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Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting

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Open Geosciences
Authors:
  • Formely Geoscientist, Geological Survey of India & HEAD, GDD, SAARC Disaster Management Centre, New Delhi

Abstract and Figures

In the proposed study, non-linear behavioral patterns in the seismic regime for earthquakes in the Himalayan basin have been studied using a complete, verified EQ catalogue comprised of all major events and their aftershock sequences in the Himalayan basin for the past 110 years [1900–2010]. The dataset has been analyzed to give better decision making criteria for impending earthquakes. A series of statistical tests based on multi-dimensional rigorous statistical studies, inter-event distance analyses, and statistical time analyses have been used to obtain correlation dimensions. The time intervals of earthquakes within a seismic regime have been used to train the neural network to analyze the nature of earthquake patterns in the different clusters. The results obtained from descriptive statistics show high correlation with previously conducted gravity studies and radon anomaly variation. A study of the time of recurrence of the numerical properties of the regime for 60 years from 1950 to 2010 for the Himalayan belt for analysis of significant EQ failure events has been done to find the best fit for an empirical data probability distribution. The distribution of waiting time of swarm events occurring in the Himalayan basin follows a power-law model, while independent events do not fit the power-law distribution. This suggests that probability of the occurrence of swarm events [M ⩽ 6.0] with frequent shaking may be more frequent than that of the occurrence of independent events of magnitude [M >6.0] in the Himalayan belt. We propose a three-layer feed forward neural network model to identify factors, with the actual occurrence of the maximum earthquake level M as input and target vectors in Himalayan basin area. We infer through a series of statistical results and evaluations that probabilistic forecasting of earthquakes can be achieved by finding the meta-stable cluster zones of the Himalayan clusters for the spatio-temporal distribution of earthquakes in the area.
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Cent. Eur. J. Geosci. 5(2) 2013 236-253
DOI: 10.2478/s13533-012-0127-6
Central European Journal of Geosciences
Evaluation of seismogenesis behavior in Himalayan
belt using data mining tools for forecasting
Research Article
Pushan Kumar Dutta1,2, O. P. Mishra3, Mrinal Kanti Naskar1,2
1 Advanced Digital Embedded System Lab, Jadavpur University, Kolkata, India
2 Electronics and Communication Dept., Jadavpur University, Kolkata, India
3 SAARC Disaster Management Centre [SDMC],New Delhi, India
Received 13 March 2013; accepted 15 May 2013
Abstract: In the proposed study, non-linear behavioral patterns in the seismic regime for earthquakes in the Himalayan basin
have been studied using a complete, verified EQ catalogue comprised of all major events and their aftershock
sequences in the Himalayan basin for the past 110 years [1900-2010]. The dataset has been analyzed to give
better decision making criteria for impending earthquakes. A series of statistical tests based on multi-dimensional
rigorous statistical studies, inter-event distance analyses, and statistical time analyses have been used to obtain
correlation dimensions. The time intervals of earthquakes within a seismic regime have been used to train the
neural network to analyze the nature of earthquake patterns in the different clusters. The results obtained from
descriptive statistics show high correlation with previously conducted gravity studies and radon anomaly variation.
A study of the time of recurrence of the numerical properties of the regime for 60 years from 1950 to 2010 for
the Himalayan belt for analysis of significant EQ failure events has been done to find the best fit for an empirical
data probability distribution. The distribution of waiting time of swarm events occurring in the Himalayan basin
follows a power-law model, while independent events do not fit the power-law distribution. This suggests that
probability of the occurrence of swarm events [M 66.0] with frequent shaking may be more frequent than that of
the occurrence of independent events of magnitude [M >6.0] in the Himalayan belt. We propose a three- layer
feed forward neural network model to identify factors, with the actual occurrence of the maximum earthquake
level M as input and target vectors in Himalayan basin area. We infer through a series of statistical results and
evaluations that probabilistic forecasting of earthquakes can be achieved by finding the meta-stable cluster zones
of the Himalayan clusters for the spatio-temporal distribution of earthquakes in the area.
Keywords: Himalayan belt seismic cycle seismic precursor power law model meta-stable cluster zone Neural Network
Model trends variation of seismicity
©Versita sp. z o.o.
E-mail:ascendent1@gmail.com
E-mail:opmishra2010.saarc@gmail.com
E-mail:mrinalnaskar@yahoo.co.in
1. Introduction
ThestudyofEQgenerationmechanismshasbeenapuz-
zlefortheentiregeo-scientificcommunitydespiteaseries
ofstudiesinthefieldofseismologyindifferentpartsof
theglobe.EQtremorshavebeenmonitoredinSouthAsia
236
P. K. Dutta, O. P. Mishra, M. K. Naskar
Figure 1. Geological map of North East India and Indo Burma Plane
after Mishra [2011].
andrecordedEQsFig.1forvariousspatio-temporalmap-
pinghavebeenfoundsubjecttoregionaltectonicsettings
reportedin[55].Aconcentratedefforttostudyspatialand
temporalvariationsinseismicactivityandusethemtorec-
ognizepatternsthatprecedelargeearthquakeshasbeen
madebyscientiststoidentifyprecursorypatterns[50,52],
seismicquiescence[30,36],swarmsinseismicactivityan-
alyzedby[31,32,83]andseismicityfluctuations[35,37].
Ongoingresearchinto earthquake processcanonlybe
improvedby thestudyof measurements ofpastearth-
quakesandsurfacedeformation. Ahighlysophisticated
statistical interpretation of instrumental, historical and
paleo-earthquakecatalogsaretheonlysystematicrecords
whichanalyzetheearthquakegenerationprocessatdepth
throughimagingtectonicenvironments. Statisticalanal-
ysisisonemethodofpredictingearthquakes. Thehis-
toryofearthquakesinagivenregionrevealsthepropen-
sityforrecurrent,orcyclical,patternsoftheearthquakes.
Ifearthquakes in agivenregionhave arecurrentpat-
tern,thenalong-termpredictioncanbemadebasedon
therecurrentpattern. Importantquestionsthatneedto
beansweredinordertounderstandtheearthquakepat-
ternsinHimalayasinvolvethestudyofformationandin-
teractionofearthquakeclusterssuchasforeshocks, af-
tershocksandearthquakeswarms[25],theroleoffluids
intheearthquakegenerationprocess[59], the study of
gravityrecordsinthestudyofrocklayerdepthswhere
earthquakesoriginate [43] andlocalizedseismicquies-
cence[85].Althoughevaluationofthelinksbetweenpre-
cursiveeventsandearthquakeshasprogressed,theex-
tremecomplexityofthesystemhassofarnotenabledthe
developmentofactualearthquakeforecastingtechniques.
