Geostatistical Simulation Methods Research Articles

Statistical and geostatistical approaches to study spatiotemporal uncertainties in earthquake catalog databases

Lack of data in time and location domain is a main problem in statistical seismology. Therefore, several methods have been developed to make synthetic catalogs to compensate these uncertainties. The approaches introduced in this paper try to decrease these uncertainties. A statistical tool has been determined to study the lack of data in time domain and revise a magnitude-frequency relationship in one of the very high-seismic regions in the world, northwest of Iran (44.00 to 48.00 E and 35.60 to 40.00 N). A geostatistical simulation method has also been utilized to reduce the uncertainties in the spatial domain. Variogram tool has been introduced as a spatial tool to assign a spatial regression among data in various directions. A geostatistical simulation produced a representative, synthetic catalog with 10,707 events to reduce spatial uncertainties (the number of data in the earthquake catalogs was 307 events). The synthetic database was classified by a geographical information system (GIS) based on simulated magnitudes to reveal the underlying seismicity patterns. Although some regions with high seismicity correspond to known faults, as far as seismic patterns are concerned, the new method could highlight locations of interest that have not been previously determined. It also suggests some previously unrecognized lineation and clusters in likely future strain release.

Multivariate Geostatistical Grid-Free Simulation of Natural Phenomena

Conventional geostatistical simulation methods are implemented in a way that is inherently gridded and sequence dependent. A variant of spectral simulation method is revisited from a linear model of regionalization standpoint to simulate realizations of coregionalized variables that are expressed as a function of the coordinates of the simulation locations, data values, and imposed spatial structure. The resulting grid-free simulation (GFS) methodology expresses a realization at any set of regularly or irregularly distributed nodes. GFS consists of two main steps: unconditional grid-free simulation and dual cokriging-based conditioning. The unconditional multivariate simulation is represented by a linear model of coregionalization, where weights are derived from the covariance function of the modeled system, and random factors are computed as a sum of equally weighted line processes within a turning bands paradigm. These stochastic line processes are expressed as a linear model of regionalization, weights are from the Fourier series decomposition of line covariance functions, and random factors have a cosine function form requiring coordinates of simulation locations and the random phases. The resulting conditionally simulated values are uniquely tied to simulation locations by an analytical form. Newly assimilated data change current realizations only locally within the correlation range. The GFS parameters are carefully chosen from a series of examples, and the associated theory is illustrated with a three-dimensional case study.

Enhancing multiple‐point geostatistical modeling: 1. Graph theory and pattern adjustment

AbstractIn recent years, higher‐order geostatistical methods have been used for modeling of a wide variety of large‐scale porous media, such as groundwater aquifers and oil reservoirs. Their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard (quantitative) data, which endow them with the capability for generating realistic realizations of porous formations with very complex channels, as well as features that are mainly a barrier to fluid flow. One group of such models consists of pattern‐based methods that use a set of data points for generating stochastic realizations by which the large‐scale structure and highly‐connected features are reproduced accurately. The cross correlation‐based simulation (CCSIM) algorithm, proposed previously by the authors, is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few CPU seconds. The method is, however, sensitive to pattern's specifications, such as boundaries and the number of replicates. In this paper the original CCSIM algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large‐scale patterns of heterogeneities in porous media. First, an effective boundary‐correction method based on the graph theory is presented by which one identifies the optimal cutting path/surface for removing the patchiness and discontinuities in the realization of a porous medium. Next, a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns. The original CCSIM algorithm is then combined with the two methods and is tested using various complex two‐ and three‐dimensional examples. It should, however, be emphasized that the methods that we propose in this paper are applicable to other pattern‐based geostatistical simulation methods.

A space-time geostatistical approach for ensemble rainfall nowcasting

Nowcasting systems are essential to prevent extreme events and reduce their socio-economic impacts. The major challenge of these systems is to capture high-risk situations in advance, with good accuracy, location and time. Uncertainties associated with the precipitation events have an impact on the hydrological forecasts, especially when it concerns localized flash flood events. Radar monitoring can help to detect the space-time evolution of rain fields, but nowcasting techniques are needed to go beyond the observation and provide scenarios of rainfall for the next hours of the event. In this study, we investigate a space-time geostatistical framework to generate multiple scenarios of future rainfall. The rainfall ensemble is generated based on space-time properties of precipitation fields given by radar measurements and rainfall data from rain gauges. The aim of this study is to investigate the potential of a framework that applies a geostatistical conditional simulation method to generate an ensemble nowcasting of rainfall fields. The Var region (south eastern France) and 14 events are used to validate the approach. Results show that the proposed method can be a solution to combine information from radar fields and rain gauges to generate nowcasting rainfall fields adapted for flash flood alert.

