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Geoscientific models are based on geoscientific data; hence, building better models, in the sense of attaining better predictions, often means acquiring additional data. In decision theory, questions of what additional data are expected to best improve predictions and decisions is within the realm of value of information and Bayesian optimal survey design. However, these approaches often evaluate the optimality of one additional data acquisition campaign at a time. In many real settings, certainly in those related to the exploration of Earth resources, a large sequence of data acquisition campaigns possibly needs to be planned. Geoscientific data acquisition can be expensive and time-consuming, requiring effective measurement campaign planning to optimally allocate resources. Each measurement in a data acquisition sequence has the potential to inform where best to take the following measurements; however, directly optimizing a closed-loop measurement sequence requires solving an intractable combinatoric search problem. In this work, we formulate the sequential geoscientific data acquisition problem as a partially observable Markov decision process (POMDP). We then present methodologies to solve the sequential problem using Monte Carlo planning methods. We demonstrate the effectiveness of the proposed approach on a simple 2D synthetic exploration problem. Tests show that the proposed sequential approach is significantly more effective at reducing uncertainty than conventional methods. Although our approach is discussed in the context of mineral resource exploration, it likely has bearing on other types of geoscientific model questions. [ABSTRACT FROM AUTHOR]

Geoscientific models are based on geoscientific data, hence building better models, in the sense of attaining better predictions, often means acquiring additional data. In decision theory questions of what additional data is expected to best improve predictions/decisions is within the realm of value of information and Bayesian optimal survey design. However, these approaches often evaluate the optimality of one additional data acquisition campaign at a time. In many real settings, certainly in those related to the exploration of Earth resources, possibly a large sequence of data acquisition campaigns need to be planned. Geoscientific data acquisition can be expensive and time consuming, requiring effective measurement campaign planning to optimally allocate resources. Each measurement in a data acquisition sequence has the potential to inform where best to take the following measurements, however, directly optimizing a closed-loop measurement sequence requires solving an intractable combinatoric search problem. In this work, we formulate the sequential geoscientific data acquisition problem as a Partially Observable Markov Decision Process (POMDP). We then present methodologies to solve the sequential problem using Monte Carlo planning methods. We demonstrate the effectiveness of the proposed approach on a simple 2D synthetic exploration problem. Tests show that the proposed sequential approach is significantly more effective at reducing uncertainty than conventional methods. Although our approach is discussed in the context of mineral resource exploration, it likely has bearing on other types of geoscientific model questions. [ABSTRACT FROM AUTHOR]

Faults are one of the building-blocks for subsurface modeling studies. Incomplete observations of subsurface fault networks lead to uncertainty pertaining to location, geometry and existence of faults. In practice, gaps in incomplete fault network observations are filled based on tectonic knowledge and interpreter's intuition pertaining to fault relationships. Modeling fault network uncertainty with realistic models that represent tectonic knowledge is still a challenge. Although methods that address specific sources of fault network uncertainty and complexities of fault modeling exists, a unifying framework is still lacking. In this paper, we propose a rigorous approach to quantify fault network uncertainty. Fault pattern and intensity information are expressed by means of a marked point process, marked Strauss point process. Fault network information is constrained to fault surface observations (complete or partial) within a Bayesian framework. A structural prior model is defined to quantitatively express fault patterns, geometries and relationships within the Bayesian framework. Structural relationships between faults, in particular fault abutting relations, are represented with a level-set based approach. A Markov Chain Monte Carlo sampler is used to sample posterior fault network realizations that reflect tectonic knowledge and honor fault observations. We apply the methodology to a field study from Nankai Trough & Kumano Basin. The target for uncertainty quantification is a deep site with attenuated seismic data with only partially visible faults and many faults missing from the survey or interpretation. A structural prior model is built from shallow analog sites that are believed to have undergone similar tectonics compared to the site of study. Fault network uncertainty for the field is quantified with fault network realizations that are conditioned to structural rules, tectonic information and partially observed fault surfaces. We show the proposed methodology generates realistic fault network models conditioned to data and a conceptual model of the underlying tectonics. [ABSTRACT FROM AUTHOR]

Increased diversity of water or energy resources has led to an increased complexity in models aimed at representing accurately dynamic behavior and geological variability in such systems. In terms of variability of properties at least, simple layered models have mostly been replaced with more complex geostatistical models. The newest trend is to replace covariance-based models with geologically more realistic models such as Boolean, multiple-point, surface-, or process-based models. In this paper, we address the following question: given some design purpose or a set of flow-based decision variables, does adding more complexity increase predictability and ultimately improve decisions based on such models? In this paper, we do not attempt to make any generalizing statements or answer this question with yes/no, but provide some initial ideas on practical workflows to discover the needed complexity. We do treat complexity only in the context of decision making under uncertainty. Two workflows are proposed: complexifying versus simplifying. In these workflows, we attempt to extract, using image transforms, relevant features of the variability between geostatistical realizations that are related to uncertainty in flow dynamics. A simple distance-based calibration between the static variability and dynamic variability provides a means to decide on what the relevant complexity of geostatistical models should be for the given purpose. [ABSTRACT FROM AUTHOR]

In pursuit of highly preorganized macrocyclic host molecules for the complexation of anions, a series of oxacalix[2]arene[2]pyrimidine-based bis(thio)ureido receptors were synthesized and fully characterized. The pincer-like 1,3-alternate conformation of the oxacalix[4]arene scaffold, essential for an efficient host-guest interaction, was visualized by single-crystal X-ray analysis and supported by variable-temperature NMR studies. The anion binding properties of the receptors were evaluated via ¹H NMR titration experiments, showing intermolecular interactions with Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., AcO-, BzO-, and Cl- ions. The host molecule bearing 4-nitrophenyl substituents on the bisurea binding pocket showed association constants in the range of 200-400 M-1 in the strongly competitive solvent mixture of DMSO/0.5% H2O. [ABSTRACT FROM AUTHOR]

Abstract: High-resolution geologic models that incorporate observed state data are expected to effectively enhance the reliability of reservoir performance prediction. One of the major challenges faced is how to solve the large-scale inverse modeling problem, i.e., to infer high-resolution models from the given observations of state variables that are related to the model parameters according to some known physical rules, e.g., the flow and transport partial differential equations. There are typically two difficulties, one is the high-dimensional problem and the other is the inverse problem. A multiscale inverse method is presented in this work to attack these problems with the aid of a gradient-based optimization algorithm. In this method, the model responses (i.e., the simulated state data) can be efficiently computed from the high-resolution model using the multiscale finite-volume method. The mismatch between the observations and the multiscale solutions is then used to define a proper objective function, and the fine-scale sensitivity coefficients (i.e., the derivatives of the objective function with respect to each node’s attribute) are computed by a multiscale adjoint method for subsequent optimization. The difficult high-dimensional optimization problem is reduced to a one-dimensional one using the gradient-based gradual deformation method. A synthetic single-phase transient flow example problem is employed to illustrate the proposed method. Results demonstrate that the multiscale framework presented is not only computationally efficient but also can generate geologically consistent models. By preserving spatial structure for inverse modeling, the method presented overcomes the artifacts introduced by the multiscale simulation and may enhance the prediction ability of the inverse-conditional realizations generated. [Copyright &y& Elsevier]