Thesolutiontothisproblemdependsprimarilyonwhether
wecanobtainreliableinformationonseismicprecursory
events[72,74]andtheirbehaviorinconnectionwithphys-
icalmechanisms. Thedetectionofaprecursoryseismic
signal[73]conformstocommonphysicalmodelsforde-
tectionofanomalieswithintheseismogeniccrustwhere
earthquakeprecursoryactivity is likelytooccur. Time
delaysbetweensuccessiveearthquakeshaveacharacter-
isticdistributionforintereventdistributionforearthquake
analyzeddata[18,58]inadenselymonitoredearthquake-
proneregion.Earthquakepatternstendtofolloweithera
mainshock,aftershocksequenceorformswarmtypeearth-
quakeclusters[46]. Inordertoinvestigatethepotential
occurrenceofprecursorsandseismiccyclesinthe,the
natureofthegenerationmechanismassociatedwiththe
statisticaldistributionofearthquakeoccurrencehastobe
formulated. Awiderangeofstatisticaldistributionscan
beusedwithessentiallynophysicaljustificationunless
anaturalmodeforpower-lawdistributionsis made for
earthquakehazardassessments[29].Thepowerlawsand
fractalpropertiesreflectthenotionofscaleinvariance[33]
thatreferstothespontaneousbreakdownofafracturefor
discretetimeperiodsforEQoccurrence.Theseproperties
areimportantandinterestingbecausetheycharacterize
systemswithmanyrelevantscalesandlong-rangeinter-
actions[70,71]ofthefaultsastheypotentiallyexistinthe
crustbeforetheoccurrenceofEQ.Intheproposedwork,
weintegrateallsuchstudiestounderstandthenatureof
seismicityintheHimalayanbelt. InSection2,weana-
lyzethecatalogtostudythespatio-temporalclusters
oftheHimalayanBasintolocateclusterswhereanoma-
lousclusteringofseismicactivityincreaseoccursinthe
region. InSection3, aprobabilitydistributionanalysis
involvingrecurrencetimeofEQfortemporalclusterse-
quenceshasbeenmadetostudythemaximumlikelihood
estimatorsforfittingthepower-lawdistributiontotimeto
studytherecurrenceintervaloftheEQdataalongwith
thegoodness-of-fitbasedapproachinthepower-lawfit
withintheclustersforindependentmainshocksandswarm
activity. InSection4,wecomparethestatisticalresults
withprecursorydatastudiesforthedescriptivestatistics
involvedinEQcataloganalysispreviouslyconducted. In
Section5,ananalysisofourresultshasbeenpresented
forfuturestudies.
2. Seismological Data and Statisti-
cal Analyses
TheHimalayanbeltisoneofthemostseismicallyactive
zonesinAsia,whichwitnessedaseriesofdeadlyearth-
quakes[EQ]inthepastcentury.Inthepresentstudy,we
analyzedacompleteEQcatalogueconsistingofallmajor
eventsandtheiraftershocksequencesintheHimalayan
basinforthepast110years[1900-2010]. Thecatalogue
forourcomprehensiveearthquakeanalysesistakenfrom
therecentlyproducedcatalogueofNathetal.[2010]that 237
Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting
Figure 2. Frequency of earthquake occurrence in Himalaya Belt.
containedseismicallymonitoredearthquakedatarecorded
duringtheyears1900-2010byvariousagenciesofthe
entireSouthAsia,whicharestatisticallyanalyzedinthis
studytounderstandthenatureandextentofseismoge-
nesisintheHimalayanbasin. Wehavecorrelatedour
resultswithotheravailablepublishedinferencestounder-
standthenatureofearthquakeswarmsandclusters[47].
InFigure2,weattemptedtoshow thecompletenessof
theearthquakedatawhichhasbeenusedinthisstudy.
Yearwiseearthquakecompletenessanalysesshowedthat
earthquakecatalogueduringtheyear19001950iscom-
pleteforthemagnitude[5.0>M>2.0]&[2.0>M<2.5]
during the year1950-2010. However, completenessof
earthquakedatafromoverallcataloguesuggeststhatit
is complete forthe eventsof magnitudes, varyingfrom
2.0to6.0[Figure3]. Figure4clearlydemonstratesthat
theoccurrenceofearthquakes[M>2.0]isdrasticallyin-
creasedduringtheyear20002010incomparisonto
pastdecades[19501999]. Thisobservationsuggests
thattheseismicactivityintherecentdecadeshasbeen
enhancedbecauseoffrequentreleaseof strainbeneath
theHimalayanbasincausingfrequentshakingduetomi-
crotomoderateearthquakes[M66.0]intherecentyears
fortheHimalayanregion.TheEQCatalogofNathetal,
2010hasbeentestedfordetaileddatafitandcanbeused
toconductapatternanalysisofseismiccycle.
ThenatureofseismogenesisintheHimalayanbasinas
hasbeen doneinother zones [7,24,41]. Inorderto
conductaseriesofstatistical analyses, ahomogeneous
datafitcatalogueisnecessarytoevaluatetheseismo-
tectonicenvironmentintheHimalayanregion. Thedata
setof4125eventsofthepast60yearscomprisesofmain-
shock,aftershockandforeshockeventsoccurringacross
variousspatial and temporalzones. Adescriptivehis-
Figure 3. Frequency Magnitude relationship of earthquakes(Y axis
number of earthquakes and X axis mag >2.0).
Figure 4. Histogram plot showing completeness of catalog and
earthquake mainshocks >5.0 in 1950 2010 for the hi-
malayan basin(Y axis as magnitude and x axis as Year).
togramplot[Fig.2]ofallmagnitude[>5.0]showsthatthe
frequencyofoccurrenceofEQsintheHimalayanbelthas
increasedoverrecentyears[51]. Thecumulativemagni-
tudeoftheEQshasbeenparticularlylowduringthepast
coupleofyears. ThenumberofEQswasonadecline
during 1960-70s after which the histogram plot shows
thatthenumberofEQshasbeen constantly rising al-
thoughtheyarescatteredinnature.Thisissignificantto
thepreviouslyconductedstudythatprovesthattheHi-
malayanearthquakeshavebeenmoderateinnature[4].
InordertostudyEQgenesisrelevanttoacertainregion,
238
P. K. Dutta, O. P. Mishra, M. K. Naskar
westudytheoccurrenceofEQsinthedifferentspatio-
temporalclustersoftheHimalayanbelt. Itisnecessary
toevaluatethespatio-temporalclustersofseismicityin
theHimalayanbasinbylookingatthe pastoccurrence
ofthesignificantEQsfromtheEQcatalog[Fig.2]that
hadasevereimpactonthetectonicsettings.Inthisstudy
weupdatethenumberofEQsasspecifiedinthespatio-
temporalclustersandconductaseriesofstatisticaland
analyticaltestsontheseclusters. Analyzingthepattern
ofearthquakeswithineachcluster,asignificantobserva-
tionestablishes[53,63]thattheclustersareconstituted
ofindependenteventsaswellasswarmsequenceandin
studyingtheircombinations we canfindaboutthena-
tureofseismiccyclesandthepatternof seismogenesis
intheHimalayas. AsthesetofreliablequantitativeEQ
catalogueshavingcompletecatalogueinformationforall
historicaleventsareverylimited,weneedtoanalyzeto
identifythebestdatasets[Fig.3] avalaible. Wehave
maderigorousstatisticalinvestigationsusingtheSPSS
toolforunderstandingthefrequencydistributionsofEQs
from1950to2010tosearchforEQhavingmagnitude>
5.0fromnEQcataloguetounderstandthenatureofEQ
patterns.Recurrenceintervalsareameansofexpressing
thelikelihoodthatagivenmagnitudeofearthquakewill
beexceededinaspecifiednumberofyearsandareanim-
portantfactorinanalyzingthehumanrehabilitationand
generalseismicresponsemechanismasin[38]. Differ-
entseismogenicfeaturesaffectthekindofseismicrelease
fortheEQdepending ontheclusteredandbackground
seismicity[2]andcanbeusedtodescribetheseismicity
ofanareainspace,timeandmagnitudedomainsandto
studythefeaturesofindependenteventsandstronglycor-
relatedones,separately.Thetwodifferentkindsofevents
givedifferent informationonthe seismicity ofanarea.
Fortheshort-term[orreal-term]predictionofseismicity
andtoestimateparametersofphenomenologicallawswe
needagooddefinitionoftheEQclusters. Metastable
clustersorblockscascade[56]orcoalescetogeneratea
largeeventinwhichlargenumberofmetastableblocks
arelost[26,57,64,65]whichexhibitsapower-lawcoa-
lescenceofmetastableclusterswhosenumber-sizedistri-
butionofclustersispowerlaw. Recurrenceintervalsare
meansofexpressingthelikelihoodthatagivenmagnitude
EQwillbeexceededinaspecifiednumberofyears[40].
