PLATE MOTIONS: BASIC CONCEPTS

PLATE MOTIONS: BASIC CONCEPTS North American plate 20 mm/yr Eurasian plate Pacific plate 35 mm/yr North American plate Iceland Spreading Center, Thingvellir San Andreas Transform Fault Carrizo Plain

BASIC CONCEPTS: RIGID PLATES 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 (about the speed at which fingernails grow) Plates are rigid in the sense that little (ideally no) deformation occurs within them, Most (ideally all) deformation occurs at their boundaries, giving rise to earthquakes, mountain building, volcanism, and other spectacular phenomena. Style of boundary and intraplate deformation depends on direction & rate of motion, together with thermo-mechanical structure

In most places we know general plate boundary geometry from geology, topography, and earthquakes PLATE BOUNDARIES: GENERALLY BUT NOT FULLY KNOWN Ideal plate boundaries very narrow Many real plate boundaries - especially continental - are deformation zones up to 1000 km wide, with motion spread beyond nominal boundary Gordon & Stein, 1992 In some places: Indian Ocean. Mediterranean, NW Asia, etc. we re still trying to figure out plate geometry

NW ASIA Not clear where North America boundary is? May be Okhotsk plate distinct from North America???? May be Amuria plate east of Baikal rift distinct from Eurasia? May be North China plate Wei and Seno, 1988

EULER VECTOR Relative motion between two rigid plates on the spherical earth can be described as a rotation about an Euler pole At a point r along the boundary between two plates, with latitude λ and longitude µ, the linear velocity of plate j with respect to plate i, v ji, is given by the vector cross product Linear velocity v ji = ω j i x r r is the position vector to the point on the boundary r ω j i is the angular velocity vector or Euler vector described by its magnitude (rotation rate) ω j i Stein & Wysession, 2003 and pole (surface position) (θ, φ)

Direction of relative motion is a small circle about the Euler pole First plate ( j) moves counterclockwise ( right handed sense) about pole with respect to second plate (i). ω 21 2 wrt 1 Boundary segments with relative motion parallel to the boundary are transforms, small circles about the pole Segments with relative motion away from the boundary are spreading centers Segments with relative motion toward boundary are subduction zones Magnitude (rate) of relative motion increases with distance from pole because v ji = ω j i r sin γ, where γ is the angle between pole and site All points on a boundary have the same angular velocity, but the magnitude of linear velocity varies from zero at the pole to a maximum 90º away. ω 12 1 wrt 2 Stein & Wysession, 2003

GPS DATA RIGID NORTH AMERICAN PLATE ROTATING ABOUT EULER POLE Direction follow small circles Rates increase as sine of angular distance from pole Velocities differ from these in nonrigid boundary zone Stein & Sella, 2002

CARTESIAN COMPONENTS OF ANGULAR VELOCITY ω AND LINEAR VELOCITY v At a point r on the plate boundary, with latitude λ and longitude µ, linear relative velocity v, is given by the vector cross product v = ω x r r is the position vector to the point on the boundary ω is the angular velocity or Euler vector described by its magnitude (rotation rate) ω and pole (surface position) (θ, φ)

LINEAR VELOCITY TYPICALLY DONE AS EITHER NS, EW COMPONENTS OR RATE & AZIMUTH Scalar (dot) product with unit vectors in NS & EW directions Gives NS & EW components of linear velocity And hence rate and azimuth

CONVERGENCE - ALEUTIAN TRENCH 54 mm/yr BOUNDARY TYPE CHANGES WITH ORIENTATION PACIFIC - NORTH AMERICA STRIKE SLIP - SAN ANDREAS PACIFIC wrt NORTH AMERICA pole EXTENSION - GULF OF CALIFORNIA Stein & Wysession, 2003

BOUNDARY TYPE CHANGES WITH ORIENTATION EURASIA - NUBIA (west Africa) NORTH AMERICA EURASIA EXTENSION TERCEIRA RIFT STRIKE-SLIP GLORIA TRANSFORM NUBIA OBLIQUE CONVERGENCE NORTH AFRICA SMALL CIRCLE ABOUT POLE + EURASIA wrt NUBIA POLE NUVEL-1 Argus et al., 1989

Until recently, done by combining different types of data from different boundaries Spreading rates from sea-floor magnetic anomalies Directions of motion from orientations of transform faults and slip vectors 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

SPREADING RATES FROM MAGNETIC ANOMALIES ANOMALY: 2 2 CENTRAL Match observed profiles to synthetics for different spreading rates Time resolution limited by magnetic reversal history NUVEL-1 uses anomaly 2 (3 ma) and so averages over that time Can t go finer than central anomaly corresponding to last reversal (780 ka) GULF OF CALIFORNIA PACIFIC - NORTH AMERICA DeMets et al., 1987

