Bayesian Markov-chain-Monte-Carlo inversion of time-lapse cross hole ground-penetrating radar data to characterize the vadose zone at the Arrenaes field site, Denmark

The ground-penetrating radar (GPR) geophysical method has the potential to provide valuable information on the hydraulic properties of the vadose zone because of its strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR traveltime data can allow for a significant reduction in uncertainty regarding subsurface van Genuchten-Mualem (VGM) parameters. Much of the previous work on the stochastic estimation of VGM parameters from crosshole GPR data has considered the case of steady-state infiltration conditions, which represent only a small fraction of practically relevant scenarios. We explored in detail the dynamic infiltration case, specifically examining to what extent time-lapse crosshole GPR traveltimes, measured during a forced infiltration experiment at the Arreneas field site in Denmark, could help to quantify VGM parameters and their uncertainties in a layered medium, as well as the corresponding soil hydraulic properties. We used a Bayesian Markov-chain-Monte-Carlo inversion approach. We first explored the advantages and limitations of this approach with regard to a realistic synthetic example before applying it to field measurements. In our analysis, we also considered different degrees of prior information. Our findings indicate that the stochastic inversion of the time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions compared with the corresponding priors, which in turn significantly improves knowledge of soil hydraulic properties. Overall, the results obtained clearly demonstrate the value of the information contained in time-lapse GPR data for characterizing vadose zone dynamics.

Genomic evidence for role of inversion 3RP of Drosophila melanogaster in facilitating climate change adaptation.

Chromosomal inversion polymorphisms are common in animals and plants, and recent models suggest that alternative arrangements spread by capturing different combinations of alleles acting additively or epistatically to favour local adaptation. It is also thought that inversions typically maintain favoured combinations for a long time by suppressing recombination between alternative chromosomal arrangements. Here, we consider patterns of linkage disequilibrium and genetic divergence in an old inversion polymorphism in Drosophila melanogaster (In(3R)Payne) known to be associated with climate change adaptation and a recent invasion event into Australia. We extracted, karyotyped and sequenced whole chromosomes from two Australian populations, so that changes in the arrangement of the alleles between geographically separated tropical and temperate areas could be compared. Chromosome-wide linkage disequilibrium (LD) analysis revealed strong LD within the region spanned by In(3R)Payne. This genomic region also showed strong differentiation between the tropical and the temperate populations, but no differentiation between different karyotypes from the same population, after controlling for chromosomal arrangement. Patterns of differentiation across the chromosome arm and in gene ontologies were enhanced by the presence of the inversion. These data support the notion that inversions are strongly selected by bringing together combinations of genes, but it is still not clear if such combinations act additively or epistatically. Our data suggest that climatic adaptation through inversions can be dynamic, reflecting changes in the relative abundance of different forms of an inversion and ongoing evolution of allelic content within an inversion.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.