First application of the failure forecast method to the GPS horizontal displacement data collected in the Campi Flegrei caldera (Italy) in 2011-2020
Andrea Bevilacqua, Abani Patra, E. Bruce Pitman, Marcus Bursik, Prospero De Martino, Flora Giudicepietro, Giovanni Macedonio, Stefano Vitale, Franco Flandoli, Barry Voight, Augusto Neri
TTitolo in italiano: Utilizzo preliminare del failure forecast method sui dati GPS di spostamento orizzontale registrati nella caldera dei Campi Flegrei dal 2011 al 2020 First application of the failure forecast method to the GPS horizontal displacement data collected in the Campi Flegrei caldera (Italy) in 2011-2020
Andrea Bevilacqua , Abani Patra , E. Bruce Pitman , Marcus Bursik , Prospero De Martino , Flora Giudicepietro , Giovanni Macedonio , Stefano Vitale , Franco Flandoli , Barry Voight , Augusto Neri . (1) Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa, Italia; (2)
Tufts University, Medford, MA, USA; (3)
University at Buffalo, Buffalo, NY, USA; (4)
Istituto Nazionale di Geofisica e Vulcanologia, Napoli, Italia; (5)
Università di Napoli Federico II, Napoli, Italia; (6)
Scuola Normale Superiore, Pisa, Italia; (7)
Pennsylvania State University, State College, PA, USA.
Introduction
Using the failure forecast method [Voight, 1988] we describe a first assessment of failure time on present ‐ ‐ established method by incorporating a stochastic noise in the linearized equations and a mean ‐ reversion property to constrain it [Bevilacqua et al., 2019]. The stochastic formulation enables the processing of decade ‐ long time windows of data, including the effects of variable dynamics that characterize the unrest of Campi Flegrei caldera. We provide temporal forecasts with uncertainty quantification, giving critical insight into a range of failure times (potentially indicative of eruption dates, see below). The basis of the failure forecast method is a fundamental law for failing materials: ẇ - α ẅ = A, where ẇ is the rate of the precursor signal, and α , A are model parameters that we fit on the data. The solution when α >1 is a power law of exponent 1/(1 − α ) diverging at time T f , called failure time [Cornelius & Voight, 1995]. In our case study, T f is the time when the accelerating signals collected at Campi Flegrei would diverge if we extrapolate their trend into the future. The interpretation of T f as the onset of a volcanic eruption is speculative [Kilburn, 2018]. Results
Figure 1 displays the modulus of the GPS horizontal displacement data collected at 11 different stations active from 2011. Three additional stations are not included in the picture because the signal collected is not clearly accelerating; seven additional stations and four GPS buoys were placed after 2011 and will be the target of future analysis. All the stations show an accelerating trend - four stations had a total displacement of ca. 30 cm, five of ca. 20 cm, two of ca. 10 cm. Short episodes of faster displacement are evident in 2012 ‐ f using the GPS data of 1/2011 ‐ 3/ f , and the annual rate of T f , i.e. its probability density function g. The function g is reported as mean values and 95 th percentile values, due to the uncertainty affecting the parameters of the linearized regression and of the noise properties [Bevilacqua et al., 2019]. The 5 th percentile values of g are negligible. igure 1. Gright cornerin year 2000GPS horizontr (UTM 33T0 for GPS 1, tal displacemT coordinates2, 5, 9, 13, 1ment modulus). The displa17, 18, in yeaus collected iacement is car 2008 for Gin 1/2011-3/2computed wiGPS 20, and 2020 at 11 sth respect toin year 2009stations mappo the day of 9 for GPS 15ped in the lodeployment,5, 19, 21. ower , i.e. igure 2.
Prate data. Tpercentile vstochastic soProbability foThe green linvalues. A bluolution pathsorecasts of Tne on the righue line bounds. The GPS sT f using the Ght is mean vds the 90% cstations are mGPS data ofvalues of theconfidence imapped in thf 1/2011- 3/2e annual probinterval of the lower right2020. Red pobability of The forecast. Gt corner (UToints on the T f , dashed linGrey dotted TM 33T coordleft are invenes mark its lines displaydinates). erse-95 th y 50 iscussion and conclusion The probability density function g, displayed in Figure 2, is distributed over many decades. The function has peaks of about 12% mean probability per year, and 95 th percentile values that can reach 25-30% probability per year. Table 1 shows the probability estimate P that the failure time is realized in 5, 10, or 25 years from 2020. We report the data from the largest to the smallest, showing three groups of estimates. In the first group P is 31-36% in 5 years, 60-64% in 10 years, 92-94% in 25 years. In the second group P is 6.0-12% in 5 years, 28-40% in 10 years, 74-82% in 25 years. In the third group P is 0.0-0.4% in 5 years, 0.2-8.6% in 10 years, 22-63% in 25 years. The three groups correspond to total displacements of ca. 30 cm, 20 cm and 10 cm, respectively. Table 1. Campi Flegrei GPS data, horiz. displ. failure time probabilities
These results provide the starting point for the improvement of short-term hazard assessments that can usemonitoring data to adapt the forecast and its uncertainty following a spatio-temporal approach, i.e. short-term vent opening maps [Bevilacqua et al., 2020; Sandri et al, 2020].It is evident that future variations of monitoring data could either slow down the increase so far observed, or suddenlyfurther increase it leading to shorter failure times than those here reported. Careful spatio-temporal interpolation canprovide a full-field view and outlier amelioration. Although we focus on the ground displacement as an example, a more robust forecasting effort should use multi-sensor data. Several types of unrest signals can be modeled with the failure forecast method, including seismic data and geochemical data [Chiodini et al., 2017; Patra et al., 2019].GPS station
P{T f < 2025} P{T f < 2030}
10 years
P{T f < 2045}
25 yearsACAE-1 36% 64% 94%
STRZ-20 35% 62% 94%
SOLO-19 32% 60% 92%
ARFE-2 31% 59% 92%
NISI-15 12% 40% 81%
VICA-21 11% 40% 82%
BAIA-5 11% 39% 81%RITE-18 7.9% 37% 82%IPPO-9 6.0% 28% 74%MORU-13 0.37% 8.6% 63%QUAR-17 0.00% 0.18% 22%
Acknowledgements
In addition to the project “Sale Operative Integrate e Reti di monitoraggio del futuro: l’INGV 2.0”, this work is supported by the Dipartimento della Protezione Civile (Italy), as part of the INGV-DPC contract 2019-2021, and by the National Science Foundation award 1821311. The manuscript does not necessarily represent official views and policies of the Dipartimento della Protezione Civile.
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