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A method of extracting group and phase velocity dispersions jointly for Love‐ and Rayleigh‐wave observations is presented. This method uses a spectral element representation of a path average Earth model parameterized with density, shear‐wave velocity, radial anisotropy, and VP/VS ratio. An initial dispersion curve is automatically estimated using a heuristic approach to prevent misidentification of the phase. A second step then more accurately fits the observed noise correlation function (NCF) between interstation pairs in the frequency domain. For good quality cross correlations with reasonable signal‐to‐noise ratio, we are able to very accurately fit the spectrum of NCFs and hence obtain reliable estimates of both phase and group velocity jointly for Love and Rayleigh surface waves. In addition, we also show how uncertainties can be estimated with linearized approximations from the Jacobians and subsequently used in tomographic inversions.

Following the linearized attenuation tomography from our previous study (Pejić et al., 2017, https://doi.org/10.1002/2016JB013692), we perform hierarchical transdimensional Bayesian tomography of the upper ≈400 km of the inner core, using 398 globally distributed t∗ estimates. The results are in good agreement with the ones obtained through linearized tomography: they show more complex attenuation pattern than the purely hemispherical one, and the noise estimated from the hierarchical inversion is in good agreement with estimates obtained from the Discrepancy Principle in the previous study. The attenuation pattern we observe gives more weight to the geodynamical models that couple the thermal anomalies of the lowermost mantle to the inner core boundary.

The use of Bayesian trans‐dimensional sampling in 2‐D and 3‐D imaging problems has recently become widespread in geophysical inversion. Its benefits include its spatial adaptability to the level of information present in the data and the ability to produce uncertainty estimates. The most used parameterization in Bayesian trans‐dimensional inversions is Voronoi cells. Here we introduce a general software, TransTessellate2D, that allows 2‐D trans‐dimensional inference with Voronoi cells and two alternative underlying parameterizations, Delaunay triangulation with linear interpolation and Clough‐Tocher interpolation, which utilize the same algorithm but result in either C0 or C1 continuity. We demonstrate that these alternatives are better suited to the recovery of smooth models, and show that the posterior probability solution is less susceptible to multimodalities which can complicate the interpretation of model parameter uncertainties.

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.

Obtaining slip distributions for earthquakes results in an ill-posed inverse problem. While this implies that only limited and uncertain information can be recovered from the data, inferences are typically made based only on a single regularized model. Here, we develop an inversion approach that can quantify uncertainties in a Bayesian probabilistic framework for the finite fault inversion (FFI) problem. The approach is suitably efficient for rapid source characterization and includes positivity constraints for model parameters, a common practice in FFI, via coordinate transformation to logarithmic space. The resulting inverse problem is nonlinear and the most probable solution can be obtained by iterative linearization. In addition, model uncertainties are quantified by approximating the posterior probability distribution by a Gaussian distribution in logarithmic space. This procedure is straightforward since an analytic expression for the Hessian of the objective function is obtained. In addition to positivity, we apply smoothness regularization to the model in logarithmic space. Simulations based on surface wave data show that smoothing in logarithmic space penalizes abrupt slip changes less than smoothing in linear space. Even so, the main slip features of models that are smooth in linear space are recovered well with logarithmic smoothing. Our synthetic experiments also show that, for the data set we consider, uncertainty is low at the shallow portion of the fault and increases with depth. In addition, a simulation with a large station azimuthal gap of 180° significantly increases the slip uncertainties. Further, the marginal posterior probabilities obtained from our approximate method are compared with numerical Markov Chain Monte Carlo sampling. We conclude that the Gaussian approximation is reasonable and meaningful inferences can be obtained from it. Finally, we apply the new approach to observed surface wave records from the great Illapel earthquake (Chile

This paper presents the application of a novel trans-dimensional sampling approach to a time domain airborne electromagnetic (AEM) inverse problem to solve for plausible conductivities of the subsurface. Geophysical inverse field problems, such as time domain AEM, are well known to have a large degree of non-uniqueness. Common least-squares optimisation approaches fail to take this into account and provide a single solution with linearised estimates of uncertainty that can result in overly optimistic appraisal of the conductivity of the subsurface. In this new non-linear approach, the spatial complexity of a 2D profile is controlled directly by the data. By examining an ensemble of proposed conductivity profiles it accommodates non-uniqueness and provides more robust estimates of uncertainties.

Most linear inverse problems require regularization to ensure that robust and meaningful solutions can be found. Typically, Tikhonov-style regularization is used, whereby a preference is expressed for models that are somehow ‘small’ and/or ‘smooth’. The strength of such preferences is expressed through one or more damping parameters, which control the character of the solution, and which must be set by the user. However, identifying appropriate values is often regarded as a matter of art, guided by various heuristics. As a result, such choices have often been the source of controversy and concern. By treating these as hyperparameters within a hierarchical Bayesian framework, we are able to obtain solutions that encompass the range of permissible regularization parameters. Furthermore, we show that these solutions are often well-approximated by those obtained via standard analysis using certain regularization choices which are—in a certain sense—optimal. We obtain algorithms for determining these optimal values in various cases of common interest, and show that they generate solutions with a number of attractive properties. A reference implementation of these algorithms, written in Python, accompanies this paper.

We address the problem of unpolarized light spectroscopy of geological materials. Using infrared radiation, the aim of this technique is to learn about the absorbing species, such as hydroxyl. The use of unoriented samples leads to the need to perform a rigorous statistical analysis, so that the three principal absorbances of the crystal can be retrieved. We present here such an analysis based on a derivation of the probability density function for a single random measurement. Previous methods for retrieval of the absorbances are shown to be suboptimal, producing biased results that are sometimes even unphysical (e.g., negative estimates for an inherently positive quantity). The mathematical structure of the problem is developed to use the maximum likelihood estimation method, and we show how to optimize for the three absorbance parameters. This leads to good parameter retrieval on both synthetic and real data sets.

Cross correlation of seismograms provides new information on the Earth both through the exploitation of ambient noise and specific components of earthquake records. Here we cross‐correlate recordings of large earthquakes on a planetary scale and identify a range of hitherto unobserved seismic phases in Earth's correlation wavefield. We show that both arrivals with the timing expected for the regular seismic wavefield and previously unexplained phases are produced by interference between seismic paths having the same ray parameter but with only a subset of propagation legs in common. This insight explains the origin and generation mechanism of the features of Earth's correlation wavefield and opens up new ways of addressing issues in global seismology. Strong similarity between observed and synthesized correlation wavefields indicates that the Earth's radial structure is remarkably well constrained in the intermediate period range.

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.