Distance-based stochastic techniques have recently emerged in the context of ensemble modeling, in particular for history matching, model selection and uncertainty quantification. Starting with an initial ensemble of realizations, a distance between any two models is defined. This distance is defined such that the objective of the study is incorporated into the geological modeling process, thereby potentially enhancing the efficacy of the overall workflow. If the intent is to create new models that are constrained to dynamic data (history matching), the calculation of the distance requires flow simulation for each model in the initial ensemble. This can be very time consuming, especially for high-resolution models. In this paper, we present a multi-resolution framework for ensemble modeling. A distance-based procedure is employed, with emphasis on the rapid construction of multiple models that have improved dynamic data conditioning. Our intent is to construct new high-resolution models constrained to dynamic data, while performing most of the flow simulations only on upscaled models. An error modeling procedure is introduced into the distance calculations to account for potential errors in the upscaling. Based on a few fine-scale flow simulations, the upscaling error is estimated for each model using a clustering technique. We demonstrate the efficiency of the method on two examples, one where the upscaling error is small, and another where the upscaling error is significant. Results show that the error modeling procedure can accurately capture the error in upscaling, and can thus reproduce the fine-scale flow behavior from coarse-scale simulations with sufficient accuracy (in terms of uncertainty predictions). As a consequence, an ensemble of high-resolution models, which are constrained to dynamic data, can be obtained, but with a minimum of flow simulations at the fine scale. [ABSTRACT FROM AUTHOR]

Multi-point geostatistics is an algorithm which complements the traditional variogram driven cell-based and object model- ling approaches to facies modelling. It is situated somewhere between the two, being a cell-based approach, but because it uses estimates of the multi-variate distribution instead of the simple bi-variate distributions that are available to variogram- driven algorithms, it is capable of capturing geometries that are more similar to those available with object modelling. This paper introduces and reviews the merits and weaknesses of this new method, particularly with regard to its ability to provide additional control in conditioning to secondary data such as may be provided from seismic data. [ABSTRACT FROM AUTHOR]

• Evaluation of the impact of uncertainty on key geothermal predictors from gravity field data in Dixie Valley geothermal field, Nevada, USA. • Geostatistical simulation used to quantify the effect of irregularly spaced gravity observations on inversion results. • Stochastic approach to gravity inversion to account for model uncertainty. Gravity field data constitute an important underlying dataset used in exploration models for new geothermal development, providing constraints on both basin geometry and fault locations. However, the impact of data and model uncertainty on gravity interpretation is often overlooked in conventional gravity modeling approaches, leading to geothermal exploration models that may be biased or undercount risk. In this study, a stochastic approach to gravity modeling is used to investigate these impacts on gravity data from Dixie Valley geothermal field in central Nevada. To address data uncertainty due to interpolation of irregularly spaced gravity measurements, realizations of the gravity field in Dixie Valley are generated by geostatistical simulation and independently inverted to show how inversion results are affected by sparse data sampling. Inversion is performed using a pseudo 3D approach in which subparallel profiles are inverted using a novel stochastic methodology that was developed to account for structural and density uncertainty. Whereas areas with high data density show relatively consistent inversion results across data realizations, areas with low data density show the opposite, indicating that data uncertainty has a marked impact on both depth-to-basement estimates as well as modeled fault locations. Inverted fault locations show high correlation with the total horizontal gravity field gradient, enabling co-simulation of fault-related properties to estimate fault location and density variation beyond profile transects. By employing stochastic modeling approaches, fault properties needed for geothermal exploration such as distance-to-fault maps are estimated with uncertainty bounds at specified depths. [ABSTRACT FROM AUTHOR]

Abstract: The probability perturbation method (PPM) is introduced as a flexible and efficient sampling technique for generating inverse solutions under a given prior geological constraint (prior model). In this paper, we present a methodology for producing software code that runs PPM within a public domain geostatistical software called the Stanford Geostatistical Earth Modeling Software (S-GEMS). The challenge in creating such code lies in the great diversity of forward models as well as prior models that can be handled by the PPM. Therefore, our software solution must be highly flexible and extensible such that it can be tailored to the various applications at hand. Our implementation has two main objectives: (1) to create an integrated working environment which provides users easy access to functionalities of the PPM through a general user interface as well as visualize results; (2) allow the users to plug-in their application specific code into the PPM algorithm workflow. We provide a two-part solution. The first part, which is hard-coded in S-GEMS as a plug-in module, runs the Dekker-Brent optimization algorithm to control the parameter perturbation needed for the inversion. It generates the PPM user interface and allows visualization of the spatial domain of interest using S-GEMS graphics capability. The second part is coded in object-oriented Python scripts and is used to control the PPM execution in S-GEMS. Users can program their particular needs in scripts and load them into S-GEMS as part of the PPM workflow. The same mechanism can be used to extend the capabilities of PPM itself by implementing new PPM variants in Python and making them a part of the base class hierarchy. Case studies are used to demonstrate the flexibility of our code. This approach requires the user to adapt only a small amount of python code, without modifying, or re-compiling the core S-GEMS code. [Copyright &y& Elsevier]

Abstract: Reservoir modeling and flow simulation are used to improve the understanding of complex flow behaviors in a reservoir and to predict future reservoir performance. History matching is an integral part of any reservoir modeling study when the reservoir has produced for some time. History matching is the process where properties in the reservoir model are changed until the production data from the model matches the field data. The multi-parameter probability perturbation method is a robust history matching technique that was developed to allow large-scales properties to be efficiently perturbed. Perturbing probabilities rather than actual petrophysical properties guarantee that the conceptual geologic model is maintained and that any history matching related artifacts are avoided. Creating reservoir models that match all types of data are likely to have more prediction power than methods where some data are not honored. Previous work with the probability perturbation method however, has been limited to only the location of geologic bodies. The current work describes a new technique that also accounts for the proportion of bodies. The proportion of geologic bodies often varies significantly throughout the reservoir, and it is a parameter that is rarely known with any certainty. The current method couples the perturbation of the location and proportion of bodies so as to improve the efficiency of the method while continuing to honor the geologic information known about the reservoir. The method is first demonstrated on a synthetic example where facies locations and proportions are simultaneously perturbed. Perturbing both of these properties results in significantly faster history matched models than perturbing facies alone. This technique is further demonstrated on a North Sea hydrocarbon reservoir. In the reservoir, a number of lenticular calcite bodies with very low permeability significantly affect fluid flow; however, the location and proportion of the bodies are generally unknown. The local proportions and positions are stochastically modeled and perturbed to match 5 1/2 yr of historical flow rate data and RFT pressure data. The history matched reservoir models more accurately reproduce the field production data, and the reservoir description of the simulation model is more realistic. [Copyright &y& Elsevier]

Abstract: In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions. [Copyright &y& Elsevier]