TRANSFORM FAULT AZIMUTH FROM BATHYMETRY AND STRIKE-SLIP EARTHQUAKE FOCAL MECHANISMS Measure azimuth from bathymetry Highresolution (Seabeam, Gloria) is best Averages over millions of years Earthquake mechanisms also used, less precise PACIFIC ANTARCTIC Stein & Wysession, 2003

NORTH AMERICA CONVERGENCE - ALEUTIAN TRENCH 54 mm/yr SUBDUCTION AZIMUTH FROM TRENCH THRUST FAULT MECHANISM SLIP VECTORS PACIFIC Common problem: for oblique (not trench normal) convergence Forearc sliver moves distinctly from both plates Slip vectors record motion of sliver relative to oceanic plate, not major plate motion Fault plane Stein & Wysession, 2003

FINDING EULER POLE FROM RELATIVE MOTION DATA Geometric conditions: Slip vectors and transform faults lie on small circles about the pole, so pole lies on a great circle at right angles to them Rate of plate motion increases with sine of distance from pole Cox & Hart, 1986

INVERSE PROBLEM - FIND EULER VECTORS FROM DATA

POSE INVERSE PROBLEM - FIND EULER VECTORS FROM DATA Set up model vector m (Euler vectors) and data vector d (observed rates and azimuths) Form partial derivative matrix G

LEAST SQUARES SOLUTION TO INVERSE PROBLEM Find change in model vector m from starting model (Euler vectors) using partial derivative matrix G to minimize misfit d to data vector (observed rates and azimuths)

Pre-NUVEL models assumed single Indo-Australian plate Deformation in Central Indian Ocean shown by large earthquakes & folding IMPROVED PLATE GEOMETRY: DISTRICT INDIA & AUSTRALIA New model: distinct Indian and Australian plates separated by a diffuse boundary zone perhaps formed by Himalayan uplift New model better fits focal mechanisms & magnetics Improved fit statistically significant, so two plates resolved Subsequent studies refined model and show that India and Australia have been distinct for at least 3 Myr and likely longer. Wiens et al., 1985

SUCCESSIVE MODELS FIT USE MORE DATA & FIT BETTER DeMets et al., 1990 More data Smaller misfit

NUVEL-1A GLOBAL RELATIVE PLATE MOTION MODEL Plate motions averaged over past 3 Ma Demets, Gordon, Argus & Stein, 1994

EULER VECTOR OPERATIONS To reverse sense of motion, use negative (same rate and with antipole: negative latitude, longitude +180 ) ω jk = -ω kj We assume that plates are rigid, so all motion occurs at their boundaries. 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 sum of 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 ω jk = ω ji - ω ki we form any Euler vector needed. Operations easily done using Cartesian components

DIFFERENT TYPES OF EULER VECTORS GLOBAL EULER VECTOR - derived using all data from all plate boundaries, assumes all plates are rigid. BEST FITTING VECTOR - for a plate pair using only data from that pair 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 for each of the three plate pairs would sum to zero. These provide tests for plate rigidity

Plate motions over a few years observed by space geodesy very similar to predictions of NUVEL-1 or similar geologic models describing average motions over past 3 Ma SPACE GEODESY & GEOLOGIC PLATE MOTION MODELS GENERALLY AGREE Hence plate motions are generally steady, presumably because viscous asthenosphere damps episodic motions at plate boundaries However, in places NUVEL-1 and space geodesy disagree. Why? Robbins et al., 1993

GLOBAL PLATE CIRCUIT CLOSURE Because we only have certain types of data for some boundaries, others are 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 at which the Cocos plate subducts beneath North America depends on measured rates of Pacific-North America spreading in the Gulf of California and Cocos-Pacific spreading on the East Pacific Rise. 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 are unclear, so the relative motion is inferred entirely from closure Motion is poorly known SOME BOUNDARIES - NO DIRECT DATA NA EU NB SA Wysession et al., 1995 Motions of plate pairs based on both rate and azimuth data are best known

AT TRIPLE JUNCTIONS, WHERE THREE PLATES MEET, ADD LINEAR VELOCITY VECTORS Direction & rate of Juan de Fuca plate subduction beneath North America found by combining: Direction & rate of Juan de Fuca-Pacific spreading at Juan de Fuca ridge Direction & rate of North America-Pacific motion from Gulf of California and San Andreas (transform) fault Plate motion showed subduction, despite no trench or thrust fault earthquakes

CASCADE VOLCANOES INDICATE JUAN DE FUCA SUBDUCTION BENEATH NORTH AMERICA Mt Saint Helens 1980 eruption USGS

