The latest generation of hydrologic models include detailed representations of ecohydrological variables to better understand and hypothesize about the connections between hydrological, ecological and energy transfer processes. Matching this is intense growth in new technologies to observe Earth’s biophysical system through satellite remote sensing or on-the-ground instruments. These new observations and models offer unsurpassed opportunities to undertake modelling experiments that are truly representative of environmental systems. However, it is not easy to directly reconcile current models with observed data because: (a) the scale of the model is generally different to the scale of the observations; (b) the data have known and unknown errors arising from instrument limitations and fluctuations; (c) the modelled variable of interest is often not directly observed but inferred from surrogate measurements. This complicates the potential power of new modelling approaches. Bayesian inference offers a potential solution, providing a convenient framework in which to calibrate multivariate environmental models while explicitly recognising data and model uncertainties. In this study, we develop a multi-objective Bayesian approach to hydrologic model inference that capitalises on a priori knowledge of observational errors to improve parameter estimation. We introduce a novel error model, which partitions observation and model residual error according to prior knowledge of the estimated uncertainty in the calibration data. We demonstrate our approach in two distinct environmental modelling case studies: an ecohydrologic model where we make use of the known uncertainty in satellite retrievals of biophysical variables, and a water quality study using proxy data for model calibration. Overall, we emphasize the usefulness of Bayesian methods for model environmental inference, especially when the errors associated with observations can be estimated independently of the model.

Structural complexity is a crucial indicator for several mineral deposit types as it marks fluid pathways and traps; however, it is frequently mapped using interpreted datasets rather than unbiased data-driven techniques. A new method to map structural complexity using circular variance and spherical dispersion is applied to two Archean greenstone belts near Dryden and Timmins in the Superior Province, Ontario, Canada. Bedding measurements and autodetected aeromagnetic lineaments are used as inputs to test if structural complexity can be used to refine and add confidence to existing geological interpretations and as an indicator of orogenic gold mineralization. The near continuous and representative nature of autodetected magnetic lineaments is effective in capturing structural complexity at a regional scale. Spherical dispersion of bedding plane vectors, however, captured the highest resolution of structural complexity at local scales (<1:30000). Key considerations when performing structural complexity analysis are scale, data density, and optimization of input parameters (e.g., neighborhood radius, lineament length, minimum neighborhood populations). Gold deposits are found <1700 m from low (< µ - 1σ) and < 1500 m from high circular variance anomalies (> µ + 1σ). Additionally, gold grade of large deposits increases with proximity to high variance anomalies. When paired with expert knowledge, statical techniques such as this will increase repeatability in future exploration endeavors, making exploration a more rigorous process with increased confidence.

When we build 3D geological models, the initial stages of modelling are often made without a clear vision of how they may control the final model. In this study we look at the impacts on the final model of systematically varying a number of parameters that strongly little influence on the final model, but are not normally systematically assessed. We focus on the choice of faults to be modelled in a regional setting, and investigate the different criteria which can be used to reduce model complexity without undermining the model’s value. This may include simple scale parameters such as fault length or the mapped width of its damage zone; intrinsic fault zone properties such as the permeability of the fault, and the presence or absence of mineralization; estimated properties such as fault throw; and finally topological constraints such as the connectivity of faults with respect to the regional fault network.  Our simple scenarios suggest that for some purposes, methods based on the input data may not be enough, and decisions as to which faults to model may not be possible without first building one or more 3D models.Given the uncertainty associated with many geological datasets, this study suggests that future model-building workflows may need to follow stochastic methodologies even to decide which input parameters should be retained to properly address the question at hand.

In this talk, I will present the statistical finite element method (statFEM) for nonlinear, time- dependent phenomena, illustrated in the context of nonlinear internal waves (solitons). Taking a Bayesian approach and admitting that the model is misspecified, we leverage the finite element method to cast the statistical problem as a (finite-dimensional) nonlinear Gaussian state–space model, updating the solution, in receipt of data, in a filtering framework. I will introduce the core ideas behind the statistical finite element method, and then present the two algorithms we have developed to implement our approach — based on the extended and ensemble Kalman filters. Throughout the talk I will discuss various simulation studies, and I will conclude with a case study on some experimental data.

Daily precipitation has an enormous impact on human activity, and the study of how it varies over time and space, and what global indicators influence it, is of paramount importance to Australian agriculture. Over 294 million daily rainfall measurements since 1876, spanning 17,606 sites across continental Australia, are analysed. We propose a Bayesian hierachical mixture model that accommodates mixed discrete-continuous data. The observational level describes site-specic temporal and climatic variation via a mixture-of-experts model. At the next level of the hierarchy, spatial variability of the mixture weights' parameters is modeled by a spatial Gaussian process prior.  We present examples of posterior inference on the mixture weights, monthly intensity levels, offsite prediction of the effects of climate drivers and long-term rainfall trends across the entire continent. 

