Math 2.0

Geophysics Definition

Plate tectonics

Builds on Rigid bodySpecial orthogonal groupEuler's rotation theorem

Definition

Model the Earth's surface as a sphere SS of radius RR centred at the origin. Plate tectonics is the kinematic model in which:

  1. the lithosphere, an outer layer about 100 km thick, is divided into finitely many plates P1,…,Pk⊆SP_1, \dots, P_k \subseteq S; their interiors are disjoint and their union is SS;
  2. each plate moves as a rigid body on SS; so its motion between two times is an element of the special orthogonal group SO(3)SO(3);
  3. deformation is concentrated on the plate boundaries, which are divergent (plates move apart), convergent (plates move together) or transform (plates slide past each other).

Remarks

By Euler's rotation theorem, the motion of a plate between two times is a rotation about an axis through the centre of the Earth. Example: the African and South American plates separate along the Mid-Atlantic Ridge, a divergent boundary, and the two plates are rigid away from the ridge and its transform faults. Non-example: a wide zone of distributed deformation, such as the Tibetan plateau, does not fit clause 2 well; such regions are treated as diffuse plate boundaries or many small blocks. The model was assembled in the late 1960s from continental drift and seafloor spreading.

Reading path

To understand this page from the ground up, read these 22 pages in order. The foundations come first.

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Determinant, concept, no evidence levelDeterminantconceptEigenvalue, concept, no evidence levelEigenvalueconceptEigenvector, concept, no evidence levelEigenvectorconceptEuclidean isometry, concept, no evidence levelEuclidean isometryconceptEuclidean plane, object, no evidence levelEuclidean planeobjectIdentity matrix, object, no evidence levelIdentity matrixobjectMatrix, definition, no evidence levelMatrixdefinitionRigid body, concept, no evidence levelRigid bodyconceptTrace of a matrix, concept, no evidence levelTrace of a matrixconceptVector space, definition, no evidence levelVector spacedefinitionRotation, 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…objectEuler's rotation theorem, statement, no evidence levelEuler's rotation theo…statementPlate tectonics, definition, no evidence levelPlate tectonicsdefinition
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. Determinant concept
  2. Eigenvalue concept
  3. Eigenvector concept
  4. Euclidean isometry concept
  5. Euclidean plane object
  6. Identity matrix object
  7. Matrix definition
  8. Rigid body concept
  9. Trace of a matrix concept
  10. Vector space definition
  11. Rotation definition
  12. Square matrix definition
  13. Transpose definition
  14. Linear map definition
  15. Multilinear map definition
  16. Orthogonal matrix definition
  17. Alternating multilinear map definition
  18. Orthogonal group object
  19. Determinant definition
  20. Special orthogonal group object
  21. Euler's rotation theorem statement
  22. Plate tectonics definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Plate_tectonics
About this page
TagA37WRP3743
URIm2://A37WRP3743
Kinddefinition
WritingW0 stub
MSC86A60, 86A04
DefinesPlate tectonics
UsesRigid body, Special orthogonal group, Euler's rotation theorem
Changed3 November 2026

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