scholarly journals Multiple-point statistical simulation for hydrogeological models: 3-D training image development and conditioning strategies

2017 ◽  
Vol 21 (12) ◽  
pp. 6069-6089 ◽  
Author(s):  
Anne-Sophie Høyer ◽  
Giulio Vignoli ◽  
Thomas Mejer Hansen ◽  
Le Thanh Vu ◽  
Donald A. Keefer ◽  
...  
Keyword(s):  
Development Strategy ◽  
Large Scale ◽  
Statistical Simulation ◽  
Training Image ◽  
Multiple Point ◽  
Data Sets ◽  
Input Information ◽  
Training Images ◽  
Voxel Model ◽  
Novel Strategy

Abstract. Most studies on the application of geostatistical simulations based on multiple-point statistics (MPS) to hydrogeological modelling focus on relatively fine-scale models and concentrate on the estimation of facies-level structural uncertainty. Much less attention is paid to the use of input data and optimal construction of training images. For instance, even though the training image should capture a set of spatial geological characteristics to guide the simulations, the majority of the research still relies on 2-D or quasi-3-D training images. In the present study, we demonstrate a novel strategy for 3-D MPS modelling characterized by (i) realistic 3-D training images and (ii) an effective workflow for incorporating a diverse group of geological and geophysical data sets. The study covers an area of 2810 km2 in the southern part of Denmark. MPS simulations are performed on a subset of the geological succession (the lower to middle Miocene sediments) which is characterized by relatively uniform structures and dominated by sand and clay. The simulated domain is large and each of the geostatistical realizations contains approximately 45 million voxels with size 100 m  ×  100 m  ×  5 m. Data used for the modelling include water well logs, high-resolution seismic data, and a previously published 3-D geological model. We apply a series of different strategies for the simulations based on data quality, and develop a novel method to effectively create observed spatial trends. The training image is constructed as a relatively small 3-D voxel model covering an area of 90 km2. We use an iterative training image development strategy and find that even slight modifications in the training image create significant changes in simulations. Thus, this study shows how to include both the geological environment and the type and quality of input information in order to achieve optimal results from MPS modelling. We present a practical workflow to build the training image and effectively handle different types of input information to perform large-scale geostatistical modelling.

scholarly journals Multiple-point statistical simulation for hydrogeological models: 3D training image development and conditioning strategies

2016 ◽  
Author(s):  
Anne-Sophie Høyer ◽  
Giulio Vignoli ◽  
Thomas Mejer Hansen ◽  
Le Thanh Vu ◽  
Donald A. Keefer ◽  
...  
Keyword(s):  
Development Strategy ◽  
Large Scale ◽  
Statistical Simulation ◽  
Training Image ◽  
Multiple Point ◽  
Data Sets ◽  
Input Information ◽  
Training Images ◽  
Voxel Model ◽  
Novel Strategy

Abstract. Most studies about the application of geostatistical simulations based on multiple-point statistics (MPS) to hydrogeological modelling focus on relatively fine-scale models and concentrate on the estimation of facies-level, structural uncertainty. Much less attention is paid to the use of input data and optimal construction of training images. For instance, even though the training image should capture a set of spatial geological characteristics to guide the simulations, the majority of the research still relies on 2D or quasi-3D training images. In the present study, we demonstrate a novel strategy for 3D MPS modelling characterized by: (i) realistic 3D training images, and (ii) an effective workflow for incorporating a diverse group of geological and geophysical data sets. The study covers an area of 2810 km2 in the southern part of Denmark. MPS simulations are performed on a subset of the geological succession (the lower to middle Miocene sediments) which is characterized by relatively uniform structures and dominated by sand and clay. The simulated domain is large and each of the geostatistical realizations contains approximately 45 million voxels with size 100 m × 100 m × 5 m. Data used for the modelling include water well logs, high-resolution seismic data, and a previously published 3D geological model. We apply a series of different strategies for the simulations based on data quality, and develop a novel method to effectively create observed sand/clay spatial trends. The training image is constructed as a small 3D voxel model covering an area of 90 km2. We use an iterative training image development strategy and find that even slight modifications in the training image create significant changes in simulations. Thus, the study underlines that it is important to consider both the geological environment, and the type and quality of input information in order to achieve optimal results from MPS modelling. In this study we present a possible workflow to build the training image and effectively handle different types of input information to perform large-scale geostatistical modelling.

