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Title Strain Analysis of Kayo Formation around Teniya-zaki,Okinawa-jima
Author(s) Hayashi, Daigoro; Baba, Sotaro
Citation 琉球大学理学部紀要 = Bulletin of the College of Science.University of the Ryukyus(56): 165-190
Issue Date 1993-10
URL http://hdl.handle.net/20.500.12000/2624
Rights
BuU、ColLSci.,Univ、Ryukyus,NC`56:165-190(1993)165
StrainAnalysisofKayoFormationaroundTeniya-zaki,
Okinawa-jima
DaigoroHAYASHI*andS⑪taroBABA…
oDepartmentofMarineSciences,UniversityoftheRyukyus,Okinawa903-01,Japan
掌中DepartmentofEarthScience,EhimeUniversity,Matsuyama790,Japan
Abstm⑰t
T1neTeniyaareainOkinawa-jimasituatedjustnorthtotheKayoareawhereHayashi
(1988,1989,1992)accomplisbedthestrainanalysis、TheKayoFormationaroundTeniya-zaki
strikesgenerallynortheasttosoutbwestanddipstothewest・T1neresultofthestrainanaly-
sisoftheareaissimiIartotllatpe㎡ormedbyHayashi(1989)ithebeddmgplanehasthe
tendencypamlleltotheXYplaneofthestrainellipsoid.、eintensityofstrainEstakes
weakervaluethanthatexpectedfromthefoldingstructu“developedinthearea・The
reasonisconsideredtobethecompetencycontrastbetweenquartzgrainsofstrainmaIker
andmatrix・AsthevaluesofI…andX2obtainedfromRl/#diagramarelargerthan
thecriticaIvalueofthem,weconcludethatthe“wasnoinitialfabricsofquartzgrains
beforedeformation.
lntmduction
Therearemanystudiesusingmineralgrainsasstrainmarker・Davidson(1983)used
feldspargrainsasthestrainmarkerandobtainedstrainellipseusingthethreeindependent
methods,theRamsay'SRI/ゆmethod(1967),Dunnet,sR1Mmethod(1969,1971)and
Elliott,smethod(1970).HeassumedthatschistosityplaneiscoincidewiththeXyplane
ofstrainellipsoidandlineationisthedirectionofXaxis・LacassineZaJ.(1983)usedblue-qu
artzgrainsasthestrainmarkertocalculatethestrainellipseusingtheFry,smethodq979).
HealsoassumedforschistosityplanetobetheXYplaneandforlineationtobe
thedirectionofXaxisofstrainellipsoiCL
Jensen(1984)treatedquartzgrainasthestrainmarkertoobtainstrainellipseusing
theRl/ウmethodHeassumedthatschistosityiscoincidewiththeXYplaneandlinea-
tionisequaltothedirectionofXaxisofstrainellipsoid・HethenconductedtheRayleigh
testwhetherthestrainmarkerhadpreferredorientationornoLSiddansetaL(1984)adopt
edthegreenspotinpeliticrockasthestrainmarkertoobtainthestrainellipse
usingtheR`ノウmethod、Thestrainellipsoidisconstructedwiththemethoddevelopedby
Owens(1984)whichisderivedfromtheleastsquaremethod
Odling(1984)usedthequartzgraininquartzo-feldsparthicgneissasthestrainmarker、
Astheshapeofquartzgrainsisdifferentfromthatofellipse0hetakessixreference
lineswith30・intervalseachotheronthemeasurementplane、Hesetupthecenterof
thequartzgrainsineyeandmeasuredthelengthofthelinewhichisparalleltothe
referencelineandpassthroughthecenterandlimitedwiththequartzgrainboundary・He
addedandaveragedthelengthofallthegrainsforeachreferencelineHeassumedthat
theellipsewhichisconstructedwiththeaveragedlengthforeachdirection,iscoincideto
Accepted:August16,1993
