Graphic Methods W L Donn J A Shimer.pdf

7/30/2019 Graphic Methods W L Donn J A Shimer.pdf

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AS

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ENCESERIES

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ERVATORY ,

TS,I NC.

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TS,I NC.

ok,orparts

ducedinany

fthepublisher.

umber:

TATESOFAMERICA

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ideauseful andfairlycompletedis-

aphicproceduresusedforsolvingprob-

Althoughwrittenprimarilyforthe

hebookmayalsoprovideaconvenient

estudentaswellas theprofessionalgeolo-

asa reviewofdescriptiveprinciples

nterpretationof geologicmapsand

alwiththequantitativegraphicpro-

allyaspectsofdescriptivegeometryap-

.Althoughthereisnothingparticularly

nt,webelievethat abookdevotedonly

tegapencounteredbytheauthorsand

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EDDEDROCKS

ROCEDURES:

N

icProjection60

68

reePoints74

ill-CoreData84

fStrata94

utcropPatterns100

PlungeandPitch;Lineation..102

ms107

ROCEDURES:

TION

onandtheStereonet126

132

erticalDrill-CoreData....138

PlungeandPitch;Lineation..140

44

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tationoftheSphereofProjection

0

tationoftheSphereofProjection

e168

1

76

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ogicmapsdependslargelyupona

esofcontactsbetweenrockunitsand

esecontactsvariesasaresult ofdiffer-

acetopography.Inotherwords,outcrop

ologicmapsresultfromtwo factors:(1)

lted,folded,andsoforth),and(2)

surfacepresent.Onflat surfacesall

velysimpleoutcroppatterns.These

plexwhenanerosionalsurface,irregular

ent.Anunderstandingofcertainbasic

theinterpretationofgeologicmapswith

plexpatterns.

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ngthegeologististhe satisfactory

nsionalsituationusingatwo-dimen-

venientmodesofillustrationarecom-

ram,thegeologicmap,andthegeologic

yusedingeologicillustrationshowa

ectionalviews,therebygivingathree-

vetrueperspective,linesextendingaway

towardavanishingpoint.Figure1A

tperspectiveblockdiagramofaneroded

ofablockmaybe truncatedtogive

s(FigureIB).Clearly,allsurfacesof

aredistorted.Twovanishingpointsmay

perspectiveblockdiagram,asin Figure

stortedfromperspective.Thus,al-

ntforillustrativepurposes,it cannotbe

onsarerequired.Forthispurpose,the

csectionmustbeused.

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ockdiagrams:(A)one-pointperspective;(B)

hcornertruncated;(C)two-pointperspective.

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uralGeology

distributionofrockformationsat the

thismapshowstheeffectsofreliefupon

ps,thereliefitself isnotdepicted.In

icmapsshowtherockpatternasitwould

herepresent,wereremoved.Theforma-

olor,orappropriatesymbols,or both.

heyindicateall compassdirectionsas

e.Thetopofageologicmapis conven-

Thesize,shape,anddistribution of

casoftheir appearanceontheearth's

ion

sthearrangementoftherockunitsin

belowtheearth'ssurface.Asthe geologic

nsions,structuresectionsareusedcom-

themtoshowthethird, ordepth,dimen-

cturesectioncorrespondstoaline onthe

onofwhichisusuallyshownon the

.Anynumberofsectionscanbedrawn

foragivenarea.Exceptfor horizontal

urewillhavea differentappearanceon

ection.

ngageologicmapandsectionin

theverticalsectionrotatedorfolded up

planeinmuchthesamemannerthatthe

nbe rotatedintotheplaneofthe box

lockshowingthesurfaceABCDand

ctions.Figure2Billustratesthisblock

tothehorizontal.ABCDis nowthe

,and1,2,3,and 4aretheundistorted

hesectionsareusuallyseparatedfrom

hichshowsamapandfour sections

ivenaboveinFigure1. Thedotshere

entical.Sectionsmaybeconstructedat

ple,thenortheast-southwestsection

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vesrocksessentiallyparalleltothe

reunderliesplainsandplateaus.A

eauwouldshowessentiallyonerock

oungest.Complicationsofthesurface

geologicmaps,areforthemost partare-

the erosion,thegreaterwillbethe num-

ew.The outcroppatternofhorizontal

conformstotheshapeofthe erosional

e 3,whichutilizesbothblockdiagrams

apinFigure3D actuallyshowstheout-

nlyfoundonaplainor plateauunder-

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erodedhorizontalstructure:(A)unerodedhori-

ywithverygentlegradient;(C) rivervalleywith

ryvalleys.

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uralGeology

cingofthegeologytakenfromthe

rionQuadrangle,Pennsylvania.The

ofthe AlleghenyPlateautothewestof

ountainbelt.ThegradientoftheClarion

e valleyhasauniformwidth.Con-

tternparallelsthecourseofthis main

egeneralizedcaseshowninFigure 3B.

onRiver haveamuchsteepergradi-

wquiterapidly awayfromthepointof

stream.Heretheoutcroppatternforms

conformingtothegeneralizedscheme

econtactsbetweenhorizontalforma-

topographiccontours.Hence,instream

ntactsalwayspointupstream,justasdo

edures

eologistdealswiththepreparationand

iptivepictureofthestructuralgeology

eaccomplishedreadilybyusingstandard

utregardtoaccuratescalesorangles.

ions,givingagoodpictureofsubsurface

tedfromageologicmap,althoughscale,

aybeonlyrelative.Conversely,ageologic

accurategeologicsection,assuming

owever,thislatterproceduremusttake

swellasstructure,andas thisinvolves

thetreatmentofsuchaproblemisre-

cedureforconstructingasectionfroma

elow.

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mapofthenorthernpart oftheClarionQuad-

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cturalGeology

gicmap(ABCD)ofaregionof horizon-

west-eastandanorth-southgeologic

helinesADand CD,respectively.

ontalrocks,thepresenceof different

onageologicmapindicatesanirregular

sion;otherwiseonlyasingleformation

n(A'D'PO)showingfiveuneroded

efivelayersshowonthemap.Thebeds

f equalthickness.

(projectionlines)connectpoints

oincidentwithpointson thelineAD.

ncanbe foundpreciselyastheyrepre-

ethat correspondtopreciselylocated

,however,thatthethreepointsmark-

fthevalleymustbeapproximated,as

tacts.Further,thedottedprojection

endiculartotheline onthemapalong

andto thehorizontallineatthe topof

oundon thesection,asshownbythe

ne isthetruetop ofthesectionand

geologicmapcannotindicate.)

sectionalongCDis constructedby

ogicsectionalongtheline XYinFigure5.

alongtheline ABonthemapin Figure6

areaasviewedfromthesouth.(Remember

ure.)Formation1 istheoldestbed,and suc-

ntsuccessivelyyoungerbeds.Thiscommoncon-

houtthebook.Again,followingcommon

aysbetowardthetopof anymapwhere

d.

talrockunitsiscutby aneast-west,V-

idthanddepth.Thestreamis flowingon

apand anorth-southstructuresection.

plateauwithasquare-shapedmesain

mesahassteepbutnotverticalsides onwhich

en.

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ileandsectionfromsimplegeologicmap.

Exercise2.

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yresultedfromthedeformationof

nits.Theymayalsobethe resultof

rofdepositiononaninclinedsurface,

ontinentalshelfor, morelocally,the

Themeasuredangleof dipcanvaryfrom

o90degrees.Areasofgentledip are

scoastalplains,whereasareasofsteep

suchas theregionsflankingmany

ed rocksisgivenbymeansofstrike

passdirectionofahorizontallineona

doftheoutcropof adippingbedacross

edipof arocklayeris theangleand

pesbeneaththe horizontal.Thisangle'

rticalplane perpendiculartothedirec-

stratestherelationbetweenstrikeand

nglayers,asmeasuredmosteasilyon

south.Thedirectionof dipisdueeast,

hismeasuredinaverticalplane per-

his case,awest-eastplane),is30de-

ntofdip mustincludethedirection

wellastheangleof dip.Notealsothat

givenspecifically,aswellastheangle

tinsuchadescription.Forexample,if

reesduesouth,then thestrike,whichis

tionofdip,mustbe east-west.Figure8

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nd dipoftiltedor dippingstrata.

whichstrikesNE-SWanddipsSE.

northeast-southwestanddipstothe

givenasbeingtowardsoutheast,then

ybenortheast-southwest.Amorede-

nddip isgiveninChapter10.

tcropPatterns

ceoftiltedbeds, whichhavenotbeen

ofdipisalwaystowardyoungerlayers.

tionshipwhichbecomesobviousupon

cture,forexample,thatin Figure7.

d asdippingeast,thedirectionin

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uralGeology

gerbedsarefound.Intheinterpretation

oldedrocksthis relationshipisof

lwidthofsurfaceexposure(out-

endson(1)theangle ofdip,(2)the

rface,and(3)the thicknessofthebeds.

