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We consider two sources of geology-related uncertainty in making predictions of the steady-state water table elevation for an unconfined aquifer. That is the uncertainty in the depth to base of the aquifer and in the hydraulic conductivity distribution within the aquifer. Stochastic approaches to hydrological modeling commonly use geostatistical techniques to account for hydraulic conductivity uncertainty within the aquifer. In the absence of well data allowing derivation of a relationship between geophysical and hydrological parameters, the use of geophysical data is often limited to constraining the structural boundaries. If we recover the base of an unconfined aquifer from an analysis of geophysical data, then the associated uncertainties are a consequence of the geophysical inversion process. In this study, we illustrate this by quantifying water table uncertainties for the unconfined aquifer formed by the paleochannel network around the Kintyre Uranium deposit in Western Australia. The focus of the Bayesian parametric bootstrap approach employed for the inversion of the available airborne electromagnetic data is the recovery of the base of the paleochannel network and the associated uncertainties. This allows us to then quantify the associated influences on the water table in a conceptualized groundwater usage scenario and compare the resulting uncertainties with uncertainties due to an uncertain hydraulic conductivity distribution within the aquifer. Our modeling shows that neither uncertainties in the depth to the base of the aquifer nor hydraulic conductivity uncertainties alone can capture the patterns of uncertainty in the water table that emerge when the two are combined.

Earthquakes are induced by man-made changes of the stress field by injection or withdrawal of fluids in hydrocarbon production, geothermal exploitation, and wastewater disposal. However, the actual perturbation of the stress field and stress release by injection-induced seismicity remains largely unknown. We provide evidence for currently not understood hydromechanical processes after shut-in of the well. We invert earthquake focal mechanisms from a massive stimulation to invert for stress resolved in time and depth to obtain changes of the stress orientation and magnitude. Prior information about fracture orientations from well logs is taken into account. Comparison with independent stress measures reveals that stresses obtained from inversion of fluid-induced seismicity are highly perturbed and not representative of the initial stress field. The horizontal stresses change by tens of megapascals, turning the stress regime from transitional normal faulting/strike-slip faulting to pure normal faulting. The observed stress changes are attributed to large-scale aseismic deformation.

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtoseconds to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth’s core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth’s surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults. A particular interesting case is discussed in detail, where out of the fluid dynamic solution, ductile compaction bands appear which are akin and can be confused with their brittle siblings. The main difference is that they require the factor time and also a much lower driving forces to emerge. These low stress solutions cannot be obtained on short laboratory time scales and they are therefore much more likely to appear in nature than in the laboratory. We finish with a multiscale description of a seminal structure in the Swiss Alps, the Glarus thrust, which puzzled geologists for more than 100 years. Along the Glarus thrust, a km-scale package of rocks (nappe) has been pushed 40 km over its footwall as a solid rock body. The thrust itself is a m-wide ductile shear zone, while in turn the centre of the thrust shows a mm-cm wide central slip zone experiencing periodic extreme deformation akin to a stick-slip event. The m-wide creeping zone is consistent with the THM feedback length scale of solid mechanics, while the ultralocalised central slip zones is most likely a fluid dynamic instability.

Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.

Trace plots for selected parameters and plots of calculated Geweke statistics

Analyzing, visualizing and communicating uncertainties are important issues as geological models can never be fully determined. To date, there exists no general approach to quantify uncertainties in geological modeling. We propose here to use information entropy as an objective measure to compare and evaluate model and observational results. Information entropy was introduced in the 50s and defines a scalar value at every location in the model for predictability. We show that this method not only provides a quantitative insight into model uncertainties but, due to the underlying concept of information entropy, can be related to questions of data integration (i.e. how is the model quality interconnected with the used input data) and model evolution (i.e. does new data – or a changed geological hypothesis – optimize the model). In other words information entropy is a powerful measure to be used for data assimilation and inversion. As a first test of feasibility, we present the application of the new method to the visualization of uncertainties in geological models, here understood as structural representations of the subsurface. Applying the concept of information entropy on a suite of simulated models, we can clearly identify (a) uncertain regions within the model, even for complex geometries; (b) the overall uncertainty of a geological unit, which is, for example, of great relevance in any type of resource estimation; (c) a mean entropy for the whole model, important to track model changes with one overall measure. These results cannot easily be obtained with existing standard methods. The results suggest that information entropy is a powerful method to visualize uncertainties in geological models, and to classify the indefiniteness of single units and the mean entropy of a model quantitatively. Due to the relationship of this measure to the missing information, we expect the method to have a great potential in many types of geoscientific data assimilation problems — beyond pure visualization.

