Under the Earth's surface is a rich array of geological resources, many with potential use to humankind. However, extracting and harnessing them comes with enormous uncertainties, high costs, and considerable risks. The valuation of subsurface resources involves assessing discordant factors to produce a decision model that is functional and sustainable. This volume provides real-world examples relating to oilfields, geothermal systems, contaminated sites, and aquifer recharge. Volume highlights include: A multi-disciplinary treatment of uncertainty quantification Case studies with actual data that will appeal to methodology developers A Bayesian evidential learning framework that reduces computation and modeling time Quantifying Uncertainty in Subsurface Systems is a multidisciplinary volume that brings together five major fields: information science, decision science, geosciences, data science and computer science. It will appeal to both students and practitioners, and be a valuable resource for geoscientists, engineers and applied mathematicians. Read the Editors' Vox: eos.org/editors-vox/quantifying-uncertainty-about-earths-resources

Under the Earth’s surface is a rich array of geological resources, many with potential use to humankind. However, extracting and harnessing them comes with enormous uncertainties, high costs, and considerable risks. The valuation of subsurface resources involves assessing discordant factors to produce a decision model that is functional and sustainable. This volume provides real-world examples relating to oilfields, geothermal systems, contaminated sites, and aquifer recharge. Volume highlights include: • A multi-disciplinary treatment of uncertainty quantification • Case studies with actual data that will appeal to methodology developers • A Bayesian evidential learning framework that reduces computation and modeling time Quantifying Uncertainty in Subsurface Systems is a multidisciplinary volume that brings together five major fields: information science, decision science, geosciences, data science and computer science. It will appeal to both students and practitioners, and be a valuable resource for geoscientists, engineers and applied mathematicians. Read the Editors’ Vox: https://eos.org/editors-vox/quantifying-uncertainty-about-earths-resources

Numerical models of flow and transport processes are heavily employed in the fields of surface, soil, and groundwater hydrology. They are used to interpret field observations, analyze complex and coupled processes, or to support decision making related to large societal issues such as the water-energy nexus or sustainable water management and food production. Parameter estimation and uncertainty quantification are two key features of modern science-based predictions. When applied to water resources, these tasks must cope with many degrees of freedom and large datasets. Both are challenging and require novel theoretical and computational approaches to handle complex models with large number of unknown parameters.

