spMC: an R-package for 3D lithological reconstructions based on spatial Markov chains

Sartore, Luca; Fabbri, Paolo; Gaetan, Carlo

doi:10.1016/j.cageo.2016.06.001

Cited by 22 publications

(13 citation statements)

References 19 publications

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“…A 3‐D model is deemed better suited for risk analysis in the VAP. Such a model could include, for instance, the hydro‐stratigraphic units of VAP subsoil reconstructed using the transition probability‐based code spMC (Fabbri et al, 2020; Sartore et al, 2016). This code allows evaluating the impact of the random spatial variability of key parameters, including peat distributions or recharge rates at regional scales.…”

Section: Discussionmentioning

confidence: 99%

Conceptual Model of Arsenic Mobility in the Shallow Alluvial Aquifers Near Venice (Italy) Elucidated Through Machine Learning and Geochemical Modeling

Libera

Pedretti

Tateo

et al. 2020

Water Resources Research

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This work proposed a novel method to elucidate the controls of As mobility in complex aquifers based on an unsupervised machine learning algorithm, Self-Organizing Map (SOM), and process-based geochemical modeling. The approach is tested in the shallow aquifers of the Venetian Alluvial Plain (VAP) near Venice, Italy, where As concentrations seasonally and locally exceed recommended drinking water limits. SOM was fed using information from two geochemical surveys on eight VAP boreholes, and continuous reading of hourly groundwater head levels and weekly geochemical analyses from three VAP boreholes between mid-October 2017 and end of January 2018. The SOM analysis is consistent with redox-controlled dissolution-precipitation hydrous ferric oxides (HFOs) as a key control of As mobility in the aquifer. Dissolved As is positively correlated to Fe and NH þ 4 and negatively to the oxidizing-reducing potential (ORP). Negative correlation between As and groundwater head levels suggests a redox control by rainfall-driven recharge, which adds oxidants to the aquifer while progressively attenuating As. This mechanism is tested using process-based geochemical modeling, which simulates different transport modalities of oxidants entering the aquifer. Starting from reducing aquifer conditions, the model reproduces correctly the observed ORP and the trends in As and Fe, when the function describing the occurrence of oxidizing events scales according to the temporal occurrence of rainfall events. Heterogeneity can strongly control the local-scale effectiveness of recharge as a natural As attenuating factor, requiring a different model analysis to be properly assessed and to be developed in a follow-up study.

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Section: Discussionmentioning

confidence: 99%

Conceptual Model of Arsenic Mobility in the Shallow Alluvial Aquifers Near Venice (Italy) Elucidated Through Machine Learning and Geochemical Modeling

Libera

Pedretti

Tateo

et al. 2020

Water Resources Research

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“…The first step simplifies the local complex heterogeneity of the available 13 stratigraphic logs into five lithologies: A = clay, G = gravel, L = silt, LS = silty sand and S = sand. All analyses are performed by the package spMC [44] implemented in R, which is a free software environment for statistical computing and graphics. Figure 3a shows the sediment distribution indicated in the subsoil G (0.34), S (0.28) and L (0.22) as more frequent than A (0.09) and LS (0.07).…”

Section: Discussionmentioning

confidence: 99%

“…In this area, the subsoil is particularly heterogeneous, representing the passage between the high and the middle Venetian Plain. The analyses of the studied area are performed by exploiting a recent implementation of MCP approach available in the spMC package [44] for the R environment [45].…”

Section: Introductionmentioning

confidence: 99%

Subsoil Reconstruction in Geostatistics beyond Kriging: A Case Study in Veneto (NE Italy)

