Are wildcat well outcomes dependent or independent?

A binary logit model is adapted to the spatial point process represented by outcomes of wildcat wells as a function of drilling history. The probability of success of the (n+1)st wildcat is made dependent on the well's location and on outcomes of wildcats previously drilled within a distanced of the well. This simple model is a device for investigating patterns of dependencies of wildcat well outcomes and for projecting probabilities of drilling success at particular locations. The model is applied to two Canadian petroleum plays.     

Oil- and gas-resource assessment in certain South American Basins—An application of ARDS (Ver. 5.0) to complex exploration and discovery histories

The modified Arps-Roberts Discovery Process Modeling System [ARDS (Ver. 4.01)] has recently been upgraded [ARDS (Ver. 5.0)] and applied to a wide variety of field discovery and wildcat drilling data with differing characteristics. ARDS is designed to forecast the number and sizes of undiscovered fields in an exploration play or basin by using historical drilling and discovery data. Fields used as input may be grown or ungrown. Two models for field growth—one offshore and the other onshore—have been implemented (Schuenemeyer and Drew, 1996). Uncertainty attributable to field growth is estimated via simulation. This upgrade of ARDS has been designed to handle situations when the data cannot be partitioned into homogeneous regions, but where estimation of the number of remaining oil and gas fields is still meaningful. In this upgrade of ARDS, many restrictions, which include those on the number of fields and wildcat wells required to forecast the size distribution of the oil and gas fields that remain to be discovered in an exploration play, a basin, or other target area, have been removed. In addition, flexibility has been gained by reforming the criteria for convergence of the model. In all, 32 basins and subbasins in South America were examined, 18 of which had sufficient data to be amenable to forecasting the field-size distribution of undiscovered oil and gas resources directly by using the Petroconsultants Inc. (1993) field discovery and wildcat drilling data. Overall, ARDS (Ver. 5.0) performed well in estimating the field-size distribution of undiscovered oil and gas resources in the 18 basins and subbasins. The aggregate volume of undiscovered petroleum resources was characterized by using histograms of the distribution of resources and the following five statistics: the mean, the 80% trimmed mean, and the 10,50 (median), and 90 quantiles. More than 38 billion barrels of oil equivalent (BOE) in fields that contain more than one million BOE individually were forecast as remaining to be discovered. The largest basin, the Campos (Brazil), is forecast to contain nearly 10 billion BOE undiscovered resources. The East Venezuela Basin (excluding the Furrial Trend) is forecast to contain about 8 billion BOE; the Austral-Magallanes Basin (Argentina and Chile), about 7 billion BOE; and the Napo (Colombia and Ecuador) and the Neuquen (Argentina) Basins, between 3 billion and 4 billion BOE. A subset of these basins that illustrate the increased flexibility of ARDS are discussed.     

Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution

For many decades the mining industry regarded resources/reserves estimation and classification as a mere calculation requiring basic mathematical and geological knowledge. Most methods were based on geometrical procedures and spatial data distribution. Therefore, uncertainty associated with tonnages and grades either were ignored or mishandled, although various mining codes require a measure of confidence in the values reported. Traditional methods fail in reporting the level of confidence in the quantities and grades. Conversely, kriging is known to provide the best estimate and its associated variance. Among kriging methods, Ordinary Kriging (OK) probably is the most widely used one for mineral resource/reserve estimation, mainly because of its robustness and its facility in uncertainty assessment by using the kriging variance. It also is known that OK variance is unable to recognize local data variability, an important issue when heterogeneous mineral deposits with higher and poorer grade zones are being evaluated. Altenatively, stochastic simulation are used to build local or global uncertainty about a geological attribute respecting its statistical moments. This study investigates methods capable of incorporating uncertainty to the estimates of resources and reserves via OK and sequential gaussian and sequential indicator simulation The results showed that for the type of mineralization studied all methods classified the tonnages similarly. The methods are illustrated using an exploration drill hole data sets from a large Brazilian coal deposit.     