scholarly journals Locality-based 3-D multiple-point statistics reconstruction using 2-D geological cross sections

2018 ◽  
Vol 22 (12) ◽  
pp. 6547-6566 ◽  
Author(s):  
Qiyu Chen ◽  
Gregoire Mariethoz ◽  
Gang Liu ◽  
Alessandro Comunian ◽  
Xiaogang Ma
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Training Image ◽  
Sensitivity Analyses ◽  
Multiple Point ◽  
Multiple Point Statistics ◽  
Training Images ◽  
Critical Issues ◽  
Probability Aggregation ◽  
Novel Strategy

Abstract. Multiple-point statistics (MPS) has shown promise in representing complicated subsurface structures. For a practical three-dimensional (3-D) application, however, one of the critical issues is the difficulty in obtaining a credible 3-D training image. However, bidimensional (2-D) training images are often available because established workflows exist to derive 2-D sections from scattered boreholes and/or other samples. In this work, we propose a locality-based MPS approach to reconstruct 3-D geological models on the basis of such 2-D cross sections (3DRCS), making 3-D training images unnecessary. Only several local training subsections closer to the central uninformed node are used in the MPS simulation. The main advantages of this partitioned search strategy are the high computational efficiency and a relaxation of the stationarity assumption. We embed this strategy into a standard MPS framework. Two probability aggregation formulas and their combinations are used to assemble the probability density functions (PDFs) from different subsections. Moreover, a novel strategy is adopted to capture more stable PDFs, where the distances between patterns and flexible neighborhoods are integrated on multiple grids. A series of sensitivity analyses demonstrate the stability of the proposed approach. Several hydrogeological 3-D application examples illustrate the applicability of the 3DRCS approach in reproducing complex geological features. The results, in comparison with previous MPS methods, show better performance in portraying anisotropy characteristics and in CPU cost.

scholarly journals Locality-based 3-D multiple-point statistics reconstruction using 2-D geological cross-sections

2018 ◽  
Author(s):  
Qiyu Chen ◽  
Gregoire Mariethoz ◽  
Gang Liu ◽  
Alessandro Comunian ◽  
Xiaogang Ma
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Training Image ◽  
Sensitivity Analyses ◽  
Multiple Point ◽  
Multiple Point Statistics ◽  
Training Images ◽  
Critical Issues ◽  
Probability Aggregation ◽  
Novel Strategy

Abstract. Multiple-point statistics (MPS) has shown promise in representing complicated subsurface structures. For a practical three-dimensional (3-D) application, however, one of the critical issues the difficulty to obtain a credible 3-D training image. However, bidimensional (2-D) training images are often available because established workflows exist to derive 2-D sections from scattered boreholes and/or other samples. In this work, we propose a locality-based MPS approach to reconstruct 3-D geological models on the basis of such 2-D cross-sections, making 3-D training images unnecessary. Only several local training sub-sections closer to the central uninformed node are used in the MPS simulation. The main advantages of this partitioned search strategy are the high computational efficiency and a relaxation of the stationarity assumption. We embed this strategy into a standard MPS framework. Two probability aggregation formulas and their combinations are used to assemble the probability density functions (pdfs) from different sub-sections. Moreover, a novel strategy is adopted to capture more stable pdfs, where the distances between patterns and flexible neighborhoods are integrated on several multiple grids. A series of sensitivity analyses demonstrate the stability of the proposed approach. Several hydrogeological 3-D application examples illustrate the applicability of our approach in reproducing complex geological features. The results, in comparison with previous MPS methods, show better performance in portraying anisotropy characteristics and in CPU cost.