Abstract: Reservoir simulation is ubiquitous in the petroleum industry, and conditioning models to production data (history matching) has become an essential job of reservoir engineers. Traditional history-matching methods directly perturb reservoir properties without regard to the existing geological continuity. When the geological heterogeneity is destroyed, the result is often a history-matched model with little prediction power. This paper presents a method for matching historical production data and, at the same time, honoring large-scale geologic information that is obtained from stratigraphic and sedimentological interpretations. Geostatistical simulation methods are used to inject the interpreted geological heterogeneity into a reservoir model. In order to maintain geological continuity in the history match models, we propose a method that perturbs the probability models used to simulate the geological model. Regional perturbations are incorporated to make the method practical for field cases that have numerous wells and local geologic differences. We demonstrate that the proposed approach does not create geological artifacts at the region borders. Additionally, a new simple yet efficient optimization method that can jointly optimize the magnitude of the perturbations for a large number of regions is proposed. A number of realistic synthetic examples demonstrate the method under various geological scenarios and several production data matching criteria. A realistic 3D synthetic simulation model based on a North Sea fluvial channel-type reservoir demonstrates how the method would work in practice. The current work provides reservoir engineers with an additional tool to use in the history-matching process. [Copyright &y& Elsevier]

Inversion of seismic amplitude into seismic impedance can be a difficult and time-consuming process. In this paper, a simple yet effective alternative approach is presented. The method relies on clustering similar seismic amplitude features, thereby exposing distinct geological features (geobodies) directly from the amplitude data. The method consists of first scanning the amplitude with a pre-defined window to obtain realizations of windowed seismic amplitude features. Next a minimum message length (MML) clustering algorithm is applied to search for similarities within the set of windowed amplitude features. Each group of similar amplitude features is given a unique cluster label. It is shown that the 3D cube of cluster labels often reveals existence of distinct geobodies. This approach is illustrated on a simple 2D synthetic case and on a real 3D seismic data set of a submarine channel deposit. [Copyright &y& Elsevier]

The application of state-of-the-art history matching methods to large heterogeneous reservoirs is hampered by two main problems: (1) reservoir models should be constrained jointly to dynamic data and a large variety of geological continuity information, and (2) CPU demand should not be prohibitive for large models. This paper proposes a method contributing to alleviating these two main concerns. By combining three existing ideas, namely gradual deformation, multiple-point geostatistics and a fast streamline-based history matching method, an algorithm is proposed that could honor a large variety of geological scenarios and is obtained with a limited amount of flow simulations. The method expands on the traditional gradual deformation methodology in three ways: (1) multiple-point geostatistics is used to generate models that are geologically more realistic than traditional variogram-based models, (2) a streamline simulator is used to define “zones-of-influence” of producers in order to locally deform an initial model toward jointly matching a large amount of wells and most importantly (3) the number of flow calculations is limited by defining a proxy to the streamline simulator in terms of streamline-based harmonic averages. Using synthetic examples of increasing complexity, the method''s efficiency and generality is assessed. [Copyright &y& Elsevier]

Prior model construction is a fundamental component in geophysical inversion, especially Bayesian inversion. The prior model, usually derived from available geological information, can reduce the uncertainty of model characteristics during the inversion. However, the prior geological data for inferring a prior distribution model are often limited in real cases. Our work presents a novel framework to create 3D geophysical prior models using soil geochemistry and borehole rock sample measurements. We focus on the Bayesian inversion, which enables encoding of knowledge and multiple non-geophysical data into the prior. The new framework developed in our research comprises three main parts, namely correlation analysis, prior model reconstruction, and Bayesian inversion. We investigate the correlations between surface and subsurface geochemical features, as well as the correlation between geochemistry and geophysics, using canonical correlation analysis for the surface and borehole geochemistry. Based on the resulting correlations, we construct the prior susceptibility model. The informed prior model is then tested using geophysical forward modeling and outlier detection methods. In this test, we aim to falsify the prior model, which happens when the model cannot predict the field geophysical observation. To obtain the posterior models, the reliable prior models are incorporated into a Bayesian inversion framework. Using a real case of exploration in the Central African Copperbelt, we illustrate the workflow of constructing the high-resolution 3D stratigraphic model conditioned on soil geochemistry, borehole data, and airborne geophysics. [ABSTRACT FROM AUTHOR]

Direct forecasting has recently been proposed as a method for uncertainty quantification in non-linear inverse problems. The method directly forecasts a desired future response without the need for full model inversion. The method has been successfully applied to a range of subsurface field cases, such as groundwater, shallow and deep geothermal and oil/gas predictions. In this paper, we extend the framework of direct forecasting to do what it was avoided to do in the first place: model inversion. The idea is simple: replace the prediction variables with the model variables. Two challenges now occur: the model dimensions, in subsurface realm at least, are much higher than data variables. This is the case in the paper where we consider dynamic data and high-dimensional spatial models for geological structure and properties. Secondly, the regression applied in the original method, being a linear regression of prediction variables on transformed data, is unlikely to lead to models that match field observations. We address these challenges first by adding a variable selection method (through global sensitivity analysis) for the model space. More specifically, we select those model components that are most sensitive to data variables only. The linear assumption is mitigated by a sequential updating of sensitive model variables. We illustrate our method on a Libyan oil reservoir with complex geological uncertainty involving structural, petrophysical and fluid model parameters. • A method for joint inversion of both global and spatial parameters. • Extension of direct forecasting to directly invert model variables. • Application to a real field oil reservoir in Libya. [ABSTRACT FROM AUTHOR]

• Development of a Bayesian framework for risk assessment in geothermal exploration. • Posterior temperature predictions generated directly without model inversion. • Quantified uncertainty for different geothermal development scenarios. The exploration and development of geothermal energy resources carries considerable financial risk. Due to the cost of drilling, there is often large uncertainty in the prediction of resource potential as well as challenges in optimizing well placement. In this paper, we propose a comprehensive Bayesian framework that accounts for high degrees of geologic uncertainty. Although Bayesian inference methods for prediction and uncertainty quantification are well-established, limitations exist, such as incorporating model realism and reducing the computational burden of simulating a large number of forward models. Using a case study problem, we demonstrate how to turn geologic understanding into a prior probability model for a basin-scale extensional geothermal system. We then use the proposed Bayesian framework, called Bayesian Evidential Learning, to generate posterior temperature predictions constrained to a temperature well without any explicit model inversion. In this approach, the relationship between data and prediction variables is learned by Canonical Correlation Analysis of a training set of models generated by Monte Carlo simulation. Sensitivity analysis results show that temperature in a geothermal target area is most sensitive to the bulk permeability of the basement and basin rock as well as the basal heat flux. [ABSTRACT FROM AUTHOR]

