BET 1.0 - Bayesian Event Tree - Istituto Nazionale di Geofisica e
Contents
1. The models and past data input panel for nodes 4 and 5 are similar to the models and past data input frames at node 1 2 amp 3 pImEMENUST P X v age Past data v Mo CO Yes Equivalent number of data Humber af known eruption SIZE 1 with this size Prior probability of eruption with this size Previa Save in the next month given that an eruption Occurs Previa NODE 5 MAIN FORM In particular the models frame left of the form works exactly as the models frame at node 4 where the locations at node 4 are substituted by the SIZEs groups at node 5 file C Program Files BET BET UPGRADE UPG_nodeSmodel html 19 02 2008 node 5 past data 5 4 2 Node 5 Past data Page l of 1 The models and past data input panel for nodes 4 and 5 are similar to the models and past data input frames at node 1 2 amp 3 Node 5 EIs C Yes Equivalent number af data HMunmber of known eruptions SIZE 1 with this size Prior probability of eruption with this size Previows Save In the next month given that an eruption Occurs Previows Save NODE 5 MAIN FORM In particular the models frame centre of the form works exactly as the past data frame at node 4 where the number of eruptions at a given location at node 4 are substituted by the number of eruption with a given SIZE at node 5 If BET finds past data for sizes defined with a pri2. 3 see in figure the case of node 1 the user can choose the number of parameters to be monitored at each node at the top of the Monitoring data frame Note that this must be done after the model and past data information have been compiled If number of monitored parameters NMP at this node is 0 the NEXT button central button in the bottom left corner of the form will link to the form relative to the next node Note that the model s and past data s information during unrest are neglected when monitoring parameters are present For this reason monitoring data must be added to BET only when they are sufficiently informative and efficient to track the evolution of the unrest at the node Fd Node 2 Magmatic intrusion EE Monitoring data Humber af monitored 3 parameters Mumber of monitored 2 Unrest episodes Prior probability of Number of known magmatic unrest given magmatic unrest an unrest in the next month 2 Equivalent number Number of unrest F of data episodes Confidence Confidence Shaw preview Show preview NODE 1 FORM If there are monitoring parameters at present node the user is also requested to input whether there are past monitored episodes relative to the node Nodes 2 and 3 only If any after having defined each one of the monitoring parameters will be requested to input the parameters measures at the time of the last episode as well as the final outcome of the episodes see below Cli
3. Confidence Confidence Equivalent number Number of unrest F of data episodes Shaw preview Show preview NODE 2 FORM Page of 1 On the bottom right of the form the user can choose to go back to the previous form button BACK to proceed to the next form once the fields have been filled button NEXT or to quit the BET UPGRADE application button EXIT This last button before quitting saves the filled fields in the file named VolcanoName rec these values can be recovered in another session through the Recover procedure file C Program Files BET BET UPGRADE UPG_nodel html 19 02 2008 model at node 1 2 3 Page 1 of 1 5 2 1 Models For node 1 2 amp 3 BET visualizes a analogous form to input the models information To input models information the user must activate the model frame the left area of the form by selecting Y ES at the top left of the frame Note that this frame must be compiled before the Monitoring data frame is v Node z Magmatic intrusion Past data Monitoring data Humber of monitored parameters Humber of monitored 2 Unrest episodes Prior probability of Number of known 2 magmatic unrest given magmatic unrest an unrest in the next month Confidence Confidence Equivalent number Number of unrest F of data episodes Shaw preview Show preview NODE 2 FORM Once activated the model frame there are two field
4. The vent location for next eruption is then assumed to fall into one and only one of these areas It is also assumed that inside an area every point has the same probability of being the site of the next eruption vent Then at node 4 of the tree BET computes a probability distribution for opening of the vent in each one of these areas during the next eruption Central volcanoes have a roughly radial symmetry in this case we usually divide the volcanic complex into 5 possible areas with location 1 being the crater and locations 2 to 5 being circular sectors oriented according to the morphology of the volcanic structure On the other hand calderas have a more complex distribution of vent locations thus in this case we usually divide the volcanic complex into a certain number depending on the geometry and size of the caldera considered of rectangular and equal areas regularly distributed The specific geometry of the vent locations is set by the user with BET UPGRADE in the geometry of vent locations form To see the areas in the upper left portion of the Event Tree and Hazard Procedure Selection form click on the SHOW VENT LOCATION button In the vent location form are reported on the left the coordinates of the volcano and the dimensional and geometrical parameters of the vent location areas On the right of the form a map of vent location areas is visualized Sit Donato s venk location Aff Donalo s vent LAT eerit
5. a histogram resembling the probability density function of the requested absolute probability e in the green box on the lower left we display the average value of the distribution and its Q 50 the median and 90 percentiles Note that when the probability distribution is peaked on very small values the x axis of the two upper plots may be in logarithmic scale When the selection of the user is all location at node 4 or node 5 BET will display also another form containing a map of the averages of conditional probabilities of vent locations file C Program Files BET BET BET absolute prob html 19 02 2008 Conditional Probability Page of 1 3 2 Selected node Conditional probability Once all monitoring measurements have been put in the monitoring form in case of monitoring data or COMPUTE CONDITIONAL PROBABILITY has been clicked in the main form in case of no monitoring data the visualization of the results of absolute probabilities will be shown Average Probability TI Donate Hade 5 Sizes Average 1 08h perc 50k perc 6 1 EN 5 BEN amp 03E 401 2 S3E 401 2 57E 1 2 E J 1 D0E i T38E 02 3 636 02 WARNING Tabled values ane appromabed wath 3 digis The pe at about 1 percent Save Back Ext Hz gar gor CONDITIONAL PROBABILITY FORMS In the table on the left form BET displays the average value and the oth 50 the median and 9 percentiles of the conditional probability of each even