Minimum Acceptance Criteria for Geostatistical Realizations

Geostatistical simulation is being used increasingly for numerical modeling of natural phenomena. The development of simulation as an alternative to kriging is the result of improved characterization of heterogeneity and a model of joint uncertainty. The popularity of simulation has increased in both mining and petroleum industries. Simulation is widely available in commercial software. Many of these software packages, however, do not necessarily provide the tools for careful checking of the geostatistical realizations prior to their use in decision-making. Moreover, practitioners may not understand all that should be checked. There are some basic checks that should be performed on all geostatistical models. This paper identifies (1) the minimum criteria that should be met by all geostatistical simulation models, and (2) the checks required to verify that these minimum criteria are satisfied. All realizations should honor the input information including the geological interpretation, the data values at their locations, the data distribution, and the correlation structure, within acceptable statistical fluctuations. Moreover, the uncertainty measured by the differences between simulated realizations should be a reasonable measure of uncertainty. A number of different applications are shown to illustrate the various checks. These checks should be an integral part of any simulation modeling work flow.     

Large-scale mineral potential estimation for blind precious metal ore bodies

Conventional evaluation of quantitative mineral potential has focused on target selection at small scales. Mapping at small scales usually results in large-area targets, which may be suitable for grass-roots exploration or regional evaluation of potential. Unfortunately, the estimates in small-scale exploration are commonly associated with large uncertainties. Large-scale estimation is used for optimal in-fill drilling design and step-out drilling target selection. In-fill drilling helps to confirm ore-grade continuities and translate a portion of geological resources into minable reserves, whereas step-out target estimation is useful for finding new orebodies in the vicinity of known ore deposits. Both of these processes are necessary for mine development and production planning. A comprehensive methodology is proposed here, particularly for large-scale mineral exploration. The central information synthesizer is canonical or indicator favorability analysis. A case study is presented to demonstrate the methodology for large-scale target selection. The study involves a gold-mining district where step-out drilling targets are being sought to expand the resource base. Several drilling targets were delineated in the study region. Two of them were tested through surface sampling with positive results.     

河流水质风险评价的灰色-随机风险率方法

提出了量化影响河流水质的随机不确定性与灰色不确定性的水质超标灰色－随机风险率概念，建立了水质超标灰色－随机风险率评价模型。在水质单项参数评价模型中，将河流污染物浓度变量的分布处理成灰色概率分布，将污染物浓度超过水质类别标准值的风险率处理成灰色概率，即水质超标灰色－随机风险率。在水质综合评价模型中，河流水环境系统被考虑为担任某一使用可能的可靠性系统，而任意一种水质参数超标意味着河流水体使用功能不能得到应有的保证，也即表明水体综合评价超标，最后借鉴系统可靠性分析的理论和方法计算水质综合超标率。该方法应用于黄河花园口断面重金属污染风险评价。     

Nonparametric Geostatistical Simulation of Subsurface Facies: Tools for Validating the Reproduction of,and Uncertainty in,Facies Geometry

Delineation of facies in the subsurface and quantification of uncertainty in their boundaries are significant steps in mineral resource evaluation and reservoir modeling, which impact downstream analyses of a mining or petroleum project. This paper investigates the ability of nonparametric geostatistical simulation algorithms (sequential indicator, single normal equation and filter-based simulation) to construct realizations that reproduce some expected statistical and spatial features, namely facies proportions, boundary regularity, contact relationships and spatial correlation structure, as well as the expected fluctuations of these features across the realizations. The investigation is held through a synthetic case study and a real case study, in which a pluri-Gaussian model is considered as the reference for comparing the simulation results. Sequential indicator simulation and single normal equation simulation based on over-restricted neighborhood implementations yield the poorest results, followed by filter-based simulation, whereas single normal equation simulation with a large neighborhood implementation provides results that are closest to the reference pluri-Gaussian model. However, some biases and inaccurate fluctuations in the realization statistics (facies proportions, indicator direct and cross-variograms) still arise, which can be explained by the use of a single finite-size training image to construct the realizations.

     

Additional Samples: Where They Should Be Located

Information for mine planning requires to be close spaced, if compared to the grid used for exploration and resource assessment. The additional samples collected during quasimining usually are located in the same pattern of the original diamond drillholes net but closer spaced. This procedure is not the best in mathematical sense for selecting a location. The impact of an additional information to reduce the uncertainty about the parameter been modeled is not the same everywhere within the deposit. Some locations are more sensitive in reducing the local and global uncertainty than others. This study introduces a methodology to select additional sample locations based on stochastic simulation. The procedure takes into account data variability and their spatial location. Multiple equally probable models representing a geological attribute are generated via geostatistical simulation. These models share basically the same histogram and the same variogram obtained from the original data set. At each block belonging to the model a value is obtained from the n simulations and their combination allows one to access local variability. Variability is measured using an uncertainty index proposed. This index was used to map zones of high variability. A value extracted from a given simulation is added to the original data set from a zone identified as erratic in the previous maps. The process of adding samples and simulation is repeated and the benefit of the additional sample is evaluated. The benefit in terms of uncertainty reduction is measure locally and globally. The procedure showed to be robust and theoretically sound, mapping zones where the additional information is most beneficial. A case study in a coal mine using coal seam thickness illustrates the method.     

