European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 Istituto Nazionale di Geofisica e Vulcanologia Istituto Nazionale di Geofisica e Vulcanologia BET: A Probabilistic Tool for Long- BET: A Probabilistic Tool for Long- and Short-term Volcanic Hazard and Short-term Volcanic Hazard Assessment Assessment Warner MARZOCCHI, Jacopo SELVA, Laura SANDRI Istituto Nazionale di Geofisica e Vulcanologia - Bologna, Italy INGV-DPC V4 Project: Conception, verification, and application of innovative techniques to study active volcanoes gv.it/V4
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Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.
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European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET: A Probabilistic Tool for Long- and BET: A Probabilistic Tool for Long- and Short-term Volcanic Hazard AssessmentShort-term Volcanic Hazard Assessment
Warner MARZOCCHI, Jacopo SELVA, Laura SANDRI
Istituto Nazionale di Geofisica e Vulcanologia - Bologna, Italy
Funded by INGV-DPC V4 Project: Conception, verification, and application of innovative techniques to study active volcanoes
www.bo.ingv.it/V4
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
WHAT IS BET?WHAT IS BET?
BET (Bayesian Event Tree)BET (Bayesian Event Tree) is a new statistical code to estimate and visualize short- to long-term eruption forecasting (BET_EF) and volcanic hazard (BET_VH) and relative uncertainties (epistemic and aleatory)
BET InputBET Input: Volcanological data, models, and/or expert opinion. These data are provided by the end-user.
BET transforms these information into probabilities BET transforms these information into probabilities
BET OutputBET Output: Time and space evolution of the probability function of each specific event in which we are interested in.
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
The method is based on three basic steps
1. Design of a generic Bayesian Event Tree
2. Estimate the conditional probability at each node
3. Combine the probabilities of each node to obtain probability distribution of any relevant event
BibliographyBibliography
Newhall and Hoblitt, Bull. Volc. 2002 (for step 1) Marzocchi et al., JGR 2004 (for steps 2 and 3) Marzocchi et al., 2006; in press IAVCEI volume on statistics in Volcanology (for steps 2 and 3) Marzocchi et al., 2006 in preparation (full description of BET)
HOW BET WORKS?HOW BET WORKS?
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
The absolute probability of the SELECTED PATH is the product of
conditional probability i at ALL SELECTED BRANCHES:
1] • [2] • [3] • [4] • [5] • …
BET STRUCTURE & ABSOLUTE PROBABILITYBET STRUCTURE & ABSOLUTE PROBABILITY
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
k(M)MONITORING PART
Monitoring Data & Models
k(NM)NON-MONITORING PART
Non-monitoring Data, Geological & Physical Models
CONDITIONAL PROBABILITY AT THE NODE:
k = k(M) + (1- k
(NM)
MONITORING DATA
State of unrest at t0through FUZZY LOGIC
CONDITIONAL PROBABILITY [CONDITIONAL PROBABILITY [KK] ] (NODE k)(NODE k)
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
At each node we account for:• Models + data• Epistemic and aleatoric uncertainities
MODELS Prior
DATALikelihood
POSTERIOR PDF
k = k(.) [H(.)|k
(.)H(.)
Bayes theorem
… … EACH PARTEACH PART
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
Through FUZZY SET theory…
• With convergence of expert opinion and past data analysis, the user defines: 1. the SET of parameters at each node2. INTERVAL OF VALUES as threshold for each param
• Smooth variation of probabilities are found for small changes in monitoring parameters (smooth thresholds)
MONITORING MEASURESMONITORING MEASURES
degree of anomaly zi
measure
State of unrest
A priori model [k(1)]
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_EF PACKAGEBET_EF PACKAGE
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
EVENT TREE for BET_EFEVENT TREE for BET_EF
Number & geometry chosen by the user Number of size groups
defined by the user
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_EF PACKAGEBET_EF PACKAGE
Volcano selection
Event selection (Unrest + Magmatic Intrusion + Eruption+Vent all loc + SIZE=4+)
Hazard procedure
OUTPUT
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
PROBABILITY VISUALIZATIONPROBABILITY VISUALIZATION
ABSOLUTE PROBABILITY CONDITIONAL PROBABILITY AT THE NODE
Probability that all the events in the selected path occur contemporaneously
Probability that the events at the selected node occur, given previous nodes
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
MONITORING MEASURESMONITORING MEASURES
Measured values are directly input in BET_EF at nodes 1, 2, 3, & 5
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
MONITORING AT Node 4: VENT LOCATIONSMONITORING AT Node 4: VENT LOCATIONS
Localization of monitored parameters When possible, the user may “localize” the anomalous measures of monitoring parameters, to identify the most “likely” position for next vent location
Map of vent locations
percent within the location
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
Major requirements to load a volcano in BET_EF are:
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET is a tool to calculate and to visualize probabilities related to eruption forecasting/hazard assessment
BET “dinamically” manages long-term (land use planning of the territory) and short-term (during emergency to help managing of short-term actions, e.g., evacuation) probabilities for each kind of possible event
BET considers all of the available information (models, state of the volcano, geologic/volcanologic/historic data, monitoring observations, expert elicitation)
BET takes properly into account the epistemic and aleatory uncertainties. This allows to highlight what we know and what we do not know about the system, indicating
future possible works to improve the scheme
BET introduces fuzzy logic to manage monitoring measurements smooth transitions in probability and overcome single threshold definition
FINAL REMARKS on BETFINAL REMARKS on BET
European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_EF will be distributed for free this yearBET_EF will be distributed for free this year after a pilot test after a pilot test carried out by volcanologists with experience in managing carried out by volcanologists with experience in managing