Geophysical applications of Natural Neighbours

Malcolm Sambridge, Jean Braun and Herbert McQueen

Research School of Earth Sciences,
Institute of Advanced Studies,
Australian National University,
Canberra, ACT 0200, Australia.


Natural neighbours are a concept from the field of Computational Geometry which describe properties of arbitrarily distributed points in any number of dimensions. They have applications in many fields. This web page describes some projects at RSES which use natural neighbours. These projects involve the application of existing algorithms and techniques as well as the development of new algorithms for a range of geophysical problems. These include triangulation and interpolation of irregular data, parameterization of Earth models in two or three dimensions, and numerical modelling of deformation and fluid flow.

Some useful links are:


  • Natural neighbour interpolation in 3 dimensions
  • Some presentation slides on this work can be found here
  • Papers

  • GJI paper: Geophysical parameterization and interpolation of irregular data using natural neighbours
  • Nature paper: A numerical method for solving partial differential equations on highly irregular evolving grids
  • Movies

  • Dynamic Lagrangian Remeshing (DLR)
  • Natural Element Method
  • Code

  • A library of fortran subroutines is available which perform all generation, bookeeping tasks, and natural neighbour interpolation in 2-D. Please contact the authors or for details.

    When you have a password you can download it from here.

  • Software for generating Delaunay and Voronoi meshes for seismic applications (e.g. seismic Tomography) can be found here.

  • The regionalized upper Mantle (RUM) seismic model of Earth is built from Delaunay and Voronoi cells in 3-D. Software for calculating seismic travel times through the RUM model can be found here.