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1. catalogue all the training period starts at start series and finishes on the date of the last event in the catalogue 10 MS series Using the training period the algorithm then determines the required magnitude cutoffs to produce the following subcatalogues CAT20 CAT10 CAT20a CAT10a and CATMS The subset CAT20 has smaller earthquakes cut out so that it has an average of 20 earthquakes per year Similarly for CAT10 though with an average of 10 events per year The subset CAT20a is the same as CAT20 except that earthquakes stronger than a half magnitude below the target magnitude are omitted Similarly for CAT10a The subset CATMS contains the events in the catalogue that have magnitudes between Mo 2 and Mp 0 2 where Mo is the target magnitude Using the vector time breaks the algorithm computes for each time interval the value of the seven series as follows Note that these series start being calculated from the date start series Series 1 is the number of earthquakes in CAT20 Series 2 is the number of earthquakes in CAT10 Series 3 and 4 are derived from series 1 and 2 respectively They are the difference between the number of earthquakes in the past 6 years and the number expected based on all data 6 years before the date when the series start being calculated Series 5 and 6 have the same lower magnitude thresholds as the first 4 series but earthquakes used in their calculation must also be a at least h2. 12 MS8 TIP Details The empirical distribution of each series is initially calculated The way this is done depends on the training mode If the training mode is moving only the threshold percentiles for declaring a TIP are calculated This is because the moving mode emulates the position of someone making real time predictions the empirical percentiles are updated with each new data point Before the empirical series are used for prediction they are smoothed by taking the maximum value over the past 3 years argument smoother 6 If the training mode is a11 the empirical distribution of the series is calculated using all avail able values of the series If the mode is user only values of series during the training period are used to calculate the empirical distribution The rts objects tops and exceeds are computed The object tops gives the threshold percentiles for each series relevant at time 2 and exceeds is a logical rts indicating whether the series exceeds the threshold percentile in the time interval J M8 TIP then looks at the decision rule for declaring a TIP For a TIP to be declared 5 out of the first 6 series must cross their 90th percentile at least once in the last 3 years and the 7th series must also cross its 75th percentile also at least once in the last 3 years This was formalised by Harte et al 2003 as follows Denote the mth series in interval J as F Ji 1 Let where Gm is the empirical distr
3. TIP declaration within the function M8 TIP is calculated by two different methods one using the quantile function and the other based on the empirical cumulative probability distribution function If they are not consistent then the time point of the TIP declaration can be different between the two methods Value A vector of the same length as q containing the cumulative probabilities Author s David Harte 2005 See Also quantile ecdf Examples n lt 10 x lt rep O n 1 print quantile x probs seq 0 1 1 n print emp cdf x x n lt 12 x lt rep O n 3 print quantile x probs seq 0 1 1 n print emp cdf x x n lt 12 x lt rnorm nt 1 print quantile x probs seq 0 1 1 n print sort x print emp cdf x sort x M8 M8 Run the M8 Algorithm Description This function runs the M8 algorithm i e calls the function M8 series to calculate the seven time series calls the function M8 TIP to calculate the Times of Increased Probabilities and finally optionally calls the function plot M8 to plot all seven series plus an eighth critical series Usage M8 catalogue centrelat mean catalogue latitude radius radius M8default M0 minday catalogue 1 time MO centrelong mean catalogue longitude start series datetimes year yearsl minday 12 month 1 day 1 hour 0 minute 0 training user end training NA time breaks Inf