ApartofthisworkwaspresentedatthelOOthAnnualMeetingoftheGeologicalSocietyofJapaninTokyo,April5,1993
DaigoroHAYAsHI・SotamBABA166
tbestrainellipse・ThestrainellipsoidwascalcUlatedwiththemethodproposedbyHext
(1963).Seno(1992)usedthegrains(gramspecieswerenotwritteninhispaper)within
tuff,conglomerateandquartziteasthestrainmarkertogetthestrainellipseusingthe
Fry,smethodHeassumedthatschistosityplaneiscoincidewiththeXYplaneofthe
strainellipsoid、Hecalculatedthestrainellipsoidusingboththestrainellipseswhichare
obtainedfromtheplaneparalleltotheschistosityandfromtheplaneperpendiculartothe
schistosity・
Manyofthemethodsdescribedhereusedthegrainswhichhavesimilarsbapetoellipse
suchasquartzgrainandtheyobtainedthestraineUipseusingtheRfMmethodorthe
Frymethod、TheyassumedthattheschistosityplaneiscoincidewiththeXYplaneand
thelineationisthedirectionofXaxisofthestrainellipsoid・Theexclusiveexamples
arethatdonebySiddansetaL(1984)usedtheOwens'smethodandthatdonebyOdling
(1984)usedtheHexfsmethod
Hayashi(1989,1992)analyzedthestrainintheKayoareausingtheSI3methodwhich
istheoreticallyclearmethodtocmstructstrainellipsoidfromthestrainellipsesonthe
mutuallyperpendicularplanes・ThepresentpaperanalyzesthestrainintheTeniyaarea
adjacenttotheKayoareausingtheSI3methodandtheLisle's0curvemethodtojudgewhetherthemarkerhasinitialfabricornot.
GeoIogicalSetting
ThePre-TertiarysystemofOkinawa-jimaiscalledtheKunchanGroupexcludedthe
formationsdistributingaroundtheMotobuPeninsula・TheKuncha曲Groupisconstructedby
theNagoFormationandKayoFormationinascendingorder・TheNagoFormationismainly
composedofphyllitesandgreenstones,andnofossilshaveyetbeenfound・Althoughthe
ageoftheNagoFormationiscontrovertial,HayashiandKizaki(1985)considereditfrom
CretaceoustoPaleogene・TheKayoFormationiscomposedofaltemationofsandstoneand
mudstone・AsNummulitesamakusaensiswasfoundfromtheformation(SuzukiandUjiie
l985),theageoftheformationisconfirmedasmiddleEoceneTheKunchanGroupiscorrelatedwiththeSouthernzoneoftheShimantoSupe堰roupfromtheabovementioned
evidenceqlayashiandKizaki,1985)
Theareawhichisanalyzedjnthepresentpaper,isthepartindicatedinFig、1along
theeasternsideofOkinawa-jima,theshorelinefromTeniyatoTeniya-zaki、Theareais
composedofflvschtypealternationofsandstoneandmudstoneoftheKayoFormation・
Isoclinalfoldimgwhoseaxialplanedipstonorthwestisseverelydeveloped・Theindicato曙
ofpolarityofbedssuchascrosslamina,tracefossilandoutcropshowingthat“soft-layer
ruptureddeposits”(Gireki-souinJapanese)gougedoutsandstonebedarewellobserved
intheflyschtypealternationofsandstoneandmudstonearoundBan-zaki(FukudaetQノ.,
1978;Hayashi,1988).Hayashi(1988)decidedwhichtoppingofthebedsisnormalorreverse
bysomesedimentarystructuresintheareaaroundBan-zaki・Onthecontrary,inthearea
aroundTeniya-zakiwecannotclearlyjudgethepolarityofbedsbecauseoftheincomple-
tenessoftheresearchperfoImedbyoneofus,S・Baba・Figures2and3illustratethe
tectonicmapoftheareaandgeologicalprofile,respectively.
