Quelle prédictibilité pour les éruptions volcaniques ?

Quelle prédictibilité pour les éruptions volcaniques ?

Foreshocks and aftershocks of eruptions 

We investigate the properties of the seismic damage around eruption time. First we compare the damage around eruption with the one corresponding to classical tectonic seismicity in order to possibly extract some specificities of the damage processes trigge red by the volcano dynamics. For that purpose we use the same method on time-space seismicity around eruption and around Mw ≥ 7 tectonic earthquakes. The pattern of the latter is therefore considered as the null hypothesis, and any result should therefore be tested against it. Second we test the dependency of the seismic damage to the eruption size. The stacked seismicity rate (for all eruptions of the dataset) attests for power law acceleration of the seismicity rate toward eruption time (Figure 3.8). The foreshocks and aftershocks sequences as a function of log(t − te), where te is the eruption time, emphasizes the short time behaviour of seismicity, i.e. close to eruption onset (figure 3.8c). The background level of seismicity is estimated as the average daily seismicity rate on [-400 ; -100] days window prior all eruptions of the dataset. The pre-eruptive pattern emerges from this background noise around ten days prior eruptions. Stacked aftershock seismicity rate remains above noise level up to 200 days after eruption onset. A power-law describes the seismicity rates after and before eruption time (figure 3.8c). This power law for damage rate, i.e. the Omori law, is a generic relaxation law observed towards and backwards failure time, from lab scale creep experiments up to tectonic activity (e.g. Andrade [1914] ; Omori [1894] ; Utsu [2002] ; Nabarro and De Villiers [1995]). To compare the brittle crust response to eruption and to earthquake respectively, we applied the same analyses on seismicity rate contemporary to both worldwide Mw ≥ 7 earthquakes (using USGS catalogue), and volcano eruptions (figure 3.9 and 3.10). We aim at extracting the influence of the size and loading rate of the trigger events on fore- and after-shocks patterns. First, we resolve the higher productivity, as seen from earthquake rate through time, for foreshocks and aftershocks from earthquakes than to the one from eruptions (see figure 3.9 and figure 3.10). The Mw ≥ 7 earthquake are contemporary of increase of seismicity rate which are at least one order of magnitude larger than the one contemporary to eruptions. In average, the VEI>3 eruptions have an aftershock rate smaller then M=5.5 time relative to eruption (days) (day−1) b. c. a. Figure 3.8 – Average seismicity rate before (blue) and after (red) eruptions : a) zoom within -20+20 days from eruption highlights the pre-eruption pattern. Note that at +20days the aftershock rate is still above the noise level, which is not the case for the eruption foreshock rate, b) log normal plots of pre and post eruption daily seismicity rate with Gaussian function smoothing. Departure from linearity rejects the exponential law to reproduce the data, c) log-log plot of pre and post eruption daily seismicity rate with Gaussian function smoothing. A power law pattern (straight line) is accepted to describe the data in the 10 days and 200 days range for foreshocks and aftershocks respectively. The seismicity background level (horizontal lines on all plots) is computed from a [-400 ; -100] days window before eruptions or Mw ≥ 7 earthquakes. The p and p’-values are maximum likelihood estimates of the Omori’s law exponent (e.g. Ogata and Katsura [1993]). They are estimated on a time window which starts at t0 and ends when the signal merges with the background noise level. Time (days) before mainshock (day−1) Figure 3.9 – Patterns of foreshocks given the type and size of main shock. Light to dark grey : mainshocks are earthquakes from worldwide catalogue for magnitude ranges in [5.5 ;7.5]. Light to dark blue : mainshocks are eruptions from worldwide catalogue for small VEI<3, all and large VEI>3. hNi is the averaged number of seismic events per day (normalized by the number of eruption in each class), prior mainshock time. We used a Gaussian function smoothing [Helmstetter et al., 2003].The seismicity background levels (horizontal dotted lines) are computed from a [-400 ; -100] days window before eruptions (blue) and before main earthquakes (grey). The p-values are the Omori’s law exponents estimated with the maximum likelihood method (e.g. Ogata and Katsura [1993]) on the seismicity starting from eruption time to the day when it merges with noise level. – Patterns of aftershocks given the type and size of main shock. Light to dark grey : mainshocks are earthquakes from worldwide catalogue for magnitude ranges in [5.5 ;7.5]. Light to dark blue : mainshocks are eruptions from worldwide catalogue for small VEI<3, all and large VEI>3. hNi is the averaged number of seismic events per day (normalized by the number of eruption in each class), prior mainshock time. We used a Gaussian function smoothing [Helmstetter et al., 2003].The seismicity background level (horizontal dotted lines) are computed from a [-400 ; -100] days window before eruptions (red) and before main earthquakes (grey). The p-values are the Omori’s law exponents estimated with the maximum likelihood method (e.g. Ogata and Katsura [1993]) on the seismicity starting from eruption time to the day when it returns to noise level. 105 CHAPITRE 3 : PROCESSUS D’ENDOMMAGEMENT AUTOUR DES ERUPTIONS earthquakes. From figure 3.10, we learn that the decrease in seismicity rate after the shocks are slower (smaller power law exponent) for eruption aftershocks than for tectonic earthquake aftershocks, respectively. In terms of brittle damage processes it accounts for a slower relaxation process after eruptions than after earthquakes. Considering the foreshocks sequences, the most striking result is the clear dependance of the earthquake forerunners rate with eruption size (figure 3.9a). It contrasts with the constant foreshocks pattern which is resolved before all earthquake sizes (see table 3.2 for the p and p’ values). The larger the VEI value, the larger the p’-value, and the longer the acceleration duration. Omori law exponent before and after eruption To analyze the dependency of the Omori law with eruptions sizes, we quantify the p’ and p exponent values of the pre- post eruption seismicity for 2 independent classes of eruptions, i.e. 172 eruptions of V EI ≥ 3, and 978 events for V EI < 3. First, we isolate the points above background noise level. Second we test when a power law is accepted, and if yes, we estimate the value of the power law exponent. For that purpose we used two different methods giving results in the same order of magnitude : the maximum likelihood method proposed by Ogata and Katsura [1993], and a Least Mean Square method. Table 3.2 sums up the estimated Omori’s law exponents for each dataset. The small number of events above the noise level imposes rough estimates of the exponent values and the standard deviations are large. Errors bars from least mean square estimations are biasses, that minimized the true error. Before small eruptions (V EI < 3), a soft acceleration of the seismicity towards eruption is characterized by p ′ = 0.51 + / − 0.26 (figure 3.11). Before V EI ≥ 3 eruption, p’= 2.06 +/-0.62, characterizes a strong acceleration towards eruption (figure 3.11). Note that for earthquakes, we resolve no change in the p’-value as a function of the upcoming mainshock’s magnitude. The lack of change in p’-value is observed for tectonic earthquakes and predicted by point process of cascading earthquake model (e.g. Helmstetter and Sornette