4. breakpoint in the vector time breaks The breaks should also be at regular intervals running total smoother by default the series are calculated with a six year running total i e 12 half years thus the M8 default is 12 integer denoting the length of the smoothing window The series are smoothed at a given point by taking their maximum value over previous values within this window The default value is 6 i e three years Requires the package ssNZ require ssNZ as catalogue subsetrect NZ minday julian 1 1 1965 maxday julian 1 1 2000 minmag 4 5 catname NZ45 decluster M8 NZ45 cutoff mag 4 5 decluster name NZ mainshocks Savpar lt par no readonly TRUE temp lt M8 NZ mainshocks MO 7 0 minday julian y 1965 x 1 d 1 start series julian y 1975 x 1 d 1 centrelong 176 centrelat 39 end training julian y 2000 x 1 d 1 par savpar 8 M8 series TIP length isthe duration of the TIP or Time of Increased Probability The M8 default is 5 years i e 10 time intervals and is independent of MO plotit logical If set to TRUE then seven plots for each of the seven smoothed series are generated There is also a plot of the largest earthquake in each 6 month interval together with the critical series The default is TRUE title character string giving a title for the page of plots The default is M8 Series and TIPs debug logical The default is FALSE Details See Detai
5. by the argument decluster name is written to the session workspace It contains the mainshock hypocentral information and an additional variable n aftershocks containing the number of aftershocks following the mainshock within 14 days Author s Li Dongfeng 1997 modified November 1999 See Also M8 M8 series M8 TIP plot M8 Examples Requires the package ssNZ require ssNZ as catalogue subsetrect NZ minday julian 1 1 1965 maxday julian 1 1 2000 minmag 4 5 catname NZ45 decluster M8 NZ45 cutoff mag 4 5 decluster name NZ mainshocks print summary NZ mainshocks emp cdf Empirical Cumulative Distribution Function Description Calculates the empirical cumulative probability distribution function This is the inverse function of quantile Usage emp cdf x q D emp cdf Arguments x is a vector containing the sample data q is a vector of points where the function is to be evaluated Details This function is an exact inverse of the quantile function when the points in q are contained in x This is not the case for the function ecdf For example say x contains 11 unique points Then according to the quantile function the minimum represents the zero th quantile and the remaining sorted values represent the 10 ile 20 ile 30 ile up to 100 ile The function emp cdf has been defined to be consistent with this This consistency is important for the evaluation of the M8 algorithm The
6. running total 12 smoother 6 TIP length 10 plotit TRUE title M8 Arguments catalogue MO centrelong centrelat radius minday start series training end training time breaks Series and TIPs debug FALSE the mainshock catalogue created by the decluster M8 function with the number of aftershocks in following 14 days numeric The aim of the algorithm is to predict earthquakes with a magnitude greater than or equal to Mo longitude of the centre of the circle of interest latitude of the centre of the circle of interest circle of interest radius The default radius is 55 5 exp Mpo 5 6 1 Julian date events earlier than this are not used in analysis By default all the data are used Julian date of end point of the first bin from which the series are generated Since the series are calculated using bins defined by time breaks the start series must coincide with an end point of one of the bins The M8 default is six month bins has three possible modes moving user and all See Details in M8 series for further explanation Julian date for the end of the training period This date should be the end point of a bin This is only used when the training mode is user a vector of Julian dates that give the bin boundaries for calculating the series The M8 default bin length is 6 months Care must be taken that the arguments minday start series and end training coincide with a
7. Package ssM8 24 September 2010 Version 2 1 8 Date 2010 09 24 Title M8 Earthquake Forecasting Algorithm Author David Harte ported to R and packaged by Ray Brownrigg Maintainer David Harte lt david statsresearch co nz gt Description This package performs the M8 calculations as in Kossobokov 1997 It was originally written for S PLUS being part of the Statistical Seismology Library Harte 1998 and was translated to R by Ray Brownrigg lt Ray Brownrigg vuw ac nz gt More information about the M8 Algorithm can be found under the topic changes along with recent modifications made to the package Depends ssBase Suggests ssNZ License GPL gt 2 URL http www statsresearch co nz software html R topics documented Changelog tb etole dears BoE gad 8G ew Bye ae Ae oy Bee 2 decl stei Mg oarso R REE ue E aw den E amp BRM ENEA a Re Se ees 4 empedi acs gis 2 ca pine Gh aorta HS Geeta Se Ke eh a a e Micha Bee K IVS HHT E NTSC ce se a E R UR a Be wt EE ea Bt E E T a aa 8 WIS SIP 5 ee e ody Be cts cored Ee hav oe ne je ae Dea ee et aes Tee Bees 11 PlOUMS ss esera i RR abe R e e R R RRR eae Soe e e T 14 Index 16 2 Change Log Change Log Changes Made to the Package Description The M8 algorithm is based on seven different time series see Keilis Borok amp Kossobokov 1990 and Kossobokov 1997 If the 7th time series and 5 out of the first 6 time series are above certain thresholds a Ti
