PLATE MOTIONS: BASIC CONCEPTS

San Andreas Transform FaultCarrizo Plain

Iceland SpreadingCenter, Thingvellir

Pacificplate

NorthAmericanplate

Eurasianplate

NorthAmericanplate

20 mm/yr

35 mm/yr

Earth's outer shell made up of ~15 major rigid plates ~ 100 km thick

Plates move relative to each other at speeds of a few cm/ yr (aboutthe speed at which fingernails grow)

Plates are rigid in the sense that little (ideally no) deformation occurswithin them,

Most (ideally all) deformation occurs at their boundaries, giving rise toearthquakes, mountain building, volcanism, and other spectacularphenomena.

Style of boundary and intraplate deformation depends on direction &rate of motion, together with thermo-mechanical structure

BASIC CONCEPTS: RIGID PLATES

In most placeswe know generalplate boundarygeometry from

geology,topography, and

earthquakes

Ideal plateboundaries very

narrowMany real plate

boundaries -especially

continental - aredeformation

zones up to 1000km wide, withmotion spread

beyond nominalboundary

PLATE BOUNDARIES: GENERALLY BUTNOT FULLY KNOWN

Gordon & Stein, 1992

In some places: Indian Ocean. Mediterranean, NWAsia, etc. we’re still trying to figure out plate geometry

NW ASIANot clear whereNorth Americaboundary isMay be Okhotskplate distinctfrom NorthAmericaMay be Amuriaplate east ofBaikal riftdistinct fromEurasiaMay be NorthChina plate

Wei and Seno, 1988

?

?

??

??

At a point r along the boundarybetween two plates, with latitudeλ and longitude µ, the linearvelocity of plate j with respect toplate i , v ji , is given by thevector cross product

v ji = ωj i x r

r is the position vector to thepoint on the boundary

ωj i is the angular velocity vectoror Euler vector described by its

magnitude (rotation rate) |ωj i |

and pole (surface position) (θ, φ)

EULER VECTORRelative motion between two rigid plates on the spherical earth can bedescribed as a rotation about an Euler pole

Linear velocity

r

Stein & Wysession, 2003

Direction of relative motion is a small circleabout the Euler pole

First plate ( j) moves counterclockwise ( righthanded sense) about pole with respect tosecond plate (i).

Boundary segments with relative motionparallel to the boundary are transforms, smallcircles about the pole

Segments with relative motion away from theboundary are spreading centers

Segments with relative motion towardboundary are subduction zones

Magnitude (rate) of relative motion increaseswith distance from pole because|v ji | = |ωj i | | r | sin γ , where γ is the anglebetween pole and site

All points on a boundary have the sameangular velocity, but the magnitude of linearvelocity varies from zero at the pole to amaximum 90º away.

ω212 wrt 1

ω121 wrt 2

Stein & Wysession, 2003

GPS DATA RIGIDNORTH AMERICANPLATE ROTATING

ABOUT EULERPOLE

Direction followsmall circles

Rates increaseas sine ofangular distancefrom pole

Velocities differfrom these innonrigidboundary zone

Stein & Sella, 2002

At a point r on theplate boundary, withlatitude λ andlongitude µ, linearrelative velocity v , isgiven by the vectorcross product

v = ω x r

r is the positionvector to the point onthe boundary

ω is the angularvelocity or Eulervector described byits magnitude(rotation rate) |ω |and pole (surfaceposition) (θ, φ)

CARTESIAN COMPONENTS OF ANGULAR VELOCITY ωAND LINEAR VELOCITY v

LINEAR VELOCITY TYPICALLY DONE AS EITHERNS, EW COMPONENTS OR RATE & AZIMUTH

Scalar (dot)product withunit vectorsin NS & EWdirections

GivesNS & EWcomponentsof linearvelocity

And hencerate andazimuth

BOUNDARY TYPECHANGES WITHORIENTATION

PACIFIC -NORTH AMERICA

PACIFIC wrt NORTH

AMERICApole

CONVERGENCE - ALEUTIAN TRENCH

54 mm/yr

EXTENSION -GULF OF CALIFORNIA

STRIKE SLIP - SAN ANDREAS

Stein & Wysession, 2003

BOUNDARY TYPE CHANGES WITH ORIENTATION

EURASIA - NUBIA (west Africa)