2areobviousfroman examinationof

vely,wherealllayersshownhavethe

fthethicknesschanged,thewidthofsur-

proportionally.

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uralGeology

ethegeneraloutcroppatternonthe

ofwhichrepresentsanerosionalsur-

hisit isevidentthatdippingbedsout-

s.If certainofthebedsare morere-

willprojectas linearridgesasindicated

illustratedinFigure7.In general,such

quenceoferosioneithertoaflat surface

hichtheerosionalformsareparallelto

rosionbysubsequentstreams.However,

opofdippingbeds resultingfromstreamerosion:

eedsgradientofstream;(B)dipofbed barely

m.

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opwherebedsdip insamedirectionbutmore

eam.

ansversetothestrike,this simpleout-

dified.Themostcommonmodificationis

nd11B,in whichthedipofthe beds

ent.Wherecutbythestreamvalleythe

byformationalcontacts,isV-shaped.

etheoutcropof thebedsmigratesinthe

ed.Clearly,thedeepertheerosion the

t,whichisgreatestat thevalleyfloor.

lowinggeneralrule(sometimescalled

pingbeds areerodedbyatransverse

tin thedirectionofdip.

eamountof migration,asmeasured

ependsonthedepthoferosion,as noted

ofdip ofthebeds.Thedeeperthe ero-

ountofmigration,andthegentlerthe

ountofmigration.Thelatterisobvious

ures11Aand11B.

ttheV'spoint inthedirectionofdip

dependonthedirectionofstream flow.

pply,however,wherethestreamflowsin

bedsandhasa gradientgreaterthanthe

stinplain orplateauareaswherethe

al.Wheresuchgently dippingbedsare

whosegradientis steeperthanthedip,

ointup-dip,asillustrated inFigure12.

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uralGeology

dtracingof thegeologicmapofthe

eApishapaQuadrangle,Colorado.This

orado,justeastof theRockyMountain

onsdipgentlynortheastward,away

howadefinitenorthwest-southeasttrend

sdirectionofdip isclearbecausethe

henortheast,andthe Vsinthestream

Althoughtherelativeages ofthebeds

elegend(a necessaryfeatureofgeo-

omeobviousoncethedirectionofdip

theTimpaslimestone(Kt)andthe

ApishapaRiver.Thiscontactis dis-

halftothenortheastin aprominentV

ftheriver valley.Atopographicmapof

valleyto beabout225feetdeephere.

ds havemigratedaboutoneandahalf

ontothisdepth.The slopeofthebeds

migrationisconsequentlyabout150feet

eetper mileisequalto onedegreefor

rmationdipsat slightlyoveroneand

logicsectionshownwiththemapexag-

forillustrationpurposes.

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thenorth-centralpartof theApishapa

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uralGeology

ologywiththatshowninFigure14,

oppatternofmoresteeplydippingbeds

entralRockyMountains(centralpartof

Wyoming).Thescaleofthismapisthe

dingone.NoteRapidCreekinthesouth-

.In crossingRapidCreekthecontact

ormation(Cd)andMadisonlimestone

wardthenortheastfora distanceof

2000feet.This correspondstoadipof

lace.However,thedipdecreasestoward

from theincreasinglengthoftheV's

the DeSmetformation(Kds).

tternofthe Amsdenformation(Ca)

scloselyspacedvalleysresultinginnar-

eslikethis besuretodeterminethe di-

outcropcrossesthestream,ratherthan

betweenstreams.Ofcourse,thedirec-

inedequallywellfromtheoutcropdis-

videorhill, solongasit isrealizedthat

soppositeto thedirectionofdip.

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cmapofthecentralpart oftheDaytonQuad-

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uralGeology

mapinFigure15,showsfive bedsout-

surface.Relativeagesareshownby num-

thandeast-weststructuresections.

bedsoutcropaslinearbands;thereforethe

tedrocks.Thestrikeis obviouslyeast-west,

thedirectionof successivelyyoungerbeds.

thusin aplaneperpendiculartothestrike,

swillshowtheactualdip. Intheeast-west

othestrike,the bedswillnotshowanydip.

eduregivenpreviouslywithhorizontal

anksection,D'C'OP.Projectformationalcon-

themapalongDCtothe topofthesection

minganyconvenientdipangle(asnone is

ationsdippingtothe southonthesection.

parallelifyouhavenoreasonto suspectthat

gewithdepth.

OPisin averticalplane.ThelineCD' is

face,identicalwithCDonthemap.POis a

eneathD'C,andbeds1-5dip duesouth,not

havingthesamedepthas thenorth-south

A'D'iscoincidentwithAD,andD'Mis coinci-

onalcontactsalongD'Pcanalso befound

eD'M.Drawthehorizontalformationalbound-

ngwith theappropriatepointsonlineD'M.

edepthtowhichthesectionis takenisarbi-

the situationinproblem1.

atternacrossthestreamvalleyonthe geo-

umethe surfacetobeflatexceptfora V-

west-eaststructuresection,assumingauni-

lineAA'inFigure14, showingclearlythe

eastandthe nonconformitybetweenthe

thegranite.

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oftiltedstrataforusewith Exercise3.

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sa structuralunitconsistingoftwo

ecaseofananticlinethe setsdipin

romthefoldaxis,whereasfora syncline

xis.Thereforealloftherules concerned

ons,widthof outcrop,anddirection

applytothe interpretationoffolded

asaunitthereare furtherrelation-

nterpretationof thestructure.Acon-

amentaldescriptiveelementsoffolds

nofstructureisreviewedfirst.

atureofFolds

soffoldsare illustratedinFigure17A,

danticlinesandaninterveningsyncline,

sameareaerodedto aflatsurface.The

etheaxialplanesof theanticlineand

otethattheaxialplanesdividethefolds

rsectionoftheaxial planewithanybed-

led theaxis.Thus,AB,XY,andactually

intheplaneABCDareaxesof theanti-

thesyncline.Notethatthe strikeofa

naltrendof theentirefoldstructure.

edlimbsorflanks.Becauseadjacent

n,AMPDrepresentstheeastlimb ofthe

estlimbofthesyncline.

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unerodedanderodedfoldshavinghorizontal

nes.

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uralGeology

hefoldshavedifferentanglesof dip.

symmetricalincontrasttothesymmetri-

ethattheaxialplaneof anasymmetrical

nstowardthesteeperflankofan anticline

yncline).

rnedfolds,thatis,folds havingthe

roughanangleofmorethan 90degrees,

anksdipinthe samedirection(although

n theoverturnedlimbthebedsarei n-

dsunderlieolder,and thetopsofbeds

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wingoverturnedfolds.

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uralGeology

picturedsofarare horizontal.Com-

Theaxis ofthefoldin 20Aisalso

he foldin20Bis inclinedtothehorizon-

othorizontalissaidto plunge.Theangle

easuredin theverticalplanewhich

gleofplungeorsimplyplunge.Note that

e 20aresymmetricalwithvertical

dsareeither asymmetricorover-

nclined,and anotherimportantfold

mely,pitch.NoteFigure21,inwhich

axialplaneof aplungingasymmetric

sof thefold.PlaneAEFGisa vertical

xis.AngleEAOisthe plunge,because

eaxisandthehorizontalmeasuredin a

AO,whichistheanglebetweentheaxis

redintheinclinedaxial plane,isthe

definedasthe anglebetweenalinein

orizontal,measuredin theinclined

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eand pitchforaplungingasymmetricfold.

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uralGeology

.Onaflaterosionalsurfacethe out-

onsistsof parallellinearbands.See

oteparticularlythatthere isasymmetri-

tanyfold axis.Theoldestexposedbeds

longtheanticlinalaxis,whereasthe

dsynclinelie alongtheaxis.Bedsdip

sandtowarda synclinalaxis,following

ardyoungerlayers.Theoutcropofthe

sof theaxisofa symmetricalfoldshows

hewidthofoutcropvarieswiththe

agivenbedonoppositesides ofan

ferentwidths.CompareFigure17Bwith

ustrationofthiseffect.Parallellinear

monlyfoundinareaswherefold struc-

erodedbysubsequentstreams.

osionalfeaturesare developedtrans-

earoutcroppatternbecomesdistorted.

tionofoutcropdownthe dip,asinthe

describedearlier,andi spictured

,whichshowsablockdiagramandgeo-

.