6. a small map of vent locations Moving the mouse over the map will be visualized the coordinates of the arrow s tip and the label of the indicated While the A is just one for all locations the average must be filled for all possible locations As the field has been filled to save the input and go at the next location the user must click SAVE With the button PREVIOUS the user can review previous locations Note that the sum of the averages over all locations must be l The memorization of the A is done as the user clicks the button NEXT Any change before of this will not be recorded The user may load values from a txt file clicking LOAD FILE The file must be composed by N records one for each vent location which contain each prior probability The j th record corresponds to location j If the file is correctly loaded BET confirms the successful process and all values are saved automatically file C Program Files BET BET UPGRADE UPG_node4model html 19 02 2008 node 4 past data Page 1 of 1 5 3 4 Node 4 Past data The models and past data input panel for nodes 4 and 5 are similar to the models and past data input frames at node 1 2 amp 3 Here we discuss only the differences dNode 4 Vent location Z Monitoring data WARNING At node 4 specific monitoring data are nat considered but ALL monitoring parameters at Made 1 2 and 3 may be used to lacalize the vent in BET Equivale
7. is composed by 5 locations The input parameters to be set are 3 1 the inner radius Ri Km 2 the Sectors strike St degree 3 the Outer radius Ro Km The location 1 1s meant to define the main crater of the volcano circle with radius Ri Then the other 4 locations are circular sectors oriented with an angle St respect to the North and with a radius Ro 2 Caldera This geometry is thought for a caldera without a main crater and consist of a grid box centred on the volcano position as defined with the volcano s coordinates The input parameters to be set are 4 Box width W Km Box height H Km Number of divisions along Width Nw Number of divisions along Height Nh Se The dimension of the box is defined by W and L and the number of locations is given by N Nw Nh The locations are labelled from 1 to N beginning from the bottom left corner to the top right corner file C Program Files BET BET UPGRADE UPG _node4locations html 19 02 2008 vent locations geometry Page 2 of 2 p Node 4 Vent location 1 Settings Geometry Degrees Central volcano Coordinates of the volcano f Caldera center Latitude 67000 i w width Km Longitud i NL N H Height Km VYolcanic area map SEES IA Map file complete path Mh divisions along H B Browse Minimum Latitude Maximum Latitude Minimum Longitude Maximum Longitude 115000 Show map NODE 4 MAP FORM caldera Once
8. is the case S d b strain rate y gt Hz dominant spectral frequency of earthquakes Tlso NM Presence of significant 510 2 Insert Exit MONITORING PAST DATA FORM Page 3 of 3 The user must fill for each one of the past monitored episodes the actual measures recorded at the time of the episode and the final outcome of the episodes Once all fields have been filled the button INSERT will point to next monitored episode if any or to the next node s main form WARNING The monitoring parameters can be recovered See recover only when all parameters at the actual node are set If the user exits BET UPGRADE from this form button EXIT in the bottom left corner the values filled for ALL monitoring parameters at the actual node will be lost file C Program Files BET BET UPGRADE UPG monitoring html 19 02 2008 weights Page l of 1 5 2 3 1 Parameters weight The weights of the monitoring parameters must be chosen according to the history of past unrest at the volcano In particular the weights control the relative importance of monitoring parameters at each node and their influence on probability computation see References Past data and model information at a given node are as much neglected as the state of unrest 1s clear given that monitoring parameters are present at the node If no monitoring parameter are present the posterior probability will be equal to the a priori probability In t
9. specific algorithm of BET where monitoring data at nodes after the first can effectively modify probabilities only proportionally to the probability of unrest at node 1 see Introduction and References for more details file C Program Files BET BET BET output conditional htm 19 02 2008 monitoring Page 1 of 2 2 1 Monitoring input values form When the Hazard Procedure selection is Monitoring BET needs the user to input the current monitoring data After having selected the Event Tree Path And Or Node and after having requested for the computation of the Absolute Probability or the Conditional Probability the series of Monitoring Data forms will appear one for each monitored node 4 Monitoring Data Mt Donato i x Mode 1 number of recorded earthquakes M gt 1 0 e e m J deformation at station DEF b temperature of fumaroles Load tile Next Show Thresholds Back MONITORING FORM 1 If the selected output is the absolute probability the user needs to fill in the monitoring values relative to the whole path selected in Event Tree Path And Or Node in the snapshot shown here the it is shown monitoring at node 1 Otherwise if the selected output is the conditional probability only the monitoring measures at first node unrest detection and at the final node are considered see Introduction and References therefore only forms relative to those two nodes are shown and must be fi
10. the specific branch selected When the user selects the path or the node and clicks on one of the two possible outputs absolute or conditional probability a confirmation window will appear as the one shown here CONFIRMATION WINDOW file C Program Files BET BET BET_ETselection html 19 02 2008 output absolute Page 1 of 1 1 4 Output the Selected Path and Absolute probability This kind of output is selected when the user wants to compute the absolute probability of a specific tree path This means that the output probability will be the product of all conditioned probabilities at the nodes along the selected tree path For example for the selection Unrest Magmatic Intrusion BET will visualize the probability of an episode of unrest due to a magmatic intrusion at the volcano considered 1 e probability of unrest multiplied by the probability of a magmatic intrusion given an unrest The selection done in figure below is Unrest Magmatic intrusion Eruption vent location 3 Size 2 Note that the selection is visualized just above the absolute probability button EJ Event tree and hazard procedure selection Target waleano r Hazard procedure F Creare ee oe rt Sabo Ad xj ae De Ho montang mr hed pn 3st daa nonno cara anm mol ped e a HI Show vent locators Maoniarng Event ee path and or node zelection Unies Magma rili un Eiupban M lae Soe Sme I Sp
