Uncertainty In Geological Models Research Articles

Probabilistic analysis of lateral behaviour of offshore wind turbine monopile considering uncertainties of geological model and loads

Due to the complex geological, meteorological and hydrological conditions, along with the limited availability of field measurements, multiple uncertainties are related to the performance analysis of the offshore wind turbine. The main sources of uncertainty are the geological model and the environmental loads. However, the geological model uncertainty and loads uncertainty were often characterized separately in previous studies. To this end, this article proposes a novel framework for the coupled characterization of the geological model and loads uncertainties. With this new framework, the geological model is generated using a conditional random field method, in which the stratigraphic and geo-properties uncertainties are characterized simultaneously. Next, environmental parameters are considered as random variables, and the cross correlation between different environmental parameters is captured with the Pearson correlation coefficient. Then, multiple realizations of the geological model and these of environmental parameters are sampled with Monte Carlo simulation. With these generated realizations as inputs, the monopile foundation performance could then be analyzed probabilistically considering uncertainties of the geological model and loads. To demonstrate the effectiveness of the new framework, a case study of an offshore site in Taiwan is conducted. Further, a comparative study is performed to quantitatively reveal the influence of different uncertainty sources on site characterization and monopile behaviour assessment, through which the superiority of the presented framework is demonstrated.

Evaluation of rock mass units using a non-invasive geophysical approach

Thorough and accurate assessment of rock mass units is important for development of engineering infrastructures and groundwater resources assessments. Rock mass units are widely evaluated by reliable geomechanical parameters namely rock quality designation (RQD) and rock core index (RCI). Conventionally, these parameters are acquired via an extensive number of geotechnical tests. Such tests, however, suffer efficiency for data coverage, cost, equipment and topographic constrictions, and hence cause ambiguity in geological models for a detailed evaluation of rock mass integrity. Conversely, geophysical surveys offer fast, more user-friendly, less invasive, more cost-effective and less time-consuming approach for geological investigations. The past research confirms a useful link between geophysical and geotechnical parameters. But, none of the past studies provides a suitable and generalized relation between these parameters which can reduce geotechnical model uncertainty mostly caused by inadequate data and subsurface heterogeneity. This paper proposes a meaningful and feasible method to obtain geomechanical parameters using a certain number of drillings and geophysical data of four different sites. Based on electrical resistivity obtained from electrical resistivity tomography (ERT) and controlled-source audio-frequency magneto telluric (CSAMT), this research provides the general and adaptable formulas for geotechnical parameter estimation and reduces geological model uncertainty for more detailed 2D/3D imaging of RQD and RCI covering the whole sites where even no drilling data exists. Thus, the investigated sites are assessed laterally and vertically along each geophysical profile via distinct value ranges of geological parameters for a thorough and reliable evaluation of rock mass units in highly heterogeneous setting. Our research reduces the ambiguity caused by structural heterogeneities and scarce data, fills the gap between inadequate well tests and the true geological models, and gives new insights into the rock mass units for proper engineering design and groundwater exploitation.

Towards quantifying uncertainties in geological models for mineral resource estimation through outside-in deposit-scale structural geological analysis

Mineral Resource downgrades can be prevented by integrating better structural geological interpretations into project evaluations. Geological modelling for Mineral Resource estimation is presented as a systematic process of structural geological analysis at the deposit-scale using drill-sampled grade data. The initial step in this process is to use Maximum Intensity Projection (MIP) rendering to interpret axial symmetry and its orientation from the grade interval mid-points at the deposit-scale, thus reducing the modelling process’s degrees of freedom to only three—estimating the prolateness of the grade or lithological distribution. This approach contrasts with the brute-force methods for assessing modelling uncertainty because the axial direction is fixed to the down-plunge orientation, thus eliminating from the outset, structurally implausible geometric configurations and unrealistic geological scenarios common in brute-force methods. Adopting this new approach of creating geological models means moving away from conventional mining industry methods that prioritise operational considerations in constructing resource estimates but fail to explain the geometric complexities of mineral deposits. We use experiments and a practical case study of a historical gold mine in Western Australia to highlight the significance of analysing the structural control of a gold deposit at the deposit-scale using raw grade data. Our research is based on anecdotal evidence suggesting that erroneous geological modelling leads to unforeseen Mineral Resource downgrades. However, we cannot confirm this hypothesis because there have been few, if any, independent public inquiries into Mineral Resource downgrades. To establish the underlying reasons for significant resource downgrades with certainty, impartial investigations (modelled on accident investigations in the aviation industry) are imperative.

