Fitting the variogram model of nickel laterite using root means square error in Morowali, Central Sulawesi

Abstract. The nickel commodity is getting popular due to its role as one of the raw materials for battery manufacture. It is estimated that this trend will continue for the next 2 - 3 years and reaching its peak when the factories that process the raw material for electric vehicle batteries are established. For this reason, the nickel mining companies are competing to explore new nickel deposits. The research location is a nickel mine in Sulawesi. The purpose of this study was to determine the most suitable Nickel variogram model based on root means square error (RMSE). To obtain an accurate number of resources, it is necessary to apply an accurate and validated estimation method to gain data that are in line with the actual conditions. Therefore, this study uses a geostatistical method that takes into account the spatial relationship of each data using a variogram which is validated by the cross-validation method and RMSE. From the results of the RSME analysis, the most suitable variogram model for nickel content in the limonite and saprolite layers is the exponential variogram model. In addition, the values of root mean square error for nickel content in the limonite and saprolite layers were 0.022 and 0.098 respectively.

Assessment of Complex Terminal Groundwater Aquifer for Different Use of Oued Souf Valley (Algeria) Using Multivariate Statistical Methods, Geostatistical Modeling, and Water Quality Index

This research aims to assess the hydrogeochemical evolution of the groundwater in Oued souf valley for drinking and irrigation purposes. To achieve this, 49 groundwater samples from the complex terminal were examined and treated concurrently with multivariate statistical methods, geostatistical modeling and the WQI (water quality index). Focusing on the physico-chemical parameters, Q mode clustering analysis detected four major water groups, where the mineralization augmented from group 1 to group 4. The hydro-chemical type was the same, Ca-Mg-Cl-SO4 for all the groups. Calcite, dolomite, anhydrite, and gypsum would be the dominant reactions with the undersaturation of evaporates minerals, based on geochemical modeling, while the carbonate minerals are precipitating. Geostatistical analysis using ordinary Kriging demonstrated the exponential semi-variogram model fitted for EC (electrical conductivity), Ca2+ (calcium), Mg2+ (magnesium), K+ (potassium), HCO3− (bicarbonate), Cl− (chloride), and SO42− (sulfate). At the same time, the rational quadratic model was the best-fitted semi-variogram model for Na+ (sodium) and NO3− (nitrate). EC, SO42−, and NO3− have a strong spatial structure, while Ca2+, Na+, K+, and HCO3− have a moderate spatial structure. Moreover, there was a weak spatial structure for Mg2+ and Cl−. The WQI shows that CT (complex terminal groundwater aquifers) are not suitable for drinking and their quality for irrigation fluctuates from excellent to moderate quality.

Accounting for Local Geological Variability in Sequential Simulations—Concept and Application

Heterogeneity-preserving property models of subsurface regions are commonly constructed by means of sequential simulations. Sequential Gaussian simulation (SGS) and direct sequential simulation (DSS) draw values from a local probability density function that is described by the simple kriging estimate and the local simple kriging variance at unsampled locations. The local simple kriging variance, however, does not necessarily reflect the geological variability being present at subsets of the target domain. In order to address that issue, we propose a new workflow that implements two modified versions of the popular SGS and DSS algorithms. Both modifications, namely, LVM-DSS and LVM-SGS, aim at simulating values by means of introducing a local variance model (LVM). The LVM is a measurement-constrained and geology-driven global representation of the locally observable variance of a property. The proposed modified algorithms construct the local probability density function with the LVM instead of using the simple kriging variance, while still using the simple kriging estimate as the best linear unbiased estimator. In an outcrop analog study, we can demonstrate that the local simple kriging variance in sequential simulations tends to underestimate the locally observed geological variability in the target domain and certainly does not account for the spatial distribution of the geological heterogeneity. The proposed simulation algorithms reproduce the global histogram, the global heterogeneity, and the considered variogram model in the range of ergodic fluctuations. LVM-SGS outperforms the other algorithms regarding the reproduction of the variogram model. While DSS and SGS generate a randomly distributed heterogeneity, the modified algorithms reproduce a geologically reasonable spatial distribution of heterogeneity instead. The new workflow allows for the integration of continuous geological trends into sequential simulations rather than using class-based approaches such as the indicator simulation technique.

