A Multi-scale Framework for Trans-dimensional Tomography

Abstract:

We present a new multi-scale framework for tomographic inversion and
compare to existing methods which use a mobile Voronoi cell
parameterisation. The new approach has a broad range of applicability.
For example, it can use any orthogonal basis functions that can be
applied to a subdivision grid, including Wavelets and related
transforms.

An implementation of the Reversible Jump Markov chain Monte Carlo
(RJMCMC) algorithm has been devised within this framework, to
stochastically refine a model by subdividing an underlying grid or
hieararchy of basis functions. In this scheme, the data drives the
resolution of the model and from this we can gain posterior
information on the scale length that the data supports. In principle,
any grid that can be continuoulys subdivided can be used resulting in
a scalable method that can be applied to different geometry, eg
cartesian or spherical, in 2 or 3 dimensions.

Numerical results indicate that the new framework generally result in
faster running times and require less sampling to obtain continuous
Earth models. It shows promise in the ability to scale to larger
inverse tomographic problems.