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geoscene3d:interpolation:2dinterpolation_krigingwithdatatransformations [2020/03/23 14:20] – rebecca130301_gmail.comgeoscene3d:interpolation:2dinterpolation_krigingwithdatatransformations [2020/11/12 11:32] (current) – external edit 127.0.0.1
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 This tutorial describes how to use the data transformation features associated with Kriging in GeoScene3D. The tutorial does not explain the mathematical foundation, only the workflow in GeoScene3d. This tutorial describes how to use the data transformation features associated with Kriging in GeoScene3D. The tutorial does not explain the mathematical foundation, only the workflow in GeoScene3d.
 +
 +For more information about basic interpolation and kriging, please look at this {{:geoscene3d:interpolation:basic_interpolation_gs3d.pdf|presentation.}}
  
 ====   ==== ====   ====
 +
  
 ==== Background ==== ==== Background ====
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 The Kriging method is based on Gaussian statistics. This means that it is assumed that the underlying data have a Gaussian distribution, a normal distribution, when performing calculating the variogram, performing the kriging, estimating the variance etc..\\ The Kriging method is based on Gaussian statistics. This means that it is assumed that the underlying data have a Gaussian distribution, a normal distribution, when performing calculating the variogram, performing the kriging, estimating the variance etc..\\
 +\\
 So, what do you do if your data have another distribution?\\ So, what do you do if your data have another distribution?\\
 \\ \\
-Examples could be:\\ +Examples could be: 
-· Chemical measurements. You have a contamination site, with a series of measurements of the concentration of a chemical compound. Such data would typically have a bi-modal distribution, with a large group of measurements (observations) having a very low value, and a separate set of observations having a very high value.\\ + 
-· Terrain surfaces with deep valleys: You have a terrain surface which is relatively smooth, but the area is crossed by deep valley structure, thus leading to a bi-modal data distribution of the elevation observations.\\ +  * Chemical measurements. You have a contamination site, with a series of measurements of the concentration of a chemical compound. Such data would typically have a bi-modal distribution, with a large group of measurements (observations) having a very low value, and a separate set of observations having a very high value. 
-\\ +  * Terrain surfaces with deep valleys: You have a terrain surface which is relatively smooth, but the area is crossed by deep valley structure, thus leading to a bi-modal data distribution of the elevation observations. 
-The answer is “data transformation”. You transform the data from “normal” space to a transformed space, where the data have a normal distribution, do the kriging, and then back transform the result.\\ + 
-\\ + \\ 
-One type of transformation is the log-transform, another is the Normal Score transform, which is part of the GSLIB library utilized by the program.\\ +The answer is “data transformation”. You transform the data from “normal” space to a transformed space, where the data have a normal distribution, do the kriging, and then back transform the result. \\  \\ 
-\\+One type of transformation is the log-transform, another is the Normal Score transform, which is part of the GSLIB library utilized by the program. \\  \\
 See separate documentation for the specific, mathematical details of each transformation. See separate documentation for the specific, mathematical details of each transformation.
  
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 Startup the interpolation wizard by using the mouse and right-clicking the point object node to be interpolated in the object manager. Startup the interpolation wizard by using the mouse and right-clicking the point object node to be interpolated in the object manager.
  
-\\ + \\ {{:tutorials:layermod:b114df8ce140eb633e665a3b64fc2168.png}}{{:tutorials:layermod:e575350890ccc04aa068a9df9031b026.png}} \\ <font inherit/inherit;;#3498db;;inherit>Figure 2. Open the Interpolation Wizard</font>
-{{:tutorials:layermod:b114df8ce140eb633e665a3b64fc2168.png}}{{:tutorials:layermod:e575350890ccc04aa068a9df9031b026.png}}\\ +
-<font inherit/inherit;;#3498db;;inherit>Figure 2. Open the Interpolation Wizard</font>+
  
-In the right-click menu, you now select “interpolation”. Step through the wizard as normal, until you reach the “Source Data” page.\\+In the right-click menu, you now select “interpolation”. Step through the wizard as normal, until you reach the “Source Data” page. \\  \\
 Press the “Get Data” button, to select the value to be interpolated. In the example here the value used to color the data points is selected. Press the “Get Data” button, to select the value to be interpolated. In the example here the value used to color the data points is selected.
  
