<< Click to Display Table of Contents >>

 

Variogram Theory Model

 

 

In fact, the γ(h) value of a variogram model is unknown. We have to estimate the γ(h) value with samples from an effective space and calculate a series of γ(h) values according to different h values. To date, the popular models in statistics are:

 

I. Spherical Model

The formula of Spherical Model is :

 

 

 

Where is the nugget constant, C+ is the Sill value, C is the structure variance, and a is the range. When =0 and C=1, this model is called Standard Spherical Model. The slope rate at the point of origin is 3C/2a, and the intersection between the Sill value and x-axis is 2a/3. The Spherical Model is the most common model in geostatistics.

 

II. Exponential Model

The formula of Exponential Model is :

       

           

Where h=3a, . It means when h=3a, , and the range of the Exponential Model is 3a. When =0 and C=1, the model is called Standard Exponential Model.

 

III. Gaussian Model

The formula of Gaussian Model is:

 

   

             

Where h=γ(h), .It means when h=, , the effective range of the Gaussian Model is. When =0 and C=1, the model is called Standard Gaussian Model.

 

 

Compared with the above three models, the Spherical Model has the smallest range, the Exponential Model has the biggest range, and the range of the Gaussian Model is in between. The Spherical and Exponential Models both have a tangent passing through the point of origin, but the Gaussian Model has no tangent.

 

 

 

©2017 Supergeo Technologies Inc. All rights reserved.