Theoutcroppatternoferodedplung-

gratherthanessentiallyparallelcontacts.

udyofFigure23,whichillustratestwo

interveningsyncline.Boththeun-

eshown.It isobviousthattheoutcrop

noseinthedirectionof plungeofthe

ectionofconvergenceornoseofaplung-

he directionofplunge.Thedifferential

produceszig-zagridges.Allotherrules

nedforfoldswithhorizontalaxesthat

utcrop,andmigrationof outcropapply

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foldedstrataerodedby atransversestreamas

mand(B)geologicmap.

wingtheoutcroppatternofa singleresistant

odedplungingfolds.Therestored,unerodedre-

ated.

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uralGeology

of ageologicmapoftheGadsden

ownin Figure24.Theprincipalfeature

allelbandsofoutcropwiththe oldestfor-

lar sequenceofprogressivelyyounger

Suchan arrangementindicatesananti-

xiswhichrunsalong themiddleofthe

xDolomite(Sk),theoldest unit.The

ormationsis broaderonthesoutheast

kofthe fold,indicatingtheanticlineto

mbofgentlerdip tothesoutheast.The

spoint awayfromtheaxisandthusalso

reofthestructure.Theyshowthat the

d axis,orinthe directionofyounger

nclinetheVswouldpointtowardthe

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cmapofpartof theGadsdenQuadrangle,

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geologicmapofportionsofLycoming,

ndcountiesinPennsylvania.Thezig-zag

fplungingsynclinesand anticlines.By

hgivesformationages,itis possibleto

romthesynclinesandthus determine

uresectionalonglineAA' showninthe

ConsiderJ theoldestlayer.

atterninthestream valleyinFigure26.

two anticlinesandonesynclineplunging

surface.Showatleastsevenformations.

e AA'inFigure24.Specificdipvaluesare

dsynclinesinFigure25. Whichwaydoes

gicmapoferodedfoldsforuse withExercise2.

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owthewaysinwhichfaultsaffectout-

cks.Thistreatment,whichemphasizes

oftiltedstructures,mayforthemost

lto thefaultingoffoldstructures.The

ofnonrotationalfaultingofhorizontal

27,whichshowsa blockdiagramof

faulting.Notethattheonly significant

erentagesareadjacenttoeachother

tersectingfaultscancomplicatethis

quitesimple.

e outcroppatternoftiltedbedsde-

estrikeof thefaultplaneandthe strikeof

mayhavethe samestrikeasthebedsastrike

thebeds atsomeangleupto 90degreesa

eangleand directionofdipofthefault

ectionof dipofthebeds.

onalongthefaultplane.

esregionsthat havebeenfaulted

tsdip inadirectionoppositetothat of

faultillustratedisnormal,andin

otethatrepetitionofbedsoccurson

ne onthemapviewofFigure 28A.

occurswheredippingbedsarecutby

dips intheoppositedirectiontothe dip

ke faultisreverse,asin Figure28B,an

otethatbed4 doesnotoutcropany-

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ds followingerosionofaregionoftilted layers

twhichdipsoppositetothebeds; (B)omission

fa regionoftiltedlayerscutby areversestrike

othe beds.

s case.Thethicknessoftheomitted

ountofdisplacement,aswellas onthe

dsandfault;this alsoistruefor thethick-

llustratedin Figure28A.

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uralGeology

9A,B,C,andD illustrateoutcrop

eerosionoftilted layerscutbystrike

directionasthebeds.InFigures29A and

eeplythanthebeds.Insuchcases,the

cesomission,asillustratedinFigure29A,

ysyieldsrepetition,as illustratedin

and29D thefaultsdipmoregently

ses,thenormalfaultalwaysproduces

Figure29C,and thereversefaultgives

igure29D.

gmovementnotparalleltothebed-

repetitionoromission.Insummary,

or(1)normal faultswhichdipopposite

ultswhichdipinthe samedirectionbut

(3) reversefaultswhichdipinthe same

thebeds.Omissionoccursfor(1) normal

medirectionbutsteeperthanthebeds

pin thesamedirectionbutgentler

ersefaultswhichdipoppositetothe

eis paralleltothebedding,as iscom-

eis neitheromissionnorrepetition.

atrepetitionoromissionof bedsinthe

orthepresenceof afault.Therepetition

asesofstrikefaults,is notsymmetrical

sontheoppositesides ofafoldaxis.

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ngomissionandrepetitionofbeds wherefaults

irection.

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uralGeology

keofa transversefaultandthestrike

gleuptoa rightangle.Whereverafault

es,asimpleoffsetrelationshipresults,

rectionsofdip ofbedsandfault,and

e faultplane.Simpleoffsetisillustrated

theoutcroppatternresulting fromthe

rockscutbyafault atrightanglesto

lifted blockproducesaneastward

thetilted beds.Ifthebedshere were

ofeastward,displacementwouldbeto

ernwouldalsodevelopif thefault

hichcasethe bedstothesouthwould

sion.Further,simplehorizontalmove-

hthe northblockmovingrelatively

tternillustrated.It israrelypossiblefor

aultplanetobe paralleltothebedding,

noapparentdisplacementwouldoccur.

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uralGeology

e strikeofthebedsobliquely,offset

exceptforthe rarecasejustdescribed.

31. Followingerosion,theeastbed

verlapofoutcropoccursalongthefault

westbed,whichdipsinthe opposite

ata gapinoutcropoccurs.Itshould

uthernblockwereraisedanderoded,

e eastbed,andtheoverlapin thewest

or offsetwithoverlapcanbeproduced

mentalongthefaultline.

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apor overlapindippingrocksbya transverse

on.

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uralGeology

r,whichhaveessentiallylinearmotion

terthestrikeof thebedstheydisplace.

ninclinedfault planeisrotational,the

edsisusuallyaltered.

ninFigures32 and33.PartsAandB

aftererosion,respectively.Thechange

sobvioushere.Naturally,the actual

articularcasedependsontherelation

of thebedsononehand andthestrike,

nthefaultplane ontheotherhand.In

ainverticalfaults,strikemaynotbe

tationalbeddingplanefaults doesthe

allothercasesthe dipischanged.For

ip ofthebedin theeasternblockis

dippingnorth insteadofsouth,itcan

hedip wouldbedecreasedunderthe

ientlyfaralongitsstrike,will befound

rfault.Afaultcannotterminateabruptly

othercrosscuttingfaultatits end.

ntiallynonrotationalmust,forthe

tionalmovementtowardtheirextremi-

ceofthedifferentialmovementinthe

sout.Obviously,theamountofrotation

thwhichthe faultmotiondecreases,so

tontheoutcroppatternmaybe promi-

Whereastrike faultdiesout,therota-

hebedstochangestrike,witheachbed

wardthefault.Thus,Figure33 canbe

eterminationofastrikefault.

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nddip producedbyarotationaltransversefault.

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uralGeology

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rsestrike faultwhichhasproduced

he mannerinwhichthemissingbeds

the faultdisplacementdecreases.The

otionisshownin thetwostructuresec-

trikenorth-south,asdothose which

islocationwherethemotionisessentially

usthatwherethe faultisdyingout,

soccurredandthedirectionofstrike

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uralGeology

rtofthe geologicmapoftheCleve-

see.Themapshowsprominentnortheast-

esefaultshaveproducedfrequentrepe-

on(r),Connasaugashale(c),and

pparently,thefaulttothesoutheastdid

lmotiontorepeattheRomeformation.

tracedtothenortheastandsouthwest,

usetheConnasaugashalelensesout

ment)againstthefault.Anasymmetric

rtheastisevidenton thesoutheastern

e relations,determinedbothfromthe

dip shownbyoutcropdisplacements

monstratethepresenceofthissynclinal

yofthesynclineisshownbythe greater

tionsonthenorthwesternflankof the

helesserwidthon thesoutheasternflank.

gicsectiongivesafurtherclarificationof

ereversefaultsmust bedrawnsteeper

thesamedirectioninorderto produce

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owingrepetitionofbedsonthe Cleve-

see.