NUVEL-1Argus et al., 1989

+ EURASIA wrt NUBIA POLE

EXTENSIONTERCEIRA

RIFT

STRIKE-SLIPGLORIA

TRANSFORM OBLIQUE CONVERGENCENORTH AFRICA

SMALL CIRCLE ABOUT POLE

EURASIA

NUBIA

NORTHAMERICA

Until recently, done by combining different types ofdata from different boundaries

Spreading rates from sea-floor magnetic anomalies

Directions of motion from orientations of transform faults and slipvectors of earthquakes on transforms and subduction zones

Problems with resulting geologic plate motion models:

No way to measure rates at subduction boundaries

Data average over different time scales:-magnetic anomalies typically 3 Myr

-transform azimuths millions of years

-slip vectors seconds

Data only at plate boundaries

Inversion assumes rigid plates

FINDING EULER VECTORS

ANOMALY: 2’ 2 CENTRALSPREADING RATESFROM MAGNETIC

ANOMALIES

Match observedprofiles to syntheticsfor different spreadingratesTime resolution limitedby magnetic reversalhistoryNUVEL-1 uses anomaly2’ (3 ma) and soaverages over that timeCan’t go finer thancentral anomalycorresponding to lastreversal (780 ka)

GULF OF CALIFORNIAPACIFIC - NORTH AMERICA

DeMets et al., 1987

PACIFIC

ANTARCTIC

TRANSFORM FAULT AZIMUTH FROM BATHYMETRY ANDSTRIKE-SLIP EARTHQUAKE FOCAL MECHANISMS

Measureazimuth frombathymetryHigh-resolution(Seabeam,Gloria) is bestAverages overmillions ofyearsEarthquakemechanismsalso used, lessprecise

Stein & Wysession, 2003

SUBDUCTIONAZIMUTH FROM

TRENCH THRUSTFAULT

MECHANISM SLIPVECTORSCONVERGENCE -

ALEUTIAN TRENCH54 mm/yr

PACIFIC

NORTH AMERICA

Common problem: for oblique (not trenchnormal) convergenceForearc sliver moves distinctly from bothplatesSlip vectors record motion of sliver relativeto oceanic plate, not major plate motion

Fault plane

Stein & Wysession, 2003

Geometricconditions:

Slip vectors andtransform faultslie on small circlesabout the pole, sopole lies on a greatcircle at right anglesto them

Rate of plate motionincreases with sineof distance frompole

FINDING EULER POLE FROM RELATIVE MOTION DATA

Cox & Hart, 1986

INVERSE PROBLEM - FIND EULER VECTORS FROM DATA

POSE INVERSEPROBLEM -FIND EULER

VECTORSFROM DATA

Set up modelvector m (Eulervectors)and data vector d(observed ratesand azimuths)Form partialderivative matrix G

LEAST SQUARESSOLUTION TO

INVERSEPROBLEM

Find change inmodel vector ∆mfrom starting model(Euler vectors)using partialderivative matrix Gto minimizemisfit ∆d to datavector (observedrates and azimuths)

IMPROVED PLATEGEOMETRY: DISTRICT INDIA

& AUSTRALIAPre-NUVEL models assumedsingle Indo-Australian plate

Deformation in Central IndianOcean shown by largeearthquakes & folding

New model: distinct Indian andAustralian plates separated by adiffuse boundary zone perhapsformed by Himalayan uplift

New model better fits focalmechanisms & magnetics

Improved fit statistically significant,so two plates resolved

Subsequent studies refined modeland show that India and Australiahave been distinct for at least 3Myr and likely longer.

Wiens et al., 1985

SUCCESSIVE MODELS FIT USE MORE DATA & FIT BETTER

More data Smaller misfit

DeMets et al., 1990

NUVEL-1A GLOBAL RELATIVE PLATE MOTION MODELPlate motions averaged over past 3 Ma

Demets, Gordon, Argus & Stein, 1994

To reverse sense of motion, use negative (same rate and with antipole:negative latitude, longitude +180°)

ωjk = -ω kj

We assume that plates are rigid, so all motion occurs at theirboundaries. We can then add Euler vectors

ω jk = ω ji + ω ik

because the motion of plate j with respect to plate k equals the sumof the motion of plate j with respect to plate I and the motion of plate i

with respect to plate k

Thus from a set of vectors with respect to one plate, e.g. i

ωjk = ω ji - ω ki

we form any Euler vector needed.