Thusouraimistostudythespatialclustersandthena-
tureofoccurrenceofforeshockandaftershocktremorsto
identifythenatureofmainshockoccurrencesinorderto
locatefutureEQevents. Identifyinglikelysourcezones
ofsuchearthquakeswouldlargelycontributeinseismic
hazardassessmentindifferentspatio-temporalclusters
inHimalayanbasin. Frequencymagnituderelationships
for4125eventsofMw>3.0werecalculated.Itwasfound
Figure 5. Logarithmic plot of the magnitude of earthquakes for n
number of events of earthquake.
thatthecatalogiscompleteabovemagnitude2[Fig.4]
whichwasthecutoffmagnitudetakenforfurtheranaly-
sis. Theestimationoftheparametersofseismicregime
wascarriedoutfromthis“cleaned”catalogue. Thestudy
hasbeendonebystudyingoccurrencesoffrequentEQs
aboveacertainthresholdiftherearemultipleeventshav-
ingspatial,preferreddistributionwithinaspecifiedpe-
riodoftime[45]. A study ofthecomplexseismicityof
theHimalayanregionbythestatisticalanalysisofhis-
toricalEQdataisineffectivewithoutthepriorcarecon-
cerningthecompletenessofhistoricalcataloguesusedin
themodeling[39]. AstudyoffrequencyoftheEQmag-
nitudes[Fig.2] over the entirepopulationrevealshigh
homogeneityofdatasets.Thecataloguehasahighrate
ofhomogeneityandfollowsthegenericMscaleframe-
worknecessarytocalculateintermagnitudeandtimeof
recurrencerelationships[10].
It has been accepted that earthquakes generally obey
Gutenberg–Richterscaling[19]. Apower-lawdecayfor
thecorrelations as afunctionoftimetranslates into a
power-lawdecayofthespectrumasafunctionfrequency.
Intheseperiodsoftime,thefunctionN[>φ]followsthe
powerlaw. N(>)-bN[>φ](1)
The slope of log-linear portions in daily distributions,
whichdeterminesthepowerexponentinequation[1]drops
duringfaulting[15]anditgrowsagainaftertheevent.The
parameterdependson
therelativeamountoflowandhigh-energyevents[the
lower,the larger the contribution ofpowerfulevents]
anditsdecreasesignalstheinvolvementofmoreimpor-
tanteventsinthefractureprocess.Thisisexplainedusing
thelogarithmicplotformagnitudeMforNevents. The
natureofthepowerlawdecayplotiscorrelatedwiththe
empiricaldataoftimerecurrencedistributionforwhich
distributiondecaysexponentially[34]Thismeans,forin-
stance,thatthereoccurlotsofsmallearthquakes,buta 239
Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting
fewbigones. Ifweconsiderearthquakesofaparticu-
larmagnitude,thereare4timesasmanywith1/2that
magnitude,anda1/4asmanywithtwicethemagnitude.
Earthquakesthataretimesaslargeintermsofenergy
comparedtoearthquakeswhosemagnitudeissmallare
alsorarerbyafactorof1/2wasshownbytheseismol-
ogistsGutenbergandRichterassimulatedinFig.5. The
exponentvariesfromonephenomenontoanother,butin
allcasesthepowerlawmeanstheeventshavenotypical
size,anditsuggeststhatallevents,largeandsmall,have
thesamecause. Thiskindofscalingappearsinnatural
systemsthatarepoisedontheedgeofchangeorinacrit-
icalstate[13]andsuchcriticalstatesseemtoarisenatu-
rallyinmanycomplexsystems.Thecumulativenumberof
earthquakesinaregionwithmagnitudesgreaterthanor
equaltoM,isrelatedtoM[28]. Usingthisobservation
analternativeapproachforthestudyofmainshockevents
hasbeenobservedforexaminingthecumulativeproba-
bilitydistributionofEQrecurrencetimefor seismically
activeEQs[Fig.5]. Westudytheoverallcharacteristics
ofthetemporalclustersinthemodelandinter-occurrence
timeintervalsbetweenevents[26]. Itisfoundthatdistri-
butionofearthquakesizefulfilsapowerlaw.Increaseof
foreshockanddecayofaftershockactivityvarieswithtime
distributionbutforanyeventrupturesizeishighlydepen-
dentonthemainshockmagnitudewhosedissipationrates
aredependentonthesizeoftherupturezone. Thiswill
shedlightonthenatureofseismicclustersfortheregion.
Onepossibleconfoundingeffectintheforegoinganaly-
sisistheunevendistributionofeventsizesinthedataset.
Thisdistributionisatypicalofearthquakecatalogs,inthat
thenumberofeventsislimitedbothonthehighenddue
tothesmallnumberofeventsatlargemagnitudes,and
atthelowendduetothedearthofsmalleventswhich
arewell-recordedenoughtobemodeled. Thephysical
significanceofthespatio-temporalstatisticalanalysesof
theseismicityintheHimalayanbasinprovidesabetter
insightintothenatureandextentofearthquakedistribu-
tionanditsbearingonthesub-surfacestructuralhetero-
geneitiesinrelationtodifferentialstrainaccumulationin
thesub-surfaceseismogenichostrocks.
Wecheckforthecumulativenumberofeventsassociated
withineachclustertoassessthefrequencyofshockoc-
currenceineveryclustersandhowvariationsarebound
toexistsignificanttoeachclusterblock.
We then analyze the cumulative distribution of earth-
quakesforeachclustershowingthetotalnumberofEQsin
theperiod1950–2010againstclusters[Fig.7].Thecluster
patternintheeightzonesrevealstemporal–spatialasso-
ciationofearthquakes[Table2].Between1964and2006,
Kashmircluster[A]experiencedthemaximumnumberof
earthquakes[250]havinganaveragemainshockperiodof
Figure 6. Spatio-temporal clusters outlined in black [A, B, C, D,
E, F, G and H] in Lesser Himalaya. The name of the
clusters are AKashmir, BKangra, CGarhwal, D
Kumaun–West Nepal, EEast Nepal, FSikkim, G
Bomdila and HEastern Syntaxis. Note the inter-
action between Himalayan Thrust planes [MFT-MBT-
MCT] and Peninsular crosscutting faults [RFRopar
fault, MDFMahendragarh–Dehradun Fault, GBFGreat
Boundary Fault, WPFWest Patna Fault, EPFEast
Patna Fault, MSRMFMunger Saharsha Ridge Marginal
Fault, MKFMalda-Kishanganj Fault and BFBomdila
Fault]. MFTmain frontal thrust, MBTmain bound-
ary thrust, MCTmain central thrust, ITSIndus-Tsangpo
Suture, JamJammu, SiSimla, LeLeh, DdDehra
Dun, NdNew Delhi, JaiJaipur, AllAllahabad,Sh
Shillong.Cluster Analysis AKashmir, BKangra, C
Garhwal, DKumaun–West Nepal, EEast Nepal, F
Sikkim, GBomdila and HEastern Syntaxis from
[Mukhopadhay et al, 2010 Fig. 1].
Table 1. Depth [km] distribution of the EQ epicenter in eight cluster
zones in Lesser Himalaya.
Cluster Numberof
mainshock
EQ NumberofEQ
[45kmdepth] Recurrence
time
tillnextEQfor
largestshock
[indays]
A
B
C
D
E
F
G
H
250
74
46
94
46
54
82
12
12
13
08
14
3
12
18
03
295
836
76
283
173
233
171
474
295daysbetweenlargesteventsofMag>4.5followedby
Kumaun–WestNepal[clusterD,74]andBomdila[cluster
G,82]sufferingmilderevents. WhileEasternSyntaxis
[clusterH]containsonly12events,theotherfourclus-
ters,Kangra[B,74],Garhwal[C,47],EastNepal[E,28]
and Sikkim [F,54], have amoderatenumber ofevents.