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uralGeology

ologicmapand atransversegeologic

mthenorthwestcornerofthe Fair-

vania.(Forclarity,thereisverticalexag-

estructureindicatedbythe mapcon-

sshownbythenatureof therepetition

he typicalplungepattern.Theaxesof

linesaremarkedwithappropriatesym-

efaultsarealsoevident.The faulttothe

esoutheast,asevidencedbyits marked

southeast(instreamvalleys).Thisfault,

mbofa syncline,hasbroughtolderbeds

hyoungerbedsonthewestside ofthe

ssion.Thedirectionofdipofthe fault

ativeagesofthe rocksoneithersideof

hangingwall oreastsidehasmovedup,

orthrustfault. Notetheuseofa con-

bol,whichisalwaysplacedonthe over-

t.Thefaultto theeastmustdipvery

ntisindicatedinthe streamvalleys.The

lt(actuallyanormalfault)hasmoved

senceof olderbedsonthisside. Con-

mbolsareusedhereto showrelative

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cmapofthenorthwestpartof theFairfield

.

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uralGeology

egeologicmapofpart oftheGettys-

vania.Offsetwithoverlapisillustrated

uttransverselyacrossthestrikeof asillin

onofrelativemovementisshownfor

warddisplacementofthesillonthe up-

obedipping tothenorthwest.

stratingthe followingconditions:(a)a

bedsdippingwest,cutbyareversefault which

-west,(b)erosionto aflatsurfacefollowing

alongline AA'inFigure35.

lockdiagramsshowingtheregionillus-

forefaulting,(b)afterfaultingbutbefore

othe presentsurface.

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cmapofpartof theGettysburgQuadrangle,

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contacts(unconformities)mayresult

ppatternsinadditionto thoseproduced

pesdiscussedabove.

commonlyusedincludesdisconform-

ngularunconformity.

sanerosionalsurfaceamongbedded

eachother,its effectisnodifferentfrom

dthusintroducesnouniquefeaturein

resenceofadisconformityismanifest

tarysequence.InFigure24theabsence

ntheSilurianandCarboniferousindi-

conformity.Theactualdisconformityis

ockwoodformation(Sr)andtheFort

tions(Cpo)andclearlyparallelsthe

ontacts.Thehiatusindicatedbythedis-

erosionornondepositionoftheincom-

ce.Actually,theeffectsofbothmaybe

tbetweenanolder massiveigneous

seriesof youngersediments.

GreyGranite(ggr)andthe Deadwood

is anonconformity.Thiscanbede-

enowhereinthisareaintrudes theDead-

mationsandthusis presumablyolder.

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eoutcropofanonconformityisaline

srockononesideand exposuresofsedi-

hareparalleltothenonconformity,on

whichseparatestwosequencesof

that anangularrelationexistsbetween

ngersequenceareparallelto theero-

ersofthe olderunderlyinggroupmeet

Anangularunconformityresultsfrom

gtheerosionofa deformedsequenceof

uentdepositionofsedimentsuponthe

ularunconformitymaybehorizontalor

urtherdeformationoccursinthearea.

viewsofthetypes ofunconformities

conformity

(D)TwoAngularUnconformities

illustratingdifferenttypesofunconformities.

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68/190

uralGeology

acingofthegeologicmapofthe north-

rksQuadrangle,Montana.TheBozeman

alrockunit whichblanketsandlies

hofthepre-Tertiaryfoldedorcrystalline

actbetweentheBozemanandall older

tcropofa surfaceofangularuncon-

ocksaremassive,suchasthe Archean

formablecontactwouldbeclassifiedas

thecontactbetweenthegraniteandthe

tion(fg)isalsoa nonconformity.The

tinformation(Cfg)andtheJefferson

blyadisconformity,owingtotheomis-

Silurianrocks.Theirregular contact

dthesedimentarybedsfromCambrianto

pofanangularunconformity.

alongthelinesAA' andBB'ofFigure39.


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cmapofpartof theThreeForksQuadrangle,


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conformablewiththeirbeddedhost

sandlaccoliths,ortheymaycut across

nthe casesofdikes,stocks,andbatho-

ormableintrusionsintroducesnomodifi-

.However,wheretheintrusioncutsa

enceisshownbya distinctiveintrusive

olderrockunits.

mapin Figure40Ainvolvesalinear

byadikecuttingtiltedor foldedrocks.

deredheretoforemayshowtheadded

sbodycuttingthe structure.Similarly,

howtheeffectofthe intrusionofastock

0B.Thelatterformsaremoreirregular

bedefinitelydistinguishedfromanon-

eddedstructuresarecutbytheintrusion.

structuresareparallel totheigneous

anonconformityoraconformableigne-

bepresent.Fieldevidencemaybeneces-

altypeof contact.

stratingintrusivecontacts.


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edures:

ucturalgeology,onthewhole,are

projectiontechniquesofdescriptivege-

phicandstereographicprojection.There

vantageinstudyingtheorthographicpro-

kesuseof thefamiliarsectionandplan

topographic,geologic,andstructure

.Also,webelievethatthe useofthe

esabetterinitialthree-dimensionalper-

tionsinvolvedinstructuralgeology.

eographicprojectionpermitsitsuseonly

rike,dip,plunge,pitch,andthelike);

measurescanonlybesolvedcompletely

atoncethestudenthaslearned to

ns,thestudyof thestereographicpro-

sier.Thesolutionofproblemsinvolving

lydifficultorimpossibleusingortho-

dilyattainablebythestereographic

tsmorerapidsolutionofmanyother

byorthographicprojection.


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Projection

rojection,isamethodofrepresent-

bjectonatwo-dimensionalsurface.In

uantitativetwo-dimensionalprojection,

st betransferred(projected)toade-

hichisperpendiculartotheplane.A

eplaneofprojection.

he centerofthedrawingisprojected

salonglinesat rightanglestothese

ointsPitoP7.The linesbetweenPand

calledprojectionlines.Note thatany

esarepossibleinaddition tothoseil-

erticalor horizontalpositions,asthose

nclinedpositions.Forthemostpartin

yonlyhorizontalandverticalplanesof

efulinillustration,showdistortedre-

edearlierinChapter1. Wewilltherefore

wingsinallofourquantitativework.(A

que,knownasisometricprojection,per-

roblemsbut israrelyusedandwill not

withverticalplanesinvolvestherota-

o thehorizontal.Thus,anyvertical

sthosein Figure41,couldberotated

osesof quantitativework.Theline

tatedis calledafoldline.This isillus-


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Projection


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uralGeology

ure42A,alinein space,AB,isprojected

R,givingtheprojectionA1B1,andonto

ivingtheprojectionA2B2.Figure42B

tatedaboutthefold line(RO)intoa

hatAiandA2 aredifferentprojectionsof

andB2aredifferentprojectionsofthe

edinasimilarmannerontothe same

nes,givingtheprojectionC1D1and

wswillbeusedtohelpin thevisualiza-

ms,allof thequantitativeworkwillbe

sofprojectionwhicharerotatedinto the,

y.Oftenmorethanoneverticalplanewill

o thatseveralfoldlinesmaybe usedin


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Projection

ngtheuseof foZdfc'nes.


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turecontoursisbasictothe quantita-

ere,becausemostofthegraphicsolutions

topographiccontoursareprojectionsof

he groundsurfaceontoahorizontal

rsareprojectionsontoahorizontalplane

n agivengeologichorizon(usuallya

ustratedinFigure 43Awhereplane

ippingformation.Thedashedlinesare

nonthebed atintervalsof100feet.

tedupto ahorizontalplane.Thepro-

ontoursfortheparticularsurfaceand

ateelevations.Sincethestrikeof abed

ofahorizontallineon adippingbed,all

elinesofstrike.

pofthissituationis showninFigure

cturecontoursareverticallyabovethe

resent.Knowingthis,it ispossibleto

theformationfroma structurecontour

calplanebeneathXY isrotatedintothe

foldline.Theangleofdip cannowbe

Drawelevationlinesparallelto thehori-

verticalscaleexactlyequaltothe

sofaprocedureessentiallythereverse

hestructurecontours,weprojectfrom

averticalplanehavingthesamevalueas

obviouslythedippingbedasit appears

diculartothe strike,andtheanglePMYi


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ngstructurecontours.

thetypeofstructurethatexistsunder-

nearparallelcontours,evenlyspaced

reasingvalues,indicatesasimplehomo-

ructuredippingi nonedirection.Figure

Ofcourse,differencesinthe angleof

acingofthecontourlines.Thisis exactly

contours,wherecloselyspacedcontours

ely-spacedcontoursmeangentleslopes.