Risk quantification with combined use of lithological and grade simulations: Application to a porphyry copper deposit

The uncertainty in the recoverable tonnages and grades in a mineral deposit is a key factor in the decision-making process of a mining project. Currently, the most prevalent approach to model the uncertainty in the spatial distribution of mineral grades is to divide the deposit into domains based on geological interpretation and to predict the grades within each domain separately. This approach defines just one interpretation of the geological domain layout and does not offer any measure of the uncertainty in the position of the domain boundaries and in the mineral grades. This uncertainty can be evaluated by use of geostatistical simulation methods. The aim of this study is to evaluate how the simulation of rock type domains and grades affects the resources model of Sungun porphyry copper deposit, northwestern Iran. Specifically, three main rock type domains (porphyry, skarn and late-injected dykes) that control the copper grade distribution are simulated over the region of interest using the plurigaussian model. The copper grades are then simulated in cascade, generating one grade realization for each rock type realization. The simulated grades are finally compared to those obtained using traditional approaches against production data.

Multivariate grid-free geostatistical simulation with point or block scale secondary data

A novel grid-free geostatistical simulation method (GFS) allows representing coregionalized variables as an analytical function of the coordinates of the simulation locations. Simulation on unstructured grids, regridding and refinement of available realizations of natural phenomena including, but not limited to, environmental systems are possible with GFS in a consistent manner. The unconditional realizations are generated by utilizing the linear model of coregionalization and Fourier series-based decomposition of the covariance function. The conditioning to data is performed by kriging. The data can be measured at scattered point-scale locations or sampled at a block scale. Secondary data are usually used in conjunction with primary data for the improved modeling. Satellite imaging is an example of exhaustively sampled secondary data. Improvements and recommendations are made to the implementation of GFS to properly assimilate secondary exhaustive data sets in a grid-free manner. Intrinsic cokriging (ICK) is utilized to reduce computational time and preserve the overall quality of the simulation. To further reduce the computational cost of ICK, a block matrix inversion is implemented in the calculation of the kriging weights. A projection approach to ICK is proposed to avoid artifacts in the realizations around the edges of the exhaustive data region when the data do not cover the entire modeling domain. The point-scale block value representation of the block-scale data is developed as an alternative to block cokriging to integrate block-scale data into realizations within the GFS framework. Several case studies support the proposed enhancements.

Change-of-Support Models on Irregular Grids for Geostatistical Simulation

In many domains, numerical models are initialized with inputs defined on irregular grids. In petroleum reservoir engineering, they consist of a great variety of grid cells of different size and shape to enable fine-scale modeling in the vicinity of the wells and coarse modeling in less important regions. Geostatistical simulation algorithms, which are used to populate the cells of unstructured grids, often have to address the problem of transition from the small-scale statistical data stemming from laboratory cores analysis and seismic processing to the multiple larger scale geological supports. The reasonable generalization of the above-mentioned problem is integrating the point-support data to simulations on irregular supports. Classical geostatistical simulation methods for generating realizations of a stationary Gaussian random function cannot be applied to unstructured grids directly, because of the uneven supports. This article provides a critical review of existing geostatistical simulation methodologies for unstructured grids, including fine-scale simulations with upscaling and direct sequential simulation algorithms, and presents two different generalizations of the discrete Gaussian model for this purpose, thereby discussing the theoretical assumptions and the accuracy when implementing these models.

Establishment of Detection and Correction Parameters for a Geostatistical Homogenisation Approach

Non-natural irregularities are an inevitable part of long-time climate records. They are originated during the process of measuring and collecting data from weather stations. In order to use those records as an input for environmental projects or climate studies, it is essential to detect and correct the irregularities through the process of homogenisation. The use of geostatistical approaches as homogenisation techniques has already been proven to be successful. The gsimcli homogenisation process is based on a geostatistical simulation method, the direct sequential simulation. This method generates a set of equally probable and independent realisations, and calculates a probability distribution function at the candidate station's location. This probability distribution function is then used in the identification and correction of irregularities. Currently, gsimcli is being developed into an open source software package. During the homogenisation process, gsimcli requires the selection of several parameters in the detection and correction of irregularities. The candidate stations’ order to be homogenised, the value of the probability used in the detection of irregularities, and the statistic value to be used in the correction of the irregularity or in the replacement of missing data, are examples of parameters to be chosen for the homogenisation with gsimcli. This work presents a sensitivity analysis of those parameters, in order to find the most suitable set of values for the homogenisation of monthly precipitation data. A benchmark data set, comprising climate records from an Austrian precipitation network, will be used in this analysis. Performance metrics are calculated to evaluate the efficiency of the homogenisation process. The set of parameters providing the best values of performance metrics will be defined as the default set of homogenisation parameters for precipitation data.

