Low temperature thermochronology and strategies for multiple samples: 2: Partition modelling for 2D/3D distributions with discontinuities

We present a new approach for modelling geological thermal histories from thermochronological data in 2D and 3D. The method allows data from multiple samples to be modelled jointly, improving the resolution of the final solution, and reduces the potential for over interpreting the data. Following from our previous work, we exploit the thermal history information contained in samples at different elevations to estimate palaeotemperature gradients. However, in this paper, we also allow for spatial discontinuities (e.g. faults) between samples, such that the thermal histories may change significantly over small distances. The major advance presented here is that the number and locations of such discontinuities do not need to be specified in advance, but can be inferred directly from the data. The problem is then to estimate the thermal histories for different clusters of samples, bounded by discontinuities, without knowing where the discontinuities are a priori. We implement the approach via Bayesian Partition Modelling, using reversible jump Markov chain Monte Carlo to deal with the changing dimensions for the number of partitions. Examples of the methodology in practice are given with both synthetic data and a real data set from Namibia.