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uralGeology

isisshownbyparallelstructurecon-

ceofvaluesthatare repeatedsymmetri-

xis.Thevaluesincreasetowardtheaxis

setowardtheaxis ofasyncline.InFigure

eisshownonthe westernpartofthe

eanticlinelies betweenthe1200-foot

portionofthemap showsanasymmetric

uthwest.

ernforanybedin anunerodedfold

semblesexactlythegeologicoutcrop

fold. TheblockdiagraminFigure45A

ionona buriedplunginganticline.These

rfaceas structurecontours.Thetrue

ustratedinFigure 45Bandshowsapat-

cmapofanerodedplunginganticline.

rsinFigure 44aredrawnforthe topofa

hickandthatthe elevationofthegroundsur-

econstructionofthesubsurfacestructurealong

icaland horizontalscalesequal.)

determinetheaverageanglesof dipfor

ntourmapoftheupper andlowersurfaces

gwest.Thesandstonelenses frommaximum

nto zerothicknessatthewestmargin.Use


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ttheangle ofinclinationofadipping

naverticalplanetakenperpendicularto

en,itisalwaysthis maximumanglethat

rectionandangleofdip aregiven,the

rightanglestothedip direction.

aturearecommonlyusedtoexpressdip

attitudeofabedin space:

givingtheangle ofdipfollowedbythe

asa bearingfromnorthorsouth.Thus,35 S

greesfromthehorizontal inadirectionthatis

south.Sincethedipdirectionis S45W,the

estrikecouldalsobe givenasS45 E,butthe

n.Theserelationshipsareshownin Figure46.

orecommonmethodconsistsofstating

angleand approximatedirectionofdip.With

napproximatenotationofdipdirectionis

directionisperpendiculartothestrike,which

seshownabovecanthenbe describedas

bedonanyverticalplanenot per-

asmalleranglethanthetrue dip.This

pparentdip.Theapparentdipbecomes

roacheszeroastheverticalplaneon

achesthestrikedirection.Thiseffectis

thedip ofaseriesof bedsappearsto

ruevalueonplane1 (whichisperpen-

eroonplane4,whichis paralleltothe


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wingquantitativerelationshipbetweenstrike

wingtrueandapparentdip.

phicprojectionprovidesaconvenient

erminingtruedip whentheapparent

wn,orfordeterminingthestrikeandtrue

sare known.

ApparentDip

edstrikeseast-westandhasa certainappar-

ewhichcrossesthestrikeata knownacute

dip.


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uralGeology

tionisanalyzed,althoughinadis-

,whichhasaneast-weststrike,hasan

newhichmakestheknownacuteangle

edip canbefoundonlyina plane

,suchasthe north-southplaneMNOP.

cturecontourlineatzero depth.Any

wthesurfaceparalleltoXYis alsoastrike

rypointB onthebedin theapparentdip

o XY.ThislinethenlocatespointC, on

MNOP.Hence,angleDXCisthedip.

thetruedipcaneasily befoundbya

on(refertoFigure48B):

thedirectionofthe apparentdipplane,

atany point,suchasY.

dipanglewithvertexat Y.(Remember

calplanerotatedup tothehorizontalabout

urecontourparallelto thestrikeline.The

recontourandFL1isdesignatedhere aspoint

rticallybelowpointA.

stothestrikeline atanypoint,suchas

hereFL2intersectsthestructurecontour.

recontourforthedepthAB,pointCmay

thverticalplaneby droppingverticallyfrom

gleDXC isthetruedip.

gure48Bare analagoustothosein

rocedureinstages 6and7involves

ftheangleofdip whentwoormore

en,asexplainedinconnectionwithFig-

eregivenit isobviousthattheap-

inedbyfollowingthe sameprocedure

gwiththeplane ofthetruedip.

TwoApparentDips

erminethe strikeandtruedipfrom

me bedfoundthrougheithersurface

edrilling.Theprocedureconsistsoffind-


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uralGeology

onaparticularbed. Thestrikeisthen

ur,andthe dipisfoundby projecting

lplanenormalto them,asgivenabove.

ftrendingN60 E,theapparentdipof a

cliffwhichtrendsN 10E,thesamebed

rikeandtrue dipofthebed.

orverticalplanes intersecteachother.

structurecontoursonaspecificbed

foldlines,suchasFL1andFL2.

ip angles,startingatthepointof inter-

wnoneitherside ofthefoldline,whichever

construction.)

A onFL1dropavertical(of depthh)

onofanequalverticalbeneathFL2thus

rethuspointsonthe surfaceprojectedfrom

bed andthereforelieona structurecontour

eparallelto thiscontourpassingthroughthe

lines(whichare surfacelines)istherefore

atthesurface.Thestrikeofeither ofthese

orth,isfoundto beN30E andgivesthe

ormaltothestrike.Followingthepro-

omtwoor morestructurecontours,thetrue

es.

nsionalanalysisofthesituationandin-

.

dshowsa dipof45 SEonaverticalplane

etruedip.

keanddipofN 55E60 NW.Findthe

aceswhichtrendnorth-southandeast-west

SWonthefaceof aminedriftoriented

wsadipof 12 SWonthefaceof adrift

ngleanddirectionofthe apparentdipof

edtotrendN 45W.

p ofanundergroundbeddeterminedfrom

outhlineis38 S.Fromtwodrillholes inan

ntdipofthe bedis55 E.Findthestrikeand


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alanalysisofsolutioninFigure49.


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oints

Elevation

determinationisto establishastruc-

ationona bed.Iftwopointsare known

onthelineofstrikeis obtainedimmedi-

opointswitha structurecontour.A

(paralleltothefirst)canbe drawn

t,whichis atadifferentelevation.The

ructioninaplaneperpendiculartothe

atopographicmapandthelocationof

agivenbed.Find thestrikeanddipof this

metopographiccontour2000feet.

C,andextendedto theedgesofthemap,

ontourwhichshowsthestriketo beN

broken,thiscontourisonthatpart ofthe

removedbyerosion.PointB locatesan

eatan elevationof1800feet.Aline

thusthe1800-footstructurecontour.

constructedinanyverticalplanenor-

justoffthemap,using FL1asthetop

mberthatthescaleused inthevertical

ontalmapscale.)Thegraphicsolution

evations

-coredatayieldrandomelevations

ses,aminimumofthreeelevationvalues


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oints

e strikeanddip.Theproblemis once

minationofa structurecontourlineon

hedbylocatingafourthpointwhose

neofthe threeknownelevations.Inthe

three-pointproblemthestrikecan be

e proceduresgivenbelow.Thecon-

tionisthe sameinallcases andwas

gure43.

FEET

trikeanddip fromthreepointswithtwoat the


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uralGeology

A,B,andCstartingfromalevelsur-

oalseam.HoleBis 1000feetS50 Eofhole

S30 WofholeA.Thedepths ofthecoal

reasfollows:A600feet,B900feet,C1600

ofthecoalseam.

oApparentDips.InFigure52, points

locationsofthedrillholes,canalso be

tothehorizontalofthe threepointson

vendepths.Clearly,theseammust be

tionfromA toC,asAis theshallowest

oles.

stpointA(the highestgivenpointon

scanbe constructedinthevertical

L1andFL2.Theapparentdip angles

tively.NotethatthedepthBBiis 300

seamisonly300feet deeperatBthanat

deeperthanA,sothat thedepthCCi

zontaland verticalscalemustbeused.

derror,a pointPonline FL2such

depthBBi,or300feet.Theline BPisa

blishesthestrike.Structurecontours,

canbe drawnthroughpointsAandC,

strike.Thetrue dipisfoundin theverti-

ennormaltothestrike,and iscon-


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oints

e-pointproblemusing twoapparentdips.


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uralGeology

ojectionMethod.Thisproblemcanalso

ectionprocedure.InFigure53,points

surfacelocationsofthethreedrillholes

onsiderthesepointstobetheprojections

ree pointsonthebed.The pointson

projectedontoanyverticalplane,such

edinto thehorizontalaboutFL1.The

eprojectionsonthisverticalplaneof the

bed.

i,simplydrawlinesfromA,B, and

ine usedanddescendtotheappropri-

ne. Anyhorizontallineorcontouron

sahorizontallinewhenprojectedto this

orizontallinedrawnthroughBi isthe

bedatthe depthofBi,or900 feet.Pi

ntalcrosseslineAiCi onthevertical

projectiontothe verticalsectionofa

hline wherethiscrossesalineon thebed

rizontalplane,drawaline fromPi

neuntil itcutslineAC.Point P,located

projectiontothehorizontalofapoint on

eet.LineBP isthereforea900-footdepth

blishesthestrike.Itshouldbe realized

wnon theverticalsectioncanbetrans-

neto giveadifferentstructurecontour.

eanyorientation,andthesamestrike

hestrikeisfoundby thisprocedure,the

ticalsectionperpendiculartothestrike.