Uncertainty assessment of 3D geological models based on spatial diffusion and merging model

AbstractThe geological model plays an important role in geophysics and engineering geology. The data source of geological modeling comes from interpretation data, borehole data, and outcrop data. Due to economic and technical limitations, it is impossible to obtain highly accurate and high-density data sources. The sparsity and inaccuracy of data sources lead to the uncertainty in geological models. Unlike the problem of probability, there is not enough samples for a geological model. Spatial diffusion model and merging model are introduced, which are more satisfied with the cognition of uncertainty than the existing methods. And then, using conditional information entropy, a quantification method of geological uncertainty, is proposed. Compared with the approaches of information entropy, this method took full account of the constraints of geological laws. Based on the uncertainty models and conditional information entropy, a framework of uncertainty assessment in geological models is established. It is not necessary in our framework to create multiple geological models, which is a time-consuming and laborious task. The application of Hashan survey located at north of China shows that the method and framework of this study are reasonable and effective.

Evaluation of geological model uncertainty caused by data sufficiency using groundwater flow and land subsidence modeling as example

Evaluation of geological model uncertainty caused by data sufficiency using groundwater flow and land subsidence modeling as example

Geophysical evaluation of geological model uncertainty for infrastructure design and groundwater assessments

Uncertainty in geological models, mainly caused by natural heterogeneity and inadequate data, often leads to substantial societal risk including failures of engineered structures, geohazards, and groundwater and environmental problems. These models mainly depend on geological knowledge about evaluation of rock mass quality, fractures/faults and clay. Traditionally, geotechnical parameters of rock mass quality classification, such as rock mass integrity index (Kv) are obtained by drilling tests. However, the boreholes approaches are time-consuming and expensive, provide limited data and have topographic constraints. Alternatively, the inexpensive integrated approaches of geophysical methods can reduce geological ambiguity by bridging the gaps between accurate subsurface models and inadequate borehole data. In this work, we incorporate electrical resistivity tomography (ERT) with inadequate drilling data, and determine Kv over large area even where no borehole exists. Our results reduce a large number of wells and evaluate the subsurface thoroughly using 2D/3D imaging of Kv. The ambiguity in water-clay differentiation caused by low resistivity was resolved by integrating ERT with induced polarization (IP). The integration of ERT, Kv and IP identified several localized fractures/faults. Our novel approach, compared with the past studies, reduces uncertainty in the geological model and provides a thorough insight into the subsurface for infrastructure design and groundwater assessments. Our approach is applicable in most cases.

Reducing the Geological Model Uncertainty in Miduk Copper Deposit by Post-processing

Geostatistical modeling, in recent years, has been widely and increasingly used in analyzing underground structures. Using the combination of uncertainty reduction techniques and modeling processes could increase the identification accuracy of underground structure models. In this study, Indicator Kriging (IK) method is employed to model four geological units comprising leached, oxidized, supergene and hypogene zones. The aforementioned units are all located within Miduk Copper Deposit. To evaluate the uncertainty index based on the modelled geological structure, Bernoulli variance is employed. In order to reduce the uncertainty amount of the executed geological model, post-processing procedure is performed using resampling of the interpolated model. This procedure is reiterated as many times as possible until a geological model with an acceptable uncertainty amount is acquired. At the final step, blast holes data is used in order for the validation of the results. The yielded results indicate that the amount of uncertainty dropped from 5.87% to 2.98% after implementing the post-processing procedure.

The role of the geological uncertainty in a geotechnical design – A retrospective view of Freeway No. 3 Landslide in Northern Taiwan

The importance of the geological model in a geotechnical engineering project has long been recognized. However, the uncertainty associated with the geological model has rarely been quantified and explicitly considered in the geotechnical design. This paper explores the role of the geological model uncertainty and the benefit of reducing such uncertainty in a geotechnical design. To this end, the landslide that occurred on 25 April 2010 at 3.3 K of Freeway No. 3 in Northern Taiwan, referred to herein as NH-3 Slope, is re-analyzed with an assumed geological model (a dip-slope model in this case) under various uncertainty scenarios. Traditionally, the design (i.e., a choice of design parameters such as slope height, slope angle, and supporting anchors) of a rock slope seeks to satisfy a target factor of safety (FS). In the case of NH-3 Slope, the apparent dip angle of the slip surface along the dip direction of slope constitutes the geological model of concern. Different survey techniques produce data with varying degrees of error (or uncertainty) in the measured apparent dip angle. For example, data from a Regional Geological Map (RGM) typically yields an estimate of the bedding plane attitude with a significant level of uncertainty due primarily to low data density. In contrast, LiDAR can significantly reduce the uncertainty of the derived bedding plane attitudes. By lowering this uncertainty, the variation (or uncertainty) in the computed FS may be reduced, which tends to yield a lower failure probability (Pf), given other conditions being the same. The benefit of lowering the geological model uncertainty in a geotechnical design is demonstrated through a retrospective analysis of the NH-3 Slope.

