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The mean land-surface temperature represents an important boundary condition for many geothermal studies. This boundary is particularly important to help constrain the models made to analyse resource systems, many of which are shallow in nature and observe relatively small thermal gradients. Consequently, a mean land-surface temperature map of the Australian continent has been produced from 13 years of MODIS satellite imagery, for the period 2003–2015. The map shows good agreement with independent methods of estimating mean land-surface temperature, including borehole surface-temperature extrapolation and long-term, near-surface ground measurements. In comparison to previously used methods of estimating mean land-surface temperature, our new estimates are up to 12 °C warmer. The MODIS-based method presented in this study provides spatially continuous estimates of land-surface temperature that can be incorporated as the surface thermal boundary condition in geothermal studies. The method is also able to provide a quantification of the uncertainties expected in the application of these estimates for the purposes of thermal modelling. [ABSTRACT FROM AUTHOR]

Abstract: We present an overview of Markov chain Monte Carlo, a sampling method for model inference and uncertainty quantification. We focus on the Bayesian approach to MCMC, which allows us to estimate the posterior distribution of model parameters, without needing to know the normalising constant in Bayes'' theorem. Given an estimate of the posterior, we can then determine representative models (such as the expected model, and the maximum posterior probability model), the probability distributions for individual parameters, and the uncertainty about the predictions from these models. We also consider variable dimensional problems in which the number of model parameters is unknown and needs to be inferred. Such problems can be addressed with reversible jump (RJ) MCMC. This leads us to model choice, where we may want to discriminate between models or theories of differing complexity. For problems where the models are hierarchical (e.g. similar structure but with a different number of parameters), the Bayesian approach naturally selects the simpler models. More complex problems require an estimate of the normalising constant in Bayes'' theorem (also known as the evidence) and this is difficult to do reliably for high dimensional problems. We illustrate the applications of RJMCMC with 3 examples from our earlier working involving modelling distributions of geochronological age data, inference of sea-level and sediment supply histories from 2D stratigraphic cross-sections, and identification of spatially discontinuous thermal histories from a suite of apatite fission track samples distributed in 3D. [Copyright &y& Elsevier]

• A quantitative method resolves the fine structure of the D″ layer. • Small-scale heterogeneities exist at CMB beneath eastern Alaska & northern Pacific. • There is a lack of correlation between D″ topography and shear velocity variation. • The D″ layer may be a mixed boundary layer comprised of thermo-chemical anomalies. • Inferred accumulated slab material suggests different mantle convection styles. The D″ layer, regarded as a thermal boundary layer and a chemically distinct region above the core-mantle boundary (CMB), has been associated with the phase transition from bridgmanite (Bm) to post-perovskite (pPv) in the lowermost mantle. However, the composition of the lowermost mantle and thermal conditions where Bm-pPv phase-transition occurs is still debatable. The methods typically used to study the fine-scale seismic features in the D″ layer has provided important information. However, trial-and-error seismic waveform modelling cannot uniquely quantify D″-layer properties because of subjective model-parameterization choices and inherent non-uniqueness of solutions and the waveform inversion method has a limited resolution of the velocity gradient and depth of the D″ discontinuity. We develop a grid-search scheme to constrain the detailed 1-D shear-wave velocity structure in the lowermost mantle beneath Alaska and the northern Pacific, accompanied with quantitative assessment of the uncertainty of 1D models. Our results show strong lateral variations of the D″ discontinuity from west to east beneath Alaska, along with the existence of smaller-scale heterogeneities in the east. We find a broad velocity increase, as thick as 240 km, at the top of D″ that indicates this region may involve a composite of downwelling thermo-chemical anomalies at the CMB. There are even smaller scale heterogeneities of approximately 120 km × 120 km in size with larger lateral variations in the lowermost mantle beneath northern Pacific. Both the magnitude and gradient of the velocity at the top of the D″ layer vastly change in adjacent regions, with an increase from 2.8% to 4.5% in magnitude and from 0.08% to 1.2% in gradient, but with a relatively consistent depth of the D″ discontinuity at ∼340 km above the CMB. The weak correlation between D″ topography and velocity variations indicate chemical heterogeneities must be present beneath the northern Pacific, which might come from north-westward subducted Pacific oceanic lithosphere. Our characterisation of the spatial pattern of small-scale heterogeneities in the lowermost mantle supports a hybrid thermo-chemical boundary layer (TCBL) model beneath Alaska and northern Pacific. [ABSTRACT FROM AUTHOR]