We introduce a workflow to image a geologically realistic sediment-basement interface using magnetotelluric (MT) data. We apply it to the area of Cloncurry, located in the Mount Isa province in Queensland, NE Australia. An MT survey was acquired in 2016 by the Geological Survey of Queensland and Geoscience Australia. It consists in 457 soundings spanning a 40 km x 80 km wide area, covered by a regolith and the Jurassic-Cretaceous sediments of the Carpentaria Basin. The workflow consists in inverting the complete dataset using a 1D trans-dimensional Bayesian algorithm, which leverages 2-D and 3-D effects present in the data. Then, we derive probability distributions on the sediment-basement interface depth for each site independently using an automated change-point analysis. Finally, a Bayesian estimate fusion algorithm is used to create a probabilistic map of the sediment-basement interface over the complete region, combining the MT probability distributions with drill-hole data and a structural model derived from aeromagnetic and geological data. Combining these different constraints and estimates allowed a significant reduction in posterior uncertainty. In certain areas, high multi-modality was observed in the change-point posterior distributions of individual MT soundings, having multiple transitions that could be associated to the sediment-basement interface. The estimate fusion process correlates these uncertainties and the combined posterior was thus much less multi-modal. Results show that the thickness of the sedimentary basin gradually increases towards the north, while towards the east the basin thickening is controlled by a two-steps fault system. This work shows the benefits of integrating MT with different types of geoscientific data within a probabilistic workflow to image a sediment-basement interface.

Multiple-point statistics (MPS) is a useful method to reconstruct three-dimensional geological models in many fields. However, non-stationary geological features, especially structural features with directional ductility, are difficult to extract and reconstruct when using the MPS-based method. In addition, the rationality of the stratigraphic sequence in the three-dimensional model cannot always be guaranteed during the MPS simulation. In this study, an MPS algorithm combined with deep learning method is presented for constructing three-dimensional geological structures, in which 2D geological sections are used as training images (TIs) and boreholes. In the presented algorithm, the 2D sections are expanded in the simulation grid within the range approximate to (equal to or larger than) the width of a pattern. The constructed 3D sections are used as TIs and the training data for deep learning in the followed process. Based on the three-dimensional TIs, the fracture zone database, stratigraphic pattern database, and stratigraphic sequence database are constructed respectively. With the fracture zone database, deep learning algorithm is used to construct the fracture zone model in the simulation grid. After that, an initial model is constructed with sequential simulation process, in which the stratigraphic information is obtained from stratigraphic sequence database. During the sequential simulation process, the spatial distribution of the strata is checked and constrained based on the stratigraphic sequences. To obtain a reasonable final realization, an GOSIM-based iterative process (Yang et al., 2016) with multi-scale strategy is implemented. The concrete examples of 3D geological structures in Xilinggang area, southern China illustrated that the presented algorithm can simulate complex non-stationary structures reasonably.

Cost-effective imaging of the subsurface requires rapid integration of different geophysical measurements with geological control and insights to generate actionable information. Multi-modal, multi-scale data sets constrained by geology can speed up the cycle time, reduce the cost, and improve the confidence of our images and interpretation of the subsurface. Decisions are taken based on Myth: narrative (e.g story line or business plan); Power: trust of authority with credibility and proven track record; Value: metrics based on expectation. Making decisions based on economic metrics is a well-studied field. Data acquisition and interpretation are undertaken to inform decisions leading to action (or inaction) that create value. Economic value can be assessed based on future expectation of the cost of acquiring and interpreting the data (including sunk costs of hardware and software), opportunity cost of not doing something, direct cost savings (e.g. time saved in seismic data processing, savings from making a bad decision, change in Probability of Success (POS), or derisking, which then influences the expected monetary value (EMV) of the prospect, play, and stock price.  Interpretation adds Value only by influencing decisions. Interpretations are essentially experiments testing one or more hypothesis. The real Power of an interpretation lies in its ability to disprove hypotheses. This presentation explores the Myth, Power, and Value of multi-physics interpretation and inversion using real examples to address the questions: How does interpretation add Value?How can poorly constrained inversion add Value?What about ambiguity in inversion?Can integrated multi-physics interpretation add Value?How can we assess that Value?How is that value communicated?

Due to the complexity of geological structures and the sparse distribution of urban drilling data, the reconstructed 3D geological model usually has randomness and uncertainty. As the core of multiple-point geostatistics, training image is often difficult to obtain and does not have stationarity assumption. Some researchers use sections (connected from boreholes) as training images, but this will increase the complexity of the modeling process. In this study we present a three-dimensional geological stochastic modeling method based on multiple-point geostatistics which directly uses urban drilling data as training images. The prior probability calculation is carried out on the neighborhood nodes of drilling data. The sequential simulation method is used to determine the simulation path. The data event of the node to be simulated is matched with the pattern in the training image, and the conditional probability distribution function of the node to be simulated is calculated using the pattern distance formula. Next, the probability aggregation method is used to aggregate each conditional probability distribution function and the previous prior probability distribution function to obtain the joint probability distribution function. A corresponding attribute value is randomly selected from the joint probability distribution function and assigned to the current node. Finally, multiple optional models are output for the same drilling data, and the spatial uncertainty of geological features is evaluated by computing the differences between the output models. As a result, the difficulty in obtaining training images and its high dependence on stationarity assumptions are solved, and the uncertainty of the urban three-dimensional geological stochastic model is evaluated. The research on actual drilling data in a certain area shows that the proposed method can realize the construction of a three-dimensional urban geological model and the uncertainty analysis of the model.