ClusterChoweveristhemostreactiveregionamongall
thefactionshavingshownageneraltendencytoproduce
eventsinthespanof76days. Analyzingthepatternof
earthquakeswithineachcluster,it isapparentthatthe
240
P. K. Dutta, O. P. Mishra, M. K. Naskar
(a) (b)
(c) (d)
(e) (f)
(g)
Figure 7. Distribution of earthquake mainshock occurrence in the various clusters[A,B,C,D,E,F,G].
clustersareconstitutedofindependenteventsaswellas
foreshock-mainshock-aftershock[FMA]sequenceandits
combinations.
Aftermakingasetofrigoroustesttoobservecharacter-
isticsoftemporalsequencesandindependenteventsin
theclusterzones,thedatashowsimportantvariationsto
revealthenatureofseismiceventoccurrenceandassoci-
atedpatternsuniquetotheclusterintheHimalayanbelt.
Havinganalyzedthepatternofearthquakeswithineach
cluster,theclustersareconstitutedofindependentevents
241
Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting
Figure 8. Analysis of events in the various cluster zones
[A,B,C,D,E,F,G,H] as from Fig. 5.
aswellasFMAsequenceanditscombinationsandhigh
swarmactivity[Table1].Intheclusters,earthquakesthat
formcompleteFMAsequenceoranycombinationofFMA
areplacedintemporalsequence,whereastheeventsthat
donotregistertoanyforeshock[FS]and/oraftershock
[AS]are treated asindependenteventswhile anevent
whichcomprisesoflocalized tremors of uniformmagni-
tudeshow swarm activityandwillbedemonstrated as
suchinFig.8. Thecharacteristicsoftemporalsequence
andindependenteventsintheclusterzonesshowinter-
estingvariations. Itisnoteworthythatinalltheclus-
ters,therearemoreindependenteventsthantheearth-
quakesclassifiedundertemporal [FMA] sequences [Ta-
ble4aand4b].Theonlyexceptionisthe‘clusterA’that
hasmoreeventsinFMAsequenceduetoKashmirearth-
quakeof08.10.2005[Mw7.6]with1FSand211AS.The
magnitudesof‘individualearthquakes’varyfrom4.5to5.8
inalltheclusters,apartfromahighermagnitudeevent
ofMw6.1[01.06.2005]inclusterH.Manyofthefolds
weretightenedwereoverturnedwhiletoppling.Thecom-
pressivestrainandthebuckledupHimalayancrustbroke
alongtheMCT.TheMCTzoneofbrittleductiledeforma-
tionshowsapureshearcomponentofdeformation.
Manyexperimentaldataaimtocharacterizedifferentas-
pectsofpre-seismicbehaviorforprecursorystrainchanges
andpreearthquakedeformationrates.Aseriesofstatisti-
caltestsonthenatureofearthquakegeneratingprocesses
associatedwithseismiccycleofEQoccurrencesinthe
Himalayanbasinareconductedusingmultidimensional
rigorousstatisticalstudies,inter-eventdistanceanalyses,
andstatisticaltimeanalysesforobtainingcorrelationdi-
mensions for seismic, radon andfocal depthpattern of
eventstobetterunderstandthenatureandextentofseis-
mogenesisintheHimalayanbelt.
3. Power-lawEQ frequency distribu-
tion
Seismicoccurrenceinclustersisaprecursoryseismicity
patternwhichhasbeenalsoobservedbeforemanystrong
EQs by several authors [60,78,79,84].Understanding
theoccurrenceofperiodsofacceleratedaswellasde-
pressedseismicity[seismicquiescence]andlocalizedclus-
teredactivity[swarmsandaftershocksequences]isimpor-
tantforunderstandingdistributionsofinter-eventtimes
betweensuccessiveearthquakesinahierarchyofspatial
domainsizesandmagnitudes. Theproposedstudypro-
videsevidenceofaninter-clustercorrelationmechanism
betweenthe different earthquakesbystudying acata-
logofseismiceventsofref.[1]. Earthquakeshavestrong
temporalcorrelationsbetweeneventsasrelatedinthis
study[8,16,76].Inthisstudy,analternativeapproachof
extrememainshockeventsthathasbeenobservedforex-
aminingthecumulativeprobabilitydistributionofEQre-
currencetime[17]andbvalueforseismicallyactiveEQs.
Thedistributionsofdistancesandwaitingtimesbetween
aquakeanditsrecurrenteventsbothfollowapower-law
decay.Ontheotherhand,[62]haveadvancedtheregion-
time-length[RTL]method, which investigates seismicity
patternchanges prior tolargeEQslooking for power-
lawdecayoftheinterevent-timedistribution. Indepen-
dentlargeeventsoverdifferent timelines do notfollow
thepowerlawasthepvalueshows.Usingthisstudywe
analyzethepowerlawdistributionmodeltofindtheset
ofparametersandstudyglobaldynamicsofruptureprop-
agationbasedontheinteractionsbetweenevents. Time
seriesofreliablemeasuressuchaswaitingtimedistri-
butionforEQandbvalueforEQscangivesignificant
accountsoftheunderlyingdynamicalbehaviorofthese
systemswithrespecttoseismicprecursors[11]especially
whentheresultingprobabilitydistributionspresentre-
markablefeaturessuchasanalgebraictail,usuallycon-
sideredthefootprintofself-organizationandtheexistence
ofcriticalpoints. Thisisadirectconsequenceofacas-
cadingfailureinvolvingseveralofitsfaultsundertheef-
fectofamainshockEQwhichisduetomagnitudecor-
relationsbetweenintereventearthquakes. Thedegree
ofdistributionplaysadefinitiveroleinnonequillibrium
criticalsystems. Apower-lawdistributionrequiresscale
invariance[self-similarity]overtherangeconsidered,and
is the only statistical distribution that does not intro-
duceacharacteristiclength/time scale. A majorques-
tioniswhetherearthquakesalsoobeypower-law[fractal]
frequency-sizestatistics.Fromstudiesitisdifficulttoin-
terpretthenatureofthestress-generatingpatternofa
region-whetherthesystemfollowsagreaternumberof
spatialmainshock-aftershockpatternsorfollowsaninde-
242
P. K. Dutta, O. P. Mishra, M. K. Naskar
pendentpatternofproducingalmostperiodicaloccurrence
ofearthquakeswarmsthatmightbehelpfulinestablish-
ingthenatureoftheclustersintheHimalayanbasinin
thepostseismicresponsestate. Thepowerexponentde-
creasesasthe‘catastrophe’approaches,andexhibitsa
trendtorestoreitsinitialvalueafterthelarge-scaleper-
turbation. Onthebasisofdamagemechanicstheory,[9]
proposedapowerlawforthetimevariationofthecu-
mulativeBenioffstrain,S[squarerootofseismicenergy],
releasedbyacceleratingpre-shocksintheregionwhere
thesepre-shocksoccurinthecriticalregion.Interevent-
timedistributionisuniversal[20]afteraccountingforthe
overall activity level it shows the existence of cluster-
ingbeyondthedurationofaftershockbursts. Recurrence
timesshouldbeconsideredforbroadareas,ratherthan
forindividualfaults,andcouldprovideimportantinsights
inthephysicalmechanismsof earthquakesoccurringin
aswarmorindependently. Inter-event-timedistribution
canbeused for anon-parametricreconstructionofthe
mainshockmagnitudefrequencydistribution.Earthquake
swarmsarestronglyclusteredinspaceandtimeandcan-
notbedescribedbydominantlawofsequences[42].Using
powerlawanalysisinempiricaldatadistributionwecan
reproducebothtypesofseismicitydependentonthepa-
rameterregionandidentifywhichoftheclusteringmech-
anismsofswarmactivityortemporalsequenceofmain-
shockscanbecharacterizedbytheintereventtimedis-
tributionwithapowerlawscale.Ananalysisofdatafrom
thedenselymonitoredearthquakeswarmregionwhichis
famousforepisodicburstsoflargenumbersofspatiallylo-
calized,smalltointermediatesizedearthquakes,showed
apower-lawdecay of theinterevent-timedistribution.