Geostatistical modeling of uniaxial compressive strength along the axis of the Behesht-Abad tunnel in Central Iran

Uniaxial compressive strength (UCS) is one of the most significant factors in the stability of rock engineering projects and is vastly used during the design and construction stages of underground excavations. Distances between exploratory boreholes is typically large during the preliminary studies of a majority of geotechnical projects. As a result, estimation of UCS values based on the scant data obtained from these distant boreholes is crucially important. Thus, the use of geostatistical estimation and simulation methods can lead to a significant reduction of errors and exploratory costs. In this regard, the present paper ties simulation and estimation of UCS values of the rock material between boreholes of the Behesht-Abad tunnel in central Iran using the Stanford Geostatistical Modeling Software (SGEMS). Variography showed the acceptable spatial distribution (9,477 m) of UCS parameters in the area under investigation. Also, cross-validation proved the high accuracy (98 %) and reliability of the results of the developed model. Then, considering the condition of the datasets and engineering judgmentvalues, the model outcomes were analyzed. It was concluded there is high similarity between the geostatistical estimation/simulation and engineering judgments. Application of geostatistical simulation methods in conjunction with estimation in rock research indicates these methods are performed in a rather different aspect from those of common validation processes. Furthermore, the combination of geostatistical estimation/simulation and engineering judgment led to better identification of the pros and cons of geotechnical explorations in each tunnel route.

WEB PERFORMANCE PREDICTION USING GEO-STATISTICAL METHOD

To provide Qos in distributed web systems, it is necessary to perform predicting in web systems. Then provide prediction technique on time and space of web resource downloaded using turning bands geostatistical simulation method. Web resources are obtained from a group of web servers worldwide by multi agent measurement systems which continuously monitor the web servers located in different geographical localization. The outcome of high-quality of Web performance calculation completed by resources of the Turning bands method, particularly in the situation when we place the Web servers were monitored by a Multi-agent Measurement Systems (MWING) localized in Poland. By means of satellite navigation system real life data like accident cases, first aid rescuers can accurately locate the place within certain specified range with maximum error control, so that the injured people can be saved as soon as possible. This method will save time or the areas in the outer part of the main zone.

A sensitivity study of FILTERSIM algorithm when applied to DFN modeling

Realistic description of fractured reservoirs demands primarily for a comprehensive understanding of fracture networks and their geometry including various individual fracture parameters as well as network connectivities. Newly developed multiple-point geostatistical simulation methods like SIMPAT and FILTERSIM are able to model connectivity and complexity of fracture networks more effectively than traditional variogram-based methods. This approach is therefore adopted to be used in this paper. Among the multiple-point statistics algorithms, FILTERSIM has the priority of less computational effort than does SIMPAT by applying filters and modern dimensionality reduction techniques to the patterns extracted from the training image. Clustering is also performed to group identical patterns in separate partitions prior to simulation phase. Various practices including principal component analysis, discrete cosine transform and different data summarizers are used in this paper to investigate a suitable way of reducing pattern dimensions using outcrop maps as training image. Because of non-linear nature of patterns present in fracture networks, linear clustering algorithms fail in determining the borders between the actual partitions; non-linear approaches like Spectral methods, however, can act more efficiently in diagnosing the right clusters. A complete sensitivity analysis is performed on FILTERSIM algorithm regarding search template dimension, type of filtering technique and the number of clusters for each clustering approach described above. Interesting results are obtained for each parameter that is changed during analysis.

