Regionalized tomography with Voronoi polyhedra and Delaunay tetrahedra
In our inversion the surface of Earth is divided into 125 regions of 8 different tectonic types according to age of crustal formation and tectonic activity. This irregular two-dimensional grid is extended in a regular fashion downward into the mantle. The regionalisation has a resolution of 2 degrees. Individual regions vary in size from 2 degrees to tens of degrees. The volume around each grid point which is closer to it than any other defines a Voronoi cell. The discrete upper mantle parameterisation we use combines all the Voronoi cells which fall within a given region and thus forms irregular polyhedra of varied sizes.
Superimposed on this is a fine representation of the volume of subducting slabs based on detailed contouring of slab seismicity in the ISC catalog. These slabs are constructed from the Delaunay tetrahedra between their definining nodes. A Delaunay tetrahedron connects each node with its natural neighbours and each tetrahedra can be assigned to a particular slab. We have complete freedom in choosing the positions of the defining nodes, and just as with the surface parameterisation we can easily select them to represent a complex slab morphology. Click here to see some of the individual slab models.
Combining these two sets of nodes we have a three-dimensional parameterisation spanning the upper mantle which is highly irregular in the shapes and sizes of its elements (1 - 10,000 km). It reflects expectations about where detail is needed and where not. It thus provides a means of inserting a-priori information into the solution to global tomography. Whatsmore all of the complex book-keeping tasks, i.e. finding the lengths of ray segments in tetrahedra or polyhedra, can solved using efficient search mechanisms devised designed for these irregular structures.
References
Jordan, T.H., 1981, Global tectonic regionalization for seismological data analysis, Bull. Seism. Soc. Am., 71, 1131-1141.Sambridge, M, Braun, J & McQueen, H., 1995, Geophysical parameterization and interpolation of irregular data using natural neighbours, Geophys. J. Int., 122, 837-857.
Images
To illustrate the work some images of the dataset and selected slabs
can be found below:
Global Delaunay Tessellation
Datasets
Slabs
The following is a set of perspective views of the tetrahedra in each slab
built from the contours of seismicity in the ISC catalogue.
Return to image list
Last modified: May 2001 malcolm@rses.anu.edu.au