# Global Inversions for a Regionalized Earth

## (The RUM model)

### Oli Gudmundsson and Malcolm Sambridge

*Research School of Earth Sciences,
Australian National University, Canberra, ACT 0200, Australia. *

*
A refinement of the Tectonic Regionalization of Jordan (1981) consisting of
125 regions categorized into 8 different tectonic types.
*
### 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.

To illustrate the work some images of the dataset and selected slabs
can be found below:
## Global Delaunay Tessellation

The Delaunay tessellation of 8548 surface nodes. These triangles are
the exterior faces of 3-D Delaunay tetrahedra that fill the upper mantle.
## Datasets

Seismicity used for contouring of slabs.
Return to image list

Slab contours from ISC catalogue.
Click here to download slab contours.
Return to image list

Volcanoes
Return to image list
## 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
Return to RUM home page

** Last modified:** May 2001
*malcolm@rses.anu.edu.au*