11. this name can be modified Once selected the folder and the file name the image will be saved by clicking on the button SAVE at the bottom left of the form the file will be saved and BET will go back to the previous window To quit the snapshot saving form without saving the user can use the button BACK at the bottom right of the form file C Program Files BET BET BET_snapshots html 19 02 2008 BET UPGRADE Page l of 1 5 BET UPGRADE To load a volcano in BET or to change the input parameters of an already loaded volcano the user may run the program BET UPGRADE The user manual of BET UPGRADE is included in the BET manual file C Program Files BET BET BET UPGRADE html 19 02 2008 Volcano Page l of 1 5 1 Volcano name This form is the first to be visualized The name of the volcano is the one that will be visualized in BET General Name of the valcana Mt Donato VOLCANO FORM In the bottom of the form there are 4 buttons Exit This button quits the application The filled data are saved in a file called volcanoname rec in the folder recover and will be recoverable through the button Recover Next It allows to proceed in upgrading your volcano Help It opens the BET and BET UPGRADE manual Recover This button loads a new form to browse an old rec file to recover old or not finished upgrading process See Recover Note that the button EXIT and NEXT plus BACK in the following forms will be
12. weights of the parameter in the BET analysis see also Introduction and References and the thresholds interval and the relationship These last 3 parameters must be chosen referring the the historical unrest of the target volcano and the background activity measured in quiet periods The relationship 1s the one relative to the state of anomaly 1 e 1f high temperature of fumaroles means an higher probability of unrest the relationship to be selected is gt As regards parameters whose value is binary 1 e presence of significant SO2 a possible choice is to set the lower and the higher threshold to be equal and the relationship to be When all field are full the user must click the INSERT button that saves the parameters characteristic and links to the next monitoring parameter or the next Node Once all parameters have been input BET links either to next node or to the past monitoring data form when they exist as input in the node s main form In the latter case a new form is loaded file C Program Files BET BET UPGRADE UPG monitoring html 19 02 2008 monitoring at node 1 2 3 PaNode 2 Monitored episode 1 A E x Was the unrest episode magmatic Ho Node 2 Monitored episode 1 Input the measures of the paramter during the unrest episode The measures must be considered as the most anomalous values recored during the episode or just before the evolution toward the magmatic unrest node 2 if this
13. BET Manual Page 1 of 2 2006 07 14 DISCLAIMER The use of the applications BET and BET UPGRADE makes the user fully responsible of its input data results and relative applications By downloading the BET and BET UPGRADE packages the user accepts that INGV and authors are not responsible for any wrong application by the user who takes his her own risks BET 1 0 Bayesian Event Tree _EF Eruption Forecasting VH Volcanic Hazard Authors Warner Marzocchi marzocchi bo ingv it Laura Sandri sandri bo ingv it Jacopo Selva selva bo ingv it Istituto Nazionale di Geofisica e Vulcanologia Sezione di Bologna via Donato Creti 12 40128 Bologna Italy http www bo ingv it warner USER MANUAL Introduction The main purpose of this software is to provide a graphically supported computation of short to long term eruption forecasting through a Bayesian Event Tree model for Eruption Forecasting BET EF The model represents a flexible tool to provide probabilities of any specific event at which we are interested in by merging all the available information such as theoretical models a priori beliefs monitoring measures and any kind of past data It is mainly based on a Bayesian procedure and it relies on the fuzzy approach to manage monitoring data The method deals with short and long term forecasting therefore it can be useful in many practical aspects as land use planning and during volcanic emergencies More details can be fou
14. E Boschi 2004 Quantifying probabilities of volcanic events The example of volcanic hazard at Mount Vesuvius J Geophys Res 109 B11201 doi 10 1029 2004JB003155 Marzocchi W Sandri L and Selva J 2006 BET EF a probabilistic tool for long and short term eruption forecasting Submitted to Bull Volcan file C Program Files BET BET_Manual html 19 02 2008 mainform Page l of 1 1 Event Tree and Hazard Procedure Selection form This is the main form in BET T Feent tree ami hazard procedure PTS E TET E E m e xj Tangel volcano r Hazard procedure l veihaul mandame dala moni Fly peabasbiihy of the selechsd At Donato Ew Momontoing PRR eee beg ate ee eM oles teats E LE condensed Usehul Far leng lem hasard assessment ducing Show vant lacaliong Monlerinc quiet pened of Ihe volcano E venit inet path and or rode selection SELECTION FORM In this page we give a general overview of this selection frame while more details on the procedures and the meaning of all the parts of BET are available following links from this page or from the index of the manual The selection form is divided in 5 parts The following 3 parts are the core of BET e the Hazard procedure frame top right e the Event tree path and or node selection frame bottom left e the Output frame centre right In extreme synthesis as first step the user must select the hazard procedure at the top right of t
15. Page 1 of 1 1 3 Event Tree Path And Or Node selection Ei Event tree and hazard procedure selection r Target volcano r Hazard procedure Without mimang data man if Af Donata f Nomordong PSs iee tien nese a rin TK LE iGonzkdened Les im h zand Sho verit katie Monto Pe Pee of Ihe vekcanc Evert tree path ando node selection z Unrnest Magmalic intrusion Enaxiion zi al locs ee 1 pese wenl lac 4 wenl kes 5 Np eruption hadian tecon unne SELECTION FORM In this frame the user chooses among all possible combinations of phenomena in the event tree structure Each node is visualized with at the corner of the branch only 1f it contains further branches There are a couple of issues to be addressed 1 the visualized tree depends on the selection done in the Hazard Procedure frame so any choice in the Event Tree Path And Or Node selection frame will be cancelled if the Hazard procedure selection changes 2 the Event Tree Path And Or Node selection is independent on whether the chosen output will be the absolute or the conditional probability see Selected Path Absolute Probability and Selected Node Conditional Probability However if the conditional probability will be chosen the output will display the probability statistics for all the possible phenomena at the selected node Otherwise in the absolute probability case the output will display the probability statistics only for
