Francesco Mulargia

Identifying different regimes in eruptive activity: An application to Etna volcano

The objective identification of different regimes in the eruptive time-history of a volcano is crucial to the understanding of its physics. While a problem well-known in statistical literature under the name of change-point or scan-point problem, no method of general applicability exists for the identification of different regimes in a time-series. In particular, the available techniques seem unsuitable to the volcanological case. We developed an original procedure based on two-sample Kolmogorov-Smirnov statistics which offers satisfactory accuracy in a broad range of conditions with a minimum of assumptions and is expressly tailored to the study of geophysical phenomena. Our procedure requires neither the a priori knowledge of the number of regimes nor of the statistical distributions governing the whole process, which can be of different type. The parent distribution of each regime is inferred through a goodness-of-fit test, and this in turn allows the confidence intervals for each of the change-points identified to be estimated by numerical simulation. This procedure is applied to the eruptive history of Mount Etna volcano. Available data allow the analysis of flank eruptions in the period 1600–1980, while the total output (summit and flank activity) can be studied only in the period 1971–1981. Information on eruptive history can be therefore obtained at two different timescales. Since no univocally accepted catalog exists except for the last few decades, we use two different sets of data, which practically exhaust all the available information. The results are interpreted by a stability analysis, and only stable results are retained. Our analysis yields that: • - The inter-event times of flank eruptions in the period 1600–1980 follow two regimes before and after year 1865, while the eruptive activity in the period 1971–1981 follows four different regimes. In each regime eruptions occur according to a Poisson process and Etna behaves as a random nonstationary volcano both at long (few centuries) and short (few years) time-scales. The eruptions appear therefore to be triggered by several combining effects with a balance showing fluctuations at both time-scales. • - The volume output of flank eruptions in the period 1600–1980 follows three different regimes, with change-points at 1670 and 1750. The volume output in the period 1971–1981 follows a single regime. Least squares regression and the related confidence bounds, calculated for each regime, suggest that, even accounting for summit activity, the output rate in the period 1971–1981 is not anomalously high. Provided that no further change in regime takes place, the confidence bounds can be used to cast estimates on the expected future activity. • - The series of the mean effusion rates (erupted volume/duration of the eruption) applied to flank eruptions in the period 1600–1980 follows two different regimes, with a change-point around year 1950. There is a net decrease in the mean effusion rate from over 24 m3 s−1 to about 7 m3 s−1, which suggests a change in the eruptive style to lower mean effusion rates. The total output (flank + summit) data of the period 1971–1981 confirms this issue, with averaged mean effusion rates lower than 12 m3 s−1. • - The points of change in regime in the time-series of the inter-eruption times and volume outputs do not coincide, thus implying that eruptions are governed by other factors than the input of magma. At the same time, the analysis of seismic activity does not suggest the stress field as a most important factor. The eruptive activity does not appear to be controlled by a single factor, but by the balance of several contributing factors, further corroborating the conclusion that Etna behaves as a random nonstationary volcano. • - The relatively small fluctuations in each of the periods identified in the flank output series suggest a constant input within each output regime, although the unavailability of both a reliable model and accurate estimates on historical summit eruptions recommends prudence in accepting this conclusion. • - There appears to be no significant correlation between the volume of a “large” flank eruption and the subsequent inter-event time. This, with the above proviso, suggests the absence of any high-level magma reservoir.

A statistical analysis of flank eruptions on Etna volcano

Abstract A singularly complete record exists for the eruptive activity of Etna volcano. The time series of occurrence of flank eruptions in the period 1600–1980, in which the record is presumably complete, is found to follow a stationary Poisson process. A revision of the available data shows that eruption durations are rather well correlated with the estimates of the volume of lava flows. This implies that the magnitude of an eruption can be defined directly by its duration. Extreme value statistics are then applied to the time series, using duration as a dependent variable. The probability of occurrence of a very long (300 days) eruption is greater than 50% only in time intervals of the order of 50 years. The correlation found between duration and total output also allows estimation of the probability of occurrence of a major event which exceeds a given duration and total flow of lava. The composite probabilities do not differ considerably from the pure ones. Paralleling a well established application to seismic events, extreme value theory can be profitably used in volcanic risk estimates, provided that appropriate account is also taken of all other variables.