A systematic sensitivity analysis of constrained cellular automata model for urban growth simulation based on different transition rules

Cellular automata (CA) have emerged as a primary tool for urban growth modeling due to its simplicity, transparency, and ease of implementation. Sensitivity analysis is an important component in CA modeling for a better understanding of errors or uncertainties and their propagation. Most studies on sensitivity analyses in urban CA modeling focus on specific component such as neighborhood configuration or stochastic perturbation. However, sensitivity analysis of transition rules, which is one of the core components in CA models, has not been systematically done. This article proposes a systematic sensitivity analysis of major operational components in urban CA modeling using a stepwise comparison approach. After obtaining transition rules, three stages (i.e. static calibration of transition rules, dynamic evolution with varied time steps, and incorporation with stochastic perturbation) are designed to facilitate a comprehensive analysis. This scheme implemented with a case study in Guangzhou City (China) reveals that gaps in performance from static calibration with different transition rules can be reduced when dynamic evolution is considered. Moreover, the degree of stochastic perturbation is closely related to obtain urban morphology. However, a more realistic (i.e. fragmented) urban landscape is achieved at the cost of decreasing pixel-based accuracy in this study. Thus, a trade-off between pixel-based and pattern-based comparisons should be balanced in practical urban modeling. Finally, experimental results illustrate that models for transition rules extraction with good quality can do an assistance for urban modeling through reducing errors and uncertainty range. Additionally, ensemble methods can feasibly improve the performance of CA models when coupled with nonparametric models (i.e. classification and regression tree).     

A framework for uncertainty assessment in simulation models

In this article, we introduce a conceptual framework for systematic identification and assessment of sources of uncertainty in simulation models. This concept builds on a novel typology of uncertainty in model validation and extends the GIScience research focus on uncertainty in spatial data to uncertainty in simulation modelling. Such a concept helps a modeller to interpret and handle uncertainty in order to efficiently optimise a model and better understand simulation results.

To illustrate our approach, we apply the proposed framework for uncertainty assessment to the TREE LIne Model (TREELIM), an individual-based model that simulates forest succession at the alpine tree line. Using this example, uncertainty is identified in the modelling workflow during conceptualisation, formalisation, parameterisation, analysis and validation. With help of a set of indicators we quantify the emerging uncertainties and assess the overall model uncertainty as a function of all occurring sources of uncertainty.

An understanding of the sources of uncertainty in an ecological model proves beneficial for: (1) developing a structurally valid model in a systematic way; (2) deciding if further refinement of the conceptual model is beneficial for the modelling purpose; and (3) interpreting the overall model uncertainty by understanding its sources. Our approach results in a guideline for assessing uncertainty in the validation of simulation models in a feasible and defensible way, and thus functions as a toolbox for modellers. We consider this work as a contribution towards a general concept of uncertainty in spatially explicit simulation models.     

Reservoir Characterization of McMurray Formation by 2D Geostatistical Modeling

There is a need to estimate reserve uncertainty for large lease areas. Detailed 3D models of heterogeneity are not necessarily required, but there is a need to integrate all available data into an in-situ reserve estimate with uncertainty. A 2D mapping approach is presented to appraise reserves accounting for multiple variables, multiple data sources, and uncertainty. The approach can be considered in three primary steps: (1) Bayesian updating is used to determine local distributions of uncertainty for each primary variable while integrating multiple secondary information, (2) matrix simulation is employed to jointly and simultaneously simulate multiple collocated variables to determine a derived variable such as OOIP, and (3) probability field simulation then is applied to permit joint simulation of multiple locations. This methodology permits local and global uncertainty assessment while integrating multiple sources of information. An application to the McMurray Formation in Alberta, Canada is demonstrated.     