8. alf a point less in magnitude than Mp the magnitude targeted for prediction Series 5 uses CAT20a and series 6 uses CAT10a These series are the average magnitude multiplied by the 2 3 power of the number of events Series 7 is based on CATMS It is the maximum number of aftershocks after any event in this magnitude range over the past year These are regular time series with intervals of 6 months and a 6 year running total incorporated into their calculation Before they are used for prediction they are smoothed again by taking the maximum value over the past 3 years Then the M8 decision rule is applied if 5 out of the first 6 series are above their 90th percentile and the 7th series is above its 75th percentile a TIP is declared Value The function produces a list object with the following components series is a regular time series rts object with n rows and 8 columns The first 7 columns are the seven series and the last is the datetime corresponding to the series values max events is a data frame with the same column structure as the catalogue However the columns are regular time series with 6 month intervals containing attributes of the largest earthquake in that 6 month period Author s Li Dongfeng 1997 modified by Maaike Vreede 1998 See Also decluster M8 M8 M8 TIP MR TIP 11 Examples Requires the package ssNZ require ssNZ as catalogue subsetrect NZ minday julian 1 1 1965 maxday
9. anged to TIP type 1 lt The earlier versions caused errors when running R CMD check in R version 1 6 2 February 2003 5 plot M8 argument M8 changed to x and argument added to fix generic method incon sistencies June 2003 6 print mainshocks has been renamed to prt mainshocks to fix generic method con fusion June 2003 7 time grid has been renamed to timegrid to fix generic method confusion June 2003 8 M8 TIP the check to see if the critical series has length less than seven now uses function nrow rather than start and end October 2003 9 decluster M8 a vector is now returned that identifies the mainshock to which each after shock belongs October 2003 10 Minor formatting corrections to manual pages December 2003 11 Minor documentation formatting changes mainly to use dQuote January 2004 12 in circle correct documentation mismatch with code 7 May 2004 13 decluster M8 PACKAGE ssM8 has been added tothe Fortran recat call within the function 7 May 2004 14 sum row renamed to sumrow 7 May 2004 Change Log 3 15 A statement require SsNZ has been added to the examples that use the NZ catalogue Hence ssNZ is no longer a package requirement of ssM8 25 May 2004 16 M8 series statement with incorrect logical syntax corrected cover breaks lt time breaks 1 lt catalogue time lt time breaks n 17 Feb 2005 17 M8 TIP make docum
10. cumentation for the Statistical Seismology Library School of Mathemati cal and Computing Sciences Research Report No 98 10 Updated Edition June 1999 Victoria University of Wellington ISSN 1174 4545 Harte D Li D F Vreede M amp Vere Jones D 2003 Quantifying the M8 prediction al gorithm Reduction to a single critical variable and stability results NZ Journal of Geology and Geophysics 46 1 141 152 URL http www rsnz org publish nzjgg 2003 010 php Harte D Li D F Vere Jones D Vreede M amp Wang Q 2007 Quantifying the M8 algorithm Model forecast and evaluation NZ Journal of Geology and Geophysics 50 2 117 130 URL http www rsnz org publish nzjgg 2007 012 php Keilis Borok V I and Kossobokov V G 1990 Premonitory activation of earthquake flow al gorithm M8 Physics of the Earth and Planetary Interiors 61 73 83 URL http dx doi org 10 1016 0031 9201 90 90096 G Kossobokov V G 1997 User manual for M8 In Algorithms for Earthquake Statistics and Prediction International Association of Seismology and Physics of the Earth s Interior IASPEI 4 decluster M8 Library Volume 6 Pages 167 222 Edited by J H Healy V I Keilis Borok and W H K Lee TASPEI Menlo Park CA Li Dongfeng 1997 M8 Splus Documentation Internal Report Institute of Statistics and Oper ations Research Victoria University of Wellington Ma L and Vere Jones D 1997 Application of the M8 and L
11. curred TIP t ype is set to CTIP continuing TIP Value A list object with the same components as that returned by M8 series but with the additional variables MR TIP 13 tops is arts with n rows and 7 columns It contains the historical top 10 percent for the first 6 series or 25 percent of values for the 7th series for each 6 month interval The percentile depends on the training mode exceeds is arts with n rows and 7 columns It is logical indicating whether each series exceeds the relevant historical percentiles for each six month interval TIP is a logical variable indicating whether a TIP is declared in each 6 month inter val see Y J in Details TIP type classifies the TIPS with the following character strings c e earthquake caused that is large earthquake gt Mo in the preceding year of the TIP declaration STIP successful warning large event occurred in the 5 year period after declaration FTIP failed warning large event did not occur in the 5 year period after declaration CTIP current warning not 5 years past since declaration STIP between STIP and FTIP strictly speaking is FTIP i e event with magnitude greater than or equal to My 0 5 occurred in the 5 year period TIP level is a number between 0 9 and 0 1 and is also referred to as the critical series see W JJ in Details Two consecutive positive values of TIP 1level is equivalent to a TIP g is th
