Uncertainty Quantification and Transdimensional Inversion

Abstract:

Over recent years transdimensional inference methods have grown in popularity and found applications in fields ranging from Solid Earth Geophysics, to Geochemistry. In all applications of inversion assumptions are made about the nature of the model parametrisation, complexity and data noise characteristics, and results can be significantly dependent on those assumptions. Often these are in the form of fixed choices imposed a priori, e.g. in the grid size of the model or noise level in the data. A transdimensional approach allows these assumptions to be relaxed by incorporating relevant parameters as unknowns in the inference problem, e.g. the number of model parameters becomes a variable as does the form of basis functions and the variance of the data noise. In this way uncertainty due to parameterisation effects or data noise choices may be incorporated into the inference process. Probabilistic sampling techniques such as Birth-Death Markov chain Monte Carlo and the Reversible jump algorithm, allow sampling over complex posterior probability density functions providing information on constraint, trade-offs and uncertainty in the unknowns.

This talk will present a review of trans-dimensional inference and its application in geophysical inversion, and highlight some emerging trends such as Multi-scale McMC, Parallel Tempering and Sequential McMC which hold the promise of further extending the range of problems where these methods are practical.