EURASIA - NUBIA (West Africa) motion Primarily derived from small differences in spreading rate & direction between North America - Eurasia and North America - Nubia motion at Mid-Atlantic Ridge NORTH AMERICA EURASIA NUBIA Eurasia - Nubia spreading at Azores Triple junction Argus et al., 1989

Relative motions between plates are most important In some applications important to consider absolute plate motions, those with respect to the deep mantle ABSOLUTE PLATE MOTIONS In general both plates and plate boundaries move with respect to the deep mantle For example, assume Africa were not moving with respect to the deep mantle. If so, as lithosphere is added by spreading at the Mid-Atlantic ridge, both the ridge and South America move westward relative to the mantle. Conversely, as the African plate lost area by subduction beneath Eurasia in the Mediterranean, the trench "rolls backwards, moving south relative to the mantle. Increasingly, it seems that such motions may have significant tectonic consequences No direct way to measure absolute motions, need to infer indirectly

NNR - NO NET ROTATION ABSOLUTE MOTIONS NNR reference frame obtained assuming no net rotation of the lithosphere as a whole, so sum of the absolute motion of all plates weighted by their area is zero NNR reference frame similar to hotspot frame Despite unresolved questions about the nature and existence of hot spots and plumes, NNR reference frames often used to infer absolute motions

ABSOLUTE MOTION CALCULATION To compute absolute motions, recognize that motions in an absolute reference frame correspond to adding a rotation to all plates Use Euler vector formulation and treat absolute reference frame as mathematically 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 North America in NUVEL-NNR reference frame Hence absolute and relative motions related by ωij = ΩI - Ωj and linear velocity in absolute reference frame at point r on plate i is Vi = Ωi x r

RIDGES TYPICALLY MIGRATE WITH RESPECT TO THE MANTLE May have effects on topography, spreading process, magma chemistry Stein et al, 1977

Hot spot hypothesis assumes certain linear volcanic trends result from plate motion over a hot spot, fixed source of volcanism, causing melting in the overriding plate. ABSOLUTE MOTION FROM HOT SPOTS If the overriding plate is oceanic, get progression from active volcanism that builds islands, to older islands, to underwater seamounts as sea floor moves away from hot spot, cools, and subsides. Get topographic swell around hotspot and volcanic age progression away from it. Direction and age of volcanic chain give motion of plate with respect to hot spot. Hot spot tracks beneath different plates and assuming hot spots fixed with respect to deep mantle (or move relative to each other more slowly than plates), yields hot spot reference frame.

Often assumed hot spots result from plumes of hot material rising from great depth, perhaps coremantle boundary HOTSPOT / PLUME HYPOTHESIS Plumes would be secondary convection mode, ~ 5% of heat transfer, bringing up deep mantle material. Would be important in Earth s thermal & chemical evolution. Would have tectonic significance - heads of new plume might cause continental breakup and flood basalts

HOTSPOT / PLUME CONTROVERSY Concepts of hot spots and plumes are attractive and widely used, but the relation between the persistent volcanism and possible deep mantle plumes is under active investigation because of many deviations from what would be expected: 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 depth extent and relation to possible plumes is difficult and controversial Convection models of plumes rising from core-mantle boundary may not correctly include pressure effects

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 VOLCANISM Trend consistent with absolute motion of North America Stein & Wysession, 2003

COMPLEXITY: additional volcanic progression to west - Newberry volcanics Proposed alternative: forced mantle flow and decompression melting resulting from local plate motions. Near subduction zone upper mantle forced to flow northwest because of corner flow driven by subducting plate. Yellowstone and Newberry magmatism follow these trends as fertile mantle flows past residuum and ascends (red-to-white arrows). Humphreys et al., 2000

MIDPLATE OCEANIC HOTSPOT: HAWAIIAN EMPEROR CHAIN Bend in the Hawaiian-Emperor chain interpreted as indicating Pacific plate changed direction about 43 Ma, leaving bend as plate moved over fixed hotspot now under Hawaii Mauna Loa

PROBLEM 1: THE 43 Ma NONEVENT No evidence for change in relative plate motions at 43 Ma, since fracture zone orientations unaffected

PROBLEM 2: HAWAIIAN HOTSPOT HAS NOT BEEN FIXED Fixed hotspot would cause all seamounts to have same paleolatitude Hawaiian hotspot actually drifted southward between 47 and 81 Ma Tarduno and Cottrell (1997)

SUMMARY Absolute motions can be defined relative to either No Net Rotation or Hotspot reference frames GPS data given in ITRF, designed to be like NUVEL-NNR Absolute motions may have roles in tectonics but details unclear Hotspot/plume model has major problems and may need to be discarded, but it s not clear what the alternatives are