The MPS Reconstruction of Porous Media Using Multiple-Grid Templates

2013 ◽  
Vol 462-463 ◽  
pp. 462-465 ◽  
Author(s):  
Yi Du ◽  
Ting Zhang
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Grid Method ◽  
Training Image ◽  
Multiple Point ◽  
Grid Data ◽  
Large Scale Structures ◽  
Complex Features ◽  
Grid Nodes ◽  
Data Template

It is difficult to reconstruct the unknown information only by some sparse known data in the reconstruction of porous media. Multiple-point geostatistics (MPS) has been proved to be a powerful tool to capture curvilinear structures or complex features in training images. One solution to capture large-scale structures while considering a data template with a reasonably small number of grid nodes is provided by the multiple-grid method. This method consists in scanning a training image using increasingly finer multiple-grid data templates instead of a big and dense data template. The experimental results demonstrate that multiple-grid data templates and MPS are practical in porous media reconstruction.

scholarly journals Contributions to uncertainty related to hydrostratigraphic modeling using Multiple-Point Statistics

2018 ◽  
Author(s):  
Adrian A. S. Barfod ◽  
Troels N. Vilhelmsen ◽  
Flemming Jørgensen ◽  
Anders V. Christiansen ◽  
Julien Straubhaar ◽  
...  
Keyword(s):  
Large Scale ◽  
Structural Information ◽  
Training Image ◽  
Multiple Point ◽  
Geological Model ◽  
Soft Data ◽  
Borehole Data ◽  
Subsurface Geology ◽  
The Impact ◽  
Neighboring Area

Abstract. Forecasting the flow of groundwater requires a hydrostratigraphic model, which describes the architecture of the subsurface. State-of-the-art Multiple-Point Statistical (MPS) tools are readily available for creating models depicting subsurface geology. We present a study of the impact of key parameters related to stochastic MPS simulation of a real-world hydrogeophysical dataset from Kasted Denmark using the snesim algorithm. The goal is to study how changes to the underlying datasets 5 propagate into the hydrostratigraphic realizations when using MPS for stochastic modeling. This study focuses on the sensitivity of the MPS realizations to the geophysical soft data, borehole lithology logs, and the Training Image (TI). The modeling approach used in this paper utilizes a cognitive geological model as a TI to simulate ensemble hydrostratigraphic models. The target model contains three overall hydrostratigraphic categories, and the MPS realizations are compared visually, as well as quantitatively using mathematical measures of similarity. The quantitative similarity analysis is carried 10 out exhaustively, and realizations are compared with each other as well as with the cognitive geological model. The results underline the importance of geophysical data for constraining MPS simulations. Relying only on borehole data and the conceptual geology or TI, results in a significant increase in realization uncertainty. The SkyTEM data used in this study cover a large portion of the Kasted model area, and are essential to the hydrostratigraphic architecture. On the other hand, the borehole lithology logs are sparse, and only 410 boreholes were present in this study. The borehole lithology logs 15 infer local changes in the immediate vicinity of the boreholes, thus providing limited large-scale structural information. Lithological information is, however, important for the interpretation of the geophysical responses. Finally, the importance of the TI was studied. An example was presented where an alternative geological model from a neighboring area was used to simulate hydrostratigraphic models. It was shown that as long as the geological setting are similar in nature, the realizations, although different, still reflect the hydrostratigraphic architecture. If a TI containing a biased geological conceptualization is 20 used, the resulting realizations will resemble the TI and contain less structure in particular areas, where the soft data show almost even probability to two or all three of the hydrostratigraphic units.

scholarly journals QuickSampling v1.0: a robust and simplified pixel-based multiple-point simulation approach

2020 ◽  
Vol 13 (6) ◽  
pp. 2611-2630 ◽  
Author(s):  
Mathieu Gravey ◽  
Grégoire Mariethoz
Keyword(s):  
Open Source ◽  
Degrees Of Freedom ◽  
State Of The Art ◽  
Training Image ◽  
Multiple Point ◽  
Spatial Structures ◽  
Continuous Variables ◽  
New Approach ◽  
Training Images ◽  
Computational Performance