Operations easily done using Cartesian components

EULER VECTOR OPERATIONS

GLOBAL EULER VECTOR - derived using all data from all plateboundaries, assumes all plates are rigid.

BEST FITTING VECTOR - for a plate pair using only data from thatpair of plates' boundary

CLOSURE FITTING VECTOR - using only data from the other plates’boundaries

Ideally, if the plates were rigid and data perfect:

- all three vectors would be the same.

-for three plates meeting at a triple junction, the best fitting vectors foreach of the three plate pairs would sum to zero.

These provide tests for plate rigidity

DIFFERENT TYPES OF EULER VECTORS

Plate motions over a few yearsobserved by space geodesy verysimilar to predictions of NUVEL-1or similar geologic modelsdescribing average motions overpast 3 Ma

Hence plate motions aregenerally steady, presumablybecause viscous asthenospheredamps episodic motions at plateboundaries

However, in places NUVEL-1and space geodesy disagree.

Why?

SPACE GEODESY & GEOLOGICPLATE MOTION MODELS

GENERALLY AGREE

Robbins et al., 1993

Because we only have certain types of data for some boundaries, othersare inferred by vector summation assuming rigid plates. In particular,convergence rates at subduction zones are estimated by global closure,combining data from all plate boundaries.

Predicted rate atwhich the Cocosplate subductsbeneath NorthAmerica depends onmeasured rates ofPacific-NorthAmerica spreading inthe Gulf of Californiaand Cocos-Pacificspreading on theEast Pacific Rise.

GLOBAL PLATE CIRCUIT CLOSURE

DeMets et al., 1990

In some cases, such as relative motion between North and South America,no direct data were used because the boundary location and geometry areunclear, so the relative motion is inferred entirely from closure

Motion is poorlyknown

SOME BOUNDARIES - NO DIRECT DATA

Motions of plate pairs based on both rateand azimuth data are best known

NA

SA

NB

EU

Wysession et al., 1995

AT TRIPLE JUNCTIONS,WHERE THREE PLATESMEET, ADD LINEARVELOCITY VECTORS

Direction & rate of Juan de Fuca platesubduction beneath North America found

by combining:

Direction & rate of Juan de Fuca-Pacificspreading at Juan de Fuca ridge

Direction & rate of North America-Pacificmotion from Gulf of California and San

Andreas (transform) fault

Plate motion showed subduction, despiteno trench or thrust fault earthquakes

CASCADE VOLCANOESINDICATE JUAN DE FUCASUBDUCTION BENEATH

NORTH AMERICA

Mt Saint Helens1980 eruption

USGS

EURASIA - NUBIA (West Africa) motion

Primarily derived from small differences in spreadingrate & direction between North America - Eurasia andNorth America - Nubia motion at Mid-Atlantic Ridge

NORTHAMERICA

EURASIA

NUBIA

Eurasia - Nubiaspreading atAzores Triplejunction

Argus et al., 1989

Relative motions between plates are most important

In some applications important to consider absoluteplate motions, those with respect to the deep mantle

In general both plates and plate boundaries movewith respect to the deep mantle

For example, assume Africa were not moving withrespect to the deep mantle. If so, as lithosphere isadded by spreading at the Mid-Atlantic ridge, boththe ridge and South America move westwardrelative to the mantle.

Conversely, as the African plate lost area bysubduction beneath Eurasia in the Mediterranean,the trench "rolls backwards”, moving south relativeto the mantle.

