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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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Page 1: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 2: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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.

Page 3: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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?

Page 4: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 5: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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)

Page 6: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 7: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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)]

Page 8: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 9: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 10: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 11: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

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

Page 12: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 13: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 14: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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:

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).

Page 15: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 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

Page 16: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

Page 17: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

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

volcanic crises. volcanic crises.

http://www.bo.ingv.it/~warnerhttp://www.bo.ingv.it/~warner

Page 18: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 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

Page 19: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 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 - exp(-(k)) Average of k

(1)

Z(k) = i zi degree of anomaly at the node

Monitoring factor

Page 20: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 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…

Page 21: Istituto Nazionale di Geofisica e Vulcanologia European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 2006 BET: A Probabilistic.

European Geosciences Union, General Assembly 2006, Vienna, Austria, 02 – 07 April 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)