Geophysical parametrization and interpolation of irregular data using natural neighbours

• DOI: 10.1111/j.1365-246x.1995.tb06841.x
• Publication Date: 2007-04-03T07:45:04Z
• Authors: Malcolm Sambridge; Jean Braun; Herbert McQueen
• Keywords: Interpolation; Parametrization (atmospheric modeling)

Summary An approach is presented for interpolating a property of the Earth (for example temperature or seismic velocity) specified at series ‘reference’ points with arbitrary distribution in two three dimensions. The method makes use some powerful algorithms from field computational geometry to efficiently partition medium into ‘Delaunay’ triangles (in 2-D) tetrahedra 3-D) constructed around irregularly spaced reference points. can then be smoothly interpolated anywhere using known as natural-neighbour interpolation. This has following useful properties: (1) original function values are recovered exactly points; (2) interpolation entirely local (every point only influenced by its nodes); and (3) derivatives continuous everywhere except In addition, ability handle highly irregular distributions nodes means that large variations scale-lengths represented easily. These properties make procedure ideally suited ‘gridding’ geophysical data, basis parametrization inverse problems such tomography. We have extended theory produce expressions function. may calculated modifying an existing algorithm which calculates information. Full details numerical given. new derivative applications range problems. it shows much promise when used finite-element solution partial differential equations.