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oints

e-pointproblemusing avariationofthe


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uralGeology

ysisofsuchaproblemisshownin Fig-

ed isrepresentedbytheplaneSTUV

splanearecircledat A2,B2,andC2.

ectionsoftheseontothehorizontal,and

onsontotheverticalsection.(Theverti-

pointC2on thebed,sothatCi andC2are

ctionisrotatedto thehorizontalabout

this rotatedsectionwillbesimilarto

thebedat depthB2andalsolies onaline

2withC2onthe bed.Thesolutionin-

tPat thesurface.ThehorizontalBiPi

projectionofthehorizontalpassing

romthe informationonthevertical

horizontalasshowninFigure 53.

ethods.Thestrikecanalsobede-

ometricmethodswhenthreepointsat

re known.InFigure55,pointsA,B,and

celocationsofthe threedrillholes.

estpointof thethree,andCthe lowest.

ACtheremustbe apointthatrepresents

thebedhavingthesamedepthas B.

rikecanbeobtained.

onforbothsolutionsisbasedonthe

ometry,"correspondingpartsofsimilar

"Itis convenienttoworkwiththediffer-

drill holesratherthantheactualdepths.

thehighestpoint),drawlineAFat an

on.Itis besttodrawthis lineroughly

pesthole,althoughalmostanydirection

Finto anumberofequalparts,using an

cale.PointCiislocatedalongline AFat

ionaltothe differenceindepthbetween

onon AFisproportionalto100feet in

valenttothatof holeBalongAFis

.Thendraw alinefromPi parallelto

thuslocatingpointP.SincepointC

jectionofthedepthscaledoffat ACi,

surfaceprojectionof thedepthscaled

edepthatB.The lineBPisa structure

0 feetandestablishesthestrike.


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e-pointproblemby ageometricmethod.


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uralGeology

nsimilargeometricreasoning,requires

ethreesurface-holelocationsareonce

ogetherwith thedifferencesindepth

beneathA andCandbeneathAand B.

realonglineACtheremust beapoint

of apointonthe bedhavingthesame

deduceataglancethat thecloserthe

nearerto AwillpointP lie.Remember-

olutionjustgivenin Figure55,wecan

nship:

toC DistanceAC

toB DistanceAP

equationexceptAP.Substituting

onwehave:

00)

3/10oflineAC,drawBPand thus

ure51areoutcropsof thesamesurface

ructure.Findthestrikeanddip ofthisdike.

from thesameelevation,encounterthe

edepths:hole12100feet,hole21200feet,

located3000feetS70E ofhole1,andhole 3

ofhole J.Findthestrikeand dipoftheseam

cribed.

famarkerhorizon fromthefollowingfield

hofhorizonLocation

N45EofA

N15WofA


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oints


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oreData

1 thatthedepthdatafromthree verti-

rkerhorizonpermitthedeterminationof

verticaldrillcoreswithknowndepthsto

able,thetrue angleofdipandtwo pos-

na specialcase)areobtainable.Ifno

ablethestrikecannotbedetermined

graphicmeans,becausetherotatingdrill

ion.However,theangleofdipcanalways

tionofthe beddingtothedrill core.If

ani nclineddrillholeaswellas froma

ip andalimitednumberofstrike direc-

nein specialcases)withoutthepres-

Thetechniquesdiscussedinthis chapter

ike.

ssolvedbelow,illustratesthegeneral

edin thesolutionofcaseswherecore

lefromonly twoverticalholes.

eon aneast-westline2500feetapart(see

leAreachesa givenbedat800feet.Hole

same layerat2000feet.Thisis showninthe

Thebeddingmakesanangleof40 degrees

ore-beddingangle).Findthepossibilitiesof


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nd dipusingverticaldrill-coredatathe

e-beddingangleisthecomplementof

ade.Thus,theangleofdip is50degrees,

otdirectlymeasurable.

rill holeextendlinestothesurfaceat

he holeaxis.Thisconstructionabout

edasectionthrougha cone,whosesides

es withtheconicaxis.Thustheactual

cludedsomewhereonthesidesofeach

onsideredseparatelygivesaninfinite

ctions.However,ifbothholesare con-


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uralGeology

scanbereducedbyfindingthe plane(s)

ntfromeachcone,asshownbelow.

oneswiththesurfaceproducesthe

e57.Thesecirclesare drawnaboutA

ii.Each circlerepresentsthelocusof

50degreesandreachthebottomof

h.The infinityoftangentstoeachcircle

kedirectionsassociatedwitheachpos-

saretherewhichifassociatedwitha

ebottomof eachholeatthegiven

epresentedbyexternaltangentscom-

this condition.Thetwopossiblestrikes

din Figure57.Dipdirectionsareshown

ostrike possibilitiesintersectinapoint

rop.Ifonly thispointweredesired,it

ngthestraightli nejoiningthebottom

e.Clearly,thislinegivestheapparentdip

section.

lcasein whichthedrillholesare on

maltothe strike,orinthe directionof

sible tangentcommontobothcircles

rike uniquely.Notealsothatinthe verti-

ip,asgivenby thelinejoiningthe bot-

eswiththetrue dipasshownbythe conic


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oreData

ticaldrill-i

eonline


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uralGeology

oleslie onalineparallelto thestrike.

auniquestrike direction,sinceboth

chother,but yieldstwopossibledip

hefactthatboth holesencounterthe

icatesthattheholesliealong thestrike.

sentanddatafromoneverticaland

able,dipand strikepossibilitiesareob-

manneras intheprecedingsection.

heanglebetweenthebeddingandthe

e thehade.Ingeneraltwovariable

weentheinclinedholeandthe bedding:

gentlerorsteeperthantheangle of

ectionofinclinationofthehole can

ke.Variationsin theserelationships

trikeanddip possibilitiesobtainablein

sibilitiesmayvaryfromonetofour.

nDip ofBeds

dipandstrike directionsisexplained

possibilitiesofstrike.

eenbeddingandaxisofa verticalholeA

f theholeisunimportant,sincenomarkeris

edfeetN30Eof holeA,holeBis drilledand

angleof50degrees withthehorizontal.The

f15 degreeswiththeaxisofthe inclined

d dippossibilities?

sly70degrees(thecomplementofthe

tionobtainedfromtheverticaldrillcore

btainedfromanyverticaldrillcorein this

zonexists,wecanimaginethe vertical

h apositionthatit willintersectthe

ybut convenientdepth.Thehypotheti-

olesmustoccurat onepointina particu-

ticalholemustlie intheverticalplane

dhole,otherwisethetwowillnot meet.

tweenholesisunimportant,sincewe

oleplacedanywhere.


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ticaldrill-coredatawhereholesare online


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uralGeology

oleB,sothatan east-westvertical

oles(seeFigure60). Thetwoholesin-

rticalsectionbelowFLl.FrompointP

of20 degreesand15degrees,respec-

andBi.Theselinesrepresentpossible

eninthissection.Againthe coneabout

ssiblebedpositionsfor eachcore.Ifboth

anagainlimitpossibilities.Thecircle

usofall outcropsfromwhichabedcan

chpointP.Theconeabouttheinclined

surfaceinanellipse, asdrawnaboutB.

thodof constructinganellipse.)This

tcropsfromwhichbedscandipat 70

whilemakingat thesametimeanangle

softheinclinedhole.

bothcircleandellipsecanbe con-

es.Inthis mostgeneralcasefourexist,

nd dipusingcoredatafromone verticaland

ralcase.


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oreData

orstrikeand dipusingcoredatafromone vertical

einclinationofthe inclinedholeislessthan the

rrowisthehorizontalcomponentofthe inclined

finclination.Theshortarrowsshow possibledip

Mead)

ossibilityexists ofobtainingthree,

direction(s).Thesecasesdepend

directionoftheinclinedhole andthe

eral procedureoutlinedabovewillsolve

riouspossibilitiesare giveninFigure61.

wisthehorizontalprojectionofthe in-

urfacetothepointofintersectionwith

that Fissimilarto thegeneralcase

elysmallsizeofthe ellipsehereoccurs

enthebedsandthe coreaxisisverysmall

ethatin Aaparabola,ratherthanan el-


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uralGeology

thanDipof Beds

hecircleand ellipseresultingfromthe

ecteachotherorlieinternallytangentto

asetwostrike anddippossibilitiesexist,

onisunique.Thepossibilitiesthat can

nsbetweenstrikeofbedsand direction

wnin Figure62.Thegeneralconstruc-

ewillagaingivespecificsolutionstoany

ntsin Figure57.Whycan'tthesebepos-

amarkerhorizonatadepth of400feet.

et N30Wof Aencountersthesamemarker

eanglebetweentheholeaxis andthebedding

drocksurfaceiscoveredby100feetofover-

ocateadrillhole totestthemarkerhorizon

den?Whatistheamountofdip, andwhatare

pand strike?

ryrocksknowntohaveauniformdip,two

deon aneast-westline,200feetapart.No

he examinationofthecores.

anangle of20degreeswiththeaxis of

ole1;inclinedN45 Eatanangle of50

l;bedsmakeanangleof 15de-

hole.

epossibilities?

possibilitiesforbedsforwhichthe follow-

ained?

eanangleof 60degreeswiththeaxisof

hole A;inclinedduewestatan angle

ontal;bedsmakeanangleof80

e hole.

llholemakesanangleof 20degreeswith

ndredfeettothenorthof thisverticalhole,a

esto thehorizontalinadirectionN 30E

he axisofthehole.Whatis theangleand

rethestrikepossibilities?


