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SUMMARY A meaningful interpretation of seismic measurements requires a rigorous quantification of the uncertainty. In an inverse problem, the data noise determines how accurately observations should be fit, and ultimately the level of detail contained in the recovered model. A common problem in seismic tomography is the difficulty in quantifying data uncertainties, and thus the required level of data fit. Traditionally, the complexity of the solution model (defined by both the number of basis functions and the regularization) is defined arbitrarily by the user prior to inversion with only limited use of data errors. In the context of multiscale problems, dealing with multiple data sets that are characterized by different noise variances and that span the Earth at different scales is a major challenge. Practitioners are usually required to arbitrarily weigh the contribution of each data type into the final solution. Furthermore, the basis functions are usually spatially uniform across the velocity field and regularization procedures are global, which prevents the solution model from accounting for the uneven spatial distribution of information. In this work we propose to address these issues with a Hierarchical Bayesian inversion. The new algorithm represents an extension of the transdimensional tomography to account for uncertainties in data noise. This approach has the advantage of treating the level of noise in each data set, as well as the number of model parameters, as unknowns in the inversion. It provides a parsimonious solution that fully represents the degree of knowledge one has about seismic structure (i.e. constraints, resolution and trade-offs). Rather than being forced to make decisions on parametrization, level of data fit and weights between data types in advance, as is often the case in an optimization framework, these choices are relaxed and instead constrained by the data themselves. The new methodology is presented in a synthetic example where both the data density and the underlying structure contain multiple length scales. Three ambient noise data sets that span the Australian continent at different scales are then simultaneously inverted to infer a multiscale tomographic image of Rayleigh wave group velocity for the Australian continent. The procedure turns out to be particularly useful when dealing with multiple data types with different unknown levels of noise as the algorithm is able to naturally adjust the fit to the different data sets and provide a velocity map with a spatial resolution adapted to the spatially variable information present in the data. [ABSTRACT FROM AUTHOR]

There is significant seismic activity in the region around Australia, largely due to the plate boundaries to the north and to the east of the mainland. This activity results in serious seismic and tsunami hazard in the coastal areas of Australia. Hence seismicity is and will be monitored in real time by Geoscience Australia (GA), which uses a network of permanent broadband seismometers. Seismic moment tensor (MT) solutions are currently determined using 1-D, radially symmetric models of Earth and this requires augmentation by recording stations located outside of Australia. A 3-D model of the Australian continent developed recently using full waveform tomography now offers the opportunity to significantly improve the determination of MT solutions of earthquakes from tectonically active regions. A complete-waveform, time-domain MT inversion method has been developed using a point-source approximation. A series of synthetic tests using first a 1-D and then a 3-D structural model has been performed. The feasibility of deploying 3-D versus 1-D Earth structure for the inversion of seismic data has been studied and the advantages of using the 3-D structural model were illustrated with examples. The 3-D model is superior to the 1-D model, as a number of sensitivity tests show. The ultimate goal of this work is an automated MT inversion system in Australia relying on GA and other international stations, although more work remains to be done before the full implementation of such a scheme in real time. [ABSTRACT FROM AUTHOR]

Conceptual uncertainty is considered one of the major sources of uncertainty in groundwater flow modelling. In this regard, hypothesis testing is essential to increase system understanding by refuting alternative conceptual models. Often a stepwise approach, with respect to complexity, is promoted but hypothesis testing of simple groundwater models is rarely applied. We present an approach to model-based Bayesian hypothesis testing in a simple groundwater balance model, which involves optimization of a model in function of both parameter values and conceptual model through trans-dimensional sampling. We apply the methodology to the Wildman River area, Northern Territory, Australia, where we set up 32 different conceptual models. A factorial approach to conceptual model development allows for direct attribution of differences in performance to individual uncertain components of the conceptual model. The method provides a screening tool for prioritizing research efforts while also giving more confidence to the predicted water balance compared to a deterministic water balance solution. We show that the testing of alternative conceptual models can be done efficiently with a simple additive and linear groundwater balance model and is best done relatively early in the groundwater modelling workflow. [ABSTRACT FROM AUTHOR]