Analysisofthemathematicalmodelofpowerlawscales
withseismicprecursoryevents. Theincreaseinnumber
offoreshockclustersshowsthatthemagnitudeoftheEQ
doesnotincreasebeyondacertainthreshold.Ithasbeen
putto study by[80]that asperitiesmaybecharacter-
izedbybvaluesandhighstressregimesmarkingplaces
susceptibletofuturelargeEQsby estimatingthelocal
recurrencetimeforactiveclustersandearthquakeswarm
activity.Theresultsareinaccordancewiththestudythat
thetemporalclusteringofindependentlargeeventshav-
ingagreatertimedistributionisabsentintheHimalayas
asthepowerlawofoccurrenceisfollowedbytheearth-
quakeswarms.Thispaperanalysesforthefirsttime,and
asfarasweknow,thestatisticsofmajorEQeventsin
aseismicfaultnetworkintheHimalayanbeltfromthis
aforementionedcomplexsystemsapproachandthelikeli-
hoodofcorrelationdimensions.TheKolmogorov-Smirnov
[KS]statisticisusedinthissense,whichisdefinedasthe
maximumdistanceDbetweenthecumulativedistribution
functionsofthedataS[x]andthefittedmodel.Theafore-
Figure 9. Cumulative distribution of earthquake swarms in Hi-
malayan basin.
Figure 10. Cumulative distribution of mainshocks of mag >5.0 in
earthquake.
mentionedKSstatisticisusedagainasagoodness-of-fit
testbetweenrealdataandsyntheticallygeneratedpower-
lawdistributeddatahavinganeffectasseismicprecursor
intheHimalayanEQdistribution. Followingthestatis-
ticalanalysis, we estimate thebasicparametersofthe
power-lawmodel,thencalculatethegoodness-of-fitbe-
tweenthedataandthepowerlawandfinallywecompare
thepowerlawwithalternativehypothesesviaalikelihood
ratiotest. Ataildistributionalsohasbeenmadetoun-
derstandtailpropertiesoftheexceedancefortheregion
withinterarrivalscanbeestimated,thenlimitingextreme
valuedistributionsgoverningthemaximumobservationor
exceedingvaluecanbeusedtostudyrecurrenceintervals
forextremeeventswithpower-lawinterarrivals.
Forthemeasureofwaiting time distributionsformain-
shock distribution and earthquake swarm, we give the
numberofoccurrences n, meanx,standarddeviation r,
maximumobservedoccurrencex, lower bound to the
power-lawbehaviorxmin,scalingparametervalueα,oc-
currencesinthepowerlawtailntailandp-value. The
lastcolumnindicatesthesupportforwhethertheobserved
dataiswell approximated by a power-lawdistribution.
Estimated uncertainties for xmin, αand ntail are also
shown.Measuressuchasntailandxminarefundamental
toestimatethespanofthepower-lawbehaviorandtode- 243
Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting
Table 2. Cumulative distribution functions P[x] and their maximum likelihood power law fits [discontinuous straight line] for the EQ catalog for
associated EQ event measure like earthquake swarm measures and waiting time between mainshocks of mag >5.0.
DatasetforPL n <x> σxmax xmin αntail p Support
Swarm 450537.23 456 600 201.04[160.07]16.8901±19.1167 47.5±25 0.12 Likely
RTime 131 127.79650.091000 126.6±722.02 ±0.2036 76.1±0.95 0 Noeffect
Figure 11. Aftershock distributions in the past 100 years.
velopfurtherquantitativemodelsandvalidationofseismic
precursorymodelslikeseismicquiescence.
4. Correlation possibility between
EQoccurrence and seismic precursor
variation
Thecorrelationbetweenprecursoryanomaliesbeforethe
eventcanbeofhelpinlocalizingEQevents. Theyare
assumedtoindicateachangeofthesystemstate[6]when
thesystemisgoingtoundergoaruptureorisgoingtoun-
dergoselforganization. Ashort-termpowerlawincrease
ofseismicactivityoccursimmediately priortothemain
shocksonaverage,e.g. groundwaterchangesorelec-
tromagneticemissions[12,6669]orforeshockclusters.
EQsoccurinclusters.Intheseclusters,thetemporaldis-
tributionofeventsseemstoberelatedtoEQmagnitude.
Twowidelyknownexamplesarethemagnitude–frequency
distribution[i.e. theGutenberg–Richterlaw]andtheaf-
tershockdecayrate[i.e.theOmorilaw].Ithasbeenfound
thatmoreisthenumberofforeshockclustersinthesource
zoneoftheearthquake,thegreaterarethechancesthat
themagnitudeoftheearthquakedoesnotexceedacertain
limitwithintheactiveregion. Westudiedthehomoge-
neousEQdatabase[2]forthedistributionofaftershocks
inspace,abundance,magnitudeandtime[Fig.10].Inves-
tigationstodateallshowthataftershocksfollowsimple
statisticalbehavior. Weconductedastudyofaftershock
distributionofmagnitude>3.0afteraseismicmainshock
occurrenceandfoundthattheaftershock distributionis
highlycorrelatedtothemainshockriseoverthetimepe-
riod.
Table 3. The total number of sequences with at least one aftershock
for different mainshock magnitude intervals.
Mainshockmagnitudeinterval 5-5.4 5.5-6.4 6.5-7.4 7.5-9.0
Numberofsequences 278 103 30 3
Thelargerthemainshock is, thefewereventsoccurin
thistimeinterval,oneobservesatransitionintheseismic
activityfromahighertoalowerlevel. Theonsetofthis
relativeseismicquiescencedependsonthesizeofthefol-
lowingmainshock,namelythelongerthedurationofthe
seismicquiescenceis,thelargerisonaveragethesubse-
quentmainshock.Theaccumulatedenergyincreaseswith
thedurationofseismicquiescence[81]thatis,theproba-
bilityforalargeeventalsoincreases.Similarstudiesto
correlategravitystudiesandgeochemicaldatawithsta-
tisticalinferencestudieshavebeendoneto understand
howanomalousvariationsofprecursorsaffectthenormal
distributionofearthquakes.
4.1. Surface plot and Gravity Studies
Usingmatlabwegeneratedasurfaceplotofthelocalized
mainshock[Fig.11]eventsofmagnitudev>6.0.Wehave
appliedasetofstatisticaltoolstoevaluatethenatureof
mainshockandaftershocktremorsthathaveoccurredin
thepast60yearsintheHimalayanBasininthelatitude
rangeof2434°Nandthelongitudeof7498°E.The
spatialplotrevealsthatmostoftheEQmainshockevents
occurredataspatialdepthof0-20kmneartothesurface
[Fig.12].Ahistogramplotforthefocal
depths shows that the spatial distribution of the focal
depthhasaneffectiveskewingcoefficienttowardstheEQs
havingsmallerfocaldepth.Therigoroussetofanalytical
investigationsmatchestheseismicprobingconductedfor
244
P. K. Dutta, O. P. Mishra, M. K. Naskar
Table 4. Earthquake swarm events in the different clusters A-G for the Himalayas.
Swarm nature corresponding to metastable Clusters[n*p]
wherenisthenumberofclustersandpisthenumberof
eventscorrespondingtocluster. ThresholdaveragemagnitudeofEQincluster
A[3*3] 5.1
B[4*2] 5.2
C[3*3] 4.9
D[3*5] 4.8
E[3*2] 5.5
F[3*1] 5.1
Figure 12. A 3D spatial plot of spatial projection depth for events in
km.
