# What are advantages of multi-point statistics compared to variogram?

Variogram is simple but effective way to investigated the spatial variation in the variable of interest in the field being studied. However it has been reported that variogram cannot be considered as the most satisfactory model especially where there are curvature (e.g., permeable channels in reservoir engineering) in the medium being studied. That is different patterns could have more and less exact copy of the same variogram.
A suggestion for development an approach was multi-point statistics (geostatistics), in which for example, a training image, a 2D matrix template is being used for inference of spatial variation. It was shown in the literature that training images are useful to dictate the output the desired pattern honoring conditioning data and being based on stochastic approaches to satisfy statistical inferences.

• Questions:

Q2: How to obtain training images?
__Q2.1: How to generate training images using existing knowledge etc?
Q3: How about 3D and further dimensions?
Q3: What is the next stage after training image?

-
Any chance of some references to where 'it has been reported' or this stuff about training images? I'm not really sure what you are on about here. –  Spacedman Dec 4 '11 at 22:44
There are many works around in literature such as (Atkinson & Lloyd, Geostatistics for Environmental Applications:P142; and Multiple-point geostatistics: a quantitative vehicle for integrating geologic analogs into multiple reservoir models, Caers & Zhang, P6) –  Developer Dec 5 '11 at 2:42

Your questions are very broad, which makes it hard to give a to-the-point answer. I'll try and provide a few pointers from my own experience using multiple point geostatistics (snesim).

The advantage is that complex geological structures, which are hard to recreate using random field techniques such as indicator kriging, can be modeled.

Q2: How to obtain training images?

__Q2.1: How to generate training images using existing knowledge etc?

Some options:

• Expert knowledge (i.e. draw them by hand)
• Digitizing existing maps
• Using model output
• etc

What is most appropriate in your situation is hard to say.

Q3: How about 3D and further dimensions?

There is no reason for multiple dimensions not to work. Fitting a pattern to a multidimensional training image becomes more and more work as the number of possible patterns grows.

Q4: What is the next stage after training image?

No sure what you are asking for here.

In general, the greatest challenge in MP geostatistics is a) find a training image and b) match patterns in the observations to the training image in a meaningful manner.

-