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

2. 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

3. 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

7. 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

8. 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)‏

9. 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

10. 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)

11. 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

14. Modelling
hotspot
motion -
an example

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

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

18. 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)‏

24. (Steinberger,
Sutherland &
O'Connell, 2004)

26. 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)

27. 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)

28. 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)

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

30. 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)

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

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

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

34. 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, …)

35. „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 Ma follows indeed approximately the „blue circle“

36. 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

37. Paleomagnetic reference frame

38. Paleomagnetic reference frame

39. 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)

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

41. 135 Ma

42. 145 Ma

43. 145 — 135 Ma
Center of mass
continents
African LLSVP
Pacific LLSVP

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

45. 110 — 100 Ma 110 — 100 Ma Center of mass continents African LLSVP
Pacific LLSVP

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

47. 195 Ma

48. 145 Ma

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

50. 250 Ma

51. 220 Ma

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

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

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

55. Rotations in paleomagnetic frame, interpreted as TPW events
Summary
Rotations in paleomagnetic frame, interpreted as TPW events
Amount time period axis of longitude
~18° Ma °-15°W (near CAMP)
~-18° Ma ´´
~-10° Ma °-40°E (near center of mass of continents)
~10° Ma ´´
Northward motion
Amount time period
~ 30° Ma
~ 15° Ma - present