EQfocal-depthdistributionintheHimalayanareasug-
gestingthatmost of theseismicactivitiesareconfined
withintheupper50km.Skewnessofthedistributionacts
asaneffectiveindicatorthatthebrittlecrustresultsina
faultrupturenearthesurface. Studiesinfocaldepthalso
leadsustotheevaluationofthespatialdepthoftheMoho
undertheHimalayas.Understandingthenatureandspa-
tialoccurrenceofEQcanhelpusinfuturetorelateevents
tovaryingmohodepth. Theductilebrittletransition[21]
regiongivesustheabilitytoanalyzethestructuralcom-
plexitiesofthesourceregion for rupture andthe seis-
mogenesisofthemohorovicdiscontinuity,formedatthe
timeofHimalayanorogenygivingthegranitegenesisof
theregion.Seismicprobingstudiescarriedoutacrossthe
highpeakregionoftheHimalayasshows75kmasthe
largestdepthoftheMohoundertheHimalayas[77].The
crustaldepthof75kmEQs[Fig.13]recordedinthisstudy
occurredbetweentheMBTandtheMCT.EQoccurrence
cangiveusgoodinsightastothecrustandmantlestruc-
turesexistingbelow surfacefeatures. Suchstudiesas
donebytheIndepthteam[82]havecontributedtoknowl-
edgeabouttheHimalayanlithosphere,includingcrustal
thicknesses.
Figure 13. Seismic probing studies with gravity to find the focal
depth of earthquakes in the himalayan front arc.
Figure 14. Statistical study of focal depth patterns from catalogue
events for the Himalayan front-arc.
Thestatisticalstudyevaluationsuggestthatthedistribu-
tionofEQarelimitedintheuppercrustofrockthatmight
betakenupforfutureanalysis. 245
Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting
Figure 15. Distribution of earthquakes across different months.
4.2. Correlation between geochemical data
and month wise earthquake distributions
Anumberofcomplexmathematicalmethodshavebeende-
velopedtoinferstressvariationsmeasuredthroughanal-
ysisofvariationsofradoncausedbytheearthquake[23].
Weconductedaseasonaltrendforthedatasetusinga
studentsamplettest. Ouranalysisofthedatasetre-
vealsthatthelikelihoodofoccurrenceofanEQhaving
magnitude6followsagreaterseasonaloccurrenceusing
theprogressivewindowapproachcomparedtomagnitude
5EQs. ThedatarevealsthatEQmainshocksarepre-
dominantlydistributedthroughouttheyears[Fig.14]but
themonthsofMarchAprilandOctoberNovemberexpe-
riencesahighseismicactivitycomparedtotherestofthe
year. Wealsoconductedastudytoidentifytherelation
betweenradondeclinelevelsandseismicity
fluctuationsthroughouttheyear.Apositivetrendbetween
EQmainshocksfrequencyformonthswiththenatureof
radonanomalychangeshowsthatseasonalstrainvaria-
tioniscorrelatedwithvariationsof geodeticstrainand
seismicity[7]. Investigationscarriedoutthroughoutthe
worldoverthepast20yearshavesubstantiatedsignif-
icantvariations of radonconcentrationswhich may oc-
curwithraregeophysicaleventssuchasEQandvolca-
noes[1,14,75]. [61]hadcarriedoutastudyinAmritsar
tostudythecorrelationofradonsoilgaswithEQs. Re-
sultsoftheanalysisofshort-termvariationsindifferent
parameterspriortothe
consideredEQconfirmtheexistingideasoninhomogene-
ityofspatialmanifestationofEQsprecursors. Theprob-
abilityofdetectingshorttermprecursorsincreasesinthe
epi-centralareaofimpendingEQs.61and27hadcarried
outextensiveradonmonitoringinnontectonic environ-
ments[Fig.16]closetotheHimalayanseismicallyactive
basintodetectincreaseinradonexhalationbeforeanEQ
occursduetostrainbuildupinthearea[54].
5. Neural Network Analysis
The relationship between two parameters d_value and
b_valuewithoccurrenceofbigearthquakesisdetected
byneuralnetwork. AnANNusuallyhasaninputlayer,
oneormoreintermediateorhiddenlayersandoneoutput
layerwhichproducestheoutputresponseofthenetwork.
Whenanetworkiscycled,theactivationsoftheinputunits
arepropagatedforwardtotheoutputlayerthroughthe
connectingweights. Inputscouldbeconnectedtomany
nodeswithvariousweights,resultinginaseriesofout-
puts,onepernode. Theconnectionscorrespondroughly
totheaxonsandsynapsesinabiologicalsystem,andthey
provideasignaltransmissionpathwaybetweenthenodes.
Statisticalestimatorsarehighlyunstableowinginestab-
lishingalinearmechanismowingtotheshorthistoryof
theforecastzones. Anonlinearmechanismoffeedback
analysisbasedonerrorestimatewillbehighlyfruitfulas
itwillbeabletograspthedifference between conven-
tionalforecastbasedontimeseriesanalysisandforecast
oflevelcrossingtimeofprecursorybehavioranalysis.The
trendoftheseismicactivitybycombiningneuralnetwork
modelandseismicfactorshasbeenstudied.Inthispaper,
avariationofseismicitywasintroducedtoreflectthecor-
respondingvariationofthefrequencyofearthquake. The
learningprocessforBPnetworkhasthefollowingfour
components.
Inputmodedesigninvolvesuseofattribute(9nodes)fully
connectedtothenodesoftheadjacentmiddlelayers.Dur-
ingthetrainingphaserecordsareselectedrandomlyfrom
thetrainingphasesetandonepassofthefileiscompleted
usingoutputerrorbackpropogationpassedthroughthe
hiddennodestotheinputlayersasfeedback.
Thisrepetioncycleinvolvesmemorytrainingthroughfor-
wardmodepropagatinganderrorbackpropagationofthe
calculationdoneforeveryalternatecycle.Afterfullneu-
ralnetworktraining;arecalltesttodeterminewhether
globalerroristendingtoaminimumvalueisdone. The
predictedvalueiscomparedwiththesuitablemagnitude
valueforthefinalresults. Asthe stability of the sys-
temisdeterminedbasedonerroroftheminimumvalue
higherminimumvalueisusedtoclassifytheseverityof
thequake.
246
P. K. Dutta, O. P. Mishra, M. K. Naskar
5.1. The three-layer BP network design is-
sues to be considered
MakingtheBPnetworkdesignshouldbeconsideredwith
thenumberoflayers,thenumberofneuronsineachlayer
ofthenetwork,theinitialvalueandthelearningrateas-
pects.
1.thenumberoflayersofthenetwork
Ithasbeenprovedthatathree-layerBPnetwork
canachievemulti-dimensionalunitcubeRmtoRn
mappingthatcanapproximateanyrationalfunc-
tion.Thisactuallygivesadesignofthebasicprin-
ciplesoftheBPnetwork.Increasingthenumberof
layerscanfurtherreduceerrorsandimproveaccu-
racy,butalsoenablesnetworkcomplexity,thereby
increasingthetrainingtimeofthenetworkweights.
Andreductionoferrortoimprovetheaccuracycan
actuallybeobtainedbyincreasingthenumberof
neurons of thehidden layer, the resultsof their
trainingismoreeasilyobservedandadjustedrather
thanincreasingthe number oflayers. Sounder
normalcircumstances,priorityshouldbegivento
increasethenumberofthehiddenlayerneurons.
2.Thenumberofhiddenlayerneurons
Networktrainingtoimprovetheaccuracycanbe
increasedbyusingahiddenlayerandoutputlayer
withlinearactivationfunction. Theevaluationofa
networkdesignquality,thefirstisitsaccuracy,the
longerthetrainingtimedependsonthenumberof
recurrencecyclesandeverycyclespenttime.