Geological uncertainty quantification is critical to subsurface modeling and prediction, such as groundwater, oil or gas, and geothermal resources, and needs to be continuously updated with new data. We provide an automated method for uncertainty quantification and the updating of geological models using borehole data for subsurface developments within a Bayesian framework. Our methodologies are developed with the Bayesian evidential learning protocol for uncertainty quantification. Under such a framework, newly acquired borehole data directly and jointly update geological models (structure, lithology, petrophysics, and fluids), globally and spatially, without time-consuming model rebuilding. To address the above matters, an ensemble of prior geological models is first constructed by Monte Carlo simulation from prior distribution. Once the prior model is tested by means of a falsification process, a sequential direct forecasting is designed to perform the joint uncertainty quantification. The direct forecasting is a statistical learning method that learns from a series of bijective operations to establish "Bayes–linear-Gauss" statistical relationships between model and data variables. Such statistical relationships, once conditioned to actual borehole measurements, allow for fast-computation posterior geological models. The proposed framework is completely automated in an open-source project. We demonstrate its application by applying it to a generic gas reservoir dataset. The posterior results show significant uncertainty reduction in both spatial geological model and gas volume prediction and cannot be falsified by new borehole observations. Furthermore, our automated framework completes the entire uncertainty quantification process efficiently for such large models. [ABSTRACT FROM AUTHOR]

We provide an automated method for uncertainty quantification and updating of geological models using borehole data for subsurface developments (groundwater, geothermal, oil & gas, and CO2 sequestration, etc.) within a Bayesian framework. Our methodologies are developed with the Bayesian Evidential Learning protocol for uncertainty quantification. Under such framework, newly acquired borehole data directly and jointly update geological models (structure, lithology, petrophysics and fluids), globally and spatially, without time-consuming model re-buildings. To address the above, an ensemble of prior geological models is first constructed by Monte Carlo simulation from prior distribution. Once the prior model is tested by means of falsification process, a sequential direct forecasting is designed to perform the joint uncertainty quantification. The direct forecasting is a data-scientific method that learns from a series of bijective operations to establish "Bayes-linear-Gauss" statistical relationships between model and data variables. Such statistical relationships, once conditioned to actual borehole measurements, allows for fast computation posterior geological models. The proposed framework is completely automated in an opensource project. We demonstrate its application by applying to a generalized synthetic dataset motivated by a gas reservoir from Australia. The posterior results show significant uncertainty reduction in both spatial geological model and gas volume prediction, and cannot be falsified by new borehole observations. Furthermore, our automated framework completes the entire uncertainty quantification process efficiently for such large models. [ABSTRACT FROM AUTHOR]

Exploring geochemical patterns based on statistical data analysis is a convenient and effective way to improve our understanding of the geochemical characteristics of the given study area. In this paper, a procedure combining factor analysis and cluster analysis in a novel way was proposed to discover geochemical patterns of interest, or more specifically, a cluster of observations most likely indicative of mineralization. Factor analysis on the entire dataset is firstly performed to obtain a baseline factor structure to be compared with. Secondly, cluster analysis based on factor scores is carried out to produce several clusters reflecting heterogeneity within the dataset. This type of heterogeneity is further investigated in more detail by implementing factor analysis upon each cluster, and comparing the factor structure of each cluster with the baseline factor structure by a defined measure. The randomization test was applied here to further test whether the difference of measures is significant or not. A case study of processing soil samples collected in Jilinbaolige district, Inner Mongolia of China, is presented to illustrate and validate this procedure. [ABSTRACT FROM AUTHOR]

Abstract: Pattern-based spatial modeling relies on training images as basic modeling component for generating geostatistical realizations. The methodology recognizes that working with the unit of a pattern aids its reproduction, particularly for large systems. In this paper improvements are made, in terms of both the computation time and conditioning, of a pattern-based simulation method that relies on the cross-correlation-based simulation (CCSIM), introduced by Tahmasebi et al. (2012). The extension lies on the use of a multi-scale (MS) representation of the training image along a pattern projection strategy that is markedly different from the traditional multi-grid methods employed in the current methodologies, and proposes acceleration of the method by carrying out most of the computations in the Fourier space. In the proposed multi-scale representation, we transform the high-resolution training image into a pyramid of consecutively up-gridded views of the same image. The pyramid allows for rapid search of the patterns that can be superimposed over a shared overlap area with previously simulated patterns. A second advantage of the multi-scale view lies in data conditioning by means of a new hard data-relocation algorithm and the use of a co-template for looking for conditioning points ahead of the raster path employed in CCSIM. Using synthetic and real-field multi-million cell examples with sparse, as well as dense datasets, we investigate quantitatively how the improved algorithm performs with respect to CCSIM, as well as the traditional MP simulation algorithms. [Copyright &y& Elsevier]

Abstract: While algorithms and methodologies to study uncertainty in the Earth Sciences are constantly evolving, there is currently no free integrated software that allows the general practitioners access to these developments. This paper presents SGEMS-UQ, a plugin for the SGEMS platform, that is used to perform distance-based uncertainty analysis on geostatistical simulations, and the resulting forward transfer function responses used in subsurface modeling and engineering. A versatile XML-derived dialect is defined for communicating with external programs that reduces the need for ad-hoc linking of codes, and a relational database system is implemented to automate many of the steps in data mining the spatial and forward model parameters. Through a graphical user interface, one can map a set of realizations and forward transfer function responses into a multidimensional scaling (MDS) space where visualization utilities, and clustering techniques are available. Once mapped in the MDS space, the user can explore linkage between simulation parameters and forward transfer function responses using a module based on a SQL database. Consideration is given to the use of software engineering paradigms and design patterns to produce a code-base that is manageable, efficient, and extensible for future applications, while being scalable to work with large datasets. Finally, we illustrate the versatility of the code-base on an application of modeling uncertainty in reservoir forecasts for an oil reservoir in the West Coast of Africa. [Copyright &y& Elsevier]

Geological characterization of naturally fractured reservoirs is potentially associated with large uncertainty. However, the geological modeling of discrete fracture networks (DFN) is considerably disconnected from uncertainty modeling based on conventional flow simulators in practice. DFN models provide a geologically consistent way of modeling fractures in reservoirs. However, flow simulation of DFN models is currently infeasible at the field scale. To translate DFN models to dual media descriptions efficiently and rapidly, we propose a geostatistical approach based on patterns. We will use experimental design to capture the uncertainties in the fracture description and generate DFN models. The DFN models are then upscaled to equivalent continuum models. Patterns obtained from the upscaled DFN models are reduced to a manageable set and used as training images for multiple-point statistics (MPS). Once the training images are obtained, they allow for fast realization of dual-porosity descriptions with MPS directly, while circumventing the time-consuming process of DFN modeling and upscaling. We demonstrate our ideas on a realistic Middle East-type fractured reservoir system. [ABSTRACT FROM AUTHOR]