16. both map and vent locations geometry are set with the button SHOW MAP map and vent locations are previewed in the left of the form file C Program Files BET BET UPGRADE UPG nodedlocations html 19 02 2008 node 4 model Page l of 1 5 3 3 Node 4 Models The models and past data input panel for nodes 4 and 5 are similar to the models and past data input frames at node 1 2 amp 3 Here we discuss only the differences fd Node 4 Vent location 7 3 E E x Monitoring data WARNING At node 4 specific monitoring data are not considered but ALL monitoring parameters at Node 1 2 and 3 may be used to localize the went in BET Equivalent number 300 of data Location 1 Location 1 Number of known Prior probability of eruption a oce eruption in this in the next month giver location that an eruption occurs INB sum to 1 Next Previgws Save Load file Previews Load file Paint the vent locations ta Exit show their NODE 4 MODEL amp DATA FORM As in the models frame at nodes 1 2 amp 3 in the models frame on the left at node 4 the user must activate the frame by selecting YES top of the frame and fill two fields the equivalent number of data A see model at node 1 2 amp 3 which controls the variance of the probability distribution on the top and the average probability best estimate on the centre of the frame On the the right part of the frame is visualized
17. can choose to go back to the previous form button BACK to proceed to the next form once the fields have been filled button NEXT or to quit the BET UPGRADE application button EXIT This last button before quitting saves the filled fields in the file named VolcanoName rec these values can be recovered in another session through the Recover procedure file C Program Files BET BET UPGRADE UPG modell html 19 02 2008 past data at node 1 2 3 Page 1 of 1 5 2 2 Past data For node 1 2 amp 3 BET visualizes a analogous form to input the past data information To input models information the user must activate the Past data frame the central area of the form by selecting YES at the top of the frame Note that this frame must be compiled before the Monitoring parameters are E zx Monitoring data Humber of monitored f parameters Humber of monitored 2 Unrest episodes Pd Node 2 Magmatic intrusion Model C Yes Prior probability of Number of known 2 magmatic unrest giver magmatic unrest an unrest in the next month Confidence Confidence Equivalent number Mumber of unrest F of data episodes Show preview Chow preview NODE 2 FORM Once activated the Past data frame there are two fields to be filled The first at top is number successes i e the number of times that the event at the actual branch happened in the past a short description is reported beside the input a
18. cking NEXT button the following form will be visualized for each one of the monitoring parameters the monitoring data form file C Program Files BET BET UPGRADE UPG monitoring html 19 02 2008 monitoring at node 1 2 3 Page 2 of 3 Node 1 parameter 1 1 Parameler name temperature Parameter description temperature al humas Parameter symbol and unite 1 PC cut and paste from Word Parameter weight Theeshalds interval Lower theeshold or Higher threshold i20 Theeshold relationship Iret Exit MONITORING DATA FORM Here all characteristics of the monitored parameter must be set From the top of the form the fields are the parameter name internal use the description of the parameter to help different users when BET is running the symbol of the parameter that will be displayed in the BET forms note that this field is a Rich Text box so that complex formats and fonts are allowed to use fonts and formats different from the default ones the user may set the symbol in a more complete editor program 1 e Microsoft Word and cut amp paste the symbol in this field Note also that for a correct visualization in BET the symbol must be reported in a single record no the EndOfRecord character that when pasted from another program may be saved even though not visible and that the visualization in BET will be identical to the one shown here same box dimension After the symbol the user must choose the
19. d al on pet daa Moniomg dala aa nol conden Ussu Far langle hazard assessment dueng quie pened of fhe volcand ETT SELECTION FORM Just below the name of the volcano there 1s a button that links to the vent locations visualization form Since BET is a general statistical tool any volcano could theoretically be uploaded in BET However the critical role played by hazard assessment in civil protection issues prevents us from leaving the user free to use all application of BET already compiled Therefore BET is provided as a general tool and the user must upgrade BET with BET UPGRADE with all the characteristics of a given volcano The use of the applications BET and BET UPGRADE makes the user fully responsible of its input data results and relative applications By downloading the BET and BET UPGRADE packages the user accepts that INGV and authors are not responsible for any wrong application by the user who takes his her own risks file C Program Files BET BET BET_Selecvolcano html 19 02 2008 vent locations Page 1 of 1 1 1 1 Show Vent location For the uploaded volcano BET assigns a probability specifically accounted for at node 4 of the tree to each vent location for the next eruption To do this the volcanic complex under study is divided into a certain number of areas depending on whether the considered volcano is a central volcano or a caldera
20. de of unrest The selection done in figure is Node 5 Sizes Note that the selection 1s visualized just above the conditional probability button Note also that even at node 4 it matters only which node is selected and it does not matter the path the branches selected at all nodes since Size distribution 1s assumed independent from the vent location see Introduction and References for more details E3 Event tree and hazard procedure selection Taiga waleana Hzd proosduire uh un rihin daa probability scieckrd Aft Dopato Ho mentang reor mr cir on pas dat jid hora ata WE Fel 1 s mt forl pam hazad azsezsmeni during Show vent ipcalons Maoniarnng re OC Event ree pah and or node selection 1 inesi Magma mliuaon Eiupban E Fipcicberrial tectonic une SELECTION FORM When conditional probability is chosen as requested output a confirmation of the selected path will appear Confirm selections Selection donesMt Donato Mode 5 Sizes oe CONFIRMATION FORM If the selected node is correct the user needs to click the OK button to proceed If monitoring data have been selected see Hazard procedure the Monitoring data form will be loaded see Monitoring data form and Thresholds form Note that 1f you choose to compute probabilities with monitoring data ALL monitoring data of the previous nodes must be compiled not only the ones of the selected node This is due to the
21. e J See J vent xc T werd loc 2 venit loc 3 went 4 went ioc 3 Ha Super hiycreberrial ectanic unrest SELECTION FORM When absolute probability is chosen as requested output a confirmation of the selected path will appear Confirm selections Selection done Donato Unrest Magmakic intrusion Eruption wert loc 1 Size 2 vate CONFIRMATION FORM If the selected path is correct the user needs to click the OK button to proceed If monitoring data have been selected see Hazard procedure the Monitoring data form will be loaded see Monitoring data form and Thresholds form Note that if you choose to compute probabilities with monitoring data ALL monitoring data of the previous nodes must be compiled not only the ones at the final node of the selected path file C Program Files BET BET BET_output_absolute htm 19 02 2008 output conditional Page 1 of 1 1 5 Output the Selected Node and Conditional probability This kind of output is selected when the user wants to compute the conditional probability of a specific tree node This means that the output probability will be the distribution relative to the last node of the selected path that is the probability of the event relative to this node conditioned to all previous ones For example for the selection Unrest Magmatic Intrusion BET will visualize the probability of a magmatic intrusion at the volcano considered given an episo