Abstract. Multiple-point geostatistics enable the realistic simulation of complex spatial structures by inferring statistics from a training image. These methods are typically computationally expensive and require complex algorithmic parametrizations. The approach that is presented in this paper is easier to use than existing algorithms, as it requires few independent algorithmic parameters. It is natively designed for handling continuous variables and quickly implemented by capitalizing on standard libraries. The algorithm can handle incomplete training images of any dimensionality, with categorical and/or continuous variables, and stationarity is not explicitly required. It is possible to perform unconditional or conditional simulations, even with exhaustively informed covariates. The method provides new degrees of freedom by allowing kernel weighting for pattern matching. Computationally, it is adapted to modern architectures and runs in constant time. The approach is benchmarked against a state-of-the-art method. An efficient open-source implementation of the algorithm is released and can be found here (https://github.com/GAIA-UNIL/G2S, last access: 19 May 2020) to promote reuse and further evolution. The highlights are the following: A new approach is proposed for pixel-based multiple-point geostatistics simulation. The method is flexible and straightforward to parametrize. It natively handles continuous and multivariate simulations. It has high computational performance with predictable simulation times. A free and open-source implementation is provided.

scholarly journals Contributions to uncertainty related to hydrostratigraphic modeling using multiple-point statistics

2018 ◽  
Vol 22 (10) ◽  
pp. 5485-5508 ◽  
Author(s):  
Adrian A. S. Barfod ◽  
Troels N. Vilhelmsen ◽  
Flemming Jørgensen ◽  
Anders V. Christiansen ◽  
Anne-Sophie Høyer ◽  
...  
Keyword(s):  
Large Scale ◽  
Structural Information ◽  
Training Image ◽  
Multiple Point ◽  
Geological Model ◽  
Soft Data ◽  
Borehole Data ◽  
Transient Electromagnetic ◽  
High Degree ◽  
The Impact

Abstract. Forecasting the flow of groundwater requires a hydrostratigraphic model, which describes the architecture of the subsurface. State-of-the-art multiple-point statistical (MPS) tools are readily available for creating models depicting subsurface geology. We present a study of the impact of key parameters related to stochastic MPS simulation of a real-world hydrogeophysical dataset from Kasted, Denmark, using the snesim algorithm. The goal is to study how changes to the underlying datasets propagate into the hydrostratigraphic realizations when using MPS for stochastic modeling. This study focuses on the sensitivity of the MPS realizations to the geophysical soft data, borehole lithology logs, and the training image (TI). The modeling approach used in this paper utilizes a cognitive geological model as a TI to simulate ensemble hydrostratigraphic models. The target model contains three overall hydrostratigraphic categories, and the MPS realizations are compared visually as well as quantitatively using mathematical measures of similarity. The quantitative similarity analysis is carried out exhaustively, and realizations are compared with each other as well as with the cognitive geological model. The results underline the importance of geophysical data for constraining MPS simulations. Relying only on borehole data and the conceptual geology, or TI, results in a significant increase in realization uncertainty. The airborne transient electromagnetic SkyTEM data used in this study cover a large portion of the Kasted model area and are essential to the hydrostratigraphic architecture. On the other hand, the borehole lithology logs are sparser, and 410 boreholes were present in this study. The borehole lithology logs infer local changes in the immediate vicinity of the boreholes, thus, in areas with a high degree of geological heterogeneity, boreholes only provide limited large-scale structural information. Lithological information is, however, important for the interpretation of the geophysical responses. The importance of the TI was also studied. An example was presented where an alternative geological model from a neighboring area was used to simulate hydrostratigraphic models. It was shown that as long as the geological settings are similar in nature, the realizations, although different, still reflect the hydrostratigraphic architecture. If a TI containing a biased geological conceptualization is used, the resulting realizations will resemble the TI and contain less structure in particular areas, where the soft data show almost even probability to two or all three of the hydrostratigraphic units.

scholarly journals Quantile Sampling: a robust and simplified pixel-based multiple-point simulation approach