et al. 2020

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The reconstruction of hydro-stratigraphic units in subsoil (a general term indicating all the materials below ground level) plays an important role in the assessment of soil heterogeneity, which is a keystone in groundwater flow and transport modeling. A geostatistical approach appears to be a good way to reconstruct subsoil, and now other methods besides the classical indicator (co)kriging are available as alternative approximations of the conditional probabilities. Some of these techniques take specifically into account categorical variables as lithologies, but they are computationally prohibitive. Moreover, the stage before subsoil prediction/simulation can be very informative from a hydro-stratigraphic point of view, as the detailed transiogram analysis of this paper demonstrates. In this context, an application of the spMC package for the R software is presented by using a test site located within the Venetian alluvial plain (NE Italy). First, a detailed transiogram analysis was conducted, and then a maximum entropy approach, based on transition probabilities, named Markovian-type Categorical Prediction (MCP), was applied to approximate the posterior conditional probabilities. The study highlights some advantages of the presented approach in term of hydrogeological knowledge and computational efficiency. The spMC package couples transiogram analysis with a maximum entropy approach by taking advantage of High-Performance Computing (HPC) techniques. These characteristics make the spMC package useful for simulating hydro-stratigraphic units in subsoil, despite the use of a large number of lithologies (categories). The results obtained by spMC package suggest that this software should be considered a good candidate for simulating subsoil lithological distributions, especially of limited areas.

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“…• Three-dimensional (3-D) transition probability models of spatial variability are readily developed from 1-D Markov chains along principal stratigraphic directions (Carle and Fogg, 1997). • Continuous-lag Markov chains have been found suitable for 3-D modeling of vertical and lateral spatial transitioning among geo-or hydro-facies (Carle 1996;Carle and Fogg, 1996;Carle and Fogg, 1997;Carle et al, 1998;Fogg et al, 1998;Zhang and Fogg, 2003;Proce et al, 2004;Ye and Khaleel, 2008;Engdahl et al, 2010a;Bianchi et al, 2011;Pozdniakov et al, 2012;Purkis et al, 2012;Bakshevskaia and Pozdniakov, 2016;Krage et al, 2016;Sartore et al, 2016;Zhu et al, 2016a;Meirovitz et al, 2017;Guo et al, 2019b).…”

Section: Transition Probability-based Indicator Geostatisticsmentioning

confidence: 99%

“…tsim-s will be made available by request as the open-source fortran code tsim has been distributed in the past. The development of the equations necessary for implementation of the tsim-s algorithm are included in this paper to fully document the methods and to facilitate coding of the tsim algorithms in higher-level languages such as R (Sartore, 2013;Sartore et al, 2016). As will be seen in the equations, the computational overhead for tsim-s is not signifcantly different from tsim because the only modifications are to the entries in the cokriging matrices and the parameters of the quenching objective function.…”

Section: Introductionmentioning

confidence: 99%

Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

Carle

Fogg

2020

Front. Earth Sci.

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Uncertain or indirect "soft" data, such as geologic interpretation, driller's logs, geophysical logs or imaging, offer potential constraints or "soft conditioning" to stochastic models of discrete categorical subsurface variables in hydrogeology such as hydrofacies. Previous bivariate geostatistical simulation algorithms have not fully addressed the impact of data uncertainty in formulation of the (co) kriging equations and the objective function in simulated annealing (or quenching). This paper introduces the geostatistical simulation code tsim-s, which accounts for categorical data uncertainty through a data "hardness" parameter. In generating geostatistical realizations with tsim-s, the uncertainty inherent to soft conditioning is factored into both 1) the data declustering and spatial correlation functions in cokriging and 2) the acceptance probability for change of category in simulated quenching. The degree or sensitivity to which soft data conditions a realization as a function of hardness can be quantified by mapping category probabilities derived from multiple realizations. In addition to point or borehole data, arrays of data (e.g., as derived from a depth-dependency function, probability map, or "prior realization") can be used as soft conditioning. The tsim-s algorithm provides a theoretically sound and general framework for integrating datasets of variable location, resolution, and uncertainty into geostatistical simulation of categorical variables. A practical example shows how tsim-s is capable of generating a large-scale three-dimensional simulation including curvilinear features.

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spMC: an R-package for 3D lithological reconstructions based on spatial Markov chains

Cited by 22 publications

References 19 publications

Conceptual Model of Arsenic Mobility in the Shallow Alluvial Aquifers Near Venice (Italy) Elucidated Through Machine Learning and Geochemical Modeling

Conceptual Model of Arsenic Mobility in the Shallow Alluvial Aquifers Near Venice (Italy) Elucidated Through Machine Learning and Geochemical Modeling

Subsoil Reconstruction in Geostatistics beyond Kriging: A Case Study in Veneto (NE Italy)

Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

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