In this thesis new methods have been developed for the recovery of past surface temperature
variations from underground temperature-depth profiles. This has been undertaken
from a Bayesian standpoint with an emphasis on model comparison, which allows
differently parameterised inverse models (inferred past temperature histories) to be automatically
constructed and compared in the light of the data and the prescribed prior
information.
In the first contribution a new method for inverting temperature-depth profiles is
presented which relies on trans-dimensional Bayesian sampling. The temperature histories
are parameterised in terms of a variable number of linear segments over time. Relying on
the natural parsimony of Bayesian inference, whereby simpler models which can adequately
explain the data are preferred, the complexity or roughness of the temperature histories
can be determined without the need for explicit a priori smoothing. This method therefore
allows a more objective inference of the past temperature changes.
These concepts are extended to the spatial domain in the following chapter using the
method of Bayesian partition modelling. This seeks to find the posterior distribution of
the number and spatial distribution of independent temperature histories given a spatially
distributed ensemble of temperature-depth profiles. The results from application
to 23 real boreholes in the UK are discussed in detail and show a clear preference for
8 or 9 independent (and mostly contrasting) temperature histories. It is thus concluded
that the majority of these data cannot be considered as reliable sources of palaeoclimate
reconstruction.
A 3D finite element heat transfer forward model is developed in the latter part of the
thesis, and is used to simulate underground temperatures. This forward model is linked to the first of the two Bayesian inverse methods described above. The effect of the reduction
in average ground surface temperature with altitude is included in the forward model and
inversion of the resultant profiles using a 1D forward model is shown to give significant
discrepancies in the inferred temperature histories. Finally the inversion results from
the Bayesian formulation are compared with those using a conventional gradient descent
method.
The thesis concludes with some possibilities for future research in this field which builds
upon the work presented herein.