Spatiotemporal scale dependency and other sensitivities in dynamic land-use change simulations

This study examines how land-use change simulation outcomes can vary based on the way the simulation model is applied, attempting to support informed model choices and model applications. This is accomplished through a series of experiments using a hypothetical model that represents the basic logic of various cell-based dynamic land-use change modeling environments. In the experiments, consideration is given to the sensitivity of the simulation results with respect to the following four application specifications: (1) the spatial resolution, (2) the temporal resolution, (3) the probability distribution, and (4) the degree of the influence of stochastic factors, under multiple growth scenarios. The experiments show that all four factors, particularly the spatiotemporal resolution and the degree to which stochastic factors are involved, can generate substantial variation in the simulation model outcomes. It is also found that the magnitude of the variation can be affected by changes in regional growth rates and the level of fluctuation, which determine the demand for new development to be allocated over the simulation time horizon.     

Geostatistical Simulation of Acoustic Log Data for Seismic Depth Conversion

Seismic reflection methods measure the time a seismic wave takes to travel through the ground, from the user defined source to a series of signal monitoring sensors known as geophones. The measured times need to be depth converted to allow for integration with other geological data. In order to convert from time to depth, an estimate of the rock volume velocity field must be made. The velocity field estimate can be made by assignment of velocity estimates to a geological model independent of the seismic processing. This article presents the results of using the acoustic geophysical log data extrapolated via sequential Gaussian simulation to derive the velocity field. The uncertainties associated with the velocity estimates were significant and provided the means to assess confidence limits for the actual depth determination. The technique is assessed by application to a major coal deposit, approximately 2.1 m thick and 210 m deep. Considering only the uncertainty associated with estimating the velocity field, half of the confidence interval values showed approximately 1 m of uncertainty in depth. The application of sequential Gaussian simulation to model the 3D distribution of acoustic velocity can be extended to other geophysical log parameters or derived estimates.     

大尺度水循环模拟系统不确定性研究进展

水循环过程受众多自然因素和人为因素影响,决定了水循环系统的变化性和复杂性。水循环系统模型作为研究流域水文循环过程及演变规律的重要工具,必然也存在较大的不确定性,特别是对于大尺度陆-气耦合下的水循环模拟系统,其不确定性来源包括输入和参数不确定性、结构不确定性、方法不确定性以及初始和边界条件不确定性。本文在分析不确定性量化方法和传统水文模型不确定性研究基础上,重点评述当前大尺度水循环系统模拟的不确定性研究进展和存在的瓶颈问题,并介绍一种针对大型复杂动力系统的不确定性量化解决方案和工具系统-PSUADE,基于此讨论PSUADE在大尺度水循环模拟系统不确定性量化过程中的优势。     

Development and test of an error model for categorical data

Abstract

An error model for spatial databases is defined here as a stochastic process capable of generating a population of distorted versions of the same pattern of geographical variation. The differences between members of the population represent the uncertainties present in raw or interpreted data, or introduced during processing. Defined in this way, an error model can provide estimates of the uncertainty associated with the products of processing in geographical information systems. A new error model is defined in this paper for categorical data. Its application to soil and land cover maps is discussed in two examples: the measurement of area and the measurement of overlay. Specific details of implementation and use are reviewed. The model provides a powerful basis for visualizing error in area class maps, and for measuring the effects of its propagation through processes of geographical information systems.     

基于粗集的知识发现与地理模拟——以深圳市土地利用变化为例

为了更有效地模拟地理现象的复杂演变过程,提出了用粗集理论来确定元胞自动机 (CA)不确定性转换规则的新方法。CA可以通过局部规则来有效地模拟许多地理现象的演变过程。但目前缺乏很好定义CA转换规则的方法。往往采用启发式的方法来定义CA的转换规则,这些转换规则是静态的,而且其参数值多是确定的。在反映诸如城市扩张、疾病扩散等不确定性复杂现象时,具有一定的局限性。利用粗集从GIS和遥感数据中发现知识,自动寻找CA的不确定性转换规则,基于粗集的CA在缩短建模时间的同时,能提取非确定性的转换规则,更好地反映复杂系统的特点。采用所提出的方法模拟了深圳市的城市发展过程,取得了比传统MCE方法更好的模拟效果。     

Propagation of positional error in 3D GIS: estimation of the solar irradiation of building roofs