Boundary simulation – a hierarchical approach for multiple categories

ABSTRACT Geological modelling is a crucial step in mineral resource evaluation. The traditional approach to modelling the volumetric limits, explicit modelling, presents a series of limitations and disadvantages which makes it costly to assess the uncertainty in relation to the location of the limits between different domains in the mineral deposit. In many cases, the geological model can be a source of crucial uncertainty, for this reason, the uncertainty associated with the geological model must be assessed. This paper proposes a method for assessing geological model uncertainty by simulating the contacts between different domains in a mineral deposit in a hierarchical manner using signed distances. The proposed method was demonstrated in a case study conducted on a porphyry copper deposit. Models generated by the proposed method do not show much noise, as this method leads to continuous contacts between domains while the volume variation and contacts characteristics can be controlled by the parameters. Results are compared to sequential indicator simulation, a traditionally used technique to model geobodies and assess its uncertainty.

Quantifying model structural uncertainty using airborne electromagnetic data

SUMMARY The ability to quantify structural uncertainty in geological models that incorporate geophysical data is affected by two primary sources of uncertainty: geophysical parameter uncertainty and uncertainty in the relationship between geophysical parameters and geological properties of interest. Here, we introduce an open-source, trans-dimensional Bayesian Markov chain Monte Carlo (McMC) algorithm GeoBIPy—Geophysical Bayesian Inference in Python—for robust uncertainty analysis of time-domain or frequency-domain airborne electromagnetic (AEM) data. The McMC algorithm provides a robust assessment of geophysical parameter uncertainty using a trans-dimensional approach that lets the AEM data inform the level of model complexity necessary by allowing the number of model layers itself to be an unknown parameter. Additional components of the Bayesian algorithm allow the user to solve for parameters such as data errors or corrections to the measured instrument height above ground. Probability distributions for a user-specified number of lithologic classes are developed through posterior clustering of McMC-derived resistivity models. Estimates of geological model structural uncertainty are thus obtained through the joint probability of geophysical parameter uncertainty and the uncertainty in the definition of each class. Examples of the implementation of this algorithm are presented for both time-domain and frequency-domain AEM data acquired in Nebraska, USA.

Utilization of multiobjective optimization for pulse testing dataset from a CO2-EOR/sequestration field

In a geological carbon storage project, leakage should be monitored to ensure safe long-term storage of injected CO2. Leakage can be detected early and cost-effectively by monitoring subsurface pressure. The uncertainty in geological models also needs to be sufficiently reduced to detect leakage based on pressure monitoring data. This study presents numerical results of field pulse testing experiments that are designed to detect leakage based on pressure monitoring data for periodical CO2 injection at a CO2 enhanced oil recovery field in Mississippi, USA. In the pulse test, sinusoidal pressure patterns are captured in transitional pressure data because CO2 injection and shut-in are repeated. The patterns are parameterized and history-matched efficiently in the frequency domain. Sensitivity analyses of pulse test parameters such as injection period and rate show that the frequency domain is more advantageous than the time domain for estimating leakage probability and well connectivity. We also conduct multi-objective history matching of pulse testing parameters in the frequency domain for reducing the uncertainty in geological models. This history matching reveals a clearer trade-off relationship between the matching qualities than conventional global-objective history matching, thereby being advantageous to yielding converged and diversified geological models for uncertainty quantification.