3.theselectionoftheinitialvalueoftherightvalue
Asthesystemis non linearandthenitialvalue
oftheselectedlearningprocessisaconstraintto
ascertainthelocalminimum,thebackpropogation
hasbeencustomized. Thebackpropogationnet-
workisaverypowerfultoolforconstructingnon-
lineartransferfunctionsbetweenseveralcontinu-
ousvaluedinputsandtheoneormorecontinuous
valuedoutputs. Itisfoundthatifinitialvalueis
toolargeorsmallitaffectslearningspeed,initial
valueof theweightsshouldpreferably uniformly
distributedfractionalexperiencevalue,valueofini-
tialweightsaresetsinthe[-1,1]domainthereare
selectarandomnumberbetween[-2.4/F,2.4/F],
whereFisthenumberofinputfeature. Toavoid
thedirectionofadjustmentoftheweightsofeach
stepinsamedirectionthatincreasestheprocessing
time,theinitialvalueissetrandomnumbers.
4.learningrate
Thelearningratedetermineseachtimetheamount
ofchangeinweightvaluethatisgeneratedinthe
loop. Afastlearningratemayleadtosystemin-
stability.However,theslowrateoflearningleads
tolongertrainingtimeandmayproduceveryfull
convergence,butitisimportanttoensurethatthe
errorvalueofthenetworkoutofthetroughofthe
errorsurfaceeventuallytendstothesmallesterror
value. So,ingeneral,wetendtochooseaslower
rateoflearninginordertoguaranteethestability
ofthesystem. Thechoiceofthelearningrateis
between0.010.8.
Asuitablelearningrateforeachspecificnetworkis
present,butformorecomplexnetworks,thediffer-
entpartsoftheerrorsurfacemayneedadifferent
learningrate. Inordertoreducetrainingtimesto
findthelearningrateandtrainingtime,themore
appropriatemethodistheuseofadaptivelearn-
ingratechanges,whereadifferentlearningrateis
automaticallysettothetrainingofthenetworkat
differentstages.Generallyspeaking,thefasterthe
learningrate,thefastertheconvergence,butwith
oscillation;whiletheslowerthelearningrate,the
slowertheconvergence.
5.theexpectederrorselect
Inthetrainingprocessofthenetwork,theexpected
errorvalueisobtainedbycomparingtheminima
with“right”,thehiddenlayernodes. Smallerex-
pectationstimesfortheinputnodesadjacenttothe
hiddenlayerandthetrainingtimetogettheerror
torely ongivesusgood results. Undernormal
circumstances,asacomparison, while two differ-
entexpectederrorofthenetworkistrained,hidden
layeroftheneuralnetworktoachieveanycontin-
uousfunctionapproximation,butsomeparameters
selecttheappropriatetrainingprocesscanspeed
upthetrainingoftheneuralnetwork,shortenthe
trainingtimeandachievedsatisfactoryresultsof
thetrainingoftheneuralnetwork.
Thisisdoeninthehiddenlayerinthe following
manner
(a)adjusttheamountproportionaltotheerror,
thatis,thegreatertheerror,thegreaterthe
magnitudeofadjustment.
(b)toadjusttheamountoftheinputvalueispro-
portional to thesize, the greatertheinput
value,inthislearningprocessbecomesmore
active,andtheirassociatedweightsadjust-
mentshouldbethegreater. 247
Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting
(c)adjustthe amount oflearningcoefficientis
proportionalto. Usuallylearningcoefficient
is0.010.8,inordertomakethewholepro-
cessoflearningtoacceleratewithoutcausing
oscillationinvariablelearningrate.
Thiswillbeusedtotakealargerlearningearlyin
thelearningcoefficientwillbegraduallyreduced
asthelearningprocessproceedsitsvalue.
5.2. Proposed Method
Inthispaperwedescribeamethodwhichhastwostages,
asapreliminarystagewehavetotakeseismicnetwork
signals,electricpre-seismicsignalsandtheaveragemag-
nitudeofpreviousearthquakes,ifanyarerecordedinthe
pastdataandinthefinalstage,thosedatacollectedinthe
preliminarystagearegiventotheANNasinputs.ANN
hastobetrainedwithearthquakeknowledgerepresenta-
tionandemploysanonlinearandbackpropagationalgo-
rithmtoproducethepreciseprediction.Wehavetotrain
theANNhiddenlayerwithearthquakeknowledgerepre-
sentation,backpropagationandautoassociativeneural
networkalgorithms. Theabovetrainingisnecessaryfor
thedesignbecausethenatureofinputdataisnonlinear.
Theanalysisoftheaftershocksaimedatonehand the
spatiotemporalcharacterization[22]byreviewingandre-
finingthehypocentrallocations,thedeterminationofthe
seismicgenerationmechanismsandidentificationofthe
mainactivestructures. Amethodologytopredictmag-
nitudeoftheearthquake[49]usingneuralnetworkhas
beendescribed. Theyhave takenseismicityindicators
inputsfortheANNmodel.[5]proposedamethodforthe
estimationofpeakgroundaccelerationusingANNbytak-
inginputslikemagnitude,hypocentraldistanceandav-
erageshearwavevelocity. [3]proposedamethodusing
ANNtoforecastearthquakesinnorthernRedSeaarea.
Theypresenteddifferentstatisticalmethodsanddatafit-
tingsuchaslinear,quadraticandcubicregression. The
studyconsideredenergeticpropertiesofseismicitywith-
outconsideringtheearthquakesdistributioninspaceand
time.Basedontheseseismicdata,theyextracted11fore-
castfactors and theactualoccurrenceof the maximum
earthquakelevelMasinputandtargetvectors.Thefore-
castfactorswere:
1.themaximumnumberofseismiclevel
2.bvalues
3.Averageearthquake’smagnitude
4.theaveragelatitude
5.Theaveragelatitudedeviation
6.AverageLongitude
7.themeanlongitudedeviation
8.MLgreaterthan115thenumberofearthquake
9.thenumberofadjacenttwo-yearearthquakeevents
istakentofindtheabsolutevalueofmorethanan
orderofmagnitudeaveragemeandividedby10and
thenroundedforabsolutevalue
10.subsequentDvalue
11.themaximumearthquakemagnitude.
TheyhavetakenseismicityindicatorsinputsfortheANN
model.Theydidnottakerecurrencetimeforoccurrenceof
earthquakeeventtothemodel.Howeveralotofin-depth
analysisisnecessaryforanalysisofprecursorybehavior
withseismicindicatoranalysis. Themainsignificanceof
neuralnetworksliesingenerationandadaptabilityand
alsoinvolvesstrengthforincorporatingnon-linearitiesto
themodelscenario.Inordertoevaluatetheperformance
oftheneuralnetworkapproach,theadjustedweightsare
thenusedtoprocessadatasamplewhosetargetvalues
arealsoknown,similartotrainingdata. Seismichazard
analysishasbeen carried outusingamulti-layerfeed
forwardnetworktrainedwithabackpropagationlearn-
ingalgorithm.Thearchitectureofthenetworkconsistsof
aninputlayerwith4neurons,oneandtwohiddenlay-
erswithappropriatehiddenneurons.Inordertoanalyze
thenatureof the earthquakeweanalyzedthe state of
earthquakebasedonthenumberofaftershocks against
therecurrencetimeofearthquakes. Theinputneurons
arefixedbythenumberofinputvariables[e.g.,thechar-
acteristicvaluesforvariousstagesofseismicitycyclefor
atimeseries].Theoutputneuronsarefixedbythenum-
berofoutputsdesired[e.g.,thepredictedcharacteristic
valuesfornumberofstagesofseismicitycyclesofinter-
est]. Iftheperformanceofthenetworkontestingdata
setsisfoundtobesatisfactory,thenetworkissupposed
tohave generalization capabilityoveranyotherset of
similardata. Thestudyoftheseismicclustersandfrac-
talpropertieswithrecurrencetimeofearthquakesinthe
zoneformthebasisforunderstandingtheself-similarityof
theseismicprocess.Oncetestedsuccessfully,thetrained
networkmaybeusedtoprocessunknowndatainorderto
predictthecharacteristicvaluesforthosedatasets. By
discoveringtherelevancebetweentwoseismicparameters
[d_valueandb_value]withoccurrenceofbigearthquakes
duringatime,wherecomplicatedandindirectrelation-
shipsaretobeidentifiedandprocessedthroughanalysis
ofthestrongestearthquakefromeachwindow.Basedon
theanalysiswehad32targetsfortrainingandtestingthe
neuralnetwork.Fromthese32pairsofinputs/targets,we
248
P. K. Dutta, O. P. Mishra, M. K. Naskar
Figure 16. Categorization of earthquakes.
