5. Stereonets - School of Ocean and Earth Science and ... · the blue circle marks this line. 9/20/17 GG303 17 Measuring the Angle Between Two Lines • Find the plane that contains

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5.Stereonets

I MainTopicsAPlo;ngaplane

BPlo;ngaline

CMeasuringtheanglebetweentwolines

DPlo;ngthepoletoaplane

E Measuringtheanglebetweentwoplanes

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Plo;ngaPlane:Overview

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•  Keyconcepts–  Aninclinedplaneplots

alongagreatcircle.–  Theendpointsofthe

cyclographictraceofaplanewithanon-zerodipareatdiametricallyopposedpointsontheprimiQvecircle;thesepointsdefinethelineofstrikefortheplane.

–  VisualizaQonoftheplane.

PrimiQvecircle

Cyclographictraceofplane

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Plo;ngaPlane:Step1

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•  Laytracingpaper(blue)overstereonet

•  Intheexamplehere,theplaneplo[edwillstrike60°anddip50°

Plo;ngaPlane:Step2

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•  TraceprimiQvecirclewithacompass

•  AddQckmarksat0°,90°,180°,and270°forreference.

•  LabeltheQckmarkat0°withan“N”torepresent“north”.

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Plo;ngaPlane:Step3

N

EQUAL-ANGLE NET(WULFF NET)

N

60°

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•  PlotaQckmarkinontheprimiQvecircleinthedirecQonofthestrikeoftheplane

•  Inthetheexamplehere,thestrikeis60°

Plo;ngaPlane:Step4

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•  NowrotatethetracingpapersuchthattheQckmarkforthestrikeliesatthe“northpole”.Thisiswhereallthegreatcirclesconverge.

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Plo;ngaPlane:Step5

•  Drawtheplanealongthegreatcirclewiththeappropriatedip(intheexamplehere,thesolidvioletcurveisaplanewithadipof50°).

•  ThedashedconstrucQonlineshowsthestrikeoftheplane;itisshownhereforillustraQononly.Itdoesnotneedtobeplo[ed.

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Plo;ngaPlane:Step6

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•  Removethestereonettoseetheresults

•  Visualizetheresults,andchecktoseeiftheymakesense.

•  Intheexample,–  Thevioletcurverepresentsaplanethatstrikes60°anddips50°.

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Plo;ngaLine:Overview

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•  Keyconcepts–  AlineliesattheintersecQonoftwoplanes:•  AverQcalplane(magenta)withastrikethatmatchesthetrendoftheline.

•  Aninclinedplane(violet)withadipthatmatchestheplungeofthelineandthatdipsinthedirecQonthelineplunges

–  VisualizaQon

Plo;ngaLine:Step1

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•  Laytracingpaperoverstereonet

•  Intheexamplehere,thelineplo[edwilltrend60°andplunge50°

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Plo;ngaLine:Step2

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•  TraceprimiQvecirclewithacompass

•  AddQckmarksat0°,90°,180°,and270°forreference.

•  LabeltheQckmarkat0°withan“N”torepresent“north”.

Plo;ngaLine:Step3

N

EQUAL-ANGLE NET(WULFF NET)

N

60°

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•  PlotaQckmarkinontheprimiQvecircleinthedirecQonofthetrendoftheline.

•  Inthetheexamplehere,thelinetrends60°.

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Plo;ngaLine:Step4

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•  NowrotatethetracingpapersuchthattheQckmarkatthetrendliesalongthesmallcirclethatprojectsasastraightline(i.e.,the“equatorialline”)

•  ThedashedpinklinerepresentsaverQcalplanecontainingtheline

Plo;ngaLine:Step5•  Markofftheplunge,counQng

fromtheprimiQvecircletowardsthecenteroftheplot.

•  Thedashedvioletcurveisaplanewithadipthatmatchestheplungeoftheline.ThisplanedipsinthedirecQonthelinetrends,anditstrikesperpendiculartothetrendoftheline.

•  ThelineofinterestisattheintersecQonoftheverQcalpinkplaneandtheplungingvioletplane.

•  ThedashedconstrucQonlinesareshownhereforillustraQononly.Theydonotneedtobeplo[ed.

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Plo;ngaLine:Step6

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•  Removethestereonettoseetheresults.

•  Visualizetheresults,andchecktoseeiftheymakesense.

