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• GEOSTATS: [Q]: 1) stationarity 2) anisothropy 3) neighb.search

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• Dear 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
Message 1 of 1 , Apr 21, 1997
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Dear 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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