StrainAnalysisofKayoFormationaroundTmiya-zaki 167
●
0
Fig.1.Indexmap
zqki
DaigoroHAYAsHI・SotaroBABA168
StrainAmlysisanditsResult
Sampling
Theorientedrocksamplesof47piecesarecollectedalongtheshorelinefromTeniya
toTeniya-zakiinthealternationofsandstoneandmudstone・Thecubesofwhichthelengthof
sideisabout5cmarecutfromthesamples、Threeplanessharingacommonapexarenamed
asA,BandCplanewhicharearbitrarilydisposedasdescribedinFi9.4.Theintersects
ofanytwoplanesofthetotalthreeplanesaredefinedas坊yandzaxis、Herewetakez
axisastheintersectofBandCplanes,andthen〃andyaxesaretakensoastoconstruct
apositivecoordinatesystem海yz、Ifwetaker”systemasmentionedabove,theplaneA
isalwaysthe〃yplaneandtheplanesBandCbecome”or誠planes・Whichplane,Band
C,becomestheplaneyzor率dependsontherelativespacialdispositionofA,BandC
X
メN14E52N
N44W58E
X
N68EO48
Fig、4.CubewiththreefacesA,BandCStrainelIipsewithXandYaxes,andthethickarrowmark
indicatingstrikeanddip・Thedirectionofarrowofthestrikemarkmeansthe”northemdirection
ofstrike".#istheanglefmmthemortherndirectionofstriketotheXaxisofstrainellipse、Thevalueof‘isalwaystakenpositive,Itisarbitrarytotakewhichfacesa1℃A,BorCplanes.
planes,Tablelshowsthestrikeanddipofeachsamplewhereェy,yzandz〃planesare
definedasdescribedabove・Table2indicatestheintersectangleofeachtwoaxes,ェand
汎yandz,andzandjrwhosevalueisexpectedtobe90。,ifwetakepreciselythe泌辨
systemorthogonally・Threethinsectionsaremadefromeachcubeoftheorientedsamples
Thetotalnumberofthinsectionis47(planes)×3(thinsections)=l41pieces・Then
micro-photographsaretakenfromthemWedraw50to200piecesofmarkerellipsesofquartzgrainineachphotograph
Thediameterofsandgrainsofthesandstoneisfine(0.1-0.2mm)andoccasionallymediumTheroundnessofsandgrainsisamgularorsub-angulartosub-roundedandthe
sortnessispoor・Themineralassembledgeofthesandstoneisquartz,plagioclase,K-feldspar,
StrainAnalysisofKayoFormationaroundTeniya-zaki 169
TableLStrikeanddipof妙耀andzェplanes. Table21ntersectamg]ebetweenanytwo
coordmateaxesofx,yandz.
microcline,muscovite,biotite,chlorite,opaqueminerals,androckflakes・Thefeatures
whichindicateanydeformationarenotseenexceptthatquartzgrainsshowfrequently
waWdistinction・Biotiteischangedalmosttochloritesothatbiotiteisrarelyfound・The
twotypesofsandstonearerecognized,oneiswackeandtheotherisarenite.
TwoDimensionaIStrainAnalySiS
ThestrainellipsesontbreesectionplanesA,BandCforeachsamplearecalculated
usingtheSImethodasshownonTable3ITheSImethodisthetecbniquetocalculate
seri21
samplenWm肘@F
original
Ba囮plemnmh⑨=
Xy
plane
yZ
plane
ZX
plane
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111111122222222333333444444455555555
N85E67N
N60W83N
N68W80S
N62W86N
N63E70N
N43W82S
N86W87S
N77W8BN
N83W84N
N72E75N
N86W30N
N62W74N
N39W81N
N56WB4N
N65W90
N34W60N
N37WB9S
N62E75S
N82WB6S
N56EB4N
N74W74S
N59W82S
N17E86N
N62W74N