2019 ◽  
Author(s):  
Mathieu Gravey ◽  
Grégoire Mariethoz
Keyword(s):  
Pattern Matching ◽  
Degrees Of Freedom ◽  
State Of The Art ◽  
Training Image ◽  
Multiple Point ◽  
Spatial Structures ◽  
Continuous Variables ◽  
Simulation Approach ◽  
Training Images ◽  
Computationally Expensive

Abstract. Multiple-point geostatistics enable the realistic simulation of complex spatial structures by inferring statistics from a training image. These methods are typically computationally expensive and require complex algorithmic parametrizations. The approach that is presented in this paper is easier to use than existing algorithms, as it requires few independent algorithmic parameters. It is natively designed for handling continuous variables, and quickly implemented by capitalizing on standard libraries. The algorithm can handle incomplete training images of any dimensionality, with categorical or/and continuous variables, and stationarity is not explicitly required. It is possible to perform unconditional or conditional simulations, even with exhaustively informed covariates. The method provides new degrees of freedom by allowing kernel weighting for pattern matching. Computationally, it is adapted to modern architectures and runs in constant time. The approach is benchmarked against a state-of-the-art method. An efficient open-source implementation of the algorithm is released and can be found here (https://github.com/GAIA-UNIL/G2S), to promote reuse and further evolution.

3D Porosity Modeling of a Carbonate Reservoir Using Continuous Multiple-Point Statistics Simulation

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 375-379 ◽  
Author(s):  
Tuanfeng Zhang ◽  
Sebastien Bombarde ◽  
Sebastien B. Strebelle ◽  
Emily Oatney
Keyword(s):  
Training Image ◽  
Carbonate Reservoir ◽  
Multiple Point ◽  
Continuous Training ◽  
Porosity Distribution ◽  
Multiple Point Statistics ◽  
Training Images ◽  
Geostatistical Approach ◽  
Porosity And Permeability ◽  
Similarity Class

Summary Training images are numerical representations of geological conceptual models that provide prior information on reservoir architecture. A new emerging geostatistical approach named multiple-point statistics (MPS) simulation allows extracting multiple-point structures from such training images and anchoring these structures to the data actually observed in the reservoir. By reproducing multiple-point statistics inferred from training images, MPS enables the modeling of complex curvilinear structures (e.g., sinuous channels) in a much more geologically realistic way than traditional two-point statistics (variogram-based) techniques. However, in the original MPS implementation, all multiple-point statistics moments computed from the training image are exported to the reservoir model without processing, which allows simulating only categorical or discretized variables. This implementation is appropriate with clastic reservoirs for which, typically, depositional facies are simulated first using MPS, then porosity and permeability are distributed within each simulated facies using traditional variogram-based techniques. But for reservoirs, in particular in carbonate environments, where porosity and permeability trends/cycles are not closely tied to any facies distribution, simulating porosity/permeability directly using corresponding continuous training images appears to be a more suitable approach. In this paper, a new filter-based implementation of MPS, named filtersim, is proposed to reproduce features from continuous variable training images. First, a set of general filters is applied to the training image to transform (summarize) each training pattern into a set of scores accounting for different aspects of the pattern, such as north-south and east-west gradients and curvatures. The training patterns are classified in the score space and grouped into a small number of similarity classes. The simulation consists then of visiting each grid node along a random path, identifying the similarity class that best fits to the local conditioning data, and patching a pattern drawn from that selected similarity class. In our study, this new approach was applied to model the 3D porosity distribution of a carbonate reservoir in Kazakhstan. First, the original "categorical" MPS program snesim was used to model the two main reservoir regions, platform and slope, where the spatial porosity distribution is characterized by significantly different features. Interpreted well markers and seismic data were used to condition the modeling of these two regions. Then porosity was distributed in the platform region using the "continuous" filter-based MPS program filtersim, as described previously. The 3D training images used in that second step displayed porosity trends/cycles controlled by the type of geological sedimentation process believed to have occurred in the reservoir.

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