Using simplified methods to explore the impact of parameter uncertainty on CO2 storage estimates with application to the Norwegian Continental Shelf

We use simplified methods to investigate how uncertainty in geological models affects practical CO2 storage capacities in large-scale saline aquifers. Our focus is on uncertainties in top-surface elevation, rock properties (porosity, permeability), fault transmissibility, and aquifer conditions (pressure and temperature). To quantify the statistical characteristics of static trapping capacity and dynamic estimates of plume migration, we create hundreds of possible realizations of the geomodel by applying Gaussian-type perturbations to the spatially correlated properties. Two different simplified methods are introduced to reduce the computational cost of simulating migration over thousands of years in all the model realizations, which each spans hundreds of kilometers. First, we use vertical-equilibrium (VE) modelling, which is orders of magnitude faster than solving the 3D flow equations. Second, we introduce a fast look-ahead algorithm that enables us to exit the VE simulation once a pseudo-steady state is reached. This algorithm uses a spill-point analysis of the top-surface's trapping structure to forecast how much CO2 will eventually become trapped and how much will leak through open boundaries of the formation. This reduces the computational cost significantly, since we seldom need to simulate long-term migration past a few hundred or thousand years.

Inverse modeling for possible rather than unique solutions

Despite the implementation of several kinematic and mechanical models for fault-related folding, and the incorporation of structural uncertainty in geological models, structural modeling is still too deterministic. The current focus is on forward modeling of a unique fit. We show the application of trishear inverse modeling, global optimization and Markov chain Monte Carlo (MCMC) methods, to a clay model of basement-involved compressional faulting, from which we know both total and incremental deformation. Global optimization and MCMC methods provide a range of possible models rather than a unique fit.Total inversions give an average of the model's deformation, while incremental inversions are more physically related to the model's evolution. Global optimization identifies the full range of possible models, while MCMC characterizes expected parameter values and their uncertainties. Structural inversions without sound geology are meaningless. A robust stratigraphy, geomorphic markers, mesoscopic structures, analogue and mechanical modeling can all greatly improve the inversions.

Seismic guided drilling technique based on seismic while drilling (SWD): A case study of fracture-cave reservoirs of Halahatang block, Tarim Oilfield, NW China

Abstract To deal with the inaccurate three-dimensional positioning of caves in the ultra-deep and high temperature Ordovician carbonate fracture-cave reservoirs in the Halahatang block, this article proposes a new integrated solution which combines seismic guided drilling (SGD) with onshore seismic while drilling (SVWD). SGD technique uses the newly acquired velocity by SVWD to update velocity model and re-place the target position in three-dimensional space to decrease the uncertainty of the target. The primary drilling targets of two wells in the Halahatang block have been selected to verify this solution. It's the first time to collect onshore SVWD date domestically. The two wells landed in the target successfully by guiding and adjusting wellbore trajectory according to near real-time prediction results obtained from SVWD data. The success of these two wells shows the solution combining SVWD with SGD is practicable in solving the misplacing of target reservoirs caused by velocity and geological model uncertainty.

Quantifying model structural uncertainty and facies prediction for locating groundwater supplies in Timor-Leste using AEM data

SUMMARY Geological structures key to understanding groundwater resources in Timor-Leste’s Baucau Plateau are mapped using an airborne electromagnetic (AEM) survey. A comprehensive assessment of model structural uncertainty is conducted using a Bayesian Markov chain Monte Carlo algorithm, and an approach for translating geophysical to geological model uncertainty is introduced. A prominent feature of the Baucau survey is a very high-contrast transition from resistive limestone materials to conductive clays, which is well-resolved from the AEM analysis. The inferred 3D geometry of potentially water-bearing limestone units that overly relatively impermeable clays is a key outcome of this analysis, and will be the focus of future ground-truthing efforts.

Climate model uncertainty versus conceptual geological uncertainty in hydrological modeling

Abstract. Projections of climate change impact are associated with a cascade of uncertainties including in CO2 emission scenarios, climate models, downscaling and impact models. The relative importance of the individual uncertainty sources is expected to depend on several factors including the quantity that is projected. In the present study the impacts of climate model uncertainty and geological model uncertainty on hydraulic head, stream flow, travel time and capture zones are evaluated. Six versions of a physically based and distributed hydrological model, each containing a unique interpretation of the geological structure of the model area, are forced by 11 climate model projections. Each projection of future climate is a result of a GCM–RCM model combination (from the ENSEMBLES project) forced by the same CO2 scenario (A1B). The changes from the reference period (1991–2010) to the future period (2081–2100) in projected hydrological variables are evaluated and the effects of geological model and climate model uncertainties are quantified. The results show that uncertainty propagation is context-dependent. While the geological conceptualization is the dominating uncertainty source for projection of travel time and capture zones, the uncertainty due to the climate models is more important for groundwater hydraulic heads and stream flow.

Uncertainties have a meaning: Information entropy as a quality measure for 3-D geological models

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.