Aftershock productivity and eruption size 

For classical tectonic seismicity, K, the aftershock productivity is resolved to scale with the size of the triggering earthquake [Helmstetter et al., 2005]. Helmstetter et al. [2003], using ETAS model, demonstrated that the average total number of aftershocks hRi (including the cascade of indirect aftershocks) is resolved to increase with the size of the triggering earthquake. Helmstetter and Sornette [2003a] demonstrate that the average total number of aftershocks hRi (including the cascade of indirect aftershocks) exponentially scales with the main shock magnitude, as hR(M)i = k0 1 − n .10α(M−M0) (3.4) where n is the branching ratio of the ETAS model. Given the smaller number of events we resolve after eruptions than after earthquakes (figure 3.10), it is more robust to test any possible scaling in aftershock production with the eruption size using the total number hNi of aftershocks on a given duration t, rather than to estimate the k0 and α parameters othe aftershock productivity from the power-law fit. As a proxy to the aftershock eruption rate, we used the number of earthquakes of magnitude M ≥ 4.8 within 200 days and 50 km from eruptions. For the V EI ≥ 3 eruptions the 200-days window corresponds to the time when the Omori decay curve reaches the background level (see fig 3.10). We may then have included a few background earthquakes in the aftershock counts. We assume it does not impact our results because the number of possible background events is small. i Table 3.3 – Parameters related to productivity in aftershocks for the different classes of eruptions. Nerup is the number of eruption in each class of VEI. Raf tershock and Rf oreshock are the total number of aftershocks over a 200 days-window after eruption and the total number of foreshocks over a 20 days window before eruption respectively, within 50 km around the volcano. hRaf tershocki and hRf oreshocki are the normalized number of aftershocks and foreshocks respectively for each eruption of each class : hRaf tershocki = Raf tershock Nerup and hRf oreshocki = Rforeshock Nerup . The number of aftershocks following V EI ≥ 2 eruptions exponentially scales with the eruption size. (figure 3.12). Similarly to regular earthquake aftershocks, our results allow us to rewrite equation (3.4) as an exponential productivity law for aftershock rate hRerupi for eruption’s aftershocks. The productivity of aftershocks triggered by a given VEI is described by hRerupi = K′ 0 .10βV EI (3.5) Using a least mean square optimization,we estimate β = 0.35 + / − 0.05 for the eruption productivity rate.