22. er esaa LON center frase Fi inner Em b c Suke degree am R2 outer Em ps pDERERRRERIEEE ERE E VENT LOCATIONS FORM When the mouse s arrow move on the vent locations will be visualized the numeral label of the vent location and the coordinates of the arrow s tip The button EXIT does not quit BET but only the Vent locations form To save a snapshot of this form by clicking the button SAVE the user may choose in a file browser the file and the folder where a BMP file will be saved file C Program Files BET BET BET_node4 html 19 02 2008 hazard procedure Page 1 of 2 1 2 Selection of the Hazard Procedure This is the first input step to be accomplished by the user The selection must be done in the Hazard procedure frame in the top right corner of the main form Here the user may choose among 2 possibilities also explained in the blue text editor at the top right position of the Event Tree And Hazard Procedure Selection form No monitoring the volcanic hazard will be computed without considering monitoring data The computed monthly probabilities will be based only on theoretical models and past data See Introduction and References for more detailed info This procedure is useful in a quiescent period when only long term hazard assessment is of interest rm a Event tree and hazard procedure selection Without monitored d north probability of ihe sieche dL d nb o ped st dala Monilonng daa a
23. he case of a clear unrest this a priori information is completely lost see Introduction and References and all probability are studied using monitoring measurements The basic assumption of this is that monitoring parameters are sufficiently efficient and informative for tracking the evolution of the unrest and that monitoring weights and thresholds have been chosen taking into account the historical unrest at the volcano file C Program Files BET BET UPGRADE UPG weights html 19 02 2008 fuzzy Page l of 1 5 2 3 2 Thresholds interval amp relationship The use of one threshold may be too rough because of several reasons At first a system can move to an anomalous state gradually rather than overcoming one specific value of a monitoring variable Secondly since the definition of a threshold is strongly subjective and that such a threshold may strongly affect the results a more fuzzy definition seems to be more appropriate For these reasons we introduce the fuzzy set theory In fact the proposition the measure 1s anomalous stands for the membership of the present measure of the parameter x to the set of anomalous values of the parameter In a fuzzy perspective this membership 1s not only TRUE or FALSE as in Boolean logic but can be true by some degree As a consequence the proposition above can be partly true and partly wrong to some extent In other words BET associates a real value between 0 and 1 to the logical sta
24. he form The next step is to choose the event tree path and or node in which he she is interested Finally the type of output which he she 1s interested 1n absolute or conditional probability has to be selected The last two parts of the form are meant to visualize and or select BET s options e the Target volcano frame top left e the control buttons bottom right On the top left of the form in the Target volcano frame the name of the target volcano 1s reported Just below the name Mt Donato in the figure the user may visualize the possible vent locations for next eruption In the bottom left corner are available several control buttons to set several options Starting from the left HELP links to this BET manual INFO visualizes information about the BET version loaded the two flags allows to change the language Italian or English the UPDATE DATA button may be used to upgrade the event tree by uploading new data or information this link is usually disabled Another procedure to update new data is to use the BET UPLOAD package Finally the button EXIT quits BET lt endif gt file C Program Files BET BET BET_ mainform htm 19 02 2008 Target volcano Page of 1 1 1 Target volcano The upper left part of the Event Tree And Hazard Procedure Selection form displays the name of the volcano currently uploaded in BET in the figure Mt Donato Ytho montonsg dale monty peababilky of the neleched 2
25. l 19 02 2008 monitoring node 4 Page 1 of 2 2 2 Monitoring at Node 4 The inference about the position of next vent is necessary when e the final node is node larger or equal to 4 if absolute probability 1s selected e the final node is node 4 if conditional probability is selected e the final node is node larger than 4 and the path includes all locations at node 4 1f conditional probability is selected In these cases for each one of the ticked parameters at nodes 1 2 and 3 a new window 1s opened where the localization of the monitoring can be input The choice of the parameters must be an expert choice 1 e the localization must be both possible and meaningful fa Monitoring for Node 4 Monitoring parameter Me Location 1 Location 2 Location 3 Location 4 Location 5 Total 1 Load file Apply Back MONITORING FORM 72 In top left part of the form is reported the symbol of the monitored parameter Just below it is located the input table The input values are the fraction of the measured quantity that can be localized in each vent location To input the fraction values select the cell relative to the vent location and input its relative value Note that all fractions must sum to 1 Remarkably this localization does not account for the actual degree of anomaly of the parameters so that anomalous measures will be as important as not anomalous measures When a cell is left BET checks both tha
26. lled in When the localization is necessary see monitoring at node 4 the user may choose to localize monitoring measures relative to parameters at all nodes through the fraction of the measured quantity in each vent location In this case all forms will be visualized and the user may select the parameters to infer the vent localization through a specific tick If actual measures at a given node are not necessary 1 e conditional probability only this selection will be allowed 1 e measures input will not be possible After having filled in all the fields the user should click on the NEXT button If the user 1s interested in checking the thresholds for the monitoring parameters he she can click on the SHOW THRESHOLDS button If Node 4 has been selected beside each field in the monitoring form BET visualize a tick relative to the monitoring at Node 4 This tick must be selected when a specific spatial distribution of the relative monitored parameter can help the localization of the eventual vent If at least one of those ticks is selected a new form is loaded monitoring at Node 4 In this form the user is requested to input the percentage of the monitoring file C Program Files BET BET BET monitoring html 19 02 2008 monitoring Page 2 of 2 parameter can be attributed to a specific vent location This operation will be done for every parameter ticked file C Program Files BET BET BET_monitoring htm