The tectonic setting of Mount Vesuvius and the correlation between its eruptions and the earthquakes of the Southern Apennines

Abstract Mount Vesuvius is emplaced on a regional NE-SW-trending fault that accommodates the stretching of the lithosphere caused by a backward retreat of the Calabrian arc. The dynamics of the Calabrian arc controls the temporal occurrence of earthquakes in the Southern Apennines and in Sicily. By means of a detailed statistical approach, we identified a significant correlation between seismic events occurring in different subsets of this geodynamic domain: seismicity changes in the Southern Apennines follow those in the Calabrian arc after 18–21 years, while seismicity changes in Sicily follow those in the Calabrian arc after 8–10 years. The seismicity changes in these three areas appear also to have affected the eruptive activity of Vesuvius in the period 1631–1944. The major effusive-explosive eruptions of this period followed the seismicity changes in the Southern Apennines after 6–13 years and those in the Calabrian arc after 36–39 years. From a tectonic point of view, this indicates a direct link between the eruptive activity of Vesuvius and the dynamics of the Calabrian arc. The backward retreat of the arc produces strain pulses propagating to adjacent areas. From a volcanological point of view, we speculate that the arrival of an extension strain pulse in the area of Vesuvius may trigger the fast movement of magma-filled cracks that stay in unstable equilibrium in the roots of the volcano.

Contour mapping of Italian seismicity

Abstract The scope of the present work is to identify the Italian seismic regions, toward a better definition of the active tectonic structures. Spatial filtering is used, together with the recently released PFG-ENEL seismic catalog which covers the period 1000–1980. Any such approach based on catalog data has to acknowledge that catalog reliability and resolving power are functions of time and position. These problems, which can potentially lead to an incorrect regionalization, can be attributed to catalog incompleteness. The effects of the latter are estimated and correlated through a new approach, which determines the completeness interval from the plot of the cumulative number of events versus time, and measures the degree of incompleteness by assuming it to be a function with a continuous first derivative. In this way, all the information present in the catalog can be used in contour mapping by an appropriate weighting of incomplete parts in spatial filtering. On the other hand, the choice of the weight factors involves some arbitrary judgement and therefore introduces a bias. In order to reach an objective result, different weighting schemes covering all feasible choices are tried, and the final regionalization is concluded to be valid only if it is stable. A fair stability is obtained and it is henceforth possible to conclude that the seismic regions identified represent an unbiased picture of the real situation. Interestingly, different areas exhibit a different seismic character, some being capable of frequent activity but never exceeding moderate magnitude values, and others being characterized by a scarcity of moderate events combined with the capability of occasional large earthquakes.

The double torsion loading configuration for fracture propagation: an improved methodology for the load-relaxation at constant displacement

Abstract For most materials the dynamics of subcritical crack propagation during stress-corrosion can be described uniquely by a relationship between the mode-I stress intensity factor K I and the crack velocity v that generally has the form of a power law. In last 30 years, the double-torsion load-relaxation test has shown to be the most reliable method for measuring such a relation. The standard analysis, developed by Evans (J Mater Sci 1972;7:1137–46), is based on an analytical approxatimation that fails to accurately describe the specimen compliance outside a narrow region in the center of the specimen. This paper deals with the implications on data inversion of the exhaustive three-dimensional finite-element analysis recently performed by Ciccotti (J Am Ceram Soc 2000, in press) on double-torsion specimens. The results are presented in terms of corrective coefficients to the classical analytical approximation. A full methodology is developed for the numerical implementation of such corrections. By numerically simulating some relaxation tests, the classical analysis based on the analytical approximation is shown to generally underestimate the stress-corrosion index up to 30% even if the most conservative operational constraints are satisfied. On the contrary, the operational constraints can be comfortably relaxed as a consequence of the capability of correcting the finite size effects in relation to the different experimental parameters.

