Math 2.0

Geophysics Definition

Plate reconstruction

Builds on Plate tectonicsEuler pole of plate motionSpecial orthogonal groupGeomagnetic reversal

Definition

Let the Earth's surface be the sphere S⊂ℝ3S \subset \R^3 centred at the origin, and let P1,…,PkP_1, \dots, P_k be the present-day plates of a plate tectonic model. Fix a reference frame, either one plate taken as fixed or an absolute frame such as the paleomagnetic frame. A plate reconstruction at a past time tt assigns to each plate PiP_i a rotation Ai(t)A_i(t) in the special orthogonal group SO(3)SO(3). The rotation Ai(t)A_i(t) must carry each point of PiP_i from its present position to its position at time tt in the reference frame. The rotation Ai(t)A_i(t) is a total reconstruction rotation, and its pole is a total reconstruction pole.

Remarks

Each Ai(t)A_i(t) is a rotation about a finite rotation pole, by the Euler pole theorem. Rotations relative to different plates compose along a chain of plates: if Ai/j(t)A_{i/j}(t) moves plate ii in the frame of plate jj, then Ai/k(t)=Aj/k(t) Ai/j(t)A_{i/k}(t) = A_{j/k}(t) \, A_{i/j}(t). Example: take two plates on the two sides of an ocean ridge. The seafloor magnetic anomalies are dated by the record of geomagnetic reversals. The rotation that superimposes the anomalies of age tt reconstructs one plate relative to the other at time tt. Non-example: a map that moves a plate by a reflection or a stretch is not a reconstruction. It is not in SO(3)SO(3), so it is not a rigid motion of a plate. Paleomagnetic data fix past latitudes and orientations but not past longitudes, so absolute reconstructions need extra assumptions.

Reading path

To understand this page from the ground up, read these 29 pages in order. The foundations come first.

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Cross product, concept, no evidence levelCross productconceptDerivative, concept, no evidence levelDerivativeconceptDeterminant, concept, no evidence levelDeterminantconceptEigenvalue, concept, no evidence levelEigenvalueconceptEigenvector, concept, no evidence levelEigenvectorconceptEuclidean isometry, concept, no evidence levelEuclidean isometryconceptEuclidean plane, object, no evidence levelEuclidean planeobjectEuclidean vector, concept, no evidence levelEuclidean vectorconceptGeomagnetic reversal, concept, no evidence levelGeomagnetic reversalconceptIdentity matrix, object, no evidence levelIdentity matrixobjectMatrix, definition, no evidence levelMatrixdefinitionPlate tectonics, concept, no evidence levelPlate tectonicsconceptTrace of a matrix, concept, no evidence levelTrace of a matrixconceptVector space, definition, no evidence levelVector spacedefinitionVelocity, concept, no evidence levelVelocityconceptRotation, definition, no evidence levelRotationdefinitionSquare matrix, definition, no evidence levelSquare matrixdefinitionTranspose, definition, no evidence levelTransposedefinitionLinear map, definition, no evidence levelLinear mapdefinitionMultilinear map, definition, no evidence levelMultilinear mapdefinitionOrthogonal matrix, definition, no evidence levelOrthogonal matrixdefinitionAlternating multilinear map, definition, no evidence levelAlternating multiline…definitionOrthogonal group, object, no evidence levelOrthogonal groupobjectDeterminant, definition, no evidence levelDeterminantdefinitionSpecial orthogonal group, object, no evidence levelSpecial orthogonal gr…objectAngular velocity, concept, no evidence levelAngular velocityconceptEuler's rotation theorem, statement, no evidence levelEuler's rotation theo…statementEuler pole of plate motion, statement, no evidence levelEuler pole of plate m…statementPlate reconstruction, definition, no evidence levelPlate reconstructiondefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Cross product concept
  2. Derivative concept
  3. Determinant concept
  4. Eigenvalue concept
  5. Eigenvector concept
  6. Euclidean isometry concept
  7. Euclidean plane object
  8. Euclidean vector concept
  9. Geomagnetic reversal concept
  10. Identity matrix object
  11. Matrix definition
  12. Plate tectonics concept
  13. Trace of a matrix concept
  14. Vector space definition
  15. Velocity concept
  16. Rotation definition
  17. Square matrix definition
  18. Transpose definition
  19. Linear map definition
  20. Multilinear map definition
  21. Orthogonal matrix definition
  22. Alternating multilinear map definition
  23. Orthogonal group object
  24. Determinant definition
  25. Special orthogonal group object
  26. Angular velocity concept
  27. Euler's rotation theorem statement
  28. Euler pole of plate motion statement
  29. Plate reconstruction definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Plate_reconstruction
About this page
Tag2GW89KY07V
URIm2://2GW89KY07V
Kinddefinition
WritingW0 stub
MSC86A60
DefinesPlate reconstruction
UsesPlate tectonics, Euler pole of plate motion, Special orthogonal group, Geomagnetic reversal
Changed3 November 2026

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