Trans-Dimensional Surface Reconstruction With Different Classes of Parameterization

The use of Bayesian trans-dimensional sampling in 2-D and 3-D imaging problems has recently become widespread in geophysical inversion. Its benefits include its spatial adaptability to the level of information present in the data and the ability to produce uncertainty estimates. The most used parameterization in Bayesian trans-dimensional inversions is Voronoi cells. Here we introduce a general software, TransTessellate2D, that allows 2-D trans-dimensional inference with Voronoi cells and two alternative underlying parameterizations, Delaunay triangulation with linear interpolation and Clough-Tocher interpolation, which utilize the same algorithm but result in either C ⁰ or C ¹ continuity. We demonstrate that these alternatives are better suited to the recovery of smooth models, and show that the posterior probability solution is less susceptible to multimodalities which can complicate the interpretation of model parameter uncertainties.