N54W80S
N77W83S
N76W86S
N48W73N
N38W88N
N17W85S
N50W88S
N48W90
N47W87N
N10W40S
N12W30S
N54W85S
N43W66N
N36W72N
N34W68N
N73W86N
N60W90
N54W90
N67W90
N63W90
NBOW58S
N38W60N
N52WBON
N16W7DS
N29E77N
N28E55N
N34E64S
N36W82S
N43E6BS
N2E43N
N77E2S
N5E10N
N21W85N
N74W57S
N39E54S
N52E82g
N33E90
N25EB7N
N78W42S
N60E52S
N55W48N
1I16E56N
II36W74S
N20E43N
N28ER⑨S
N73W90
N58E29S
N46E47N
N21E82S
N13E8DS
N42E90
N61E4S
BI73E82S
N38E67N
N38E31S
N34E2BS
N43W54N
N46W62N
N30E4BN
N52E85S
NB4E31S
N58E86N
N8E88N
N29E43N
N40E50N
N34E2N
N27E8N
N58W40N
N57E82S
N40E60N
N3BE32S
N51E19S
N21E34S
N22mRN
N6盆石兜DR
N67E25N
NS50W
N14E90
N33m2s
N8Bm2S
N9E90
N15E35N
N34E21N
N65W7S
N12E10S
N45E66N
N52E35N
N18W51S
N1W30N
N21W18N
N6E40S
NBOW13N
N20E6S
N21E66N
N22E46S
N43E11N
N33E9N
N43W16S
N52E85N
N78E1BN
N48E27S
N42E56N
N43E67N
N60E72S
N53E73S
N31E50S
N23W24S
N44E65N
N44W21S
N12E8S
N34E48S
N28E32S
N25E88S
N30E80S
N22E75N
N32W26S
N48E30S
Xy,
yAZo Zハエ●
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DaigoroHAYAsHI・SotaroBABA170
tectonicstrainellipsedevelopedbyShimamotoandIkeda(1976).Thevalueoflongaxis
XandshortaxisYofstrainellipsearenormalizedasnovolumechange(Xy=1).The
parameterRistheaxialratioofstrainellipse(R=X/Y)and#istheanglebetweenthedirectionofXとaxisandthenortherndirectionofstrikeoftheplaneconcerned、The
Table3.Valuesofstrainellipse.X:IengthoflongaxisofstraineIlipse-Y:lengthofshortaxis
of…、。Ⅱipse"…,FatiooI…(+)。:angI…m1h…rthemd…ionoist『ik・totheXaxisofstrain
northerndirectionofstrikemeans,forexample,ifweconsiderthestrikeN40。E,there
aretwodirectionswhichthestrikeindicates,oneisN40oEandtheotherisS40・W
WecallN40・Easthenorthemdirectionofstrike.
ThreeDimensimualStrainAnalysis
ThestraineUipsoidisconstructedusingtheSI3methodfromthestrainellipsesof
threesectionsineachsample・TheSI3methodisthetechniquetocalculatetectonic
strainellipsoiddescribedbyShimamotoandIkeda(1976).ThevaluesoflongestaxisX
inteImediateaxisYandshortestaxisZarenormalizedsoastonovolumechange(XYZ=
1)assbownonTable4・EachparameterindicatedonTable4isdefinedasfollows.
Ba■PlG
nHmDhgr ~i-1
XyPlano
可一面可一万丁 ̄
yZPlanG
X Y R 。.
ZZplanD
X Y R ①。
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StrainAnalysisofKayoFormationaroundTeniya-zaki 171
’’○・』囚脛一
V●|z||やログR
XlYllv●工R Rェ,-1
(Rxy-1)2十(Ry@-1)2。=Ryz-1
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LRy2
1-K,〃==ES
l+K
soid.Y:lengthofilutermediateTable4ValuesofstraineuipsoidX:Iengthoflongaxisofstrainellipsoid.Y:lengthofilutermediat
…。fstraineⅡipsokLZ:lengthofsh。…so…in。ⅡipsoidR…xi…i。。…、(+LL…iaI噸Moof…、(き)Meanimgsofth…he蕨……風…f…。‘。…
TheFlinndiagramisshowninFi9.5.Wecansayfromthefigure,
(1)Themaximumvalueofstrainintensitydis0.6andtakethevaluerangingq3to
O4frequentlv・Thesevaluesindicatethatthedeformationoftheareawasweakerthan
theotherfoldedarea,forexample,theAlps.
