scholarly journals Application of the Modified Shepard’s Method (MSM): A Case Study with the Interpolation of Neogene Reservoir Variables in Northern Croatia

Stats ◽  
2020 ◽  
Vol 3 (1) ◽  
pp. 68-83 ◽  
Author(s):  
Tomislav Malvić ◽  
Josip Ivšinović ◽  
Josipa Velić ◽  
Jasenka Sremac ◽  
Uroš Barudžija
Keyword(s):  
Cross Validation ◽  
Statistical Properties ◽  
Inverse Distance Weighting ◽  
Geological Mapping ◽  
Interpolation Methods ◽  
Geometrical Features ◽  
Distance Weighting ◽  
Northern Croatia ◽  
Inverse Distance

Interpolation is a procedure that depends on the spatial and/or statistical properties of the analysed variable(s). It is a particularly challenging task for small datasets, such as in those with less than 20 points of data. This problem is common in subsurface geological mapping, i.e., in cases where the data is taken solely from wells. Successful solutions of such mapping problems depend on interpolation methods designed primarily for small datasets and the datasets themselves. Here, we compare two methods, Inverse Distance Weighting and the Modified Shepard’s Method, and apply them to three variables (porosity, permeability, and thickness) measured in the Neogene sandstone hydrocarbon reservoirs (northern Croatia). The results show that cross-validation itself will not provide appropriate map selection, but, in combination with geometrical features, it can help experts eliminate the solutions with low-probable structures/shapes. The Golden Software licensed program Surfer 15 was used for the interpolations in this study.

scholarly journals Application of Modified Shepard's Method (MSM) case study with interpolation of Neogene reservoirs variables in the Northern Croatia

2019 ◽  
Author(s):  
Tomislav Malvić ◽  
Josip Ivšinović ◽  
Josipa Velić ◽  
Jasenka Sremac ◽  
Uroš Barudžija
Keyword(s):  
Cross Validation ◽  
Statistical Properties ◽  
Inverse Distance Weighting ◽  
Geological Mapping ◽  
Interpolation Methods ◽  
Geometrical Features ◽  
Distance Weighting ◽  
Northern Croatia ◽  
Inverse Distance

Interpolation is procedure that depends on spatial and/or statistical properties of analysed variable(s). It is special challenging task for data that included low number of samples, like dataset with less than 20 data. This problem is especially emphasized in the subsurface geological mapping, i.e. in the cases where data are taken solely from wells. Successful solutions of such mapping problems ask for knowledge about interpolation methods designed primarily for small datasets and dataset itself. Here are compared two methods, namely Inverse Distance Weighting and Modified Shepard’s Method, applied for three variables (porosity, permeability, thickness) measured in the Neogene sandstone hydrocarbon reservoirs (Northern Croatia). The results showed that pure cross-validation is not enough condition for appropriate map selection, but also geometrical features need to be considered, for datasets with less than 20 points.

scholarly journals Interpolation of Small Datasets in the Sandstone Hydrocarbon Reservoirs, Case Study of the Sava Depression, Croatia

Geosciences ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 201 ◽  
Author(s):  
Tomislav Malvić ◽  
Josip Ivšinović ◽  
Josipa Velić ◽  
Rajna Rajić
Keyword(s):  
Inverse Distance Weighting ◽  
Challenging Problem ◽  
Interpolation Methods ◽  
Distance Weighting ◽  
Hydrocarbon Fields ◽  
Northern Croatia ◽  
First Time ◽  
Inverse Distance ◽  
Selection Of