The subglacial bed topography is critical for modelling the evolution of Thwaites Glacier in the Amundsen Sea Embayment (ASE), where rapid ice loss threatens the stability of the West Antarctic Ice Sheet. However, mapping of subglacial topography is subject to uncertainties of up to hundreds of metres, primarily due to large gaps of up to tens of kilometres in airborne ice-penetrating radar flight lines. Deterministic interpolation approaches do not reflect such spatial uncertainty. While traditional geostatistical simulations can model such uncertainty, they become difficult to apply because of the significant non-stationary spatial variation of topography over such large surface area. In this study, we develop a non-stationary multiple-point geostatistical (MPS) approach to interpolate large areas with irregular geophysical data and apply it to model the spatial uncertainty of entire ASE basal topography. We collect 166 high-quality topographic training images (TIs) of resolution 500 m to train the gap-filling of radar data gaps, thereby simulating realistic topography maps. The TIs are extensively sampled from deglaciated regions in the Arctic as well as Antarctica. To address the non-stationarity in topographic modelling, we introduce a Bayesian framework that models the posterior distribution of non-stationary TIs assigned to the local line data. Sampling from this distribution then provides candidate training images for local topographic modelling with uncertainty, constrained to radar flight line data. Compared to traditional MPS approaches that do not consider uncertain TI sampling, our approach results in a significant improvement in the topographic modelling quality and efficiency of the simulation algorithm. Finally, we simulate multiple realizations of high-resolution ASE topographic maps. We use the multiple realizations to investigate the impact of basal topography uncertainty on subglacial hydrological flow patterns. [ABSTRACT FROM AUTHOR]

Geologic uncertainties and limited well data often render recovery forecasting a difficult undertaking in typical appraisal and early development settings. Recent advances in geologic modeling algorithms permit automation of the model generation process via macros and geostatistical tools. This allows rapid construction of multiple alternative geologic realizations. Despite the advances in geologic modeling, computation of the reservoir dynamic response via full-physics reservoir simulation remains a computationally expensive task. Therefore, only a few of the many probable realizations are simulated in practice. Experimental design techniques typically focus on a few discrete geologic realizations as they are inherently more suitable for continuous engineering parameters and can only crudely approximate the impact of geology. A flow-based pattern recognition algorithm (FPRA) has been developed for quantifying the forecast uncertainty as an alternative. The proposed algorithm relies on the rapid characterization of the geologic uncertainty space represented by an ensemble of sufficiently diverse static model realizations. FPRA characterizes the geologic uncertainty space by calculating connectivity distances, which quantify how different each individual realization is from all others in terms of recovery response. Fast streamline simulations are employed in evaluating these distances. By applying pattern recognition techniques to connectivity distances, a few representative realizations are identified within the model ensemble for full-physics simulation. In turn, the recovery factor probability distribution is derived from these intelligently selected simulation runs. Here, FPRA is tested on an example case where the objective is to accurately compute the recovery factor statistics as a function of geologic uncertainty in a channelized turbidite reservoir. Recovery factor cumulative distribution functions computed by FPRA compare well to the one computed via exhaustive full-physics simulations. [ABSTRACT FROM AUTHOR]

Abstract: A multiscale adjoint (MSADJ) method is developed to compute high-resolution sensitivity coefficients for subsurface flow in large-scale heterogeneous geologic formations. In this method, the original fine-scale problem is partitioned into a set of coupled subgrid problems, such that the global adjoint problem can be efficiently solved on a coarse grid. Then, the coarse-scale sensitivities are interpolated to the local fine grid by reconstructing the local variability of the model parameters with the aid of solving embedded adjoint subproblems. The approach employs the multiscale finite-volume (MSFV) formulation to accurately and efficiently solve the highly detailed flow problem. The MSFV method couples a global coarse-scale solution with local fine-scale reconstruction operators, hence yielding model responses that are quite accurate at both scales. The MSADJ method is equally efficient in computing the gradient of the objective function with respect to model parameters. Several examples demonstrate that the approach is accurate and computationally efficient. The accuracy of our multiscale method for inverse problems is twofold: the sensitivity coefficients computed by this approach are more accurate than the traditional finite-difference-based numerical method for computing derivatives, and the calibrated models after history matching honor the available dynamic data on the fine scale. In other words, the multiscale based adjoint scheme can be used to history match fine-scale models quite effectively. [Copyright &y& Elsevier]

The subglacial bed topography is critical for modeling the evolution of Thwaites Glacier in the Amundsen Sea Embayment (ASE), where rapid ice loss threatens the stability of the West Antarctic Ice Sheet. However, mapping of subglacial topography is subject to high uncertainty. This is mainly because the bed topography is measured by airborne ice-penetrating radar along flight lines with large gaps up to tens of kilometers. Deterministic interpolation approaches do not reflect such spatial uncertainty. While traditional geostatistical simulation can model such uncertainty, it may be difficult to apply because of the significant non-stationary spatial variation of topography over such large surface area. In this study, we develop a non-stationary multiple-point geostatistical approach to interpolate large areas with irregular geophysical data and apply it to model the spatial uncertainty of entire ASE basal topography. We collect 166 high-resolution topographic training images (TIs) to train the gap-filling of radar data gaps, thereby simulating realistic topography maps. The TIs are extensively sampled from deglaciated regions in the Arctic as well as Antarctica. To address the non-stationarity in topographic modeling, we introduce a Bayesian framework that models the posterior distribution of non-stationary training images to the local modeling domain. Sampling from this distribution then provide candidate training images for local topographic modeling with uncertainty, constrained to radar flight line data. Compared to traditional MPS approaches without considering TI sampling, our approach demonstrates significant improvement in the topographic modeling quality and efficiency of the simulation algorithm. Finally, we simulate multiple realizations of high-resolution ASE topographic maps. We use the multiple realizations to investigate the impact of basal topography uncertainty on subglacial hydrological flow patterns. [ABSTRACT FROM AUTHOR]

Although most landslides are precipitation‐triggered, a number of other complex conditions simultaneously predispose any given slope to failure, with the impact of urbanization posing particular scientific challenges. We use panel regression with fixed effects—which controls for observed and unobserved time‐variant and time‐invariant influences—to quantify the effect of precipitation accumulation on landslide concentration across the Pacific Coast region of the United States. We find that landslide hazard is most sensitive to precipitation variations in urbanized areas. This finding is robust across 1‐day, 10‐day, and 30‐day periods of precipitation accumulation, among individual Pacific Coast states, and when the analysis is confined to the San Francisco Bay Area (a subregion with both urban and rural areas). Our results corroborate existing hypotheses that urbanization increases landslide hazard, while demonstrating the importance of considering interactions with urbanization when predicting landslide hazard in the current climate, and under climate change scenarios. Plain Language Summary: Generalizable understanding of where and how landslides occur may inform efforts to adapt to these devastating natural disasters. While most landslides are triggered by precipitation, a number of other complex factors also play a role in slope destabilization. Employing an empirical framework that accounts for these confounding factors, we find that landslide hazard is most sensitive to precipitation variations in urbanized areas. Our results enhance understanding of the impact of urbanization on precipitation‐triggered landslide hazard and highlight the importance of considering urbanization when predicting landslide hazard, particularly in response to global warming and climate change. Key Points: We quantify the effect of precipitation on landslide concentration within distinct land use types across the US Pacific CoastLandslide hazard is most sensitive to precipitation variations in urbanized areasResults highlight the importance of considering interactions with urbanization when predicting landslide response to climate [ABSTRACT FROM AUTHOR]