Increasingly, it seems that such motions may havesignificant tectonic consequences

No direct way to measure absolute motions, need toinfer indirectly

ABSOLUTEPLATE MOTIONS

NNR reference frame obtained assuming no net rotation of the lithosphereas a whole, so sum of the absolute motion of all plates weighted by theirarea is zero

NNR reference frame similar to hotspot frame

Despite unresolved questions about the nature and existence of hot spotsand plumes, NNR reference frames often used to infer absolute motions

NNR - NO NETROTATIONABSOLUTEMOTIONS

To compute absolute motions, recognize that motions in an absolutereference frame correspond to adding a rotation to all plates

Use Euler vector formulation and treat absolute reference frame asmathematically equivalent to another plate

For example, given NNR Euler vector relative to North America ωNNR-NA its negative ω NA-NNR is the absolute Euler vector ΩNA for NorthAmerica in NUVEL-NNR reference frame

Hence absolute and relative motions related byωij = ΩI - Ωj

and linear velocity in absolute reference frame at point r onplate i is

Vi = Ωi x r

ABSOLUTE MOTION CALCULATION

RIDGES TYPICALLY MIGRATE WITH RESPECT TO THEMANTLE

May have effects on topography, spreading process,magma chemistry

Stein et al, 1977

Hot spot hypothesis assumes certainlinear volcanic trends result from platemotion over a hot spot, fixed source ofvolcanism, causing melting in theoverriding plate.

If the overriding plate is oceanic, getprogression from active volcanism thatbuilds islands, to older islands, tounderwater seamounts as sea floormoves away from hot spot, cools, andsubsides. Get topographic swell aroundhotspot and volcanic age progressionaway from it.

Direction and age of volcanic chain givemotion of plate with respect to hot spot.

Hot spot tracks beneath different platesand assuming hot spots fixed withrespect to deep mantle (or move relativeto each other more slowly than plates),yields hot spot reference frame.

ABSOLUTE MOTIONFROM HOT SPOTS

HOTSPOT / PLUME HYPOTHESISOften assumed hotspots result fromplumes of hot materialrising from greatdepth, perhaps core-mantle boundary

Plumes would besecondary convectionmode, ~ 5% of heattransfer, bringing updeep mantle material.

Would be important inEarth’s thermal &chemical evolution.

Would have tectonicsignificance - headsof new plume mightcause continentalbreakup and floodbasalts

Concepts of hot spots and plumes are attractive and widely used, but therelation between the persistent volcanism and possible deep mantle plumes isunder active investigation because of many deviations from what would beexpected:

Some hot spots move significantly

Some chains show no clear age progression

Oceanic heat flow data show little or no thermal anomalies at the swells

Seismological studies find low-velocity anomalies, but assessing their depthextent and relation to possible plumes is difficult and controversial

Convection models of plumes rising from core-mantle boundary may notcorrectly include pressure effects

HOTSPOT / PLUME CONTROVERSY

HOTSPOT TYPES:MIDPLATE CONTINENTAL (Yellowstone,…)MIDPLATE OCEANIC (Hawaii, Bermuda,…)

ON OR NEAR RIDGE (Iceland, Azores, Easter…)

YELLOWSTONE NATIONAL PARK, WYOMING USA

Type example of continental hot spot?

AGE PROGRESSIVE VOLCANISMTrend consistent with absolute motion of North America

Stein & Wysession, 2003

COMPLEXITY: additionalvolcanic progression towest - Newberryvolcanics

Proposed alternative:forced mantle flow anddecompression meltingresulting from local platemotions. Near subductionzone upper mantle forced toflow northwest because ofcorner flow driven bysubducting plate. Yellowstoneand Newberry magmatismfollow these trends as fertilemantle flows past residuumand ascends (red-to-whitearrows).

Humphreys et al., 2000

Bend in the Hawaiian-Emperorchain interpreted as indicatingPacific plate changed directionabout 43 Ma, leaving bend asplate moved over fixed hotspotnow under Hawaii

MIDPLATE OCEANICHOTSPOT: HAWAIIAN

EMPEROR CHAIN

Mauna Loa

PROBLEM 1:THE 43 Ma

“NONEVENT”

No evidence forchange inrelative platemotions at 43Ma, sincefracture zoneorientationsunaffected

Fixed hotspotwould cause allseamounts tohave samepaleolatitudeHawaiian hotspotactually driftedsouthwardbetween 47 and81 Ma

Tarduno and Cottrell(1997)

PROBLEM 2:HAWAIIANHOTSPOTHAS NOT

BEEN FIXED

SUMMARYAbsolute motions can be defined relative to either No NetRotation or Hotspot reference framesGPS data given in ITRF, designed to be like NUVEL-NNRAbsolute motions may have roles in tectonics but detailsunclearHotspot/plume model has major problems and may need tobe discarded, but it’s not clear what the alternatives are