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## [ai-geostats] kriging with trend

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• Dear list, Just a simple question... I m trying to produce a contour map from a structural surface. This surface is highly non-stationary (actuaally dips
Message 1 of 3 , Jan 5, 2006
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Dear list,

Just a simple question...

I'm trying to produce a contour map from a structural surface. This
surface is highly non-stationary (actuaally dips towards NW)
I wolud like to know which could be the best solution for getting a
reliabel map:

1) Fit a plyonomial surface to the sample values, which is used as a
drift. Substract the drift from the observations to get the residuals.
Estimate the variogram of the residuals (now the residual variable is
stationary). Perform OK on the residuals. Add the polynomial surface to
the residuals to get the interpolated surface.

2) Compute variograms from the observations. Use universal kriging to
get the interpolated surface.

Thank you

Oriol
--

______________________________________

Oriol Falivene
ofaliven@...
http://www.ub.es/ggac

tel. (+34) 93 4021373
fax (+34) 93 4021340

Fac. de Geologia,
Univ. de Barcelona
• Dear Oriol Falivene, If you could assume a linear (or polynomial trend) for the dip, the situation you are talking about, is the classical situation for the
Message 2 of 3 , Jan 5, 2006
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Dear Oriol Falivene,

If you could assume a linear (or polynomial trend) for the dip, the situation
you are talking about, is the classical situation for the use of intrinsic
random functions, IRKk-kriging and generalized covariances or generalized
variograms. The theory is quite good explained in the thick standard books
on Geostatistics such as that of Cressie or of Chiles and Delfiner. In
pratice it is quite difficult to actually estimate the generalized variograms
and to find good software for that.

Can anyone hint me and Oriol to good software for IRK-k kriging, especially
regarding the estimation and modelling of the generalised variograms? The
IRKk/Universal kriging is present everywhere, but the modelling...?

In case of nonpolynomial trend, the estimation of the variogram gets even more
tricky.
> I wolud like to know which could be the best solution for getting a
> reliabel map:
> 1) Fit a plyonomial surface to the sample values, which is used as a
> ...
1) is wrong, since removing the trend removes the assumption of stationarity,
which often also results in strange behavior of the variogram (e.g. dropping
for long distances again)

2) is not strictly wrong, however whenever a trend is really present, you can
not fit a ordinary variogram model, due to a quadratic increase in the
variogramm. You will need a generalized variogram model and than we are back
at IRFk-kriging.

Best regards,
Gerald v.d. Boogaart

Am Donnerstag, 5. Januar 2006 10:57 schrieb Oriol Falivene:
> Dear list,
>
> Just a simple question...
>
> I'm trying to produce a contour map from a structural surface. This
> surface is highly non-stationary (actuaally dips towards NW)
> I wolud like to know which could be the best solution for getting a
> reliabel map:
>
> 1) Fit a plyonomial surface to the sample values, which is used as a
> drift. Substract the drift from the observations to get the residuals.
> Estimate the variogram of the residuals (now the residual variable is
> stationary). Perform OK on the residuals. Add the polynomial surface to
> the residuals to get the interpolated surface.
>
> 2) Compute variograms from the observations. Use universal kriging to
> get the interpolated surface.
>
> Thank you
>
> Oriol
> --
>
>
>
> ______________________________________
>
> Oriol Falivene
> ofaliven@...
> http://www.ub.es/ggac
>
> tel. (+34) 93 4021373
> fax (+34) 93 4021340
>
> Fac. de Geologia,
> Univ. de Barcelona

--
-------------------------------------------------
Prof. Dr. K. Gerald v.d. Boogaart
Professor als Juniorprofessor fuer Statistik
http://www.math-inf.uni-greifswald.de/statistik/

office: Franz-Mehring-Str. 48, 1.Etage rechts
e-mail: Gerald.Boogaart@...
phone: 00+49 (0)3834/86-4621
fax: 00+49 (0)89-1488-293932 (Faxmail)
fax: 00+49 (0)3834/86-4615 (Institut)

paper-mail:
Ernst-Moritz-Arndt-Universitaet Greifswald
Institut f�r Mathematik und Informatik
Jahnstr. 15a
17487 Greifswald
Germany
--------------------------------------------------
• Oriol If you can get a semi-variogram from the observations which does not contain a parabolic upturn (diagnostic of polynomial type trend) then your trend is
Message 3 of 3 , Jan 5, 2006
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Oriol

If you can get a semi-variogram from the observations which does not contain a parabolic upturn (diagnostic of polynomial type trend) then your trend is weak enough to ignore.

You can download a free tutorial on dealing with polynomial type trend at http://geoecosse.bzland.com/softwares

Isobel

Oriol Falivene <oriolfalivene@...> wrote:
Dear list,

Just a simple question...

I'm trying to produce a contour map from a structural surface. This
surface is highly non-stationary (actuaally dips towards NW)
I wolud like to know which could be the best solution for getting a
reliabel map:

1) Fit a plyonomial surface to the sample values, which is used as a
drift. Substract the drift from the observations to get the residuals.
Estimate the variogram of the residuals (now the residual variable is
stationary). Perform OK on the residuals. Add the polynomial surface to
the residuals to get the interpolated surface.

2) Compute variograms from the observations. Use universal kriging to
get the interpolated surface.

Thank you

Oriol
--

______________________________________

Oriol Falivene
ofaliven@...
http://www.ub.es/ggac

tel. (+34) 93 4021373
fax (+34) 93 4021340

Fac. de Geologia,
Univ. de Barcelona

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