Reconstruction of Incomplete Data Sets or Images Using Direct Sampling

Mariethoz, Grégoire; Renard, Philippe

doi:10.1007/s11004-010-9270-0

Cited by 115 publications

(57 citation statements)

References 39 publications

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“…In the literature, a groundwater divide is noted along the eastern corridor of the aquifer (Bennett 1976), so this corridor was truncated and an entering flux equal to the recharge was assigned. The recharge of the aquifer was distributed according to the distribution of the geological units and remained within the range of values provided for historical studies of the region (Manning et al 1970;Betts 1982;Kalin and Roberts 1997): where Sherwood Sandstone outcrops it ranges from 73 to 100 mm yr −1 ; below the Mercia Mudstone 7-10 mm yr −1 and below the basalt 4 mm yr −1 Within those zones, ranges were required to account for variations in bedrock K, urbanization and glacial till cover.…”

Section: Numerical Groundwater Modellingmentioning

confidence: 94%

“…The Lagan Valley Aquifer has been studied for many decades (Bennett 1976;Cronin et al 2000Cronin et al , 2005Hartley 1935;Kalin and Roberts 1997;Kalin et al 1998;Manning et al 1970;McNeill et al 2000;Robins 1996;Yang et al 2004) and the region is well documented to contain Tertiary dykes. The effect of dykes on groundwater flow is acknowledged by previous authors as acting as relative barriers to flow: the hydraulic effect is described in Bennett (1976), Kalin and Roberts (1997), Burns et al (2010), Wilson (2011) and numerous consultancy studies involving hydraulic testing.…”

Section: Multiple-point Statistics and Direct Sampling Techniquementioning

confidence: 99%

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Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models

et al. 2015

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The process of accounting for heterogeneity has made significant advances in statistical research, primarily in the framework of stochastic analysis and the development of multiple-point statistics (MPS). Among MPS techniques, the direct sampling (DS) method is tested to determine its ability to delineate heterogeneity from aerial magnetics data in a regional sandstone aquifer intruded by low-permeability volcanic dykes in Northern Ireland, UK. The use of two two-dimensional bivariate training images aids in creating spatial probability distributions of heterogeneities of hydrogeological interest, despite relatively 'noisy' magnetics data (i.e. including hydrogeologically irrelevant urban noise and regional geologic effects). These distributions are incorporated into a hierarchy system where previously published density function and upscaling methods are applied to derive regional distributions of equivalent hydraulic conductivity tensor K. Several K models, as determined by several stochastic realisations of MPS dyke locations, are computed within groundwater flow models and evaluated by comparing modelled heads with field observations. Results show a significant improvement in model calibration when compared to a simplistic homogeneous and isotropic aquifer model that does not account for the dyke occurrence evidenced by airborne magnetic data. The best model is obtained when normal and reverse polarity dykes are computed separately within MPS simulations and when a probability threshold of 0.7 is applied. The presented stochastic approach also provides improvement when compared to a previously published deterministic anisotropic model based on the unprocessed (i.e. noisy) airborne magnetics. This demonstrates the potential of coupling MPS to airborne geophysical data for regional groundwater modelling.

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Section: Numerical Groundwater Modellingmentioning

confidence: 94%

Section: Multiple-point Statistics and Direct Sampling Techniquementioning

confidence: 99%

Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models

et al. 2015

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“…The order in which pixels are simulated is defined by a random path which is different for each realization. by directly sampling the training image in a random manner, attempting to find one pixel y in the training image with a replicate Ny that is similar to Nx [31]. As soon as a pixel y is obtained with a neighborhood similar to Nx, the sampling process stops and the value of y is assigned to x.…”

Section: Direct Sampling Methodsmentioning

confidence: 99%

“…When the distance is less than a given threshold t, Ny is regarded similar as Nx and the value of y is assigned to x. The distance can be computed in different ways (further discussion on this can be found in Mariethoz et al [31]). are the values at corresponding locations; d is the distance between two data events Nx and Ny, which can be denoted as d{Nx, Ny}.…”