The interpolation of small datasets is challenging problem regarding the selection of interpolation methods and type of datasets. Here, for such analysis, the analysed data was taken in two hydrocarbon fields (“A” and “B”), located in the western part of the Sava Depression (in Northern Croatia). The selected reservoirs “L” (in the “A” Field) and “K” (“B”) are of Lower Pontian (Upper Miocene) age and belong to the Kloštar-Ivanić Formation. Due to strong tectonics, there are numerous tectonic blocks, each sampled with only a few wells. We selected two variables for interpolation—reservoirs permeabilities and injected volumes of field water. The following interpolation methods are described, compared and applied: Nearest Neighbourhood, Natural Neighbour (for the first time in the Sava Depression) and Inverse Distance Weighting. The last one has been recommended as the most appropriate in this study. Also, the presented research can be repeated in similar clastic environments at the same level hydrocarbon of exploration.

scholarly journals Assessment of Ordinary Kriging and Inverse Distance Weighting Methods for Modeling Chromium and Cadmium Soil Pollution in E-Waste Sites in Douala, Cameroon

2020 ◽  
Vol 10 (26) ◽  
pp. 200605
Author(s):  
Romaric Emmanuel Ouabo ◽  
Abimbola Y. Sangodoyin ◽  
Mary B. Ogundiran
Keyword(s):  
Urban Areas ◽  
Ordinary Kriging ◽  
Cross Validation ◽  
Interpolation Method ◽  
Waste Recycling ◽  
Inverse Distance Weighting ◽  
P Value ◽  
Interpolation Methods ◽  
Distance Weighting ◽  
Inverse Distance

Background. Several studies have demonstrated that chromium (Cr) and cadmium (Cd) have adverse impacts on the environment and human health. These elements are present in electronic waste (e-waste) recycling sites. Several interpolation methods have been used to evaluate geographical impacts on humans and the environment. Objectives. The aim of the present paper is to compare the accuracy of inverse distance weighting (IDW) and ordinary kriging (OK) in topsoil analysis of e-waste recycling sites in Douala, Cameroon. Methods. Selecting the proper spatial interpolation method is crucial for carrying out surface analysis. Ordinary kriging and IDW are interpolation methods used for spatial analysis and surface mapping. Two sets of samples were used and compared. The performances of interpolation methods were evaluated and compared using cross-validation. Results. The results showed that the OK method performed better than IDW prediction for the spatial distribution of Cr, but the two interpolation methods had the same result for Cd (in the first set of samples). Results from Kolmogorov-Smirnov and Shapiro-Wilk tests showed that the data were normally distributed in the study area. The p value (0.302 and 0.773) was greater than 0.05 for Cr and for Cd (0.267 and 0.712). In the second set of samples, the OK method results (for Cd and Cr) were greatly diminished and the concentrations dropped, looking more like an average on the maps. However, the IDW interpolation gave a better representation of the concentration of Cd and Cr on the maps of the study area. For the second set of samples, OK and IDW for Cd and Cr had more similar results, especially in terms of root mean square error (RMSE). Conclusions. Many parameters were better identified from the RMSE statistic obtained from cross-validation after exhaustive testing. Inverse distance weighting appeared more adequate in limited urban areas. Competing Interests. The authors declare no competing financial interests

scholarly journals Interpolation of Small Datasets in the Sandstone Hydrocarbon Reservoirs, Case Study from the Sava Depression, Croatia

2019 ◽  
Author(s):  
Tomislav Malvić ◽  
Josip Ivšinović ◽  
Josipa Velić ◽  
Rajna Rajić
Keyword(s):  
Laboratory Tests ◽  
Secondary Phase ◽  
Inverse Distance Weighting ◽  
Tectonic Block ◽  
Interpolation Methods ◽  
Distance Weighting ◽  
Hydrocarbon Fields ◽  
First Time ◽  
Inverse Distance

Here are analysed data taken in two hydrocarbon fields ("A" and "B"), located in the western part of Sava Depression (North Croatia). They are in the secondary phase of production. The selected reservoirs "L" (in the “A” Field) and "K" (“B”) are of the Lower Pontian (Upper Miocene) age and belong to Kloštar-Ivanić Formation. Due to strong tectonics, there are numerous tectonic block, relatively rarely sampled with well and laboratory tests. Here are selected two variables for interpolation - reservoirs permeabilities and the injected volumes of field water. The following interpolation methods are described, compared and applied: Nearest Neighbourhood, Natural Neighbour (the first time in the Sava Depression) and Inverse Distance Weighting. The last one has been proven as the most appropriate for datasets with size lower than 20 points.