Injection of water-based hydraulic fracturing fluid (HFF) into tight shale gas/oil formations can increase formation permeability and enhance production rates, but this process frequently causes mineral scale formation that can occlude pore space and hinder flow. To identify the most important factors that control the formation of mineral scales, we applied a novel global sensitivity analysis method—distance-based generalized sensitivity analysis (DGSA)—to a reactive transport model (RTM) that was previously built and calibrated to simulate precipitation of barite [BaSO4] and iron (hydr)oxide [Fe(OH)3] in shale matrices and on fracture surfaces. Reactive transport simulations were run with model parameters randomly sampled based on assigned uncertainties. Modeling results for barite and Fe(OH)3 formation were clustered using machine-learning algorithms. A list of ranked critical input parameters was obtained after statistical quantification of cumulative distribution functions of input parameters. We found that barite formation is most sensitive to the rate of sulfate ion generation, which is determined by the pyrite dissolution rate coefficient and oxidant availability. In addition, barite formation is sensitive to the initial amounts of barite in HFF and shale, followed by barite thermodynamics/kinetics. For Fe(OH)3 formation, the ranked factors are Fe(OH)3 precipitation rate coefficients, initial HFF pH, initial Fe(OH)3 amount in HFF, and oxidant availability. Our results provide insights into managing mineral scale formation during hydraulic fracturing to enhance production. Meanwhile, this study serves as an example of global sensitivity analysis of RTMs using the efficient, straightforward, and open-source DGSA method. [ABSTRACT FROM AUTHOR]

This paper introduces a method to generate conditional categorical simulations, given an ensemble of partially conditioned (or unconditional) categorical simulations derived from any simulation process. The proposed conditioning method relies on implicit functions (signed distance functions) for representing the categorical spatial variable of interest. Thus, the conditioning problem is reformulated in terms of signed distance functions. The proposed approach combines aspects of principal component analysis and Gibbs sampling to achieve the conditioning of the unconditional categorical realizations to the data. It is applied to synthetic and real-world datasets and compared to the traditional sequential indicator simulation. It appears that the proposed simulation technique is an effective method to generate conditional categorical simulations from a set of unconditional categorical simulations. [ABSTRACT FROM AUTHOR]

Computational modeling is frequently incorporated into environmental decision-making in order to capture inherently complex relationships and system dynamics. The complexity of such models often lies in various heterogeneous effects that arise due to the interaction of different input factors or due to designed structural variation in the model. In the past, various sensitivity analysis approaches have been implemented in attempts to identify essential decision factors. However, existing sensitivity analysis methods fail to capture critical information in the presence of heterogeneous effects. In this paper, the recently introduced simulation decomposition (SimDec) visualization method is extended to include quantitative sensitivity analysis. The framework is tested on several decision-making problems and is shown to capture heterogeneous behavior. A formal definition and classification of heterogeneous effects for computational models is introduced. The framework is open-sourced in a variety of scientific programming languages. • Sensitivity analysis methods fail to capture heterogeneous effects. • A novel quantitative SimDec framework is able to address heterogeneous model behavior. • Three case studies exhibit various types of heterogeneous effects. • The definition of heterogeneous effects in computational models is introduced. • SimDec open-source packages in Python, Julia, R, and Matlab are created. [ABSTRACT FROM AUTHOR]

Many Earth-surface processes are studied using field, experimental, or numerical modeling datasets that, although realistic, only represent a small subset of possible outcomes observed in nature. Acquiring statistically significant quantities of data is often time- and/or cost intensive. Therefore it is not uncommon that a quantitative statement of uncertainty is missing in predictions made from geomorphic datasets. To access such uncertainty for partially or unobserved states of a system, a stochastic model is needed that can mimic spatial as well as temporal variability. In this paper, we propose such a stochastic model for morphodynamic datasets. One component of the model represents long time-scale behavior using extreme value statistics that describe large but infrequent morphological changes; a second component models short time-scale behavior by means of multiple-point geostatistics. We propose a Bayesian protocol to first falsify the stochastic model based on the statistical similarity to the dataset thereby improving physical plausibility. Then, we use approximate Bayesian computation to infer the stochastic model parameters from the temporally limited geomorphic data. We apply the model to a single flume experiment of braided river channels evolving under steady water and sediment flux. Realizations of the stochastic model allow quantifying uncertainty on the movement of channels in the flume and on the occurrence of rare extreme events. [ABSTRACT FROM AUTHOR]

Abstract For many geoscience applications, prediction requires building complex 3D surface models. Because of such complexity, often only a single model is built, possibly with a small set of variants to represent the uncertainty. Recent advancement in implicit modeling has made the construction of 3D geological models simpler; however, automatic assessment and visualization of uncertainty constrained by input geological rules and data constraints is still an active research topic. In this paper, we propose a new method that directly assesses and visualizes the uncertainty of geological surfaces by the means of stochastic motion. We represent the geological surfaces as the addition of stochastic implicit conceptual models and residual functions subject to the constraints of data and geological age relationships. Two sampling approaches to create the stochastic motion are proposed: Monte Carlo and Markov chain Monte Carlo (McMC). The uncertainty is assessed by independent realizations drawn by Monte Carlo sampling. The uncertainty is visualized by a "smooth" movie of gradually evolving geological surfaces that have the same stationary distribution as Monte Carlo, sampled by Markov chain Monte Carlo (McMC). This idea is integrated into the level set equation. Level sets are an ideal way to represent mathematically complex surfaces without explicit grid representations, thereby having the advantage of avoiding tedious topological computations such as defining the connectivity of a surface. We illustrate this new idea with simple synthetic 3D examples, taking the constraints of data and geological age relationships into consideration. Finally, we illustrate the idea using a synthetic data set from a copper deposit, where dense drillholes constrain an ore body with seven different lithologies. Our method provides a direct assessment and visualization of the uncertainty of 3D geological surfaces. Highlights • A new method for direct uncertainty assessment of geological surfaces is presented. • Enhanced visualization of uncertainty using movies. • Proof of gradual deformation method as a McMC sampler. • Realizations of a complex case exhibit large surface variability. [ABSTRACT FROM AUTHOR]

Modeling complex geological interfaces is a common task in geosciences. Many data sources are available for geological interface modeling, including borehole data and geophysical surveys. Geological knowledge, such as the delineation from geologists, is difficult to quantify but likely adds value to geological interface modeling. To integrate all information, we present a data-knowledge-driven trend surface analysis method to construct stochastic geological interfaces. We design a Metropolis–Hastings sampling framework to sample stochastic trend interfaces and quantify the uncertainty of geological interfaces given all information sources. This method is suitable for both explicit and implicit representations of geological interfaces. We demonstrate our method in three different test cases: modeling stochastic interfaces of Greenland subglacial topography, magmatic intrusion, and buried river valleys in Australia. • This new trend surface analysis method integrates various data types and geological knowledge. • A Markov chain Monte Carlo sampler is used for explicit and implicit geological interfaces. • Stochastic geological interfaces are sampled in three studies: subglacial topography, magmatic intrusion, and palaeovalley modeling. [ABSTRACT FROM AUTHOR]