Uncertainty quantification for subsurface flow problems is typically accomplished through the use of model inversion procedures in which multiple posterior (history-matched) geological models are generated and used for flow predictions. These procedures can be demanding computationally, and it is not always straightforward to maintain geological realism in the resulting history-matched models. In some applications, it is the flow predictions themselves (and the uncertainty associated with these predictions), rather than the posterior geological models, that are of primary interest. This is the motivation for the data-space inversion (DSI) procedures developed in this work. In the DSI framework, an ensemble of prior model realizations, honoring prior geostatistical information and hard data at wells, are generated and then (flow) simulated. The resulting reservoir responses (e.g., time-series of flow rate data at wells, and/or limited spatial saturation fields) are assembled into data vectors that represent prior `realizations' in the data space. The conditional distribution of data variables given observed data is then constructed within a Bayesian framework. This distribution is directly sampled using a data-space randomized maximum likelihood method. Due to the non-Gaussian characteristics of the data variables, we introduce pattern-based mapping operations, or histogram transformation, along with principal component analysis. These treatments allow us to represent the data variables using a set of low-dimensional variables that are closer to multivariate Gaussian, which is shown to improve the performance of DSI. We present extensive numerical results for two example cases involving oil-water flow in a bimodal channelized system and oil-water-gas flow in a Gaussian permeability system, in which the quantities of interest (QoI) are time-series data at wells. DSI results, with pattern-based mapping operations, for uncertainty quantification (e.g., P10, P50, P90 posterior predictions) are compared with those obtained from a strict rejection sampling (RS) procedure. Reasonable agreement between the DSI and RS results is consistently achieved, even when the (synthetic) true data to be matched fall near the edge of the prior distribution. Computational savings using DSI are very substantial in that RS requires O(10^5--10^6) flow simulations, in contrast to 500 for DSI, for the cases considered. We then apply the DSI procedure, with the histogram transformation treatment for data reparameterization, for naturally fractured reservoirs (NFRs), represented as general discrete-fracture-matrix (DFM) models. This DSI procedure is first tested on two-dimensional DFM systems involving multiple fracture scenarios. Comparison with an approximate rejection sampling procedure for this case indicates the DSI results for the P10, P50 and P90 responses are again consistent with RS results. The DSI method is then applied to a realistic NFR that has undergone 15 years of primary production and is under consideration for waterflooding. To construct the DSI representation, around 400 prior DFM models, which correspond to different geologic concepts and properties, are simulated. Two different reference `true' models, along with different data-assimilation durations, are considered. In all cases, the DSI predictions are shown to be consistent with the forecasts from the `true' model, and to provide reasonable quantification of forecast uncertainty. Finally, we investigate the application of DSI to quantify the uncertainty associated with carbon storage operations, in which the QoI is the spatial distribution of CO2 saturation in the top layer of a storage aquifer, and the observed data are pressure and CO2 saturation measurements from a few monitoring wells. We also introduce a procedure to optimize the locations of monitoring wells using only prior-model simulation results. This approach is based on analytical DSI results, and determines monitoring well locations such that the reduction in expected posterior variance of a relevant quantity is maximized. The new DSI procedure is applied to three-dimensional heterogeneous aquifer models involving uncertainties in a wide range of geological parameters, including variogram orientation, porosity and permeability fields, and regional pressure gradient. Multiple monitoring scenarios, involving four to eight monitoring wells, are considered in this evaluation. Application of DSI with optimal monitoring wells is shown to consistently reduce the posterior variance in predictions of the average CO2 saturation in the top layer, and to provide detailed saturation fields in reasonable correspondence with the `true' saturation distribution.

This text combines the science and engineering of hydrogeology in an accessible, innovative style. As well as providing physical descriptions and characterisations of hydrogeological processes, it also sets out the corresponding mathematical equations for groundwater flow and solute/heat transport calculations. And, within this, the methodological and conceptual aspects for flow and contaminant transport modelling are discussed in detail. This comprehensive analysis forms the ideal textbook for graduate and undergraduate students interested in groundwater resources and engineering, and indeed its analyses can apply to researchers and professionals involved in the area.

Using isotopes as a tool for understanding Earth processes From establishing the absolute age of the Earth to providing a stronger understanding of the nexus between geology and life, the careful measurement and quantitative interpretation of minor variations in the isotopic composition of Earth’s materials has provided profound insight into the origins and workings of our planet. Isotopic Constraints on Earth System Processes presents examples of the application of numerous different isotope systems to address a wide range of topical problems in Earth system science. Volume highlights include: examination of the natural fractionation of non-traditional stable isotopes utilizing isotopes to understand the origin of magmas and evolution of volcanic systems application of isotopes to interrogate and understand Earth’s Carbon and Oxygen cycles examination of the geochemical and hydrologic processes that lead to isotopic fractionation application of isotopic reactive transport models to decipher hydrologic and biogeochemical processes The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.

A comprehensive picture of the architecture of crustal magmatic systems The composition of igneous rocks – their minerals, melts, and fluids – reveals the physical and chemical conditions under which magmas form, evolve, interact, and move from the Earth’s mantle through the crust. These magma dynamics affect processes on the surface including crustal growth and eruptive behaviour of volcanoes. Crustal Magmatic System Evolution: Anatomy, Architecture, and Physico-Chemical Processes uses analytical, experimental, and numerical approaches to explore the diversity of crustal processes from magma differentiation and assimilation to eruption at the surface. Volume highlights include: Physical and chemical parameterization of crustal magmatic systems Experimental, theoretical and modelling approaches targeting crustal magmatic processes Timescales of crustal magmatic processes, including storage, recharge, and ascent through volcanic conduits The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals. Find out more about this book in a Q&A with the Editors.