracturing stress measurements have been carried out to about 0.4 km in two boreholes in Quaternary volcanic rocks in Reykjavik, Iceland, on the flank of the Reykjanes-Langjokull continuation of the Mid-Atlantic Ridge. The measurements indicate a dominant orientation of σH max approximately perpendicular to the axial rift zone, in contrast to earthquake focal mechanism solutions from within the axial rift zone of the Reykjanes Peninsula. In one hole (H32) a depth-dependent change in stress orientation is indicated, with σ1 horizontal above a depth of about 0.25 km, and vertical below it; however the orientation of σH max remains unchanged. The data thus suggest reconciliation of an apparent conflict between the dominantly compressive indications of shallow overcoring stress measurements and dominant extension as required by focal mechanism solutions. The measured stresses are supported by the more reliable of overcoring measurements from southeast Iceland, and by recent focal mechanism solutions for the intraplate Borgarfjordur area. A fundamental change in crustal stresses appears therefore to occur as a function of distance from the axis of the axial rift zone. The data seem reasonably explicable in terms of a combination of thermoelastic mechanisms associated with accretion and cooling of spreading lithosphere plates. Stresses directly associated with the driving mechanisms of plate tectonics apparently do not dominate the observed stress pattern.

The relationship Ω·–α Ω¨ – A = 0 describes the behaviour of materials in terminal stages of failure, where Ω is an observable quantity such as strain, and A and α are empirical constants. Drawing on analogies between failure mechanics and eruption processes at volcanoes, Ω is interpreted in terms of conventional geodetic, seismic or geochemical observations. Manipulation of Ω provides a consistent analytical basis for eruption prediction.

The elastic response (i.e., displacement fields, strain and stress distributions) has been determined by structural matrix analysis for a homogeneous rock layer subjected to two-dimensional distributions of vertical displacement applied along a basal boundary. The results obtained compare favorably with biharmonic function solutions obtained bySanford [42]2) and the authors. The analysis was then extended: the effects of different magnitudes of superposed gravitationally-induced stresses, release of a constrained side boundary, and introduction of pronounced heterogeneity were each quantitatively evaluated. Each of these changed conditions effected important alterations in response characteristics, e.g., in configuration of stress trajectories, predicted locations and configurations of initial fracture surfaces, shear stress distributions, and displacement fields.

Knowledge of spatial variations (concerning both magnitude and orientation) and temporal variations of the stress tensor at various points in the earth's crust is crucial to our understanding of the fundamental nature of tectogenesis, The means by which this data can be acquired forms the principal subject of a newly developed field of endeavor concerned with thein- situ measurement of stress. This field of research is expanding, with rapid advances in development of techniques, numbers of personnel, and acquisition of field data. Although primarily motivated by engineering and mining operations (because of the immediate applicability of this data to subsurface ground control), the geologic implications — thus far largely ignored — appear enormous. Determinations of stress have been made in every continent. The purpose of this paper is to emphasize the geological (and geophysical) relevance of current stress measurement work, which imposes conditions with which adequate theories of tectogenesis must comply.