(2)Thenumberofstainellipsoidwhichbelongstotheprolatetypeis25andthatof
oblatetypeis22・Astheyareroughlythesamenumber,wecannotsaywhichtypeofdeformationwasdominantinthearea・
Thedistributionofprmcipalaxesofstrainellipsoidisdrawnasthelowerhemisphe塵
projectionontotheSchmidtnetinFig6,WecollectsomanysamplesintheareaAandBthatwedrawthedistributionofprincipalaxesintheseparatesheets,thatis,inFig.7
fortheareaAandinFig、8fortheareaBThedistributionofZLaxisofallthestrain
BmPlQnumber。 X Y Z R且7 Ry■ k 。 G3コ ど■。 X 、 ご■ ソ
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1.093
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1.495
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DaigoroHAYAsHl・SotaroBABA172
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Fig.5,FlinndiagramOpencircle8sclmpIeSCCI]ectedfromhingepart,SoIidcircle:samplescollectedfromlimbpart
ellipsoidsisillustratedinFig9・AstheZaxesareseenrandomlydistributed,weconsider
thattherearenotendenciesaboutthedirectionofZaxeswhicharenotclassifiedbut
asawhole、Table5indicatestheintersectangleofeverytwoprmcipalstrainaxes,X
andZYandzandZandXTheangIevalueexceedinglO゜differencefrom90・isseen
intbesample9(intersectanglebetweenZandX=78.1゜)andsamplel3(intersect
anglebetweenYandZ=78.9゜).Wethinkthatthewobbleofintersectangledependson
theincompleteorthogonalcoordinatesystem兀爽・Infacttheintersectangleofzandェ
withregardtothesample9is65、5゜andthatofエandyforsamplel3is780o,which
mustbe90゜iftheエァsystemisorthogonaL
1,.exofSymmetry
Asthestrammarkeristhequartzgrainofsedimentaryrock,thereisapossibility
thatthestrainmarkerhasaninitialfoliation,inotherwordsinitialpreferredorientation・
Weknowwhetberthestraimmarkerhasapreferredfoliationornot,byexaminingthe
symmetryoftheR〔/#diagram(Lisle,1985).Thesymmetryisdescribedbythe”indexofsymmetry”(abbreviateditasLy”hereafter).Table6sbowsthevaluesof恥,
calculatedoneachsectionplaneofthesamples・AsmanyvaluesofL,風areoverq8in
Table6,weconcludethatinitialmarkersofquartzgrainarerandomlyoriented・Inorder
toperformmoredetaildiscussion,weuseTable41ofLisle,sbook(Lisle,1985,pl5).
LislecalculatedthevaluesofI…wherehechangedintensityoftectonicstrainL5,2.0,
3.0,5.0and10.0,andchangedthesamplesize20,35,60,100and200whereinitial
markersarerandomlydistributed、Heobtainedthecriticalvaluesof心圃for5%and
10%ofthelevelofsignificance・Forexample,withregardtothetectonicstrainR=1.5
StrainAnaIysisofKayoFormationaroundTeniya-zaki 173
圭髻rli③④催勘
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④砂
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②
i≦'碁Ti二V、二mm!&Zn)
A
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ZarCtheprincipalstrain
theXZsectionofstrain
andBareillustratedo、
Fig.6.DistributionofstrainellipsoidCircleistbeSchmidtnet、XYand
axesprojectedonthelowerhemisphereofthenet・Ellipserepresents
ellipsoid.*meanstbesamplecolIectedfrom]imbpart・TheareasA
theseparatefiguresbecauseoftheirlargenumberofsamples.
⑨⑫
②
②⑭小
Fig.7.DistributiomofstrainellipsoidintheareaA・OtherexplanationsaresameasinFi9.6.
DaigoroHAYAsHI・SotaroBABA174
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Fig.8.DistributionofstrainellipsoidintheareaB,OtherexpIanationsaresameasinFi9.6.
N
Fig.9.Zaxesof47strainellipsoidsprojectedontheIowerbemisphereoftheSchmidtnet、Solid
circle:samplecollectedfromlimbpart,OpencircIe:sampIecoIIectedfromhingepart.