Pattern recognition applied to volcanic activity : identification of the precursory patterns to Etna recent flank eruptions and periods of rest

Abstract Computational pattern recognition is an invaluable tool in understanding the phenomenology of complex processes and represents the first step towards their effective physical modeling. So far it has never been used in volcanology. We discuss in detail pattern recognition algorithms of the “logic” type and present an application to the recent eruptive activity of Mount Etna volcano. The specific aim is a characterization of the intermediate-term precursory patterns to its flank eruptions. A comparatively successful recognition is obtained, providing the combinations of parameters which have been precursory to eruptions and periods of rest in the last fifteen years. The recognized patterns yield two main results: (a) the seismicity in the Gulf of Patti is identified as the most important precursor, and a further correlation study confirms this issue as highly significant, implying that regional tectonic stress, and in particular the structures around the Tindari-Giardini lineament, play a fundamental role in triggering Etna flank activity; (b) an operative prediction-oriented application of the recognized precursory patterns is tentatively possible.

Statistical identification of physical patterns which accompany eruptive activity on Mount Etna, Sicily

Abstract A new statistical nonparametric pattern recognition algorithm is used to identify the phenomenology which accompanies summit and flank eruptions on Mount Etna, Sicily. This algorithm allows us to solve some of the operational problems typical of logic-type pattern recognition algorithms. Volcanic activity is parametrized through 12 variables concerning seismicity, past eruptive history, and precipitation, which practically exhaust the presently available data. In the 40 days which precede and follow the onset of each eruption, we identified no pattern whatsoever for summit eruptions, and a single significant pattern for flank activity. This indicates different eruptive mechanisms for flank and summit events. The latter appear to be independent of all the phenomena considered, and should therefore be ascribed either to magma feeding processes, a variable which we were not able to consider in our analysis due to the lack of data, or to random behaviour, without any repetitive scheme. Flank activity appears to be linked to the state of regional tectonic stress, but is independent of past eruptive history and groundwater level. This means that eruptions of the size Etna recently experienced, do not perturb the system, which must have a much larger capacity, at least of the order of 10 9 m 3 .

The seismic noise wavefield is not diffuse.

Passive seismology is burgeoning under the apparent theoretical support of diffuse acoustics. However, basic physical arguments suggest that this theory may not be applicable to seismic noise. A procedure is developed to establish the applicability of the diffuse field paradigm to a wavefield, based on testing the latter for azimuthal isotropy and spatial homogeneity. This procedure is then applied to the seismic noise recorded at 65 sites covering a wide variety of environmental and subsoil conditions. Considering the instantaneous oscillation vector measured at single triaxial stations, the hypothesis of azimuthal isotropy is rejected in all cases with high confidence, which makes the spatial homogeneity test unnecessary and leads directly to conclude that the seismic noise wavefield is not diffuse. However, such a conclusion has no practical effect on passive imaging, which is also possible in non-diffuse wavefields.

Anthropogenic Triggering of Large Earthquakes

The physical mechanism of the anthropogenic triggering of large earthquakes on active faults is studied on the basis of experimental phenomenology, i.e., that earthquakes occur on active tectonic faults, that crustal stress values are those measured in situ and, on active faults, comply to the values of the stress drop measured for real earthquakes, that the static friction coefficients are those inferred on faults, and that the effective triggering stresses are those inferred for real earthquakes. Deriving the conditions for earthquake nucleation as a time-dependent solution of the Tresca-Von Mises criterion applied in the framework of poroelasticity yields that active faults can be triggered by fluid overpressures < 0.1 MPa. Comparing this with the deviatoric stresses at the depth of crustal hypocenters, which are of the order of 1–10 MPa, we find that injecting in the subsoil fluids at the pressures typical of oil and gas production and storage may trigger destructive earthquakes on active faults at a few tens of kilometers. Fluid pressure propagates as slow stress waves along geometric paths operating in a drained condition and can advance the natural occurrence of earthquakes by a substantial amount of time. Furthermore, it is illusory to control earthquake triggering by close monitoring of minor “foreshocks”, since the induction may occur with a delay up to several years.

Precursor candidacy and validation: The VAN Case so far

A reliable identification of seismic precursors requires a two-step statistical approach: a retrospective “learning” step to establish the candidate precursors on the basis of ad hoc chosen laws of the game, and a “validation” step which evaluates candidate precursors on an independent data set according to the previously established laws of the game. No published work has so far provided a sound support to the candidacy of the VAN signals as earthquake precursors. The problem is complicated by a chronic fuzziness in the text of VANs predictions, which often allows different interpretations, and by the absence of any clear statement by VAN of the laws of the game.