Section: Direct Sampling Methodsmentioning

confidence: 99%

Gap-Filling of Landsat 7 Imagery Using the Direct Sampling Method

2016

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Abstract:The failure of the Scan Line Corrector (SLC) on Landsat 7 imposed systematic data gaps on retrieved imagery and removed the capacity to provide spatially continuous fields. While a number of methods have been developed to fill these gaps, most of the proposed techniques are only applicable over relatively homogeneous areas. When they are applied to heterogeneous landscapes, retrieving image features and elements can become challenging. Here we present a gap-filling approach that is based on the adoption of the Direct Sampling multiple-point geostatistical method. The method employs a conditional stochastic resampling of known areas in a training image to simulate unknown locations. The approach is assessed across a range of both homogeneous and heterogeneous regions. Simulation results show that for homogeneous areas, satisfactory results can be obtained by simply adopting non-gap locations in the target image as baseline training data. For heterogeneous landscapes, bivariate simulations using an auxiliary variable acquired at a different date provides more accurate results than univariate simulations, especially as land cover complexity increases. Apart from recovering spatially continuous fields, one of the key advantages of the Direct Sampling is the relatively straightforward implementation process that relies on relatively few parameters.

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“…More realistic training images and more reliable stochastic models will be generated if wide and accurate prior information about the reservoir is available. Pattern-based methods like SimPat (Arpat, 2005), FilterSim (Zhang, 2006), Direct Sampling (Mariethoz and Renard, 2010), DisPat (Honarkhah, 2011), and WaveSim (Chatterjee et al, 2012) are 25 generally best methods for MPS reservoir modeling. The SimPat algorithm is time-consuming and in the FilterSim, defining the filters adds complexity to the algorithm.…”

Section: Model Multiplicities By the Mps Methodsmentioning

confidence: 99%

Sparsity-based compressive reservoir characterization and modeling by applying ILS-DLA sparse approximation with LARS on DisPat-generated MPS models using seismic, well log, and reservoir data

Hosseini

Riahi

2016

Preprint

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Abstract. In the earth sciences, there is only one single true reality for a property of any dimension whereas many realization models of the reality might exist. In other words, a set of interpreted multiplicities of an unknown 10 property can be found but only one unique fact exists and the task is to return from the multiplicities to the uniqueness of the reality. Such an objective is mathematically provided by sparse approximation methods. The term 'approximation' indicate the sufficiency of an interpretation that is close enough to the true mode, i.e. reality.In geosciences, the multiplicities are provided by multiple-point statistical methods. Realistic modeling of the earth interior demands for more sophisticated geostatistical methods based on true available images, i.e. the training 15 images. Among available MPS methods, the DisPat algorithm is a distance-based MPS method which generate appealing realizations for stationary and nonstationary training images by classifying the patterns based on distance functions using kernel methods. Advances in nonstationary image modeling is an advantage of the DisPat method.Realizations generated by the MPS methods form the training set for the sparse approximation. Sparse approximation is consisted of two steps, i.e. sparse coding and dictionary update, which are alternately used to 20 optimize the trained dictionary. Model selection algorithms like LARS are used for sparse coding. LARS optimizes the regression model sequentially by choosing a proper number of variables and adding the best variable to the active set in each iteration. Out of numerous training dictionary methods given in the literature, the ILS-DLA is a variant of the MOD algorithm where the latter is inspired by the GLA and the whole trained dictionary is sequentially updated by alternating between sparse coding and dictionary training steps. The ILS-DLA is different 25 from the MOD for addressing the internal structure of the dictionary by considering overlapping or nonoverlapping blocks and modifying the MOD algorithm according to the internal structure of the trained dictionary.The ILS-DLA is faster than the MOD in the sense that it inverts for smaller blocks constructing the trained dictionary rather than inverting for the entire block. The subject of this paper is an integration study between sparse approximations from image processing and compressed sensing, multiple-point statistics from the field of 30 geostatisitcs, and the geophysical methods and reservoir engineering from the branch of petroleum science. This paper specifically emphasizes the utilization of image processing in solving reservoir complexities and enhancing reservoir models.

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Reconstruction of Incomplete Data Sets or Images Using Direct Sampling

Cited by 115 publications

References 39 publications

Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models

Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models

Gap-Filling of Landsat 7 Imagery Using the Direct Sampling Method

Sparsity-based compressive reservoir characterization and modeling by applying ILS-DLA sparse approximation with LARS on DisPat-generated MPS models using seismic, well log, and reservoir data

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