•  Intheexample,–  Theline(markedbythesmallred

circle)trends60°andplunges50°.–  Thedashedpinklinerepresentsa

planethatstrikes60°anddips90°.–  Thevioletdashedcurverepresents

aplanethatstrikes330°anddips50°towardsthenortheast.

–  Theplanesintersectattheline.–  Theplanes(dashed)areshownfor

illustraQonpurposesonly.Theytypicallywouldnotbeshownifonlythelineisoffinterest.

MeasuringtheAngleBetweenTwoLines

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•  Keyconcepts–  Theanglebetweenthelinesismeasuredalongthecyclographictraceoftheplanethatcontainsthelines.

–  Theprocedureisexactlyanalogoustomeasuringtheanglebetweentwolineswithaprotractor.

PrimiQvecircle

“Coloredprotractorsofdifferentdip”

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•  Plotthelines•  Intheexample,onelinetrends78°andplunges36°;theredcirclemarksthisline.

•  Theotherlinetrends146°andplunges49°;thebluecirclemarksthisline.

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•  Findtheplanethatcontainsbothlines–  Rotatethetracingpaper

suchthatbothlineslieonasinglegreatcircle.Thisrequirescare.

–  Measuretheanglealongthegreatcirclebetweenthetwolines.Here,theangleis50°.

–  Bycoincidence,thecommonplane(green)dips50°.

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•  HereistheplotrestoredtoitsoriginalorientaQon.

•  Thecommonplane(green)hasastrikeof40°.

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•  Hereistheplotwithoutthestereonet–  Checktoseewhethertheplotlookscorrect(i.e.,visualize).

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Plo;ngthePoletoaPlane

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•  Keyconcepts–  Thepoletoaplaneisaline

thatcanbeplo[edlikeanyotherline.

–  ThepoletoaplaneofinterestliesinaverQcalplaneperpendiculartotheplaneofinterest.

–  Thepolealsomakesa90°angle(asmeasuredintheverQcalplane)withrespecttothe“dipvector”oftheplaneofinterest.

Plo;ngthePoletoaPlane

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•  Example•  Consideraplaneofinterestthat

strikes330°anddips50°totheNE.Itisplo[edinblue.

•  ItspolecanbefoundbysimplecalculaQons.Thepoletrends240°andplunges40°.Thisisplo[edattheredcircle.

•  ThepoletoaplaneliesinaverQcalplaneperpendiculartotheplaneofinterest.

•  Thepolealsomakesa90°angle(asmeasuredintheverQcalplane)withrespecttothe“dipvector”oftheplaneofinterest.

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MeasuringtheAngleBetweenTwoPlanes

•  Keyconcepts–  Theanglebetweentwo

planes(blueandred)istheanglebetweenthepolestotheplanes.

–  Theanglebetweentheplanesismeasuredintheplane(green)containingthepoles.

–  TheanglebetweentangentstothecyclographictracesonanequalareprojecQonalsogivestheanglebetweentheplanes,butdrawingthetangentsaccuratelyisdifficult.

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•  Plottheplanesandthepoles

•  Example–  Theblueplanestrikes330°

anddips50°totheNE.–  Theredplanestrikes30°

anddips20°totheSE.–  Thebluepoletrends240°

andplunges40°totheSW.–  Theredpoletrends300°

andplunges70°totheNW.

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•  Measuretheanglebetweenthepolesintheplanecontainingthepoles–  Rotatethetracingtofind

thecommonplane(green)thatcontainsthetwopoles.

–  Theanglebetweentheplanesismeasuredintheplane(green)containingthepoles.

–  Theangledeterminedgraphicallyis43°(measuredtothenearestdegree).

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•  Appearanceofplotwithoutstereonet–  Theplotisbusy.–  TheanglebetweentangentstothecyclographictracesonanequalareprojecQonalsogivestheanglebetweentheplanes,butdrawingthetangentsaccuratelyisdifficult.

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>>Tr=300*pi/180;>>Tb=240*pi/180;>>Pr=70*pi/180;>>Pb=40*pi/180;>>[bx,by,bz]=sph2cart(Tb,Pb,1);>>[rx,ry,rz]=sph2cart(Tr,Pr,1);>>blue=[bx,by,bz];>>red=[rx,ry,rz];>>angle=acos(dot(blue,red))*180/piangle=42.6907

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Accuracy

ThisangleisconsistentwiththegraphicalsoluQon

Documents

5. Stereonets - School of Ocean and Earth Science and ... · the blue circle marks this line. 9/20/17 GG303 17 Measuring the Angle Between Two Lines • Find the plane that contains