Improved Strategies for BeiDou Ultrarapid Satellites’ Clock Bias Prediction Using BDS-2 and BDS-3 Integrated Processing

GNSS ultrarapid clock biases are key inputs of rapid high-accuracy applications, especially for its prediction parts. With the fast development of the BeiDou system (BDS), the system performances are mainly represented by orbit and clock products. However, it is suggested that the BDS-predicted clock biases cannot meet the requirement of real-time or near real-time services. In this research, the BDS satellite-predicted ultrarapid clock bias products are optimized with three methods, namely, one-step strategy, intersatellite correlation, and variogram model, using the combined estimation of BDS-2 and BDS-3 satellites. Firstly, considering the traditional two-step strategy for modelling clock bias prediction, we take all terms (including trend and periodic terms) into one-step solution of model estimation based on the sparse modelling in machine learning. Secondly, because of the much more stable on-board atomic clock of BDS-3 satellites, the intersatellite correlations between BDS-2 and BDS-3 are utilized to enhance the solution of model coefficients. Thirdly, to further improve the model, the temporal correlations in model residuals are used to reconstruct the stochastic function obtained by variogram. In addition, to verify the proposed improved strategies, 12 schemes of BDS clock bias prediction experiments are designed and analyzed with different conditions. According to the results of predicted clock biases, it is indicted that (1) the stability of BDS-3 on-board clocks is more optimal compared with BDS-2, which can be used to strengthen the solution of the clock bias prediction model; (2) the one-step estimation of the clock bias model by sparse modelling can slightly increase the accuracy of prediction results; (3) both BDS-2- and BDS-3-predicted clock biases benefited each other by inserting the intersatellite correlations into the weight matrix, in which the accuracy of 18-hour period with one-step strategy can be improved by 28.6% and 27.2% for BDS-2 and BDS-3, respectively; and (4) after the introduction of the variogram model in updating the weight matrix, the clock bias prediction model is further corrected by 8.0% and 11.1% for BDS-2 and BDS-3. In summary, improved strategies for BDS ultrarapid satellites’ clock bias prediction using BDS-2 and BDS-3 integrated processing are meaningful for the current BDS ultrarapid satellites’ clock bias prediction products.

Relationship between Spatial Variability Pattern of Wheat Yield and Soil Properties

Aims: Determining effects of spatial variation of some soil properties on wheat quantity and quality variation in order that proper soil and inputs management can be applied for sustainable wheat production. Study Design: Analyzing data of a field with center pivot irrigation system and uniform management using the geostatistical method. Place and Duration of Study: Soil and Water Research Department, Fars Agricultural and Natural Resources Research and Education Center, Darab, Iran, from September 2013 to February 2014. Methodology: Wheat yield data harvested by class lexion 510 combine from 25 m2 plots (11340 locations) with the corresponding geographical location were used. Besides, soil properties and wheat yield were measured at 36 randomly selected points on the field. Interpolation of parameters was predicted with the best semi-variogram model using kriging, inverse distance weighted (IDW), and cokriging methods. Results: Results showed that wheat yield varied from 2 to 10.08 tons per hectare. Cokriging with cofactor of kernel weight interpolator had more accuracy compared to the combine default interpolator (kriging). A logical, linear correlation was found between different parameters. The best variogram model for pH, OC, and ρb was exponential, for EC, TNV, SP, soil silt and clay percentage was spherical, and for soil, percentage sand was Gaussian model. Data of soil sand, silt, and clay percentage, EC, TNV, and SP had strong spatial structure, and soil pH, OC, and ρb had moderate spatial structure. The best interpolation method for soil pH, EC, sand and silt percentage was kriging method; while, for TNV, SP, OC, ρb, and clay percentage was IDW. Conclusion: There was a close relationship between wheat yield variation and changes in the soil properties. Soil properties and wheat yield distribution maps provided valuable information which could be used for wheat yield improvement in precision agriculture.