Conetividade e modelos de transporte de domínio único/duplo: experiências num análogo de um aquífero de depósitos de meandro/canal

In porous aquifers, groundwater flow and solute transport strongly depend on the sedimentary facies distribution at fine scale, which determines the heterogeneity of the conductivity field; in particular, connected permeable sediments could form preferential flow paths. Therefore, properly defined statistics, e.g. total and intrinsic facies connectivity, should be correlated with transport features. In order to improve the assessment of the relevance of this relationship, some tests are conducted on two ensembles of equiprobable realizations, obtained with two different geostatistical simulation methods—sequential indicator simulation and multiple point simulation (MPS)—from the same dataset, which refers to an aquifer analogue of sediments deposited in a fluvial point-bar/channel association. The ensembles show different features; simulations with MPS are more structured and characterised by preferential flow paths. This is confirmed by the analysis of transport connectivities and by the interpretation of data from numerical experiments of conservative solute transport with single and dual domain models. The use of two ensembles permits (1) previous results obtained for single realizations to be consolidated on a more firm statistical basis and (2) the application of principal component analysis to assess which quantities are statistically the most relevant for the relationship between connectivity indicators and flow and transport properties.

Effective and Efficient Method for Web System Performance Forecasting

Recent development of computer systems (DCSs) in networked industrial and manufacturing applications on the World Wide Web (WWW) platform, including service-oriented architecture and Web of Things QoS-aware systems, it has become important to predict the Web performance prediction in time and in space .In this paper, we present Web performance prediction in time by making a forecast of a Web resource downloading using the Turning Bands (TB) geostatistical simulation method. Real-life data for the research were obtained from our own website named Distributed forecasting system. We generate log file form our website and performing monitoring of a group of Web clients from connected LAN. For better web forecasting we used spatio temporal prediction method with time utility for downloading particular file from website with locations. Also perform comparison study in between spatio temporal method & TB methods. The results show good quality of Web performance prediction using the TB method. Keyword: Computer System ,Turning Band,, Qos-Aware Systems, Geostatistics, Spatio-Temporal Prediction.

Geostatistical Methods for Lithological Aquifer Characterization and Groundwater Flow Modeling of the Catania Plain Quaternary Aquifer (Italy)

Sedimentary heterogeneity conditions of Catania Plain quaternary aquifer (CPQA), the wider alluvial multi-aquifer system of Sicily, were rebuilt to simulate and quantify groundwater flow. Transition probabilities based on a Markov Chain (MC) and Sequential Indicator Simulation (SIS) are the structure-imitating simulators utilized for generating stochastic distributions of hydraulic conductivity fields of CPQA, basing on borehole data: plausible equiprobable solutions of the complex geological structure of the CPQA were simulated. This study highlights that the choice of geostatistical simulation method plays a fundamental role in predictive scenarios for groundwater resources managing of CPQA. Indeed, simulated characteristics of the sedimentary heterogeneity constituted the basis of finite difference models for simulating the groundwater flow of CPQA. In heterogeneous systems such as CPQA, SIS may be inadequate for reproducing the macrostructures. Instead, MC adequately reproduced spatial connection of lithofacies, representing a more realistic solution dealing to the proposed geological model of CPQA. MC and SIS models were utilized to both assess the uncertainty of the generated hydraulic conductivity fields of CPQA and predictions about its behavior under normal stress conditions induced by urbanization. The calibration of CPQA groundwater flow models based on MC and SIS simulations allowed to achieve a realistic feedback about the quality of the geostatistical reconstructions of the geological heterogeneity field.

Application of geostatistical simulation models in the charac- terization of complex geological structures

Geostatistical simulation methods are able to generate numerical models or relations of the spatial distribution of a continuous geologic variable (grade, thickness, density, etc.) or a categorical variable (geological units and lithofacies or rock types). In this work, a review of traditional simulation techniques, as the Sequential Indicator Simulation (SIS), reveals a major pitfall that comes from theoretical difficulties in the development of a valid cross covariance model. On the contrary, a valid indicator cross covariance model is automatically defined in the framework of the Truncated Gaussian Simulation Method (TGS). This method is based on the concept that the categorical variables are obtained by truncating one standard multigaussian random variable at different thresholds. Plurigaussian Simulation Method (PGS) is an extension of the TGS Method but based on the simultaneous truncation of several multigaussian variables. An application of Plurigaussian method to simulate the lithofacies in the alluvial formations of the West Thessaly Basin is finally presented. This method was shown to be effective in reproducing the spatial characteristics of the different lithofacies and their distribution across the studied area.