scholarly journals Analysis of Mapping Techniques for Mountain Precipitation: A Case Study of Alpine Region, Austria

2018 ◽  
Vol 8 (4) ◽  
pp. 3213-3217
Author(s):  
A. N. Laghari ◽  
G. D. Walasai ◽  
D. K. Bangwar ◽  
A. H. Memon ◽  
A. H. Shaikh
Keyword(s):  
Cross Validation ◽  
Geographical Information ◽  
Missing Information ◽  
Local Data ◽  
Consistency Test ◽  
Distance Weighting ◽  
Map Generation ◽  
Mapping Techniques ◽  
Inverse Distance

Truly representative precipitation map generation of mountain regions is a difficult task. Due to poor gauge representativity, complex topography and uneven density factors make the generation of representative precipitation maps a very difficult task. To generate representative precipitation maps, this study focused on analyzing four different mapping techniques: ordinary kriging, spline technique (SP), inverse distance weighting (IDW) and regression kriging (RK). The generated maps are assessed through cross-validation statistics, spatial cross-consistency test and by water balance approach. The largest prediction error is produced by techniques missing information on co-variables. The ME and RMSE values show that IDW and SP are the most biased techniques. The RK technique produced the best model results with 1.38mm and 72.36mm ME and RMSE values respectively. The comparative analysis proves that RK model can produce reasonably accurate values at poorly gauged areas, where geographical information compensated the poor availability of local data.

scholarly journals Spatial interpolation methods for estimating monthly rainfall distribution in Thailand

2021 ◽  
Author(s):  
Nawinda Chutsagulprom ◽  
Kuntalee Chaisee ◽  
Ben Wongsaijai ◽  
Papangkorn Inkeaw ◽  
Chalump Oonariya
Keyword(s):  
Spatial Interpolation ◽  
Cross Validation ◽  
Monthly Rainfall ◽  
Rainfall Distribution ◽  
Mathematical Concepts ◽  
Interpolation Methods ◽  
Distance Weighting ◽  
Inverse Distance ◽  
Fold Cross Validation ◽  
Spatial Interpolation Methods

Abstract Spatial interpolation methods usually differ in their underlying mathematical concepts, each with inherent advantages and drawbacks depending on the properties of data. This paper, therefore, aims to compare and evaluate the performances of well-established interpolation techniques for estimating monthly rainfall data in Thailand. The selected methods include the inverse distance-based method, multiple linear regression (MLR), artificial neural networks (ANN), and ordinary kriging (OK). The technique of searching nearest stations is additionally imposed for some aforementioned schemes. The k -fold cross-validation method is exploited to assess the efficiency of each method, then the metric scores, RMSE, and MAE are used for comparisons. The results suggest the ANN might be the least favorite as it underperforms in many folds. While the OK method provides the most accurate prediction, the inverse distance weighting (IDW), particularly inverse exponential weighting (IEW), and MLR are considerably comparative. Overall, IEW is plausible for monthly rainfall estimation of Thailand because it is less computationally expensive than the OK and its flexible computation.

scholarly journals Aiming for the Optimum: Examining Complex Relationships Between Sampling Regime, Sampling Density and Landscape Complexity to Accurately Model Resource Availability

2021 ◽  
Author(s):  
Ira L. Parsons ◽  
Melanie R. Boudreau ◽  
Brandi B. Karisch ◽  
Amanda E. Stone ◽  
Durham Norman ◽  
...  
Keyword(s):  
Landscape Heterogeneity ◽  
Inverse Distance Weighting ◽  
Universal Kriging ◽  
Systematic Sampling ◽  
Sampling Density ◽  
Interpolation Methods ◽  
Landscape Characteristics ◽  
Distance Weighting ◽  
Inverse Distance