StrainAnalysisofKayoForlnationamundTeniya・zaki 175
Table5.1,te鱈ectanglebetweenanytwoprincipalstrainaxesofXYandZ
andthesamplesize〃=l00inthelevelofsignificanCe5%,wefindoutacriticalvalue
ofI…0.74.Thismeansthatwehaveonechancetogetthevalueunder0.74ofI…
intotal20challengesandthereforewejudgethatthiscasewillhappenrarely、Wededuce
thatifthevalueofI…isoverO74,thedirectionoflongaxisofinitialmarkersis
randomlydistributedinthelevelofsignificance5%、Thismeansthattherewerenoinitial
fabricsintheareaconcerned・ThecriticalvalueofLvmforR=1.5is0.6(samplesize
"=60,5%L、0.s.=levelofsignificaInce)and0.74(、=100,5%L0.s.)fromtheLisle's
Table4.1.WehaveaplanewherethevalueofLymisunderthecriticalvalue,thatis,
wearebettertothrowawaythestrainanalysisontheplanebecausetherewasinitial
fabricontheplane・Theplanefittothecaseis43-jFy(〃=74,L,函=0.65).Inthe
conditionR>1.5,wehave22planesasfollows、6旨"y(R=1.53,〃=39,L画=0.92),11-:ry
(R=1.64,,,=68,1sy風=0.94),12-juy(R=1.51,打=71,Lym=0.93),21-難y(thevalues
ofR,〃andLmarereferredtoTable6,hereafter),32-.6,1,35-範洗40-郡41-灘弘44-jUjI
BnmplenHnmlL9r X負Y・ Y▲Z。 ZへX・
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DaigoroHAYAsHl・SotaroBABA176
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100,5%L・OS.),thevaluesofLym,of22planesarehigherthanthecriticalvalue・
Therefore,therewerenoinitialfabricsonthe22planes.
InitialMakerEUipse
TheinitialmarkerellipsesarerestoredfromboththemarkerellipsesandthestrainellipseforeachplaneTheimportantparametersarealsoshownonTable6.The
parametersRandiaretheaxialratioofstrainellipseobtainedwithSImethodand
theangleoflongaxisofthestrainellipsefromthereferenceline・Theparameter#is
theangleofthelongaxisofthestrainellipseobtainedwiththeRI/jmethod(Vector
meanofangleofallthepointsineachRIMdiagram)fromthereferenceline・The
parameterI…isthesymmetricindexandthe,'size厨isthenumberofmeasurement・The
parametersソ,凡,XやandX28arethedegreeoffreedom,axialratioofstrain
eUipseobtainedwiththe8curvemethodbyLisle(1985),X2-valueattheR《/‘
diagramandX匙valueattheR/,diagram,respectively・ThevaluesofXぎゆandX20
arecalculatedusingtheFORTRANprogramdevelopedbyPeachandLisle(1979).Asthe
valuesofaxialratioofstrainobtainedfromthesamplesintheareaarealmost
underthevalueL5,wedonotrecognizesignificantchangesonthefeatureanddistribution
ofthestrainmarkersofmanysamplesbeforeandafterdeformation・
FigurelOindicatesthefrequencygraphoftheaxialratioofinitialmarkerellipse
Rl、Figurellillustratestherosediagramoftheangle0betweenlongaxisofinitial
markerellipseandthereferencelinewhere工払yzand鉱planesarearrangedfromthe
lefthandsidetotheright・ThefrequencydiagramofR,isshowninFig・10wherethe
valuesofR1arecalculatedforthedivided40partsofO,1intervalsthroughoutthe
rangeLOt05.0.Thenumberofmarkerisrepresentedbythepercentageoftbetotal
numberofmarker・Thepercentagevalueisplottedasthefrequencyonordinatewhere
onetwentiethofthelengthofabscissabecomes1%、FigurelOshowsthatthedistribution
ofRiofmanysamplesformsaclusterbetweenl.Oto2.0.Thedirectionoflongaxisof
initialmarkerellipsesisrepresentedontherangebetweenO・tol80・inFig.11.The
numberofthedirectionoflongaxisiscountedforthel8partsofeachlO゜intervals
andisdescribedintheformofpercentofthetotalnumberofmarker・Thepercentage
numberisplottedasthefrequencyforeverydirectionasthelengthof1%beComesone
fortiethofthediameterofcircle・
ThefrequencydiagramofRintheareaAisshowninFi9.12andtherosediagram
oflongaxisofinitialmarkerellipseintheareaAisdrawninFig.13.Thefrequency
diagramofRandtherosediagramoflongaxisofinitialmarkerellipsewithregardto
theareaBareillustratedinFigs、14and15,respectivelv・
Table7sbowstheparameters,”stハウ…,β…Rノハ.andRi…andtheymeanexceptfor
"s〃,,thevectormeanangleofp,vectormeamangleof8,harmonicmeanofRiandRi,
respectively、Theparameter“W',isthenorthemdirectionofstrikeofbefore
deformationmeasuredfromthedirectionofthestrikeafterdeformation・TheRIMand
RJ0diagramsaredrawnusi、gtheparametersdescribedonTable7.Wedecidenotto
showthediagramsR,/jandRi/Fbecauseitgivesnoprofittous.