In this paper we propose Universal trace co-kriging, a novel methodology for interpolation of multivariate Hilbert space valued functional data. Such data commonly arises in multi-fidelity numerical modeling of the subsurface and it is a part of many modern uncertainty quantification studies. Besides theoretical developments we also present methodological evaluation and comparisons with the recently published projection based approach by Bohorquez et al. (Stoch Environ Res Risk Assess 31(1):53-70, 2016. 10.1007/s00477-016-1266-y). Our evaluations and analyses were performed on synthetic (oil reservoir) and real field (uranium contamination) subsurface uncertainty quantification case studies. Monte Carlo analyses were conducted to draw important conclusions and to provide practical guidelines for all future practitioners. [ABSTRACT FROM AUTHOR]

Geophysical data have proven to be very useful for lithological characterization. However, quantitatively integrating the information gained from acquiring geophysical data generally requires colocated lithological and geophysical data for constructing a rock-physics relationship. In this contribution, the issue of integrating noncolocated geophysical and lithological data is addressed, and the results are applied to simulate groundwater flow in a heterogeneous aquifer in the Prairie Waters Project North Campus aquifer recharge site, Colorado. Two methods of constructing a rock-physics transform between electrical resistivity tomography (ERT) data and lithology measurements are assessed. In the first approach, a maximum likelihood estimation (MLE) is used to fit a bimodal lognormal distribution to horizontal crosssections of the ERT resistivity histogram. In the second approach, a spatial bootstrap is applied to approximate the rock-physics relationship. The rock-physics transforms provide soft data for multiple point statistics (MPS) simulations. Subsurface models are used to run groundwater flow and tracer test simulations. Each model's uncalibrated, predicted breakthrough time is evaluated based on its agreement with measured subsurface travel time values from infiltration basins to selected groundwater recovery wells. We find that incorporating geophysical information into uncalibrated flow models reduces the difference with observed values, as compared to flow models without geophysical information incorporated. The integration of geophysical data also narrows the variance of predicted tracer breakthrough times substantially. Accuracy is highest and variance is lowest in breakthrough predictions generated by the MLE-based rock-physics transform. Calibrating the ensemble of geophysically constrained models would help produce a suite of realistic flow models for predictive purposes at the site. We find that the success of breakthrough predictions is highly sensitive to the definition of the rock-physics transform; it is therefore important to model this transfer function accurately. [ABSTRACT FROM AUTHOR]

Process-based modeling offers a way to represent realistic geological heterogeneity in subsurface models. The main limitation lies in conditioning such models to data. Multiple-point geostatistics can use these process-based models as training images and address the data conditioning problem. In this work, we further develop image quilting as a method for 3D stochastic simulation capable of mimicking the realism of process-based geological models with minimal modeling effort (i.e. parameter tuning) and at the same time condition them to a variety of data. In particular, we develop a new probabilistic data aggregation method for image quilting that bypasses traditional ad-hoc weighting of auxiliary variables. In addition, we propose a novel criterion for template design in image quilting that generalizes the entropy plot for continuous training images. The criterion is based on the new concept of voxel reuse—a stochastic and quilting-aware function of the training image. We compare our proposed method with other established simulation methods on a set of process-based training images of varying complexity, including a real-case example of stochastic simulation of the buried-valley groundwater system in Denmark. [ABSTRACT FROM AUTHOR]

The conventional paradigm for predicting future reservoir performance from existing production data involves the construction of reservoir models that match the historical data through iterative history matching. This is generally an expensive and difficult task and often results in models that do not accurately assess the uncertainty of the forecast. We propose an alternative re-formulation of the problem, in which the role of the reservoir model is reconsidered. Instead of using the model to match the historical production, and then forecasting, the model is used in combination with Monte Carlo sampling to establish a statistical relationship between the historical and forecast variables. The estimated relationship is then used in conjunction with the actual production data to produce a statistical forecast. This allows quantifying posterior uncertainty on the forecast variable without explicit inversion or history matching. The main rationale behind this is that the reservoir model is highly complex and even so, still remains a simplified representation of the actual subsurface. As statistical relationships can generally only be constructed in low dimensions, compression and dimension reduction of the reservoir models themselves would result in further oversimplification. Conversely, production data and forecast variables are time series data, which are simpler and much more applicable for dimension reduction techniques. We present a dimension reduction approach based on functional data analysis (FDA), and mixed principal component analysis (mixed PCA), followed by canonical correlation analysis (CCA) to maximize the linear correlation between the forecast and production variables. Using these transformed variables, it is then possible to apply linear Gaussian regression and estimate the statistical relationship between the forecast and historical variables. This relationship is used in combination with the actual observed historical data to estimate the posterior distribution of the forecast variable. Sampling from this posterior and reconstructing the corresponding forecast time series, allows assessing uncertainty on the forecast. This workflow will be demonstrated on a case based on a Libyan reservoir and compared with traditional history matching. [ABSTRACT FROM AUTHOR]

Sensitivity analysis plays an important role in geoscientific computer experiments, whether for forecasting, data assimilation or model calibration. In this paper we focus on an extension of a method of regionalized sensitivity analysis (RSA) to applications typical in the Earth Sciences. Such applications involve the building of large complex spatial models, the application of computationally extensive forward modeling codes and the integration of heterogeneous sources of model uncertainty. The aim of this paper is to be practical: 1) provide a Matlab code, 2) provide novel visualization methods to aid users in getting a better understanding in the sensitivity 3) provide a method based on kernel principal component analysis (KPCA) and self-organizing maps (SOM) to account for spatial uncertainty typical in Earth Science applications and 4) provide an illustration on a real field case where the above mentioned complexities present themselves. We present methods that extend the original RSA method in several ways. First we present the calculation of conditional effects, defined as the sensitivity of a parameter given a level of another parameters. Second, we show how this conditional effect can be used to choose nominal values or ranges to fix insensitive parameters aiming to minimally affect uncertainty in the response. Third, we develop a method based on KPCA and SOM to assign a rank to spatial models in order to calculate the sensitivity on spatial variability in the models. A large oil/gas reservoir case is used as illustration of these ideas. [ABSTRACT FROM AUTHOR]

Scientific curiosity, exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity. This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydrogeological data. Modern geostatistical simulation algorithms can produce multiple subsurface realizations that are in agreement with conceptual geological models and statistical rock physics can be used to map these realizations into physical properties that are sensed by the geophysical or hydrogeological data. The inverse problem consists of finding one or an ensemble of such subsurface realizations that are in agreement with the data. The most general inversion frameworks are presently often computationally intractable when applied to large-scale problems and it is necessary to better understand the implications of simplifying (1) the conceptual geological model (e.g., using model compression); (2) the physical forward problem (e.g., using proxy models); and (3) the algorithm used to solve the inverse problem (e.g., Markov chain Monte Carlo or local optimization methods) to reach practical and robust solutions given today's computer resources and knowledge. We also highlight the need to not only use geophysical and hydrogeological data for parameter estimation purposes, but also to use them to falsify or corroborate alternative geological scenarios. [ABSTRACT FROM AUTHOR]