While error propagation in GIS is a topic that has received a lot of attention, it has not been researched with 3D GIS data. We extend error propagation to 3D city models using a Monte Carlo simulation on a use case of annual solar irradiation estimation of building rooftops for assessing the efficiency of installing solar panels. Besides investigating the extension of the theory of error propagation in GIS from 2D to 3D, this paper presents the following contributions. We (1) introduce varying XY/Z accuracy levels of the geometry to reflect actual acquisition outcomes; (2) run experiments on multiple accuracy classes (121 in total); (3) implement an uncertainty engine for simulating acquisition positional errors to procedurally modelled (synthetic) buildings; (4) perform the uncertainty propagation analysis on multiple levels of detail (LODs); and (5) implement Solar3Dcity – a CityGML-compliant software for estimating the solar irradiation of roofs, which we use in our experiments. The results show that in the case of the city of Delft in the Netherlands, a 0.3/0.6 m positional uncertainty yields an error of 68 kWh/m²/year (10%) in solar irradiation estimation. Furthermore, the results indicate that the planar and vertical uncertainties have a different influence on the estimations, and that the results are comparable between LODs. In the experiments we use procedural models, implying that analyses are carried out in a controlled environment where results can be validated. Our uncertainty propagation method and the framework are applicable to other 3D GIS operations and/or use cases. We released Solar3Dcity as open-source software to support related research efforts in the future.     

An uncertainty and sensitivity analysis approach for GIS-based multicriteria landslide susceptibility mapping

GIS-based multicriteria decision analysis (MCDA) methods are increasingly being used in landslide susceptibility mapping. However, the uncertainties that are associated with MCDA techniques may significantly impact the results. This may sometimes lead to inaccurate outcomes and undesirable consequences. This article introduces a new GIS-based MCDA approach. We illustrate the consequences of applying different MCDA methods within a decision-making process through uncertainty analysis. Three GIS-MCDA methods in conjunction with Monte Carlo simulation (MCS) and Dempster–Shafer theory are analyzed for landslide susceptibility mapping (LSM) in the Urmia lake basin in Iran, which is highly susceptible to landslide hazards. The methodology comprises three stages. First, the LSM criteria are ranked and a sensitivity analysis is implemented to simulate error propagation based on the MCS. The resulting weights are expressed through probability density functions. Accordingly, within the second stage, three MCDA methods, namely analytical hierarchy process (AHP), weighted linear combination (WLC) and ordered weighted average (OWA), are used to produce the landslide susceptibility maps. In the third stage, accuracy assessments are carried out and the uncertainties of the different results are measured. We compare the accuracies of the three MCDA methods based on (1) the Dempster–Shafer theory and (2) a validation of the results using an inventory of known landslides and their respective coverage based on object-based image analysis of IRS-ID satellite images. The results of this study reveal that through the integration of GIS and MCDA models, it is possible to identify strategies for choosing an appropriate method for LSM. Furthermore, our findings indicate that the integration of MCDA and MCS can significantly improve the accuracy of the results. In LSM, the AHP method performed best, while the OWA reveals better performance in the reliability assessment. The WLC operation yielded poor results.     

多智能体与元胞自动机结合及城市用地扩张模拟

运用多智能体(Agent)和元胞自动机(CA)结合来模拟城市用地扩张的方法,将影响和决定用地类型转变的主体作为Agent引进元胞自动机模型中,Agent在CA确定的城市发展概率的基础上,通过自身及其周围环境的状况,综合各种因素的影响做出决策,决定元胞下一时刻的城市发展概率。运用Agent的决策结果,对CA模型中以随机变量体现的不确定性通过Agent决策行为给予地理意义的新解释。以城市郊区—樟木头镇为例,对1988～1993年城市用地扩张进行了模拟研究,取得了良好的模拟效果。     

Sequential Simulation Approach to Modeling of Multi-seam Coal Deposits with an Application to the Assessment of a Louisiana Lignite

There are multiple ways to characterize uncertainty in the assessment of coal resources, but not all of them are equally satisfactory. Increasingly, the tendency is toward borrowing from the statistical tools developed in the last 50 years for the quantitative assessment of other mineral commodities. Here, we briefly review the most recent of such methods and formulate a procedure for the systematic assessment of multi-seam coal deposits taking into account several geological factors, such as fluctuations in thickness, erosion, oxidation, and bed boundaries. A lignite deposit explored in three stages is used for validating models based on comparing a first set of drill holes against data from infill and development drilling. Results were fully consistent with reality, providing a variety of maps, histograms, and scatterplots characterizing the deposit and associated uncertainty in the assessments. The geostatistical approach was particularly informative in providing a probability distribution modeling deposit wide uncertainty about total resources and a cumulative distribution of coal tonnage as a function of local uncertainty.