Conditioning Surface-Based Geological Models to Well and Thickness Data

Geostatistical simulation methods aim to represent spatial uncertainty through realizations that reflect a certain geological concept by means of a spatial continuity model. Most common spatial continuity models are either variogram, training image, or Boolean based. In this paper, a more recent spatial model of geological continuity is developed, termed the event, or surface-based model, which is specifically applicable to modeling cases with complex stratigraphy, such as in sedimentary systems. These methods rely on a rule-based stacking of events, which are mathematically represented by two-dimensional thickness variations over the domain, where positive thickness is associated with deposition and negative thickness with erosion. Although it has been demonstrated that the surface-based models accurately represent the geological variation present in complex layered systems, they are more difficult to constrain to hard and soft data as is typically required of practical geostatistical techniques. In this paper, we develop a practical methodology for constraining such models to hard data from wells and thickness data interpreted from geophysics, such as seismic data. Our iterative methodology relies on a decomposition of the parameter optimization problem into smaller, manageable problems that are solved sequentially. We demonstrate this method on a real case study of a turbidite sedimentary basin.

Neural network stochastic simulation applied for quantifying uncertainties

Generally the geostatistical simulation methods are used to generate several realizations of physical properties in the sub-surface, these methods are based on the variogram analysis and limited to measures correlation between variables at two locations only. In this paper, we propose a simulation of properties based on supervised Neural network training at the existing drilling data set. The major advantage is that this method does not require a preliminary geostatistical study and takes into account several points. As a result, the geological information and the diverse geophysical data can be combined easily. To do this, we used a neural network with multi-layer perceptron architecture like feed-forward, then we used the back-propagation algorithm with conjugate gradient technique to minimize the error of the network output. The learning process can create links between different variables, this relationship can be used for interpolation of the properties on the one hand, or to generate several possible distribution of physical properties on the other hand, changing at each time and a random value of the input neurons, which was kept constant until the period of learning. This method was tested on real data to simulate multiple realizations of the density and the magnetic susceptibility in three-dimensions at the mining camp of Val d'Or, Québec (Canada).

Distributed Web Systems Performance Forecasting Using Turning Bands Method

With the increasing development of distributed computer systems (DCSs) in networked industrial and manufacturing applications on the World Wide Web (WWW) platform, including service-oriented architecture and Web of Things QoS-aware systems, it has become important to predict the Web performance. In this paper, we present Web performance prediction in time and in space by making a forecast of a Web resource downloading using the Turning Bands (TB) geostatistical simulation method. Real-life data for the research were obtained in an active experiment conducted by our multi-agent measurement system MWING performing monitoring of a group of Web servers worldwide from agents localized in different geographical localizations in Poland. The results show good quality of Web performance prediction made by means of the TB method, especially in the case when European Web servers were monitored by an MWING agent localized in Gliwice, Poland.

Application of Bayesian geostatistics for evaluation of mass discharge uncertainty at contaminated sites

Mass discharge estimates are increasingly being used when assessing risks of groundwater contamination and designing remedial systems at contaminated sites. Such estimates are, however, rather uncertain as they integrate uncertain spatial distributions of both concentration and groundwater flow. Here a geostatistical simulation method for quantifying the uncertainty of the mass discharge across a multilevel control plane is presented. The method accounts for (1) heterogeneity of both the flow field and the concentration distribution through Bayesian geostatistics, (2) measurement uncertainty, and (3) uncertain source zone and transport parameters. The method generates conditional realizations of the spatial flow and concentration distribution. An analytical macrodispersive transport solution is employed to simulate the mean concentration distribution, and a geostatistical model of the Box‐Cox transformed concentration data is used to simulate observed deviations from this mean solution. By combining the flow and concentration realizations, a mass discharge probability distribution is obtained. The method has the advantage of avoiding the heavy computational burden of three‐dimensional numerical flow and transport simulation coupled with geostatistical inversion. It may therefore be of practical relevance to practitioners compared to existing methods that are either too simple or computationally demanding. The method is demonstrated on a field site contaminated with chlorinated ethenes. For this site, we show that including a physically meaningful concentration trend and the cosimulation of hydraulic conductivity and hydraulic gradient across the transect helps constrain the mass discharge uncertainty. The number of sampling points required for accurate mass discharge estimation and the relative influence of different data types on mass discharge uncertainty is discussed.

Joint simulation of a building stone deposit using minimum/maximum autocorrelation factors

Quality of a natural building stone deposit can be characterised by some attributes such as tensile strength, uniaxial compressive strength and unit volume weight. There are spatial cross-correlations between these variables that should be reproduced when the geostatistical simulation methods are used for modelling such deposits. So it is needed to use multivariate techniques in that cases. Minimum/maximum autocorrelation technique which offers great advantages over standard full cosimulation, principal component simulation and stepwise techniques is used in this study to estimate quality-extractable area curves in a building stone deposit.