Low temperature thermochronology and modeling strategies for multiple samples 1: Vertical profiles

Low-temperature thermochronology is a powerful method for constraining the time-temperature history of rocks and provides constraints on denudation chronologies, landscape evolution and tectonic history of geological terrains. We present a strategy for modelling thermal histories constrained by thermochronological data from multiple samples in vertical profiles. The thermal history is specified to be similar in form for each sample, and we include extra parameters to determine the offset temperature between the uppermost and lowermost samples. We combine the likelihood from each sample to produce a joint likelihood for all samples together, and using initially stochastic search then directed search methods we try to identify a maximum likelihood solution. We also implement a test (Bayesian Information Criterion) which allows us to assess whether we have overparameterised the thermal history and potentially introduced unwarranted complexity. This test allows us to simplify the thermal history model without compromising the acceptable data fit. Subsequently, we use a sampling approach to determine the uncertainty or resolution of the thermal history. Markov chain Monte Carlo is straightforward to implement and is used to produce joint and marginal probability distributions, and from these we can infer credible intervals on the model parameters. We demonstrate that combining the samples is preferable in that the final model is easier to interpret and generally has smaller uncertainties than the case where we model all samples independently. We consider both synthetic and real data examples, focusing on apatite fission track analysis, but the general approach is applicable to other analytical methods such as (U-Th) / He dating and 40Ar / 39Ar analysis and in principle it is straightforward to combine these different data types into one joint thermal history model.