StrainAmalysisofKayoFomlationaroundTeniya-zaki 177
Table6.Resultsoftwodimensiona】strainanalysis、Anglesaretakenanticlockwiseaspositive・R3
axialratioofstrainellipsecalculatedwithSImethod.①:anglemeasuredfromtbenorthem
directionofstrikeofafterdefomlationtotbeXaxisofstrainelIipsecalcuIatedwithSIInethod.
‘:vectormeanofallthedatapointsimtheRfノゥdiagram・Theanglejtakesideallythe
samewLlueof。L画:indexofsymmetryafterLisle・傘e:samplesize・し:degreeoffreedom
inthe8curvemeth0..Ro:axialratioofstraineⅡipseobtainedwiththe8cuwemethod.Xや
:X鰹vaIuecalculatedfromtheR,/‘diagram・X28:X2valuecaIcuIatedfromtheRJ8diagram.
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AvemgedlnitialEllipse
AccordingtoShimamotoandlkeda(1976),theclosertheaxialratioRiofaveraged
ialellipseistobeunity,themoreprecisethestrainanalysis(axialratiooftectonicinitialellipseistobeunity,themoreprecisethestramanalysis(axialratiooftectonic
strainR,anglebetweenthelongaxisofstrainel1ipseandthereferencelineα)is・The
closertheabsolutevalueofanglell-albetweenthedirectionaoflongaxisXof
strainellipseandthedirectionOoflongaxisoftheaveragedinitialeJlipse,themore
precisethestrainanalysis(R,α)withregardtothesamevalueRi,Table8sbowsthe
valuesofFi,。〃。lターα’(indicatedasjinTable8)ofthesamplesinthepresent
area、ThemanyvaluesRiareclosetol・O00wherethedeflectionfromthevalueLOOOis
theorderof0.001.ItmeansthatthevalueofstrainaxialratioRispreciseemoughin
thepracticalsense
Figurel6showsthegraphofRiandthesamplesize・AlthoughShimamotoandlkeda
(1976)saidthatthenegativerelationbetweenRiandsamplesizewasexpected,were-
cogmizenoclearrelationshipsbetweenthem.
FoIiationandXYPlane⑪fStminElIipSoid
ThebeddingfoliationatthesamplingpointandtheXYplaneofstrainellipsoid
calculatedfromthecollectedsamplesaredrawnasgreatcimlesoflowerhemisphere
projectionontheSchmidtnetinFigl7withregardtothewholearea・Thesamekind
▼
DaigoroHAYAsHI・SotaroBABA180
?LLL'0LL卜
DImLL
StrainAnalysisofKayoFormationaroundTeniya-zaki 181
⑨
,jjJirliTiJlii⑥
B
⑱
⑨ ④④④
26⑥⑨
A
③⑥
Fig.11Distributionmapoftherosediagramof6・OtherexplanationsaresameasinFi9.10.
LL
麺L
の
jOLL
八Fig.12.DistributionmapofthefrequencydiagramofRiintheareaA・Otherexplanationsaresame
asmFi9.10.
DaigoroHAYAsHI・SotaroBABA182
窪④④⑨
⑫⑰駒八
④ ④ ⑭ GI,
⑥
、、
⑥
Fig.13.Distributio血mapoftherosediagramofOintheareaA、Otherexplanationsaresameasin
Fi9.10.
