Exploiting 3D spatial sampling in inverse modeling of thermochronological data
Gallagher K., Stephenson J., Brown RW., Holmes C., Ballester P.
We have given an overview of a modeling strategy aimed at exploiting the spatial geometry of the sample distributions in order to maximize the retrieval of thermal history information from the thermochronological data. Philosophically, we aim to find thermal history solutions that fit the observations well, but do not have unwarranted complexity. These two requirements are quantified through the Bayesian Information Criterion, which combines the data likelihood and the number of model parameters. The overall approach relies on exploiting the spatial geometry of the sample locations to combine data from individual samples and identify a common thermal history. The combination of different data sets has the advantage of improving the resolution in the inferred thermal history, and also reducing the complexity. Markov chain Monte Carlo sampling provides a means of constructing reliable representations on the probability distributions for the parameters. 1D modeling is relevant to vertical profiles, and provides an estimate of the paleotemperature gradient directly from the data. The 2D approach relies on a partition model, in which each partition contains a subgroup of the samples with a common thermal history. The partition model approach allows for an unknown number of discontinuities, whose locations are also unknown. The extension to 3D combines the 1D and 2D approaches to find partitions in which samples at different elevations have experienced a common form of thermal history, but the actual temperatures depend on the elevation. As presented here, it is implicit that the spatial relationship between samples has not changed over time, at least not in a way that will lead to differential thermal histories. The approach presented here is different to 3D thermal models (Braun 2003, 2005; Ehlers 2005) but complementary. Thus, we infer the thermal history directly from the data, while the other 3D models are specified and certain parameters are adjusted to match the observed data. Both approaches assume thatthe predictive models for fission track annealing or helium diffusion in apatite are correct. In principle, this assumption can be relaxed and appropriate predictive model parameters can be estimated as part of the modelling process. However, this will lead to significant trade-off between annealing of diffusion parameters and the thermal history (Gallagher and Evans 1991). Future modifications to this approcah will include more generalized sampling of the thermal histories during th MCMC sampling of the partition structure, incorporation of mutiple data types (e.g., apatite fission track and (U-Th)/He data) and potentially allowing for irregularly shaped partition boundaries. Copyright © Mineralogical Society of America.