27. n the left of the form file C Program Files BET BET UPGRADE UPG_node4map html 19 02 2008 Map Page 2 of 2 FX Node 4 Vent location 1 Settings Geometry greet f Central volcano f Caldera Degrees eee Coordinates of the volcano center Latitude BFo00 Longitude 59000 Yolcanic area map Ai Inner radius K m St Sectors strike Degree Ro Outer radius Km Map file complete path Browse Minimum Latitude n Id aximum Latitude 130000 Back Minimum Longitude n Next Maximum Longitude 115000 NODE 4 SHOW MAP file C Program Files BET BET UPGRADE UPG node4map html 19 02 2008 vent locations geometry 5 3 2 Node 4 Geometry of vent locations Page 1 of 2 In the central frame of the Node 4 form the user must select the geometry of the vent locations p Node 4 Vent location 1 x Settings Geometry C Degrees DTM f Central volcano Coordinates of the volcano Caldera center Latitude B 7000 Ri Inner radius Km Lenet 59000 St Sectors strike Degree Volcano SUO Hn Outer radius Km M ap file complete path Browse Minimum Latitude I4 asimum Latitude Minimum Longitude Maximum Longitude Exit Show map NODE 4 MAP FORM central volcano In BET two possible vent location geometries are available 1 Central volcano This geometry is thought for a central volcano with a main crater It has a circular symmetry and it
28. nd in References BET 1 0 1 Event Tree And Hazard Procedure Selection form 1 1 Target Volcano 1 1 1 Show Vent Locations 1 2 Selection of the Hazard Procedure 1 3 Selection of the Event Tree Path And Or Node 1 4 Output the Selected Path 1 5 Output the Selected Node file C Program Files BET BET_ Manual html 19 02 2008 BET Manual 2 Monitoring data 2 1 Monitoring input values form 2 2 Monitoring at Node 4 2 3 Monitoring Thresholds form 3 Displaying the output results 3 Selected Path Absolute Probability 3 2 Selected Node Conditional Probability 3 3 The Vent Location Map 4 Snapshots saving form 5 BET UPGRADE 5 1 Volcano name 5 1 1 Recover 5 2 Node 1 2 amp 3 5 2 1 Models 5 2 2 Past data 5 2 3 Monitoring data 5 2 3 1 Weights 5 2 3 2 Thresholds interval and relationship 5 3 Node 4 vent locations 5 3 1 Coordinates amp map 5 3 2 Geometry of vent locations 5 3 3 Models at node 4 5 3 4 Past data at node 4 5 4 Node 5 VEIs 5 4 1 Models at node 5 5 4 2 Past data at node 5 5 5 Summary Page 2 of 2 WARNING AII figures and examples in this manual are completely invented They refer to an inexistent volcano that we named Mt Donato All parameters and settings are invented and none of this material has the intent of suggestion and or true values REFERENCES Marzocchi W L Sandri P Gasparini C Newhall and
29. ne nior oncadened Useful for langebeme hazard assessment dung gui periods of the volcano SELECTION FORM No monitoring Monitoring the volcanic hazard will be computed taking into account also monitoring data Thus the computed monthly probabilities will be evaluated both through past data and theoretical models and monitoring data See Introduction and References for more detailed info This procedure is useful when anomalous signals are recorded at the volcano and during an unrest so that the user might be interested in the estimation of short term hazard EDIDI tree and hazard procedure selection Without monitor d ond probability of the seiche 22 04 bead nb on pel a Moran j dais are nor oreadered Useful ior kngtere harard arpesarmerit du mg que penoge oi ini vol T file C Program FilessBETWIBET BET Haz procedure html 19 02 2008 hazard procedure Page 2 of 2 SELECTION FORM Monitoring Based on this choice the Event Tree visualization changes Because of this the choice of the Hazard Procedure needs to be made before the selection of the event tree path and or node in the Event Tree Path And Or Node frame Otherwise if the user selects first the event tree path and or node and then the Hazard Procedure the event tree path and or node selection will be cancelled as soon as the Hazard Procedure changes file C Program Files BET BET BET Haz procedure html 19 02 2008 path node selection
30. nt number 300 gF data Location 1 Location 1 Number of known m Prior probability of eruption a oce eruption in this in the nest month given location that an eruption occurs NB sum to 1 Previmws Save Load file Previows Save Load file Paint the vent locations ta Exit show their NODE 4 MODEL amp DATA FORM In the past data frame on the right at node 4 the user must activate the frame by selecting YES top of the frame and fill just 1 field the number of times an eruption occurred at the location on the centre of the frame On the the right part of the frame is visualized a small map of vent locations Moving the mouse over the map will be visualized the coordinates of the arrow s tip and the label of the indicated The number of eruption at the location must be filled for all possible locations As the field has been filled to save the input and go at the next location the user must click SAVE With the button PREVIOUS the user can review previous locations The user may load values from a txt file clicking LOAD FILE The file must be composed by N records one for each vent location which contain the number of eruptions recorded at each location The j th record corresponds to location j If the file 1s correctly loaded BET confirms the successful process and all values are saved automatically If BET finds past data in locations defined with a prior probability equal to 0 a warning message will be
31. or probability equal to 0 a warning message will be visualized BET will run anyway but this choice 1s quite illogical since some past eruptions occurred with a size that the user defined not possible in the future 1 e with a theoretical 0 probability of occurrence file C Program Files BET BET UPGRADE UPG_nodeSdata html 19 02 2008 summary amp finish Page l of 1 5 5 Summary amp finish In this final form a synthesis of the previous choices is displayed To save and finish the upgrade click on the button FINISH on the bottom right of the form Pa Check input and Finish E X Target volcano Mt Donato LAT 6000 LON 59000 MODEL DATA MONITORING MODE 1 Unrest es Tes 3 parameter z NODE Magmatic unrest Ho es 3 parameters NODE 3 Eruption es Ma 1 parameter z NODE 4 Vent locations 5 Yes No No monitoring NODE 5 SIZE lt 2 Mn Ma Mo monitoring Finish SUMMARY A final message will be shown that confirms the successful upgrade SAVE FORM If no map file has been selected will be shown also another analogous message recalling this After these messages the program BET UPGRADE quits Now BET is ready to be run To recover the entire set of choices done just launch the BET UPGRADE application and browse the rec file relative to the volcano previously upgraded file C Program Files BET BET UPGRADE UPG_ summary html 19 02 2008