-{{:tutorials:layermod:d07d975e5dc94db7f22b421b2f9fe079.png}}\\ +{{:tutorials:layermod:d07d975e5dc94db7f22b421b2f9fe079.png}} \\ <font inherit/inherit;;#3498db;;inherit>Figure 3 Select the value to be interpolated. Here the color value used for the XYZ points.</font>
-<font inherit/inherit;;#3498db;;inherit>Figure 3 Select the value to be interpolated. Here the color value used for the XYZ points.</font>+
  
-On the “Source Data” page, you have tools available for checking the distribution, the statistics, of your data.\\ +On the “Source Data” page, you have tools available for checking the distribution, the statistics, of your data. \\  \\ 
-Press the “Statistics…” button, to inspect the statistics of the selected value.\\ +Press the “Statistics…” button, to inspect the statistics of the selected value. \\
-\\+
 Note that if you have a large amount of data, it may take a while to process the statistics of the data. Note that if you have a large amount of data, it may take a while to process the statistics of the data.
  
-{{:tutorials:layermod:e9365723622958da22b3e95d99c4ddb0.png}}\\ +{{:tutorials:layermod:e9365723622958da22b3e95d99c4ddb0.png}} \\ <font inherit/inherit;;#3498db;;inherit>Figure 4. Distribution of chemical contaminant data. Clearly not Gaussian.</font>
-<font inherit/inherit;;#3498db;;inherit>Figure 4. Distribution of chemical contaminant data. Clearly not Gaussian.</font>+
  
-{{:tutorials:layermod:13a284b78471f767bc2fd537122233b3.png}}\\ +{{:tutorials:layermod:13a284b78471f767bc2fd537122233b3.png}} \\ <font inherit/inherit;;#3498db;;inherit>Figure 5. Select "Normal Score Transform" and press "Apply".</font>
-<font inherit/inherit;;#3498db;;inherit>Figure 5. Select "Normal Score Transform" and press "Apply".</font>+
  
-{{:tutorials:layermod:de0879ce8292ff6f929b56da2c3857e2.png}}\\ +{{:tutorials:layermod:de0879ce8292ff6f929b56da2c3857e2.png}} \\ <font inherit/inherit;;#3498db;;inherit>Figure 6. Data distribution after "Normal Score Transform" has been applied.</font>
-<font inherit/inherit;;#3498db;;inherit>Figure 6. Data distribution after "Normal Score Transform" has been applied.</font>+
  
-The statistics of the chemical contaminant, shown in Figure 4, is clearly not Gaussian. A large amount of the data values has very low concentrations of the chemical compound, while a significant amount has a very high concentration.\\ +The statistics of the chemical contaminant, shown in Figure 4, is clearly not Gaussian. A large amount of the data values has very low concentrations of the chemical compound, while a significant amount has a very high concentration. \\  \\ 
-\\ +To use kriging correctly on these data, we have to perform a data transformation. \\  \\ 
-To use kriging correctly on these data, we have to perform a data transformation.\\ +Close the Statistics window. \\  \\ 
-Close the Statistics window.\\ +Select the “Normal Score Transformation”, as shown in Figure 5. Now press “Apply” and the values are transformed into normal score space. \\  \\
-\\ +
-Select the “Normal Score Transformation”, as shown in Figure 5. Now press “Apply” and the values are transformed into normal score space.\\ +
-\\+
 Open the statistics window again to inspect the result, se Figure 6. The distribution of the transformed values now has a mean value of 0 and standard deviation (STD) of 1. A perfect Gaussian distribution. Open the statistics window again to inspect the result, se Figure 6. The distribution of the transformed values now has a mean value of 0 and standard deviation (STD) of 1. A perfect Gaussian distribution.
  
 ==== Step 2. ==== ==== Step 2. ====
  
-You now complete the rest of the Wizard as you would normally do, noting that the estimation of the variogram is particularly easy now, as you now that your data have STD of 1, which corresponds to the Sill value of your variogram.\\ +You now complete the rest of the Wizard as you would normally do, noting that the estimation of the variogram is particularly easy now, as you now that your data have STD of 1, which corresponds to the Sill value of your variogram. \\  \\ 
-\\ +The program automatically handles the back transform of the interpolated values to normal space from Normal score space, so you do not have to worry about that. \\  \\
-The program automatically handles the back transform of the interpolated values to normal space from Normal score space, so you do not have to worry about that.\\ +
-\\+
 Note: The variance grid constructed is an approximation, as the STD of the Kriging values are values in Normal Score Space. Note: The variance grid constructed is an approximation, as the STD of the Kriging values are values in Normal Score Space.
  
  

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