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The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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.
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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?
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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)
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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)]
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_EF PACKAGEBET_EF PACKAGE
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
PROBABILITY VISUALIZATIONPROBABILITY VISUALIZATION
ABSOLUTE PROBABILITY CONDITIONAL PROBABILITY AT THE NODE
Selection done: (1) unrest -> (2) magmatic intrusion -> (3) eruption -> (4) location all -> (5) SIZE=4+
Probability that all the events in the selected path occur contemporaneously
Probability that the events at the selected node occur, given previous nodes
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
Major requirements to load a volcano in BET_EF are:
1. Models and/or theoretical believes, and/or expert elicitation
2. Catalog of past volcanic events and related phenomena
3. Monitoring parameters and relative threshold intervals
4. Number and geometry of vent locations
APPLICATION TO VOLCANOESAPPLICATION TO VOLCANOES
ALL VOLCANOES can be loaded in BET_EF with the BET_UPGRADE PACKAGE
Until now, we have (preliminary) implemented BET_EF for Mt. Vesuvius, and we are doing the same for Campi Flegrei
(INGV-DPC V3_2 and V3_4 projects).
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_ UPGRADE (ES. NODE 1)BET_ UPGRADE (ES. NODE 1)
models data monitoring monitoring thresholds
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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
volcanic crises. volcanic crises.
http://www.bo.ingv.it/~warnerhttp://www.bo.ingv.it/~warner
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
STATE OF UNRESTSTATE OF UNREST
zi degree of anomaly the i-th parameter
The user: input measures at node 1
BET computes:
1 - i (1 - zi)
k = k(M) + (1- k
(NM) Conditional probability at the node
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
FROM MONITORING TO PROBABILITYFROM MONITORING TO PROBABILITY
k(M)|H] = k
(1)[H(1)|k(1)H
zi degree of anomaly the param
The user: input measures
BET computes:
<k(1)>1 - a exp(-b (k)) Average of k
(1)
Z(k) = i zi degree of anomaly at the node
Monitoring factor
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
MONITORING & FUZZY #1MONITORING & FUZZY #1ne = 0 [27-120] -> pU = 0.0025
ne = 30 -> pU = 0.033
ne = 30 & Md = 3.6 [3.5,4.1] -> pU = 0.19
Changes on 1 parameter induce changes in probability of unrest depending on the THRESHOLDS INTERVAL
When changes occur on 2 or more parameters at the same time, the probability of unrest increases…
The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
MONITORING & FUZZY #2MONITORING & FUZZY #2
ne = 100 -> pU = 0.78
ne = 150 -> pU = 1.00
ne = 75 [27-120] -> pU = 0.51When the measured value approach the higher threshold, the probability reach 1 (NODE 1: UNREST)
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