## AI-GEOSTATS: Modeling anisotropy with GSTAT

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• Dear members of ai-geostats, I must apologize for posting such a ill-typed mail. I have edited a new one and hope this will be more readable. Thank you very
Message 1 of 1 , Dec 1, 2002
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Dear members of ai-geostats,

I must apologize for posting such a ill-typed mail.
I have edited a new one and hope this will be more readable.
Thank you very much for your patience to read this long post.

I am new in geostatistics and this is my first time to use GSTAT.
My knowledge realted to geostatistics came from Burrough's
"principles of GIS" and Issack's "Applied Geostatistics".
I have several questions about anisotropy modeling and
I would be very grateful if someone could help me.

I have an exhaustive dataset of 900*1000 grids with grid size 30 m
I want to use the GSTAT's unconditional simulation to generate random fields
that have similar spatial autocorrelation with my exhaustive dataset.
Here are my steps to generate such a random field:

1) log-transform my dataset since it is highly postively skewed.

2) Set the cutoff = 9000 and width = 30

3) Plot the omnidirectional experimental variogram and fit it.
It has three componets and can be fit by the following equation:
gamma (h) = 0.048 nug(0) + 0.324exp(1101)+ 0.086sph(247)

4) Plot directional experimental variograms of 36 directions with
angle tolerance 10 degree.
Here are the maximum partial range and partial sill for
different componets and total sill I found :

Direction P.Sill P.Sill Range P.Sill Range Total
Nug() Exp() Exp() Sph() Sph() Sill

70 0.068 0.322 1604 0.093 413 0.483
30 0.073 0.282 1398 0.111 464 0.467

110 0.066 0.354 1333 0.063 280 0.482
40 0.054 0.289 1318 0.113 357 0.457

80 0.044 0.348 1577 0.100 268 0.491

Here are the minimum partial range and partial
sill for different componets and total sill I found :

Direction P.Sill P.Sill Range P.Sill Range Total
Nug() Exp() Exp() Sph() Sph() Sill

170 0.040 0.323 726 0.066 170 0.430
170 0.040 0.323 726 0.066 170 0.430

30 0.073 0.282 1398 0.111 464 0.467
150 0.065 0.332 847 0.046 231 0.442

170 0.040 0.323 726 0.066 170 0.430

5) Perform unconditional simulation.

My questions are:

1) Is that make sense to log-transform my dataset? My intuition is that
since the result I get from a unconditional simulation is normal
distributed. So I shall provide a spatial information comes from
normal distributed dataset. Is my thougt correct?

2) The nugget varies with different orientations. How can this happen?
(the nugget is omnidirectional as far as I know)
Shall I use the nugget from omnidirectional experimental variogram or
the average nugget from different orientations for the simulation?

3) The orientation of the maximum range for exp() and sph() componets
is different.
Is it correct that I model them independently? for example:
0.322 Exp(1604, 70, 0.47) + 0.11 Sph(464, 30, 0.53)

4) For geometry anisotropy,
the maximum and minimum ranges seems not perpendicular exactly
to each other.
How shall I determine the anisotropy ratio?
(I use the ratio of maximum range and range perpendicular to it)

ai-geostats and gstat-info.
But I am afraid that I did not catch the points.
How shall I deal with the zonal anisotrpoy in combination with
geometry anisotropy?
Model it from total sill or model it for each componet independently?
for example: 0.032 Exp(133300, 20, 0.01) + 0.002 Sph(35700, 130, 0.01)

I have also attach my command file and hope you can correct me.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# gstat command file, Win32/Cygwin version 2.3.7 (12 July 2002)
# Fri Oct 18 04:41:45 2002
#
data(ln_zn_dummy): dummy, sk_mean=0, max=10;
variogram(ln_zn_dummy):
0.068 Nug(0) + 0.322 Exp(1604, 70, 0.47) + 0.11Sph(464, 30, 0.53) +
0.032 Exp(133300, 20, 0.01) + 0.002 Sph(35700, 130, 0.01);

method: gs; # Gaussian simulation instead of kriging
predictions(ln_zn_dummy): 'drandom';
variances(ln_zn_dummy): 'ran_van';
set nsim=100;

set cutoff = 9000;
set width = 30;
set fit = 2;
set output = 'errs.est';
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thanks very much for your help and reading such a long post.

Pei-Chun Chang

__________________________________________________

Pei-Chun Chang