全LⅢL
L卜烏
345
串LL
2hL
1卜丙
'4鳥Lh~
t5LLL
Fig.14.DistriblltiommapofthefrequelBcydiagramofR,intheareaBOtherexpIanationsaresame
asinFig、10.
StrainAnaIysisofKayoFomlationaroundTeniya-zaki 183
⑨
」~-
11‐‐11
④鰯
③
④
②
⑤
盆~
盆
Fig.15.Distributionmapoftberosediagramof8intheareaBOtherexplanationsaresameasin
FiglO.
1.010
1.005
1.00015050100
numberofmeqsurem臼11s
0
Fig.16.DiagramoftheaxialmtioRiofaveragedinitialelIipseandthesamplesize、ThetotaIplottednumberoftheaveragedinitialeⅡipsesis47x3=141
DaigoroHAYAsHI・SotaroBABA184
Table7.IndexvaluesintheRIノウandR,/0diagram・Theanglesindicatedhereafteraremeasured
fromthenortherndirectionofstrikeofafterdeformation、Anglesaretakenanticlockwiseas
poslitives灯:northerndirectionofstrikeofbeforedeformation.#…:vectormeanof抄.poslitive.sけ:northerndirectionofstrikeofbeforedeformation.#…:vecto]Rfmm:harmonicmeanofR1.8…:vectormeanofaR1A風:harmonicmeanofRi.
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StrainAnalysisofKayoFormationaroundTeniya-zak 185
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DieterichandCarter(1969)saidthattheXYplanebecomestobeparalleltothe
wageplaneatlimboftheisoclinalfoldofthemultilayerfoldsystemOnthecontrary,cleavageplaneatlimboftheisoclinalfoldofthemultilayerfoldsystemOnthecontrary,
theXYplaneandcleavageplaneareobviouslyobliqueeachotherwhenbulkstrainis
notsolargeandtbeviscouscontrastisgreatbetweeRllaverandmatrixinthesingle
layersystem、Thus,therelatiombetweencleavageplaneandtheXYplaneofstrain
ellipsoidisimportant,butwecannotcorrelatethenumericalexperimentalresultsobtained
byDieterichandCarter(1969)withthe]argescalenaturalfolds,becausewefoundno
cleavagesinthehomoclmalpartwhichisthelimbpartofthelargescalefoldinthearea.
(2)Thestrainvalueobtainedbythestrainanalvsisusingquartzgrainmarkerissmall
comparedwiththatoftheotherfoldedarea,forexample,theAlpsTheprincipalvalue
ofstraineIlipsoidismuchsmallerthanthevalueexpectedfromthegeologicalstructure
(Hayashi,1988,1989)Oneofthereasonisalargecompetencycontrastbetweenfolded
layerandmatrix・Thereasonofsmallstrainvaluedoesnotdependonthenonconsolidation
ofstratathatHayashi(1988,1989)forecasted,becausetheXYplaneofstrainellipsoid
isroughlydisposedparalleltothebeddingandsotheXYplanereflectsdeformation
lfthestrataissoftandnotyetconsolidated,quartzgrainsarenotdeformedbutonlv
rotatedThestrataofsocalledShimantotypealternationofsandstoneandmudstonelike
theKayoFormationwassufferedtectonicmovementundertheconsolidatedconditionWe
StrainAnalysiSofKayoFormationaroundTeniya-zaki 187
Table8.Va】uesoftheaveragedinitialelIipse.s礎e:samplesize.R,:axialratiooftheaveraged
initialellipse.⑩(=|ターα|):absolutevalueofthedifferencefromthedirectionofthe
longaxisoftheavemgedinitialellipseandtheIongaxisofstrainellipse.
wonderwhythevalueofE,takesalwaysaroundO2(0.1-0.5)whenweanalyzethestrain
usingthequartzgrainasstrainmarker・Thevalueofe、showssimilarquantitytothat
obtainedfromthesampleofthemetasedimentscollectedfromtheMidlandzoneintbe
NepalHimalaya・TheparameterEoistheamountofstraindefinedbyNadai(1963),and
isth…Iuemultipliedth…ahedralunitshoarγ⑭by県Wec・nsiderthatthe…・ロoflowEova]uedependsonthecompetencycontrast.
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