Pitney Bowes MapInfo Vertical Mapper - Manual (Page 49)

Chapter 3: Creating Grids Using Interpolation
User Guide
47
Understanding Kriging Techniques
Vertical Mapper provides three variations of kriging interpolation that you can apply in two forms,
although they all operate in a similar way. The three methods are ordinary kriging, simple kriging,
and universal kriging, and all three of these techniques can be applied in one of two forms: punctual
or block.
Ordinary Kriging
This method assumes that the data has a stationary variance and a non-stationary mean value
within the search radius. Ordinary kriging is highly reliable and is recommended for most data sets.
Simple Kriging
This method assumes that the data has a stationary variance and a stationary mean value and
requires you to enter the mean value.
Universal Kriging
This method represents a true geostatistical approach to interpolating a trend surface of an area.
The surface representing the drift of the data is built first, then the residuals for this surface are
calculated. With universal kriging, you can set the polynomial expression used to represent the drift
surface. The most general form of this expression is:
F(x, y) = a
20
* x 2 + a
11
* xy + a
02
* y 2 + a
10
* x + a
01
* y + a
00,
where a
00
is always present but rarely set to zero in advance of the calculation. However, the other
coefficients can also be set to zero. The recommended setting is a first degree polynomial which will
avoid unpredictable behaviour at the outer margins of the data.
Punctual and Block Kriging
All three kriging interpolation techniques can be applied in one of two forms: punctual or block. The
most commonly used is punctual kriging (the default), which estimates the value at a given point.
Block kriging uses the estimate of the average expected value at a given location (such as a “block”)
around a point. Block kriging provides better variance estimation and has the effect of smoothing
interpolated results.
Using the Kriging Interpolation Technique
There are four basic steps in the kriging process:
• aggregate the data
• choose the kriging parameters
• complete the variogram analysis
• perform the kriging estimation