32. present in all forms of BET UPGRADE with the same meaning file C Program Files BET BET UPGRADE UPG volcano html 19 02 2008 recover Page 1 of 1 5 1 1 Recover Not finished upgrading process are automatically saved as BET UPGRADE is quitted Data are saved in a file called volcanoname rec in the folder recover sub folder of the application folder From the volcano amp coords form clicking the button Recover the user is asked to browse a rec file 4 Documerts and Settings jacopo ae ME Donata rec SABET upload maet Prog peu RECOVER FORM Once a file is selected single click on the file list on the left of the form clicking the button SELECT or double clicking the file name in the list all data saved will be loaded in BET UPGRADE These data can be confirmed and or changed in the BET UPGRADE procedure file C Program Files BET BET UPGRADE UPG recover html 19 02 2008 node 1 2 3 5 2 Nodel1 2 amp 3 The forms to set values at node 1 2 and 3 are equal Each form is divided into three frames 1 On the left the MODEL 2 In the centre the PAST DATA catalogue of past events 3 Onthe right the MONITORING parameters for the node Pd Node 2 Magmatic intrusion Monitoring data Humber af monitored 3 parameters Mumber of monitored 2 Unrest episodes Prior probability of Number of known 2 magmatic unrest given magmatic unrest an unrest in the next month
33. rea The second field is the total number of measures 1 e the number of times an observation has been done If model s information is present this number must be compared to the equivalent number of data A In the bottom of the Past data frame with the button SHOW PREVIEW the user can visualize a Cumulative Distribution Function CDF of the probability given by past data at the present node The median is given by the intersection of CDF red line with horizontal solid line An idea of the dispersion of the distribution around the median is given by percentiles which are the intersections of CDF red line with horizontal dashed lines 10th 20th 30th 40th 60th 70th 80th and 90th percentiles from bottom to top A sharp and sudden increase of the CDF means high confidence on the model while a smoother increase means more uncertainty on the past data s results On the bottom right of the form the user can choose to back to the previous form button BACK to proceed to the next form once the fields have been filled button NEXT or to quit the BET UPGRADE application button EXIT This last button before quitting saves the filled fields in the file named VolcanoName rec these values can be recovered in another session through the Recover procedure file C Program Files BET BET UPGRADE UPG datal html 19 02 2008 monitoring at node 1 2 3 Page 1 of 3 5 2 3 Monitoring data On the right of the main form at nodes 1 2 amp
34. resholds Page of 1 2 3 Monitoring Thresholds form The Monitoring Threshold form shows the low and high thresholds used to compute the degree of anomaly of each monitoring parameter at the node according to the fuzzy approach see Introduction and References These thresholds are chosen by the user during the installation of BET made through BET UPGRADE Here we show a conceptual example for Mt Donato P dMonitoring thresholds Mt Donato Node 1 T C 9 50E 01 1 20E 02 Ne 3 006 011 50E 02 Pem Ezam d gt 4 006 00 1 006 01 THRESHOLDS FORM file C Program Files BET BET BET_ Threshold html 19 02 2008 Absolute Probabilities Page 1 of 1 3 1 Selected Path Absolute probability Once all monitoring measurements have been put in the monitoring form in case of monitoring data or COMPUTE ABSOLUTE PROBABILITY has been clicked in the main form in case of no monitoring data the visualization of the results of absolute probabilities will be shown E2 COF amp POF Cail GCumaLrree Destrrburticur Farchion Probability Density Function ee amp E TEE E E y AR ae WHGKANING Tabled values ae approamalsd wath 3 dcr ABSOLUTE PROBABILITY FORM In this window we show statistics for the absolute probability distribution requested In particular e in the left upper panel we show the cumulative distribution of the requested absolute probability e in the right upper panel we show
35. s to be filled The first at top 1s the average probability of the event of the node a short description 1s reported beside the input area The second field is the confidence of the models average given in terms of equivalent number of data A The A is the weight that BET will assign to the models information and it controls the uncertainty relative to the estimated average A is mainly a measure of the epistemic uncertainties of models at the present node Therefore the A must be chosen by taking into account the confidence of the model judging approximately the number of data that would lead the user to reject the models results Note that 1f both model and past data are present at the node the A will be compared to the number of past data In the bottom of the Model frame with the button SHOW PREVIEW the user can visualize a Cumulative Distribution Function CDF of the probability given by models at the present node The median is given by the intersection of CDF red line with horizontal solid line An idea of the dispersion of the distribution around the median is given by percentiles which are the intersections of CDF red line with horizontal dashed lines 10th 20th 30th 40th 60th 70th 80th and 90th percentiles from bottom to top A sharp and sudden increase of the CDF means high confidence on the model while a smoother increase means more uncertainty on the model s results On the bottom right of the form the user
36. t at the selected node Note that BET visualizes these values for all the possible branches 1 e all the possible events at the selected node On the right form BET displays a pie chart showing the averages of all the possible outcomes at that node Clearly being a set of mutually exclusive and complete outcomes the sum of the averages 1s one This windows may be sized by the user to magnify the chart This form 1s not visualized when at the node are present more than 14 branches 1 e node 4 depending on the user definitions Note that values in the visualization table are approximated with 3 digits and values in the pie chart are visualized only when greater than about 1 percent If the user selected node 4 BET will also display a third form where it is drawn a map of the average conditional probabilities of vent locations file C Program Files BET BET BET conditional prob html 19 02 2008 Absolute Probabilities Page 1 of 1 3 3 The Vent Location Map The Vent Location Map is visualized if all locations 1s selected either for Absolute or Conditional probability or if Node 4 is selected for Conditional probability The map represents the conditional probability of eruption in each vent location given that an eruption occurs jj Conditional prob of the event in a specific location See i manual for more details VENT LOCATION MAP The map is drawn with the averages of the conditional probability distribu
