A genetic algorithm for resizing and sampling reduction of non-stationary soil chemical attributes optimizing spatial prediction

Aim of study: To evaluate the influence of the parameters of the geostatistical model and the initial sample configuration used in the optimization process; and to propose and evaluate the resizing of a sample configuration, reducing its sample size, for simulated data and for the study of the spatial variability of soil chemical attributes under a non-stationary with drift process from a commercial soybean cultivation area. Area of study: Cascavel, Brazil Material and methods: For both, the simulated data and the soil chemical attributes, the Genetic Algorithm was used for sample resizing, maximizing the overall accuracy measure. Main results: The results obtained from the simulated data showed that the practical range did not influence in a relevant way the optimization process. Moreover, the local variations, such as variance or sampling errors (nugget effect), had a direct relationship with the reduction of the sample size, mainly for the smaller nugget effect. For the soil chemical attributes, the Genetic Algorithm was efficient in resizing the sampling configuration, since it generated sampling configurations with 30 to 35 points, corresponding to 29.41% to 34.31% of the initial configuration, respectively. In addition, comparing the optimized and initial configurations, similarities were obtained regarding spatial dependence structure and characterization of spatial variability of soil chemical attributes in the study area. Research highlights: The optimization process showed that it is possible to reduce the sample size, allowing for lesser financial investments with data collection and laboratory analysis of soil samples in future experiments.

A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series

Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect.

Geomechanical and Fracture Network Interpretation of a Devonian Outcrop

Summary The Duvernay Formation is an unconventional reservoir characterized by induced seismicity and fluid migration, with natural fractures likely contributing to both cases. An alpine outcrop of the Perdrix and Flume formations, correlative with the subsurface Duvernay and Waterways formations, was investigated to characterize natural fracture networks. A semiautomated image-segmentation and fracture analysis was applied to orthomosaics generated from a photogrammetric survey to assess small- and large-scale fracture intensity and rock mass heterogeneity. The study also included manual scanlines, fracture windows, and Schmidt hammer measurements. The Perdrix section transitions from brittle fractures to en echelon fractures and shear-damage zones. Multiple scales of fractures were observed, including unconfined, bedbound fractures, and fold-relatedbed-parallel partings (BPPs). Variograms indicate a significant nugget effect along with fracture anisotropy. Schmidt hammer results lack correlation with fracture intensity. The Flume pavements exhibit a regionally extensive perpendicular joint set, tectonically driven fracturing, and multiple fault-damage zones with subvertical fractures dominating. Similar to the Perdrix, variograms show a significant nugget effect, highlighting fracture anisotropy. The results from this study suggest that small-scale fractures are inherently stochastic and that fractures observed at core scale should not be extrapolated to represent large-scale fracture systems; instead, the effects of small-scale fractures are best represented using an effective continuum approach. In contrast, large-scale fractures are more predictable according to structural setting and should be characterized robustly using geological principles. This study is especially applicable for operators and regulators in the Duvernay and similar formations where unconventional reservoir units abut carbonate formations.

Effect of Savanna windrow wood burning on the spatial variability of soil properties

ABSTRACT Tropical Savannas cover an area of approximately 1.9 billion hectares around the word and are subject to regular fires every 1 to 4 years. This study aimed to evaluate the influence of burning windrow wood from Cerrado (Brazilian Savanna) deforestation on the spatial variability of soil chemical properties, in the field. The data were analysed by using geostatistical methods. The semivariograms for pH(H2O), pH(CaCl2), Ca, Mg and K were calculated according to spherical models, whereas the phosphorus showed a nugget effect. The cross semi-variograms showed correlations between pH(H2O) and pH(CaCl2) with other variables with spatial dependence (exchangeable Ca and Mg and available K). The spatial variability maps for the pH(H2O), pH(CaCl2), Ca, Mg and K concentrations also showed similar patterns of spatial variability, indicating that burning the vegetation after deforestation caused a well-defined spatial arrangement. Even after 20 years of use with agriculture, the spatial distribution of pH(H2O), pH(CaCl2), Ca, Mg and available K was affected by the wood windrow burning that took place during the initial deforestation.

Theory of Intrinsic Random Functions

Chapter 3 discusses intrinsic random functions Y(x) of the space variable x, i.e. functions whose mean and variance of the increments Y(x + h) − Y(x) depend on h only. Half of this variance defines the variogram γ‎(h). The behaviour of the variogram near the origin, such as continuity, the nugget effect, etc., expresses the regularity of these functions. Regularisations of them, by grading and convolutions, produce new variograms, via the same rules as for transitive methods. When Z(v) and Z(v′) are the averages of these functions in v and v′, respectively, then the variance of Z(v) − Z(v′) by attributing to v′ the grade in v is called extension variance. Its formal expression is given and calculated for various patterns of sampling v, in dimensions 1, 2, or 3, via the de Wijsian scheme and the spherical scheme, and for various models of variograms, such as the semi-variogram.

SPATIAL DEPENDENCE INDEX FOR CUBIC, PENTASPHERICAL AND WAVE SEMIVARIOGRAM MODELS

This study aims to propose a spatial dependence index (and its classification), from the concept of spatial correlation areas, for the Cubic, Pentaspherical and Wave models. The index, called Spatial Dependence Index (SDI), covers the following parameters: the range (a), the nugget effect (C 0 ) and the contribution (C 1 ), beyond considering the maximum distance (MD) between sampled points and the model factor (MF). The proposed index, unlike the most used in the literature, considers the influence of the range parameter to describe the spatial dependence, highlighting the importance of this formulation. The spatial dependence classification, based on the observed asymmetric behavior in the SDI, was performed considering categorizations from the median and the 3rd quartile of the index. We obtain the spatial dependence classification in terms of weak, moderate, and strong, just as it is usually described in literature.