12. e number of different types of measures exceeding their critical value in the last 3 years h is the number of measures exceeding their critical value in the last 3 years Author s Li Dongfeng 1997 modified by Maaike Vreede 1998 See Also decluster M8 M8 M8 series Examples Requires the package ssNZ require ssNZ as catalogue subsetrect NZ minday julian 1 1 1965 maxday julian 1 1 2000 minmag 4 5 catname NZ45 decluster M8 NZ45 cutoff mag 4 5 decluster name NZ mainshocks templ lt M8 series NZ mainshocks MO 7 0 minday julian y 1965 x 1 d 1 start series julian y 1975 x 1 d 1 centrelong 176 centrelat 39 end training julian y 2000 x 1 d 1 temp2 lt M8 TIP templ MO 7 0 end training julian y 2000 x 1 d 1 print cbind time templSseries time TIP temp2STIP TIP type temp2STIP type TIP level signif temp2 TIP level digits 3 quote FALSE 14 plot M8 plot M8 Plot MS Series Description Plot the seven M8 series plus the eighth critical series Usage S3 method for class M8 plot x title M8 Series and TIPs Arguments x a list object produced by the function M8 TIP title a title to be placed at the top of the matrix of eight graphs other options for formatting datetimes objects Details This produces a 4 x 2 grid of graphs The first seven are graphs of the seven series and the eighth is the critical series When the trai
13. entation consistent with Harte et al 2003 17 Feb 2005 18 M8 TIP method of calculating the quantiles in variable tops incorrect redone using the function quantile Values of g and h included in output list object Variable initialisation rewritten Code included to calculate TIP level when training moving previ ously not working for this option 24 Mar 2005 19 emp cdf completely rewritten see documentation 11 Apr 2005 20 Old package stepfun not now required Part of base 19 Apr 2005 21 decluster M8 on manual page units added for space and time windows 9 Jul 2006 22 All occurences of subset rect in the Examples have been changed to subset rect See Changes in ssBase 8 Nov 2007 23 ssNZ added to Suggests in the DESCRIPTION file Corresponding changes made to ex amples on manual pages 10 Jan 2008 24 Use of require ssNZ in examples made consistent with package ssEDA 28 Jan 2008 25 References updated below 28 Jan 2008 26 Package vignettes added 28 Jan 2008 27 Removal of LaTeX markups from DESCRIPTION file 31 May 2009 28 Minor manual page changes to conform to R 2 10 0 13 Nov 2009 29 M8 TIP called a function st opt mp non existent changed to stop 13 Nov 2009 30 timegrid internal function not used deleted 17 Nov 2009 31 Changes correct hyperlink from package vignettes 11 Feb 2010 32 Add CITATION file 24 Sep 2010 References Harte D 1998 Do
14. ibution function of the mth series Then 100 U J is the percentile value corresponding to the series value Fm J 2 Find the maximum for each in the preceding 3 years i e Vin Ji max Um Ji Um Ji 1 maa Um Jes 3 Now let Vig J denote the second smallest of the six values V J Ve J Then the TIP level is defined as W J min Vig Ji 0 9 V7 J 0 75 We refer to W J as the critical series see Harte et al 2003 Values are listed in the output object as TIP level A TIP is declared if W J gt 0 for two consecutive intervals Hence by letting Y Ji mint W Ji 1 W Ji a TIP is declared in time interval J if Y J gt 0 and then the value of TIP in the output object is TRUE otherwise FALSE The duration of a TIP is specified by the argument TIP length which is 5 years by default If an earthquake with magnitude greater than or equal to the target magnitude occurs the character variable TIP type is set to STIP successful TIP If an earthquake with magnitude smaller than Mo but gt Mp 0 5 occurs TIP type is set to STIP nearly successful TIP If the TIP is triggered by an earthquake with magnitude greater than or equal to the target magnitude TIP type is set to c e If no earthquake with magnitude gt M occurs TIP t ype is set to FETIP false TIP and if the 5 year duration of the TIP has not come to an end and no earthquake gt Mo has oc
