Application of the Modified Shepard’s Method (MSM): A Case Study with the Interpolation of Neogene Reservoir Variables in Northern Croatia
Abstract
:1. Introduction
2. Geological Settings of the Analysed Field “B” (Sava Depression, Northern Croatia)
3. Basics of the Applied Interpolation Methods
3.1. Inverse Distance Weighting (IDW)
3.2. Modified Shepard’s Method (MSM)
3.3. CrossValidation (CV)
4. Interpolation Results in Reservoir “K” for Variables of Porosity, Thickness and Permeability
5. Discussion
6. Conclusions
 The MSM could be recommended for subsurface geological mapping of Neogene deposits in northern Croatia;
 This method is valid for datasets smaller than 20 measured values, i.e., for the early exploration phase of hydrocarbon reservoirs or the later development phase when the number of measurements of a selected property is small, but quick insight in the spatial distribution of such variables is necessary;
 The selected variables could be porosity, permeability and thickness, measured in Neogene lithostratigraphic units by laboratory analysed well data (cores) or interpreted logs;
 The interpreters need to be aware of: (a) the IDW method resulted in the lowest crossvalidation of all applied methods without a spatial model (variogram), i.e., namely the Nearest neighbourhood and the Natural neighbour, (b) the MSM interpolation eliminated all the unwanted geological features and did not result in a crossvalidation 250 % higher than in the IDW, for the same variable.
 Based on the visual (geometric) criteria, the sets with less than five measured points are too small for interpolation (using the IDW or MSM methods), and they are only appropriate for zonal estimation.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Description  No Data  Min  Max  Mean 

Porosity  19  0.217  0.315  0.232 
Permeability (10^{−9} m^{2})  18  29.6  121.2  85.7 
Thickness (m)  14  1  24  7.7 
Well’s No.  Surface X  Surface Y  Porosity (Parts of Unit)  Thickness (m)  Permeability (mD) 

J101  6,421,096  5,028,877  0.217  1  121.2 
J120  6,420,658  5,029,068  0.272  15.7  29.6 
J161  6,420,957  5,028,870  0.217  3  29.6 
J162  6,421,034  5,028,593  0.217  6.5  121.2 
J167  6,420,529  5,028,674  0.217  14.8  121.2 
J168  6,420,699  5,028,475  0.315  1  121.2 
J169  6,420,724  5,028,825  0.217  18.4  121.2 
J170  6,420,349  5,028,926  0.223  7  29.6 
J174  6,421,298  5,028,863  0.217  1.1  29.6 
J175  6,420,475  5,029,136  0.223  3.2  121.1 
J158  6,420,303  5,028,910  0.223  7.3  29.6 
J171  6,420,576  5,028,970  0.223  24  29.6 
J172  6,420,928  5,029,147  0.223  0.5  29.6 
J102  6,421,208  5,028,926  0.217  121.2  
J148  6,421,126  5,028,437  0.217  
J149  6,420,959  5,028,501  0.217  121.2  
J166  6,420,771  5,028,650  0.217  121.2  
J25  6,420,546  5,028,460  0.315  3.8  121.2 
J173  6,420,539  5,028,382  0.217  121.2 
Description  No Data  CrossValidation  

Inverse Distance (IDW)  Modified Shepard’s Method (MSM)  
Porosity  19  0.00119  0.00345 
Permeability  18  480.8  516.1 
Thickness  14  40.7  60.5 
Number of Data  Applicability of Interpolation Method  

Inverse Distance Weighting  Nearest Neighbourhood  Natural Neighbour  
1–5  Yes  Yes  No 
6–10  Yes  Yes  Yes 
11–19  Yes  Yes  Yes 
Number of Data  Applicability of Interpolation Method  

Inverse Distance Weighting  Modified Shepard’s Method  
Criteria 


5–20  Yes  Yes 
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Malvić, T.; Ivšinović, J.; Velić, J.; Sremac, J.; Barudžija, U. Application of the Modified Shepard’s Method (MSM): A Case Study with the Interpolation of Neogene Reservoir Variables in Northern Croatia. Stats 2020, 3, 6883. https://doi.org/10.3390/stats3010007
Malvić T, Ivšinović J, Velić J, Sremac J, Barudžija U. Application of the Modified Shepard’s Method (MSM): A Case Study with the Interpolation of Neogene Reservoir Variables in Northern Croatia. Stats. 2020; 3(1):6883. https://doi.org/10.3390/stats3010007
Chicago/Turabian StyleMalvić, Tomislav, Josip Ivšinović, Josipa Velić, Jasenka Sremac, and Uroš Barudžija. 2020. "Application of the Modified Shepard’s Method (MSM): A Case Study with the Interpolation of Neogene Reservoir Variables in Northern Croatia" Stats 3, no. 1: 6883. https://doi.org/10.3390/stats3010007