37. t the sum of all fields is larger than 1 and that the last input field is correctly spelled Press RETURN to visualize the sum of all fractions already filled in and BACK SPACE to reset the selected fraction to 0 Note that numbers must be input with the decimal separator 1 e dot in English comma in Italian as defined in the International settings of the OS An alternative choice simpler for high numbers of vent locations 1s to load a txt file where fractions are stored The file must have a txt extension and must be formatted as a single column file with a list of the N percentages relative to the N vent locations To load the file click the LOAD FILE button and select the file from the browser file C Program Files BET BET BET_ monitoring4 html 19 02 2008 monitoring node 4 Page 2 of 2 ETN C4 Documents ard Settings J jacopo Jj jecopo backup 20060124 BET FILE BROWSER When all fields are input a field left empty means 0 if they do not sum to 1 BET normalizes them to 1 The buttons APPLY and BACK may be used to move forth to next monitoring parameters for the localization or to the visualization of results and back On the top right part of the form is reported a map of the vent location When the mouse s arrow move on the vent locations will be visualized the numeric label of the vent location and the coordinates of the arrow s tip file C Program Files BET BET BET_ monitoring4 html 19 02 2008 th
38. tement representing the degree of truth of the statement 1 e the degree of anomaly z of a given measure of x In practice for each monitoring parameter x a function called membership function u x 1s defined u x associates to each measurable value of x its relative degree of anomaly z W x The functional form of p is set and specifically is a linear membership function with corners defined with the lower and the higher thresholds 1 e the threshold intervals the relationship define whether the anomalous measurements are the ones on the right or on the left side of the threshold interval 1 e greater or lower values respectively In practice 1f the parameter 1s expected to have lower values during a quiet period and greater during unrest the relationship to be chosen is gt If the parameter is boolean 1 e presence of significant SO a possible choice is to set the lower and the higher threshold to be equal and the relationship to be In this case the fuzzy logic works in the same way as boolean logic does See References for more details file C Program Files BET BET UPGRADE UPG fuzzy html 19 02 2008 Map Page of 2 5 3 1 Node 4 Coordinates amp Map The coordinates are the basis to locate the volcano and its possible vent locations For central volcanoes these coordinates are meant to indicate the center of the main crater In the case of calderas the coordinates indicate the geometrical cen
39. ter of the caldera ba Node 4 Yent location 1 Settings Geometry Degrees f UTM f Central volcano t Caldera Coordinates of the volcano center Latitude Eun Ri Inner radius Km Longitude 59000 St Sectors strike Degree Ro Outer radius Km Yolcanic area map Map file complete path Browse Minimum Latitude Masimum Latitude 120000 Minimum Longitude Maximum Longitude Show map NODE 4 MAP FORM The map file must be a GIF file with transparent background if a map file is chosen the visualization box defined in Minimum Maximum Latitude Longitude must correspond to the limits of the map Coordinates may be given in ordinary degrees 90 90 0 360 or through UTM coordinates m To choose between these two options the user has to tick the preferred option at the top of the frame Note that this option controls the metric on the map The map file may be selected through a file browser for more details see the Recover browser description that is opened when the user clicks the button BROWSE FILE FORMAT g mag vennan copy gi map wvesundaes gi 29g BET upload CAEveniTies anap 2 Select Back BROWSE MAP FILE BET may run also without a map file in this case the visualization box is chosen by the user Note that a visualization box must be defined in any case Once both map and vent locations geometry are set with the button SHOW MAP vent locations are visualized i
40. tions at node 4 Note that the palette limits change dynamically so they are not fixed a priori In the top of the form the button SAVE permits to save a bmp snapshot of the form in a file and visualize a browse form to select name and folder where the image will be saved When the mouse tip is over the map BET visualize the geographical position LAT and LON the vent location s number and the value of the average probability at the location file C Program Files BET BET BET location map html 19 02 2008 snapshots Page 1 of 1 4 Snapshot saving form In both absolute and conditional probabilities output forms and in the vent locations showing form the button SAVE links to a new form that allows to store the snapshot of the preceding form in a BMP file fiSave map Mt Donato Node 5 Sizes MM PIE A amp ggiomalalti hm Aggiomalat le she 5s Dres frs calceli manpa bas DD v1 dataFL coordinahbe bas mg vi dataMD dichiarazioni bac ADincuments and SertngssjacopawacaposBE T Mit Donato Hode 5 Sez HM FIE bmp SNAPSHOT SAVING FORM On the left there 1s a classical browser to select the folder in which to save the image In the centre a ist of the files in the selected folder is visualized On the right a preview of the image is visualized At the bottom left of the form is reported the name of the file that 1s going to be saved BET proposes a name that recalls to the path selected and the choices done but
41. visualized BET will run anyway but this choice 1s quite illogical since past data are found in location where the user defined a theoretical 0 probability of vent opening file C Program Files BET BET UPGRADE UPG_node4pastdata html 19 02 2008 node 5 Page l of 1 5 4 Node 5 Eruption magnitude At first the user must set the number of sizes expected at the target volcano Sizes may be defined by the user 1 e VEI by grouping sets of eruptions using a given definition of how to measure the size of each eruption T Hode 5 Minimum size Insert the maximum SIZE A expected For the volcana P Hari Jie SEE cjue sg aur OEE Ae ME aor Pam atm Faces Cooke 4 Back Next NODE 5 MINIMUM VEI FORM The definition of size classes depends on the specific interest of the user and from the eventual next nodes Usual choices are VEI magnitude intensity Note that the SIZE distribution is considered independent from the vent location 1 e all vent locations have the same VEI distribution This means that the size distribution 1s assumed equal in all vent locations so that the expected size 1s completely independent from the localization of the unrest Note also that is not possible to input monitoring parameters at node 5 This choice is due to the lack of reliable precursory signals to the size of eruptions file C Program Files BET BET UPGRADE UPG_node5 html 19 02 2008 node 5 model Page of 1 5 4 1 Node 5 Models
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