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oreData

eddingandthe axisofthecoretakenfrom

es.Westoftheverticalhole,ata distanceof

nedduewestat anangleof55degreeswith

akeanangleof 10degreeswiththeaxisof

pandstrikepossibilities?

olutionswheretheinclinationofthe inclined

pofthebeds.(Modifiedfrom Mead)


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ata

ocalculatethedepthto agivenbed

ssif thewidthofoutcropandangleof

ustratesthe relationshipbetweenwidth

D;angleofdipEAG;depth tothetop

epthtothe bottomofthebedEG;and

wnbyaverticaldrill holeFG.Ifthestrike

n,itsdepthfromany pointonthesurface

onshipbetweenthicknessandwidthof

yasimple graphicprocedurewhichin-

datato scale.Thedesiredinformation

fromthe graph.

acommonsituationwhereadippinglayer

PointA liesonthebottom,andpoint Bon

nowntohavea dipof30 Eandastrike

edepthstothetopand bottomofthebedat

ofthebed.


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ata

essof,anddepthto, agivenbedwhenwidthof

are known,andgroundsurfaceishorizontal.


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uralGeology

ingaverticalsectionatright angles

thissectionmustbethe sameasthatof

owsthe truedip.ThemaplocationsA,

ntotheverticalsection,arerepresented

mandtoplinesof thebedaredrawn

spectively,atthe properdip.The

eddirectly,usingthesamescaleas the

Fisthe desireddepthtothetop ofthe

othebottomof thebed.

onsimilartothatabovewiththe excep-

eis notlevelbutslopesat anangleof10

onas thedipinthe bed.

uantitiesis showninFigure65,where

akendirectlyfromthe sectionandcon-

ns,usingthescale.Notethat pointsA

e horizontalofpointsAiandBi, whose

utcropon thegroundsurface.

onsimilartothefirst exampleabove,with

hat thegroundslopesatanangle of15de-

eto thedipofthe bed.

gure66.


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ata

hat ofFig.64,butgroundslopes oppositeto


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uralGeology

ttomof abedwhichstrikesN10 Wand

elevationof1000feet.PointB onthetopof

tN50E ofpointAandis atanelevationof

knessofthebed,andwhatis itsdepthat

vationof1450feetand lies1000feetdueeast

ndParelocated,usinga convenient

oughA marksthebottomofthebedat

ndthelineofstrike drawnthroughB

tthe900-footelevation.Thethreepoints

erticalsectiondrawnat rightanglesto

Pi arethethreepointsprojectedonto

awnthroughAiand Pnatanglesof30

ebottomandtop ofthebed,respectively.

canbescaledoffdirectly.Thedepth

wpointP isthedistancePiP2,measured

f35 degrees.Thesurfaceofthegroundis

weentheupperandlower contactsofthebed

othe strikeis200feet.Findthe thicknessof

bedifthewidth ofoutcropbetweenupper

eetas measuredatrightanglestothe strike.

20 E,andthebed dips45 E.

tionsasin theproblem2,butwiththe

pes20degreesi nadirectionoppositetothe

e bed.

fabedwhichstrikes east-westisatan

distanceof 700feetS30 Wofthispoint is

ebed.Theelevationhereis 1500feet.Ifthe

uethicknessand,also,theapparentthickness

verticaldrillhole.


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ata

rthicknessof,anddepth to,agivenbedwhen

rop(A,B)is knownandwherethegroundsurface


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opPatterns

ayeredrocksisknownor canbede-

ppatterncanbedrawnby graphicpro-

pographicmapofthearea.This pro-

edrockis mostlycoveredorwhenparts

e.Itmust beassumedthattheattitude

tionsisuniformoverthe givenarea.

hatthecontactsbetweenhorizontal

to topographiccontours.Thus,ifthick-

nforonelocality,the entireoutcroppat-

y extrapolatingthecontactsparallelto

d,ifbedsare vertical,thecontactswill

ndingacrosscountry,regardlessofto-

quiresgraphicconstructionwhenthe

ngle otherthan90degrees.Thispro-

to foldedrocksbyconsideringeachflank

oftiltedbeds.

heproceduretobeusedis giveninFigure

mapof anerodedarea.PointsA,B,andC

ofthreepointson thetopofa sandstone

e strikeanddipofthe sandstonebedand

ern,orarealdistribution.

s,usingthe benchmark(2150feet)

whichare bothonthe1800-footcon-

econtourfortheuppersurfaceof the

fstrike(east-west).

ormalto thestrikebelowFL1and

gtothesurfacecontourlines,usingthe

e.


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opPatterns101

eappropriatelevelsatpointsAi,Ci,

andCiareidentical.Thelineconnect-

dipofthetop ofthebed(24 S).

on,wecanprojectstructurecontours

hesandstonelayer.Thecontoursare

ebeneathpresenttopography,and

actuallybeeneroded.Onlyatpoints

crosstopographiccontoursofthesame

ofthetop ofthesandstonebedoccur.

gpointswitha continuousline.This

tcropofthe topofthesandstonelayer.

bottomof thebedparalleltothe

nttoa thicknessof100feet.(Notethat

ngalinenormalto thetopandbottom

ine.)

sforthebottomof thebedand,using

the top,markpointswherethestructure

opographiccontours.Thesepointsare

butthestructurecontourson thebot-

dsoasnotto complicatethedrawing.

thacontinuousline,whichmarksthe

e bed.

EET

ompletionofarealoutcroppatternwhenstrike,

ven.


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ngeandPitch;

ntlydescribethepositioninspace

Thismaybe thelineofintersectionor

res,suchasthe traceof(1)a faultwith

rotherlayeredstructure;(2)the axial

ngsurfaces;(3)cleavagewithbedding;

rther,thesubsurfacelinesmaybeslick-

r someformoflineation.

hlineis usuallygivenbythecompass

rojection(azimuthorbearing)and its

ithrespectto adippingplaneisdesired,

thatplane isgiven.Rememberthat

edin theverticalplanebetweenthehori-

and pitchistheanglebetweenthe hori-

measuredin adippingplanewhich

mswereusedear hertodescribefold

ccurswhereavein crossesastandstone

patthe surface.TheveinstrikesN40E and

sN 50Wandhasa dipof40 SW.Find(1)

lungeof theorezone;(2)the surfaceloca-

meettheorezoneat adepthof300 feet;(3)

zoneifit runsoutbelowthe500-footdepth;

emeasuredonthevein;and (5)theshortest

aft)fromtheoutcropof theveintothe ore

.


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ngeandPitch;Lineation103

gintersectingsurfaces.

deredasthezoneofintersectionofthe

edurewhichfollows,wewillworkonly

hesedipping structures.

psofveinand bed,asinFigure69A.

sforanarbitrarydepth hforbothvein

urfaceoutcropsofvein andbedlo-

orebody.ThepointofintersectionPof

slocatesthehorizontalprojectionofa

dy,at hdepth.LineAP,continuedsouth-

surfaceprojectionoftheore body,or

oneachother.


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ucturalGeology

f theorebodyissimply thebearing

.

t befoundinthe verticalplanein-

nthediagramwewill useA'P'asthe

lineAP.Ontheverticalsectionbelow

thh. ThusA'Banditscontinuationrep-

ofthe orebody,andangleP'A'Bisthe

00feetmeetstheorebody belowFL3.

urfaceatO'andthusO onthecontinua-

rfacelocationofaverticalshaftto meet

300feet.

orebody500feet verticallybelow

totallengthoftheore body.

he veinbetweenthesurfaceoutcrop

neisthe desiredangleofpitch.Theangle

ofthe pitchangle.Inordertomeasure

theinclinedplaneofthevein,we must

aceaboutlineAX.Forsimplicityinil-

nisgiveninFigure 69B.

dlineFL1andequalto XY.This

to thesurface.