All geological models are subject to several kinds of uncertainty. These can be classified into three different types: data imprecision and quality, inherent randomness and incomplete knowledge. With our approach, we address uncertainties introduced by input data quality in complex three-dimensional (3D) models of subsurface structures (geological models). As input data, we consider parameters of geological structures, i.e. formation and fault boundary points and orientation measurements. Our method consists of five steps: construction of an initial geological model with an implicit potential-field method, assignment of probability distributions to data positions and orientation measurements, simulation of several input data sets, construction of several model realisations based on these simulated data sets and finally the visualisation and analysis of the uncertainties. We test our approach in two generic models, a simple graben setting and a complex dome structure. The first model shows that our approach can evaluate uncertainties from different structures and their interaction. Furthermore, it indicates that the final uncertainty of the model is not simply the sum of all input data uncertainties but complex interactions exist. The second example demonstrates that our approach can handle full three-dimensional settings with overturned surfaces. Results of the uncertainty simulation can be visualised and analysed in several ways, ranging from borehole histograms to uncertainty maps. For complex 3D visualisation and analysis, we use indicator functions. When we apply these, we can treat the visualisation of uncertainties in complex settings in a self-consistent manner. With our simulation method, it is possible to analyse and visualise the uncertainties directly introduced by imprecision in the input data. Our approach is intuitive and straight-forward and suitable in both simple and complex geological settings. It enables detailed insights into the model quality, even for the non-expert. In cases where a geological model is the basis for geophysical simulation, it opens-up the way to geological data-driven ensemble modelling and inversion.

We present a novel methodology for performing experiments with subsurface structural models using a set of flexible and extensible Python modules. We utilise the ability of kinematic modelling techniques to describe major deformational, tectonic, and magmatic events at low computational cost to develop experiments testing the interactions between multiple kinematic events, effect of uncertainty regarding event timing, and kinematic properties. These tests are simple to implement and perform, as they are automated within the Python scripting language, allowing the encapsulation of entire kinematic experiments within high-level class definitions and fully reproducible results. In addition, we provide a~link to geophysical potential-field simulations to evaluate the effect of parameter uncertainties on maps of gravity and magnetics. We provide relevant fundamental information on kinematic modelling and our implementation, and showcase the application of our novel methods to investigate the interaction of multiple tectonic events on a pre-defined stratigraphy, the effect of changing kinematic parameters on simulated geophysical potential-fields, and the distribution of uncertain areas in a full 3-D kinematic model, based on estimated uncertainties in kinematic input parameters. Additional possibilities for linking kinematic modelling to subsequent process simulations are discussed, as well as additional aspects of future research. Our modules are freely available on github, including documentation and tutorial examples, and we encourage the contribution to this project.

European Geosciences Union General Assembly 2015 - Division Energy, Resources and Environment, EGU 2015 / Edited by Maria Ask, Suzanne Hangx, Viktor Bruckman and Michael Kühn European Geosciences Union General Assembly 2015, EGU 2015, Vienna, Austria, 12 Apr 2015 - 17 Apr 2015; Amsterdam [u.a.] : Elsevier, Energy procedia 76, 321-330 (2015). doi:10.1016/j.egypro.2015.07.869, Published by Elsevier, Amsterdam [u.a.]