Figure 17. Adaptive competing networks to predict the seismic rat-
ing.
select16pairsfortrainingnetwork,and16pairsfortest-
ingit.Resultoftrainingandtestingfortheneuralnetwork
indicatedinearthquakeswasfoundthroughsimulation.A
relationshipbetweentwoparametersd_valueandb_value
withtheoccurrenceofbigearthquakesisdetectedbythe
neuralnetwork. Howeversomeexitoftherealvariation
canbeobservableintheoutputofneuralnetwork,because
ofthecomplexitynatureofthisphenomenon.
These results may have important implications for the
study of dynamical behavior of earthquake generating
mechanismintheHimalayas. TheHimalayantimese-
riesofearthquakesofsizewithmagnitude4andhigheris
modeledbyhighnumberofvariablesi.e.,bettermodeled
bythestochasticorahigh-dimensionalprocess.
Basedontheactualdata,wecandividetheearthquake
levels. Inthisarticle,thefirstcategorycorrespondsto
the“generallevel", the second category correspondsto
"medium-level"thirdcategorycorrespondstothe“sever-
itylevel”withaclassificationleveldifferenttoregression
analysis.
6. Conclusion
Our interpretation of geophysical, geological and geo-
chemicaldataforEQgenesispatternsintheHimalayan
basinsuggestthatinter-seismicuppercrustaldeformation
maybelocalizedalongshallowthrustfaultswithintense
groundmotionwithlargedisplacementandhighaccel-
erationalongthebrittlefracturezonesintheHimalayas.
Theabovesetofstatisticalanddescriptiveanalysisforex-
tractingthenatureofseismicpatternsintheHimalayan
beltrevealsthatthefrequencyofEQshasincreasedwith
theyears.ThenumberofEQsmainshocksof5.0ormore
hasbeen high inthepast few years. Theinterevent
timelydistribution plays averyeffectiverolein earth-
quakemainshockdistributionintheclusterearthquakes.
Utilizingneuralnetworksasatoolintheanalysisofb
value,dvalueandrecurrencedistributionsformainshock
andaftershockeventsfortheseismicregimetoforecast
earthquakesgivesinsighttotheearthquakesizevariation
inthevariousclustersofHimalayas.Thepatternofmain
shockswithmag>5.0hasapositivecorrelationwiththe
aftershockpatterndistribution. Thedistributionoffocal
depthoftherecordedEQshadanegativeskewshowing
thattheEQsweremorelikelytoemergenearthesurface
ofthebrittlecrust.TheseasonaltrendofEQmainshocks
respondfavorablywiththeradonanomalyobserved. The
numberofEQsofmagnitudes greater than 5aremore
inthe month ofSeptemberOctober when radonpeaks
aremore. Thisshowsthatsecularinter-seismicstrainis
modulatedbystrongseasonalvariationsthatdependson
localsurfaceloadvariations.ThefrequencytableforEQs
ofmag>5.0andthatofmag>6.0wasinvestigatedus-
ingtheindependenttsampletest.Theresultsshowthat
theEQmainshocksofmag>6.0tendstofollowasignif-
icantlypredictabletimewindowcomparedtomag>5.0
populations. Theaftershockpatternswereclustered in
the20002010decadeproducingthehighestnumberof
aftershocksaround2008forallpopulationofmainshock
pattern.Therestillexistmanycomplexitiesnotexplained
inthissystem.Theoverallstudyusingseismicprecursors
hasgivenussufficientinsightovertheHimalayanearth-
quakesoccurringinclusterbelts.Theindependentearth-
quakesarebasicallyrandomoccurrenceintheHimalayan
regionandfollownostrictdistribution. Onthecontrary
earthquakeswarmsaremorefinelydistributedandself
organizemore.Ongoingresearchwillbefocusedinana-
lyzingthestructureandtopologyoffaultnetworksatthe
stateofseismicquiescenceandhowinter-eventdistribu-
tionaffectsthestressdynamicsofaftershockdistributions
andwhetherastatisticalinferencecanbedrawntofind
arelationshipgeneratedbytheaftershockofaprevious
earthquakeintheclusterandthecomingevent. 249
Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting
Table 5. Seismic Annual value of seismic activity indicators
YearsHighestnumber
of The magni-
tude BvalueAverage
MagnitudeLatitude
Deviation Longitude
Deviation Average
Latitude Average
Longitude Number
oftimes Number
oftimes
Poor Dvalue Maximum
Magnitude
1997 0.3125 0.45 0.4902 0.7639 0.93 0.4643 0.1765 0.0473 0.5 0.1 3.9
1998 0.3125 0.49 0.3333 0.8611 0.57 0 0 0.8581 12. 2.4 6.3
1999 0 0.65 0.7647 1.0000 0.96 0.1786 0.0588 0.2462 0.03 0.28 3.5
2001 0 0.60 0.0196 0.8889 0.94 0.3214 0.1765 0.1081 0.2 0.4 3.9
2002 0.1875 0.50 0.3137 0.5972 0.80 0.1786 0.3529 0.1419 1.0 1.1 5.0
2003 0 0.62 0 0.8194 0.96 1.0000 0.2353 0 0.2 0.15 3.5
2004 1.0000 0.36 1.0000 0 0.53 0.1786 1.0000 1.0000 15.0 2.8 6.3
2005 0.5000 0.43 0.5686 0.1528 0.7 0.1429 0.9412 1.0000 0 0.22 4.1
2006 0.1875 0.42 0.6471 0.7917 1.12 0.2857 0.5882 0.0405 0.02 1.0 5.1
2007 0.5000 0.43 0.6078 0.6528 0.89 0.3214 0.6471 0.0405 0 0.3 5.4
2008 0.3125 0.43 0.6078 0.8333 1.05 0.4286 0.5882 0.0878 1.00 0.14 4.0
2009 0.3161 0.45 0.5000 0.7853 1.00 0.4424 0.1825 0.0501 0.4 0.12 4.1
Acknowledgements
AaronClausetforenlightening comments andclarifica-
tionsaboutdistributionswithheavy tailsandaspecial
thanksforthereviewersfortheirinformativecommentsin
comprehensiveanalysisoftheseismicprocess.
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... Melting of the thicker ice sheets leads to the reduction in weight on the crust, allowing faults contained therein to slide more easily, which may promote increased earthquake activity in the Himalayan region during recent decades (Mishra, 2014). It is, however, felt that a detailed study on seismogenesis in the glaciated belts of the entire Himalaya needs to be carried out using archival earthquake data recently compiled by different institutes of South Asia based on data mining tools applied to neural network model (Dutta et al., 2013), which would furnish good correlation between glacial mass changes and earthquakes to ascertain GMCIMS as one of the additional efficient proxies of climate change along with temperature, precipitation, sea-level rise, global warming, and erratic extreme weathers, reflecting local impacts of regional climate change. Conversely, it has also been argued that great earthquakes (M $ 8.0) are capable to tilt the axis of rotation of the earth, influencing the secular motion of the earth that significantly controls seasonal changes, which, in turn, contributes to climate change for a longer recorded period. ...
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