ThefigureXZSRthusrepresentsa

thedepthhrotatedto thesurfaceabout

theactualcontourat thisdepth.

oftheorebody(of whichAPisthe

herotatedsurface.RememberthatY'

nsfromthesame depthh.AspointY

afterrotationtothe surface,thepoint

onmust,byanalogy,appearatf.

e actualorezoneontherotatedvein,

pitch.

ncefromlineAXtoO' istheshortest

the300-footlevel,measuredfromthe

ddips 70 SE.AveinstrikesN 60Wand

tionandangleof plungeoftheline ofinter-


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ngeandPitch;Lineation

gintersectingsurfaces.

es.Whatis theshortestdistancetorunan

ltsurfacetomeetthe veinatadepthof 500

perinch.)

agestrikesN75 Wanddips60 SW.The

imbstrikesN 20Wanddips 75 SW.What

thefoldaxis andthepitchofthe foldaxis

g?

ofa faultwhichstrikesN10E anddips

nddueeast.Findthe directionandplungeof

measuredonthe faultsurface.


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offaultproblemsinvolvesprimarily

oftwoinitiallyadjacentpointsinthe

icprojectionmethodisproperlyappli-

are translationalalongthefaultzoneor

ementispresent,thismethodcanbe

almotioncanbeapproximated.

beessentiallyparalleltothedip ofthe

hestrikeofthe fault(strikeslip),orat

ongthefaultsurface(obliqueslip).Al-

mon,dip-slipandstrike-slipfaultsare

eslip.Owingto theirlackofverticalmo-

entmuchsimplerproblemscomparedto

osestrikeanddipare N65Wand 30 SW,

wedsoutheastwardalongitsstrikeatthe

iscutoffabruptlywherei tiscrossedbyan

hatdips50 south.Fromthiscut-offpoint

ctlydownthefaultencounterstheseamagain

Wherealongthefaultline wouldtheveinbe

000-footlevel?

1000-footlevel.Theprojectionto

eseamonthe faultisdeterminedby

ntoursdrawnforanarbitrarydepth h.

themaplevelof thepointatwhichthe

e150-footinclinedshaft.It isfound

thefaultcontourcorrespondingtothe

et.


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uralGeology

dP'were coincident.Therefore,point

e tracewiththefaultlinemust have

n suchawaythatO'OequalsP'P.From

toO'A.OBisthusthe displacedvein

traceof theintersectionoftheseamand

kmustbe PO.

ramofthissituationshowinganalo-

reedimensions.

ybenormalor reverse,theproce-

applicabletoeithertype.The variables

aregenerally(1)the dipandstrikeof

andstrikeofthe displacedstructure,

strikeseparation(alongthe fault

msresultingfromfaultinginvolvethe

enetslip orthestrikeseparationif allthe

n.


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nalanalysisofFigure70A.


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p-slipfaultwhichdips65 Scausesastrike

a veinthatstrikesN35 Eanddips40 SE.

thiscaseisthe dipslip.

nFigure71, whichrepresentsthe

e,whichmaybeconsideredasthesur-

esiredminelevel.Notethatthe north

ectionofdip(tothe east),relativeto

evelsurface,thenorth blockmusthave

cementtooccur.Thus,the faultisnor-

emustlocateapoint atdepthonthe

eadjacenttopointE onthenorthvein.

ectionofthetraceofthe southvein

cedurefromChapter8.Aisthe location

ndBath depth.ADisthedesiredtrace.

Eisthe horizontalprojectionofthe

thefault.Beforefaulting,lineEFwasin

sis adip-slipfault,motionwasnormal

hus,ifwedrawa linenormaltothe

intersectlineADat C,thepositionof

ECisthe horizontalcomponentofthe

et slip(dipslip),whichlies inthe

averticalsectionnormaltothefault

owFL2.E'G isthedesirednet slip

C'Gisthethrow.Thethree-dimensional

mareshownin Figure72.Itshouldbe

uldbesolved inthesamemanner,work-

p,sideofthefault.In thiscaseAJis the

ld befoundbydrawingthefaultup-dip

PublicDomain,

Google-d

igitized

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oogle


124/190

uralGeology

heabovecaseanothervein(A)which

NEisfoundonlyon thesouthsideofthe

thenorth ofthefault.

enet slipwasdetermined.Thisin-

iedinthe solutionofthenewproblem.

down-orup-dipsideofthe fault.

showsthefault andveinA,whose

fthe faultistobe found.Bymeansof

zontalprojectionofthetraceofthe vein

thefault islocated.Thestructurecon-

opriatethrowforthenet slipintersects

tP.After faulting,apointoriginallyin

blockhasbeencarriedtopointQ.Thus,

d paralleltoveinAlocatesthe dis-

alanalysisofFigure71.


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113


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oogle


127/190

djust asreadilybyworkingonthe

fault(Figure73B).PointRis displaced

nceequaltotheheave,sothat veinA2

newposition,verticallyhigherthanvein

theprojectionofthetrace ofthevein

mpointRi,it willintersecttheoriginal

kstheintersectionoftheveinto befound

alsobefoundbydrawinga structure

throwdepth(theoriginallevelof vein

ntersectsthefaultat Q.Ofcourse,this

nationofauniquepointonthe traceRiQ.


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generalcasein whichthemovement

astrike-slipanda dip-slipcomponent.

thesameasthose fordip-slipfaults.

rmalfaultdips55 S.Thedirectionof

rfaceisN 30E,andthe netslipis 500feet.

Wanddips40 SWisfoundon thesouth

ocationoftheveinnorth ofthefault.

byusingtwovariationsofthe ortho-

ure.

rojectionofthetraceofthe southvein

Figure74.Thetruedip ofthefaultis

FL1.Fromthis,constructtheapparent

calplanewhichincludestheslickensides

,thisapparentdipisalso theplungeof

engthofthe netslipcanbemeasured

cturecontour(PQ)correspondingtothe

wnasshown.Theintersectionofthiscon-

onofthetracegivesapoint (B)which,

ultline paralleltothedirectionofthe

isplacednorthveinatA.

olvedequallywell byworkingonthe

wasdoneforthe dip-slipfaults,above.


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ternatesolutionoftheproblemgiven

zontalprojectionofthetraceofthesouth

previoussolution(Figure74), using

hh.Then,rotatethe faultplaneintothe

epresentedbytheh structurecontour

he pointPontheprojectionof thetrace

ceofthenorthvein onthefaultas

planeis thusthelinefrom OthroughP'.

glebetweenOP'andthefaultline isthe

dinthe planeofthefault.)

onoftheslickensidesonthefault

projectionoftheslickensides,N30 E.

ensidesath depthisshownatpoint T,

planeis atpointT'.All motionalong

alleltotheline ST'.SU,whichis500feet,

. AlinethroughUparallelto thefault

swhichweredisplacedthenet-slip dis-

meof faulting.Thislinecutsthetrace

pointonthenorthblockoriginallyin

topointX whichcanbefoundbydraw-

t lineparalleltoUS.PointX thuslo-

hblock.Notewellthatthepreviousprob-

dalso besolvedbyfollowingtheabove

aultplaneinto thehorizontal.


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uralGeology

heoriginalanddisplacedpositionsof two

venstrikeanddip areshownonopposite

trikeanddip,in Figure76.Findthedirection

winadvancewhetherthefaultisdip

iskindofdata isavailable,butthetype

bviousinthesolution.By inspectionof

esoutheastblockmovedup,sothat

ansofstructurecontourson veins

urfaceforthehangingwall,locatethe

eachofthese veinsonthefaultsurface.

A'CandB'C.Forsimplicity,theconstruc-

ut theprocedureisthesameas thatused

ThendrawACandBC paralleltoA'C

andBCaretheprojectionsofthe traces

ltsurfaceofthe footwall.

of intersectionofthetwosetsof

ebeen incontact.Thus,lineCCmust

sliponthefault surface.Thedirection

thenetslip.It becomesclearatthis

obliquemotion.Theamountofnetslip

alplane,whichincludesthenetslipCC,

epresentedbypointsCandC mustbe

ly,mustlieonthe twofaultsurface

CE',whosetruedepthsare foundin

FL1,normaltothefaultl ine.Thus,the

surfacetothefault,correspondtothe

CE',respectively,andhencetothe

everticalplanethroughthesepoints,

pectively.ForconvenienceinFigure

,whichis paralleltoCC.Thedistance

uirednetslipand isscaledfromthedia-


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Graphic Methods W L Donn J A Shimer.pdf