- View SourceDear all,

I have three questions, as follows (supposed I have non-evenly

distributed point data)

1) is that true that stationarity of data is just a question of

scale?

If I make a search window too small, a mean of the data in this

window will be very different from global mean , so I have

non-stationarity.

If I make a search window large enough, a mean of the data in the

window will be close to the global mean, so I have stationarity.

Usually stationarity will be also checked through the form of

variogramm. Variogramms without sill are said to be from

non-stationary random process. Typical such are power variograms,

including a linear one. But if I take into account, that spherical

and exponential variograms are linear and gaussian model is parabolic

NEAR THE ORIGIN, it looks to me, as such variograms were just a part

of transition variograms (with a sill) near origin, so my region is

just not large enough to show stationarity of data. So should one use

exponential and gaussian variograms with a large range (larger as

size of the region) to fit experimental variogram without sill?

2) the next question is about modelling an anisotropy for kriging. If

I have very different variograms in different directions, I can

transform coordinates and calculate equivalent models with reduced

distances to deal with it.

The question is: why just not use different theoretical variograms for

different directions. If one builds an ordinary kriging system, one

could just pick up different variograms depending on the angle

between i-th and j-th point?

3) and the last question: should one use all data points for kriging

or restrict to the nearby of them? Isaaks&Srivastava vote for the

neighbourhood searching, and Peter Kitanidis in "Introduction to

Geostatistics" write:

Another motivation has been the estimate at x0 dependent only on

observations in its neighbourhoods, which is often a desirable

characteristic. However, the same objective can be achieved by using

all data with an appropriate variogram(such as the linear one) that

assigns vary small weights to observations at distant points. If the

weights corresponding to points near the border of the neighbourhood

are not small and the moving neighborhood method is applied in

contouring, the estimated surface will have discontinuities that are

unsightly as well as unreasonable, if they are the artifact of the

arbitrarily selection of a moving neighbourhood.

So - moving neighbourhood - is it good or bad ( beside of the question of

computational effectiveness)?

Thanx,

Konstantin.

Konstantin Malakhanov, wiss. Mitarbeiter/research engineer

IWW, RWTH Aachen

Tel. 0241-807343

Fax. 0241-8888348

E-Mail: kosta@...-aachen.de

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