Reference frames for plate motions and true polar wander Bernhard Steinberger Deutsches GeoForschungsZentrum, Potsdam and Centre for Earth Evolution and Dynamics, Univ. Oslo

Why “absolute” plate motions? Need appropriate reference frame to link surface and deep mantle LIPs reconstructed in palaeomagnetic and global moving/fixed hotspot (for the Pacific) frame

How to obtain „absolute“ plate motions? Use „hotspot tracks“ (geometry, age progression) Consider modelled hotspot motion Analyse plate motion properties for the times when hotspot tracks are available in order to proceed towards „absolute“ plate motions for times before the oldest hotspot tracks 0 Ma 49 Ma 47 Ma 56 Ma 61 Ma 76 Ma

Insert plume conduit in large-scale flow: Initiall vertical (because established by fast rising head)‏ Advection of conduit in large-scale flow + buoyant vertical rising Plume source moves with flow at source depth

Predicted plume sources to move with flow at depth towards large-scale upwellings above LLSVPs Yet no direct comparision with tomography, but statistical analysis reveals better agreement with slow anomalies for tilted, compared to vertical plumes (Boschi, Becker, Steinberger, G-Cubed 2007, PEPI 2008)‏ Tristan Meteor (Bouvet)‏

Hotspot surface motion Predicted intersection of plume conduit with surface vs. time Initially motion away from large- scale upwelling (corresponding to flow at shallower depth Increasingly towards upwelling with time More towards upwelling for higher buoyant rising speed

Buoyant plume rising speed I Step 1: plume centerline temperature anomaly: Computed following Albers and Christensen (1996) anomalous mass flux 1, 2 and 3 x 103 kg/s (Iceland, Tahiti, Hawaii) Basal temperature anomaly 500 K consistent with plumes rising from top of chemically distinct basal layer Temperature anomaly decreses with height, even for adiabatic plume Decreases more strongly for smaller plumes Step 2: plume viscosity (temperature and depth dependence)

Buoyant plume rising speed II anomalous mass flux 1, 2 and 3 x 103 kg/s Step 3: thermal plume radius Larger radius for higher viscosity Smaller plumes may actually be thicker, because of lower temperature, hence higher viscosity Step 4: plume buoyant rising speed

Modelling hotspot motion - an example

Combine (1) computed hotspot motion (2) plate motions (also time dependent)‏ to models of hotspot tracks

Combine (1) computed hotspot motion (2) plate motions (also time dependent)‏ to models of hotspot tracks

Construction of absolute plate motion reference frame Find absolute (African) plate motions which, combined with given relative plate motions, gives best fit between model tracks and observations (seamount/island ages, locations)‏

(Steinberger, Sutherland & O'Connell, 2004)

Constructing the global mantle reference frame Hawaii hotspot moving southward (> 1 cm/yr) Other hotspots moving slower Can fit hotspot tracks globally after ~ 65 Ma, but only with plate circuit Model 2 (through Lord Howe rise) (Steinberger, Sutherland & O‘Connell, 2004)

Constructing the global mantle reference frame Hawaii hotspot moving southward (> 1 cm/yr) other hotspots moving slower can fit hotspot tracks globally after ~ 65 Ma, but only with plate circuit Model 2 (through Lord Howe rise) (from Torsvik et al., Rev. Geophys., 2008; following Steinberger, Sutherland & O'Connell, Nature, 2004)

Apparent polar wander Paleomagnetism (declination, inclunation)  „Virtual Geomagnetic Pole“ (VGP) Relative plate motions  common reference frame (here: South Africa) Group data in age bins („running mean“) to obtain global apparent polar wander path (APWP) A (from Torsvik et al., 2008; Reviews of Geophysics)

True polar wander in mantle reference frame converted from African apparent polar wander path (Torsvik et al., 2008, Reviews of Geophysics)

For times earlier than hotspot tracks: Paleomagnetic reference frame, but: cannot constrain coherent East-West motion cannot distinguish plate motions and true polar wander For East-West reconstruction I: Deep mantle reference frame (Torsvik et al., 2014)

Slab fitting (van der Meer et al., 2010) 1325 km 2650 km 120 Ma 240 Ma

Pick reference plate and assign zero longitude motion Africa appears most suitable (Torsvik et al. 2008, „Longitude“) (after Sobel, 1995)

Other approaches: Trench advance vs. Trench rollback (Williams et al., 2015)

TPW vs. plate motions – a bit of history Both are old ideas Detailed TPW discussion by Darwin (1876) „Continental drift“ Wegener (1915) Supported by paleomagnetism in the 1950‘s Qualitative theory of true polar wander by Gold (1955) Plate tectonics in the 1960‘s TPW „Renaissance“ since 1990s (Kirschvink, 1997, …)

„True polar wander“ in mantle reference frame Converted from African apparent polar wander path (Torsvik et al., 2008; Rev. Geophys.) Colors for lowermost mantle seismic anomalies (smean) Event at 100-110 Ma follows indeed approximately the „blue circle“

Constructing the reference frame further back in time Reconstruction based on paleomagnetism 100 Ma reconstruction longitude based on moving hotspot reference frame Coherent rotation of all continents in paleomagnetic, but not in hotspot reference frame Therefore indication of true polar wander

Paleomagnetic reference frame

Paleomagnetic reference frame

TPW unplugged: the tool For each time step, compute, for all continents combined center of mass Inertia tensor I angular momentum L mean rotation w (L = I ˖ w) Three components Along Earth‘s spin axis (coherent E-W motion Equatorial axis; longitude at center of mass (coherent rotation) Equatorial axis; longitude 90° from center of mass (coherent N-S motion)

TPW unplugged Mean rotation Mean N-S motion Paleomagnetic global mantle African mantle reference frame

135 Ma

145 Ma

145 — 135 Ma Center of mass continents African LLSVP Pacific LLSVP

Center African LLSVP Center Pacific LLSVP (antipode) (Burke et al., 2008) Geotectonic Centers A and P (antipode) (Pavoni, 1969)

110 — 100 Ma 110 — 100 Ma Center of mass continents African LLSVP Pacific LLSVP

TPW unplugged Mean rotation Mean N-S motion Paleomagnetic global mantle African mantle reference frame

195 Ma

145 Ma

Center of mass continents African LLSVP Pacific LLSVP (antipode) CAMP (200 Ma) 195 – 145 Ma

250 Ma

220 Ma

Center of mass continents African LLSVP Pacific LLSVP (antipode) CAMP (200 Ma) 250 – 220 Ma

Center of mass continents African LLSVP Pacific LLSVP (antipode) CAMP (200 Ma) 195 – 145 Ma

TPW unplugged Mean rotation Mean N-S motion Paleomagnetic global mantle African mantle reference frame

Rotations in paleomagnetic frame, interpreted as TPW events Summary Rotations in paleomagnetic frame, interpreted as TPW events Amount time period axis of longitude ~18° 250-220 Ma 10°-15°W (near CAMP) ~-18° 195-145 Ma ´´ ~-10° 145-135 Ma 20°-40°E (near center of mass of continents) ~10° 110-100 Ma ´´ Northward motion Amount time period ~ 30° 320-190 Ma ~ 15° 190 Ma - present