Reservoir Simulation Technology by Streamline-based Methods

Detailed geological models can now be developed by interpreting different data in a consistent and integrated manner with the advances in computer technology and stochastic methods. Reservoir simulation is important for reducing uncertainties in geological models by history matching with dynamic data. Streamline-based simulation has advantages over conventional finite-difference models in computation speed, accuracy, and visualization. Faster computation is attributed to less frequent solutions of the pressure equation, one-dimensional solutions along streamlines replacing three-dimensional flow calculations, and operator splitting. Streamline-based simulation is particularly suited to repeated history matching for multiple equi-probable geological models. Applications are demonstrated with model development for upscaling, tracer flow simulation, automatic history matching, and dual-porosity modeling.

Inter‐tuff correlation and architecture within the Moor Cliffs Formation, Lower Old Red Sandstone, southwest Wales: a multi‐disciplinary approach for reservoir characterization

AbstractThe laterally continuous coastal exposures of the Moor Cliffs Formation of the Anglo‐Welsh Basin have allowed a highly detailed 2D reconstruction of the floodplain. Whole‐rock trace element geochemical and spectral gamma‐ray (SGR) correlation are combined with traditional sedimentological analysis allowing outcrop and subsurface techniques to be compared. Micaceous, quartz‐rich and well‐sorted fluvial channel sandstones form up to 10% of the thickness in this low net‐to‐gross succession. High Th/K ratios derived from SGR analysis distinguish sandstones from the surrounding fine‐grained sediments, but lateral facies variations prevent the correlation of fluvial channel intervals using SGR without outcrop control. Red‐brown micaceous siltstone and claystone constitute 65 to 95% of the outcrop thickness and contain abundant pedogenic features characteristic of modern Vertisols. The most mature Vertisol horizons and the non‐pedogenically altered siltstones/claystones do not show significant differences in their SGR response. Intraformational conglomerates comprising carbonate and siltstone clasts within a siltstone matrix are common above laterally extensive erosion surfaces, and can be clearly recognized from a sharp spike in Nb/Y and Zr/Y ratios. Major tuff horizons, which form chronostratigraphic marker horizons throughout the Moor Cliffs Formation, are also characterized by a distinctive geochemical signature, enabling calibration of the geochemical and sedimentological datasets. Geochemical and SGR analytical techniques are complementary and assist in enhancing the confidence of correlations created by traditional techniques in the Moor Cliffs Formation. Where multiple correlation scenarios have been interpreted due to a lack of diagnostic marker beds or biostratigraphic control, the SGR and geochemical data can increase confidence in a particular interpretation and hence decrease uncertainty in geological models of low net‐to‐gross systems in the subsurface. Copyright © 2004 John Wiley & Sons, Ltd.

The Quality Map: A Tool for Reservoir Uncertainty Quantification and Decision Making

SummaryThe parameters that govern fluid flow through heterogeneous reservoirs are numerous and uncertain. Even when it is possible to visualize all the parameters together, the complex and nonlinear interaction between them makes it difficult to predict the dynamic reservoir responses to production. A flow simulator may be used to evaluate the responses and make reservoir management decisions, but normally only one deterministic set of parameters is considered, and no uncertainty is associated with the responses or taken into account for the decisions.This paper introduces the concept of a "quality map," which is a 2D representation of the reservoir responses and their uncertainties. The quality concept may be applied to compare reservoirs, to rank stochastic realizations, and to incorporate reservoir characterization uncertainty into decision making (such as choosing well locations) with fewer full-field simulation runs.The data points necessary to generate the quality map are obtained by running a flow simulator with a single vertical well completed in all the layers and varying the location of the well in each run to have good coverage of the entire horizontal grid. The quality of the horizontal cell in which the well is located is the cumulative oil production after a long production time.The geological model uncertainty is captured by generating multiple stochastic realizations and building a quality map for each realization. The quality maps of all the realizations provide a distribution of quality values for each cell of the map grid. A mean quality map can be obtained by taking the expected value for each cell, and a map of quality uncertainty can be obtained by taking the standard deviation of the distribution for each cell.If a loss function is specified, an L-optimal quality map can be generated by retaining, for each cell, the quality value that minimizes the expected loss. This map allows us to locate wells accounting for the geological uncertainty as well as for the risk profile of the decision maker.The methodology for building the quality map is presented in detail, and the applications of the map are demonstrated with 50 realistic reservoir models.