15. in Lin algorithms to New Zealand Earthquake data NZ Journal of Geology and Geophysics 40 77 89 URL http www rsnz org publish nzjgg 1997 7 php decluster M8 Decluster Catalogue Using M8 Method Description The function reads an earthquake catalogue with class catalogue deletes events with mag nitude below a cutoff level and all aftershocks optionally deletes events with depth too deep or too shallow and counts the number of aftershocks in the 14 days following each remaining mainshock The output is also a catalogue object containing the mainshock information and an additional variable with the corresponding number of aftershocks Usage decluster M8 catalogue cutoff mag 4 minday min catalogueStime mindepth Inf maxdepth Inf debug FALSE decluster name magn window c 3 3 5 4 4 5 5 5 5 6 6 5 7 7 5 8 space window c 30 40 40 40 50 50 50 100 100 150 200 time window c 6 11 23 46 91 183 183 365 730 913 1096 Arguments catalogue the catalogue It should be a catalogue object decluster nam character string containing the name of the declustered catalogue cutoff mag he magnitude below which the record is cutoff before going through the mainshock aftershock separation Default 4 0 minday number of days from 1 January 1970 julian If specified then after main shocks have been separated out mainshocks before this date are dropped If not specified n
16. julian 1 1 2000 minmag 4 5 catname NZ45 decluster M8 NZ45 cutoff mag 4 5 decluster name NZ mainshocks temp lt M8 series NZ mainshocks MO 7 0 minday julian y 1965 x 1 d 1 start series julian y 1975 x 1 d 1 centrelong 176 centrelat 39 end training julian y 2000 x 1 d 1 print temp series M8 TIP M8 Times of Increased Probability Description Calculates the times of increased probability for the M8 Algorithm Usage M8 TIP series MO training user end training NA smoother 6 TIP length 10 debug FALSE Arguments series a list object produced by the function M8 series MO numeric The aim of the algorithm is to predict earthquakes with a magnitude greater than or equal value to this value training has three possible modes moving user and all See Details in M8 series for further explanation end training Julian date for the end of the training period This date should be the end point of a bin This is only used when the training mode is user smoother integer denoting the length of the smoothing window The series are smoothed at a given point by taking their maximum value over previous values within this window The default value is 6 i e three years TIP length 19 the duration of the TIP or Time of Increased Probability The M8 default is 5 years i e 10 time intervals and is independent of MO debug logical The default is FALSE
17. ls in M8 series for an explanation of how the M8 series are calculated and M8 TIP for how the Times of Increased Probabilities are calculated Value The same object as that returned by the function M8 TIP Author s Li Dongfeng 1997 modified by Maaike Vreede 1998 See Also decluster M8 M8 series M8 TIP Examples M8 series Calculates the Seven M8 Series Description This functions calculates the seven time series of the M8 Algorithm MS8 series Usage M8 series catalogue M0 centrelong mean catalogue longitude centrelat mean catalogue latitude radius radius M8default M0 minday catalogue 1l time start series datetimes year yearsl minday 12 month 1 day 1 hour 0 minute 0 training user end training NA time breaks Inf running total 12 debug FALSE Arguments catalogue MO centrelong centrelat radius minday start series training end training time breaks the mainshock catalogue created by the decluster M8 function with the number of aftershocks in following 14 days numeric The aim of the algorithm is to predict earthquakes with a magnitude greater than or equal value to Mo longitude of the centre of the circle of interest latitude of the centre of the circle of interest circle of interest radius The default radius is 55 5 exp Mpo 5 6 1 Julian date events earlier than this are not used in analysis By default all the da
18. me of Increased Probability or TIP is declared This means there is an increased probability of an earthquake of or greater than Mo in the next 5 years Details for the calculation of the seven series can be found in under M8 series and details for the calling of a TIP can be found under M8 TIP Li 1997 converted the original M8 FORTRAN code in Kossobokov 1997 into S PLUS which was then included into the Statistical Seismology Library Harte 1998 Ray Brownrigg subse quently packaged it into R Analyses using the M8 Algorithm applied to New Zealand data have been carried out by Ma amp Vere Jones 1997 Harte et al 2003 and Harte et al 2007 This page contains a listing of recent changes made to functions and known general problems Details 1 decluster M8 The line near the bottom within an else loop class minday lt datetimes has been commented March 2002 2 plot M8 Main title now uses default cex main vertical lines t ype h have been removed horizontal reference line changed to dashed 1t y 2 colours removed from plotted symbols and 8th graph plots only critical series January 2003 3 Occurrences of T and F have been changed to TRUE and FALSE respectively January 2003 4 M8 TIP When training moving the line TIP type 1 7 lt NA has been changed to TIP type 1 7 lt When training user training all the line TIP type 1 lt NA has been ch