• Groundwater remediation planning and decision problem formulated as a partially observable Markov decision process (POMDP). • Comparison between POMDP and the conventional state-of-the-art optimization approaches, such as one-shot optimization and model predictive control (closed loop) optimization. • DESPOT, a state-of-the-art POMDP solver, outperforms optimization solution methods using PSO and hand-crafted heuristic solutions. • Optimizing the trade-off between information gathering and the performance of possible future scenarios via POMDP formulation. • Importance of belief updates, also known as inversion problems or history matching, in groundwater problems. Groundwater contamination causes significant groundwater supply risks that severely affect humans and livestock, especially in the era of climate change. Consequently, the need to develop and optimize remediation strategies such as pump and treat is indispensable. An effective and efficient strategy can reduce the spread of contaminants and cost of clean-up. However, developing such a strategy is challenging due to the inherent uncertainty and sequential nature of the problem. For example, taking actions such as drilling wells is interwoven with information gathering over time. In this paper, we formulate the groundwater remediation planning and decision problem as a partially observable Markov decision process (POMDP). A POMDP formulation allows planning by optimizing the trade-off between information gathering and the performance of possible future scenarios. We use a state-of-the-art POMDP solver called DESPOT for planning remediation strategies. The results show that DESPOT can yield much better remediation strategies than hand crafted heuristics and optimization methods. The superior performance of DESPOT is due to the incorporation of both previous information and future reward into the current decision. We also demonstrate the robustness of the POMDP formulation to measurement error. [ABSTRACT FROM AUTHOR]

Computationally efficient updating of reservoir models with new production data has received considerable attention recently. In this paper however, we focus on the challenges of updating reservoir models prior to production, in particular when new exploration wells are drilled. At this stage, uncertainty in the depositional model is highly impactful in terms of risk and decision making. Mathematically, such uncertainty is often decomposed into uncertainty of lithological trends in facies proportions which is typically informed by seismic data, and sub-seismic variability often modeled geostatistically by means of training images. While uncertainty in the training image has received considerable attention, uncertainty in the trend/facies proportion receives little to no consideration. In many practical applications, with either poor geophysical data or little well information, the trend is often as uncertain as the training image, yet is often fixed, leading to unrealistic uncertainty models. The problem is addressed through a hierarchical model of probability. Total model uncertainty is divided into first uncertainty in the training image, then uncertainty in the trend given the uncertain training image. Our methodology relies on an efficient Bayesian updating of these model parameters (trend and training image) by modeling forward-simulated well facies profiles in low-dimensional metric space. We apply this methodology to a real field case study involving wells drilled sequentially in the subsurface, where as more data becomes available, uncertainty in both training image and trend require updating to improve characterization of the facies. [ABSTRACT FROM AUTHOR]

Uncertainty quantification is currently one of the leading challenges in the geosciences, in particular in reservoir modeling. A wealth of subsurface data as well as expert knowledge are available to quantify uncertainty and state predictions on reservoir performance or reserves. The geosciences component within this larger modeling framework is partially an interpretive science. Geologists and geophysicists interpret data to postulate on the nature of the depositional environment, for example on the type of fracture system, the nature of faulting, and the type of rock physics model. Often, several alternative scenarios or interpretations are offered, including some associated belief quantified with probabilities. In the context of facies modeling, this could result in various interpretations of facies architecture, associations, geometries, and the way they are distributed in space. A quantitative approach to specify this uncertainty is to provide a set of alternative 3D training images from which several geostatistical models can be generated. In this paper, we consider quantifying uncertainty on facies models in the early development stage of a reservoir when there is still considerable uncertainty on the nature of the spatial distribution of the facies. At this stage, production data are available to further constrain uncertainty. We develop a workflow that consists of two steps: (1) determining which training images are no longer consistent with production data and should be rejected and (2) to history match with a given fixed training image. We illustrate our ideas and methodology on a test case derived from a real field case of predicting flow in a newly planned well in a turbidite reservoir off the African West coast. [ABSTRACT FROM AUTHOR]

The spatial modeling of geo-domains has become ubiquitous in many geoscientific fields. However, geo-domains' spatial modeling poses real challenges, including the uncertainty assessment of geo-domain boundaries. Geo-domain models are subject to uncertainties due mainly to the inherent lack of knowledge in areas with little or no data. Because they are often used for impactful decision-making, they must accurately estimate the geo-domain boundaries' uncertainty. This paper presents a geostatistical implicit modeling method to assess the uncertainty of 3D geo-domain boundaries. The basic concept of the method is to represent the underlying implicit function associated with each geo-domain as a sum of a random implicit trend function and a residual random function. The conditional simulation of geo-domains is performed through a step-by-step approach. First, implicit trend function realizations and optimal covariance parameters associated with the residual random function are generated through the probability perturbation method. Then, residual function realizations are generated through classical geostatistical unconditional simulation methods and added to implicit trend function realizations to obtain unconditional implicit function realizations. Next, the conditioning of unconditional implicit function realizations to hard data is performed via principal component analysis and randomized quadratic programming. Finally, conditional implicit function simulations are transformed to conditional geo-domain simulations by applying a truncation rule. The proposed method is constructed to honor hard data and stated rules of how geo-domains interact spatially. It is applied to a lithological dataset from a porphyry copper deposit. A comparison with the classical sequential indicator simulation (SIS) method is carried out. The results indicate that the proposed approach can provide a more reliable and realistic uncertainty assessment of 3D geo-domain boundaries than the traditional sequential indicator simulation (SIS) approach. • A new geostatistical implicit modeling framework. • Honor hard data and stated rules of how geo-domains interact spatially. • Integrate volume proportion constraints on the geo-domains. • Easily handle a large number of geo-domains. • Provide reliable uncertainty assessment of geo-domain boundaries. [ABSTRACT FROM AUTHOR]

The development of geostatistics has been mostly accomplished by application-oriented engineers in the past 20 years. The focus on concrete applications gave birth to many algorithms and computer programs designed to address different issues, such as estimating or simulating a variable while possibly accounting for secondary information such as seismic data, or integrating geological and geometrical data. At the core of any geostatistical data integration methodology is a well-designed algorithm.Yet, despite their obvious differences, all these algorithms share many commonalities on which to build a geostatistics programming library, lest the resulting library is poorly reusable and difficult to expand.Building on this observation, we design a comprehensive, yet flexible and easily reusable library of geostatistics algorithms in C++.The recent advent of the generic programming paradigm allows us elegantly to express the commonalities of the geostatistical algorithms into computer code. Generic programming, also referred to as “programming with concepts”, provides a high level of abstraction without loss of efficiency. This last point is a major gain over object-oriented programming which often trades efficiency for abstraction. It is not enough for a numerical library to be reusable, it also has to be fast.Because generic programming is “programming with concepts”, the essential step in the library design is the careful identification and thorough definition of these concepts shared by most geostatistical algorithms. Building on these definitions, a generic and expandable code can be developed.To show the advantages of such a generic library, we use GSTL to build two sequential simulation programs working on two different types of grids—a surface with faults and an unstructured grid—without requiring any change to the GSTL code. [Copyright &y& Elsevier]