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This paper presents the application of a novel trans-dimensional sampling approach to a time domain airborne electromagnetic (AEM) inverse problem to solve for plausible conductivities of the subsurface. Geophysical inverse field problems, such as time domain AEM, are well known to have a large degree of non-uniqueness. Common least-squares optimisation approaches fail to take this into account and provide a single solution with linearised estimates of uncertainty that can result in overly optimistic appraisal of the conductivity of the subsurface. In this new non-linear approach, the spatial complexity of a 2D profile is controlled directly by the data. By examining an ensemble of proposed conductivity profiles it accommodates non-uniqueness and provides more robust estimates of uncertainties. [ABSTRACT FROM AUTHOR]