19. ning mode is not moving the 90th and 75th percentiles for the first 6 and 7th series are plotted respectively These percentiles represent the thresholds for each of the seven series When the training mode is moving the threshold values are not constant over time and are not plotted The plot of the critical series has a reference line marked at zero A TIP is called if this series exceeds zero in two consecutive time periods Points are marked on all plots where a TIP is in effect the symbols having the following interpretations e Successful TIP STIP pch 5 e Near Successful TIP STIP pch 2 e False TIP FTIP pch 4 e Continuing TIP CTIP pch 3 s TIP caused by quake of target magnitude c e pch 0 Note that the plotting symbols may be different on different plotting devices see the argument pch in the graphics function par Value NULL Author s Li Dongfeng 1997 modified by Maaike Vreede 1998 See Also M8 M8 series M8 TIP plot M8 15 Examples Requires the package ssNZ require ssNZ as catalogue subsetrect NZ minday julian 1 1 1965 maxday julian 1 1 2000 minmag 4 5 catname NZ45 decluster M8 NZ45 cutoff mag 4 5 decluster name NZ mainshocks temp lt M8 NZ mainshocks MO 7 0 minday julian y 1965 x 1 d 1 start series julian y 1975 x 1 d 1 centrelong 176 centrelat 39 end training julian y 2000 x 1 d 1 plotit FALSE savpar lt pa
20. o mainshocks are dropped mindepth all events with depth less than mindepth are deleted before entering algorithm Default is Inf maxdepth all events with depth greater than or equal to maxdepth are deleted before enter ing algorithm Default is Inf magn window a vector giving the magnitude window boundaries The default c 3 3 5 4 0 Aaby 5 0 3535 6 0 6 5 7 0 7 9 8 0 time window a vector giving the time window boundaries days The default is c 6 11 23 46 91 183 183 365 730 913 1096 space window a vector giving the space window boundaries km The default is c 30 40 40 40 50 50 50 100 100 150 200 debug boolean default is FALSE emp cdf 5 Details All events with magnitude less than magn window 1 are assumed to have no aftershocks Those events with magnitude less than magn window i 1 but greater than or equal to magn window i have aftershock time and space windows given by time window i and space window i respectively fori 1 length magn window 1 All events with magnitude greater than or equal to magn window length magn window have aftershock time and space windows given by time window length magn window and space window length magn window respectively Value The value returned is the vector identifying the mainshock to which each aftershock belongs The mainshocks themselves are identified by zeros A catalogue object with name given
21. r no readonly TRUE plot temp title M8 Analysis of NZ events par savpar Index Topic distribution emp cdf 5 Topic documentation Change Log 2 Topic hplot plot M8 14 Topic methods plot M8 14 Topic ts decluster M8 4 M8 7 M8 series 8 M8 TIP 11 Change Log 2 Changes 3 Changes Change Log 2 decluster M8 2 3 4 7 10 13 ecdf 6 emp cdf 3 5 in circle 2 M8 5 7 10 13 14 M8 series 2 3 5 7 8 8 9 11 14 M8 TIP 2 3 5 8 10 11 12 14 par 14 plot M8 2 5 7 14 prt mainshocks 2 quantile 3 5 6 stop 3 subsetrect 3 sumrow 2
22. ta are used Julian date of end point of the first bin from which the series are generated Since the series are calculated using bins defined by time breaks the start series must coincide with an end point of one of the bins The M8 default is six month bins has three possible modes moving user and all See Details in M8 series for further explanation Julian date for the end of the training period This date should be the end point of a bin This is only used when the training mode is user a vector of Julian dates that give the bin boundaries for calculating the series The M8 default bin length is 6 months Care must be taken that the arguments minday start series and end training coincide with a breakpoint in the vector time breaks The breaks should also be at regular intervals running total debug Details by default the series are calculated with a six year running total i e 12 half years thus the M8 default is 12 Gl logical The default is FALSI Initially a training period is defined This period is used to estimate various magnitude cutoffs described below Three time points are specified in the arguments to this function minday lt start series lt end training Further there are three possible training modes usr the training period starts at start series and finishes atend training moving the training period starts at minday and finishes on the date of the last event in the
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