Abstract Context Obtaining accurate maps of landscape features often requires intensive spatial sampling and interpolation. The data required to generate reliable interpolated maps varies with spatial scale and landscape heterogeneity. However, there has been no rigorous examination of sampling density relative to landscape characteristics and interpolation methods.ObjectivesOur objective was to characterize the 3-way relationship among sampling density, interpolation method, and landscape heterogeneity on interpolation accuracy in simulated and in situ landscapes. MethodsWe simulated landscapes of variable heterogeneity and sampled at increasing densities using both systematic and random strategies. We applied each of three local interpolation methods: Inverse Distance Weighting, Universal Kriging, and Nearest Neighbor — to the sampled data and estimated accuracy (R2) between interpolated surfaces and the original surface. Finally, we applied these analyses to in situ data, using a normalized difference vegetation index raster collected from pasture with various resolutions.Results All interpolation methods and sampling strategies resulted in similar accuracy; however, low heterogeneity yielded the highest R2 values at high sampling densities. In situ results showed that Universal Kriging performed best with systematic sampling, and inverse distance weighting with random sampling. Heterogeneity decreased with resolution, which increased accuracy of all interpolation methods. Landscape heterogeneity had the greatest effect on accuracy.ConclusionsHeterogeneity of the original landscape is the most significant factor in determining the accuracy of interpolated maps. There is a need to create structured tools to aid in determining sampling design most appropriate for interpolation methods across landscapes of various heterogeneity.

scholarly journals COMPARISON THE PERFORMANCE OF ORDINARY KRIGING AND INVERSE DISTANCE WEIGHTING METHODS FOR MAPPING NICKEL LATERITE PROPERTIES

KURVATEK ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 57-67
Author(s):  
Hendro Purnomo
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Ordinary Kriging ◽  
Cross Validation ◽  
Inverse Distance Weighting ◽  
Mean Square ◽  
Nickel Laterite ◽  
Distance Weighting ◽  
Inverse Distance ◽  
Weighting Methods

Pemilihan metode interpolasi yang sesuai untuk memprediksi kadar bijih pada lokasi yang tidak tersampel merupakan hal yang penting untuk pemetaan sebaran anomaly kadar dan estimasi sumberdaya. Tujuan penelitian ini dilakukan untuk mengevaluasi hasil estimasi metode ordinary kriging (OK) dan inverse distance weighting (IDW) dalam pemetaan distribusi dan potensi sumberdaya nikel (Ni) dan cobalt (Co) pada zona limonit dan saprolit. Dalam penelitian ini digunakan aplikasi perangkat lunak ArcGis 10.2 dengan Geostatistical Analyst Extention untuk menganalisis data. Untuk pemilihan model variogram dan interpolasi yang terbaik digunakan nilai parameter root mean square error (RMSE) yang diperoleh dari prosedur cross validation. Fitting variogram eksperimental dilakukan dengan model spherical, exponential dan gaussian, sedangkan pemilihan model variogram terbaik dilakukan berdasarkan nilai RMSE terkecil. Pada zona limonit, metode IDW dengan power 2 mempunyai performa terbaik untuk kadar Ni dan Co, sedangkan prosedur OK menghasilkan performa terbaik untuk  ketebalan. Pada zona saprolit metode IDW dengan power 5 mempunyai performa terbaik untuk kadar Ni dan IDW power 1 menunjukkan performa terbaik pada kadar co dan ketebalan. Hasil interpolasi menunjukkan bahwa distribusi nikel dan potensi tambahan sumberdaya pada zona limonit dan saprolit masih terbuka ke arah timur laut dan barat daya daerah penelitian.Kata Kunci: ArcGIS, cross validation, IDW, OK, RMSE

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