International audience; Existing 3D geological systems are well adapted to high data-density environments, such as at the mine scale where abundant drill core exists, or in basins where 3D seismic provides stratigraphic constraints, but are poorly adapted to regional geological problems. There are three areas where improvements in the 3D workflow need to be made: in the handling of uncertainty; in the model building algorithms themselves; and in the interface with geophysical inversion. All 3D models are under-constrained, and at the regional scale this is especially critical for choosing modelling strategies. The practice of only producing a single model ignores the huge uncertainties that underlie model-building processes, and underpins the difficulty in providing meaningful information to end-users about the inh erent risk involved in applying the model to solve geological problems. Future studies need to recognize this and focus on the characterization of model uncertainty, spatially and in terms of geological features, and produce plausible model suites, rather than single models with unknown validity.

SEG Conference on Keystone - Building Exploration Capability for the 21st Century, Keystone, CO, SEP 27-30, 2014; International audience; Existing three-dimensional (3-D) geologic systems are well adapted to high data-density environments, such as at the mine scale where abundant drill core exists, or in basins where 3-D seismic provides stratigraphic constraints but are poorly adapted to regional geologic problems. There are three areas where improvements in the 3-D workflow need to be made: (1) the handling of uncertainty, (2) the model-building algorithms themselves, and (3) the interface with geophysical inversion. All 3-D models are underconstrained, and at the regional scale this is especially critical for choosing modeling strategies. The practice of only producing a single model ignores the huge uncertainties that underlie model-building processes, and underpins the difficulty in providing meaningful information to end-users about the inherent risk involved in applying the model to solve geologic problems. Future studies need to recognize this and focus on the characterization of model uncertainty, spatially and in terms of geologic features, and produce plausible model suites, rather than single models with unknown validity. The most promising systems for understanding uncertainty use implicit algorithms because they allow the inclusion of some geologic knowledge, for example, age relationships of faults and onlap-offlap relationships. Unfortunately, existing implicit algorithms belie their origins as basin or mine modeling systems because they lack inclusion of normal structural criteria, such as cleavages, lineations, and recognition of polydeformation, all of which are primary tools for the field geologist that is making geologic maps in structurally complex areas. One area of future research will be to establish generalized structural geologic rules that can be built into the modeling process. Finally, and this probably represents the biggest challenge, there is the need for geologic meaning to be maintained during the model-building processes. Current data flows consist of the construction of complex 3-D geologic models that incorporate geologic and geophysical data as well as the prior experience of the modeler, via their interpretation choices. These inputs are used to create a geometric model, which is then transformed into a petrophysical model prior to geophysical inversion. All of the underlying geologic rules are then ignored during the geophysical inversion process. Examples exist that demonstrate that the loss of geologic meaning between geologic and geophysical modeling can be at least partially overcome by increased use of uncertainty characteristics in the workflow.

The ability to understand and predict how thermal, hydrological, mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal–Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties, stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.

The calibration of large-scale geothermal models for entire sedimentary basins is challenging as direct measurements of rock properties and subsurface temperatures are commonly scarce and the basal boundary conditions poorly constrained. Instead of the often-applied trial-and-error manual model calibration, we examine here the use of an automatic model calibration method, implemented in iTOUGH2, for a large-scale conductive geothermal simulation of the Perth Basin, Australia. The application shows that we obtain valuable insights into parameter sensitivities and correlations. In addition, outlier analysis, parameter bounds and the spatial variation of temperature residuals provide indication for convective heat transport in the basin. These interesting results will be addressed with future work.

Several stochastic approaches have recently been developed to evaluate uncertainties in 3-D geological models based on imprecise geological data. Multiple models are generated through random changes of input parameters, according to defined probability distributions. This leads to a new problem: randomly generated realizations might be topologically different or they might be in contrast to expected geological constraints or settings. We present here a method to enable automatic checks of models based on reliability filters encapsulating aspects of geological knowledge. We apply those filters to a model of a graben structure and obtain an ensemble of acceptable realizations, representing the range of uncertainty, but preserving expected geological features.