## [ai-geostats] modelling trend and kriging type

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• Dear ai-geostats members When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal
Message 1 of 10 , Jun 30, 2005
Dear ai-geostats members

When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal kriging, kriging with a trend, regression kriging etc).
If this is the case, does one should use the same type of kriging or different depending on modeling the trend using coordinates of target variable or using other (namely, secondary or auxillary) variables such as elevation or topography ? That is , are there a dinstinction depending on the type of variables to model the trend while kriging?

Best regards
Recep

Yahoo! kullaniyor musunuz?
http://tr.mail.yahoo.com
• ... I believe not. There s a fourth term, kriging with external drift , which also is the same, in my view. Some people may like to distinguish the case where
Message 2 of 10 , Jun 30, 2005
Recep kantarci wrote:
> Dear ai-geostats members
>
> When the data used has a trend, it is needed to model trend and in this
> case there exists various types of kriging to apply (universal kriging,
> kriging with a trend, regression kriging etc).
> If this is the case, does one should use the same type of kriging or
> different depending on modeling the trend using coordinates of target
> variable or using other (namely, secondary or auxillary) variables such
> as elevation or topography ? That is , are there a dinstinction
> depending on the type of variables to model the trend while kriging?
>
I believe not. There's a fourth term, "kriging with external drift",
which also is the same, in my view. Some people may like to distinguish
the case where external variables are (powers of) coordinates or not,
but mathematically it's all identical.

If we were to choose a name now, maybe I would prefer "regression
kriging", but being the (newest) fourth name for an old technique, I
don't like it. We also stick to "simple" and "ordinary" kriging.

There's also the other issue of doing regression and
residual kriging separately and adding the results, which may be
coined regression kriging.
--
Edzer
• Dear Recep, I don t think the type of variable has any impact on the choice of the detrending algorithm. There is indeed a whole collection of methods and one
Message 3 of 10 , Jun 30, 2005
Dear Recep,

I don't think the type of variable has any impact on the choice of the
detrending algorithm. There is indeed a whole collection of methods and
one can also cite the various methods in which the trend is modelled by
neural networks (e.g. Kanevski's NNRK Neural Network Residual Kriging).
NN can be very useful for complex detrending but less, in my eyes at
least, if you want to understand the mathematical/physical expression of
your drift. If you do care, then I would propose to use more simple
polynomial functions that may be more easy to understand when analysing
the drift.

You may find the following report useful

Hengl, T., Heuvelink, G.B.M. and Stein, A., 2003. Comparison of kriging
with external drift and regression-kriging. Technical report,
International Institute for Geo-information Science and Earth
Observation (ITC), Enschede, pp. 18.
http://www.itc.nl/library/Papers_2003/misca/hengl_comparison.pdf

The first author has also on the web a practical guide to
regression-kriging explaining how to do it with various software. See
http://hengl.pfos.hr/RKguide.php

Hope this helps,

Gregoire

-----Original Message-----
From: Recep kantarci [mailto:recep_kantarci_1978@...]
Sent: 30 June 2005 15:39
To: ai-geostats@...
Subject: [ai-geostats] modelling trend and kriging type

Dear ai-geostats members

When the data used has a trend, it is needed to model trend and in this
case there exists various types of kriging to apply (universal kriging,
kriging with a trend, regression kriging etc).
If this is the case, does one should use the same type of kriging or
different depending on modeling the trend using coordinates of target
variable or using other (namely, secondary or auxillary) variables such
as elevation or topography ? That is , are there a dinstinction
depending on the type of variables to model the trend while kriging?

Best regards
Recep

Yahoo! kullaniyor musunuz?
Yahoo! Posta'da
http://tr.mail.yahoo.com
• To add to the excellent comments by Edzer and Gregoire, 1. Universal kriging = kriging with a trend. The second terminology has been proposed by Andre Journel
Message 4 of 10 , Jun 30, 2005

1. Universal kriging = kriging with a trend. The second terminology has been proposed by Andre
Journel who felt that the term "universal" was vague and misleadingly "ambitious".

2. Kriging with an external drift (KED) is mathematically the same as universal kriging (UK). Secondary variables
are simply replacing the spatial coordinates used in UK.

3. Regression kriging denotes all the techniques where the trend is modeled outside the kriging algorithm.
There are various methods that can be used to model that trend, ranging from linear regression
to neural networks. Kriging is used to interpolate the residuals. In practice these techniques have more
flexibility than universal kriging in term of modeling the trend: multiple variables either categorical or
continuous can be incorporated easily and many sofwtare are available for this trend modeling.
The only limitation is that the trend is modeled globally (i.e. the regression coefficients are constant
in space) while in KED the coefficients are reestimated within each search window.

Cheers,

Pierre

Pierre Goovaerts

Chief Scientist at Biomedware

516 North State Street

Ann Arbor, MI 48104

Voice: (734) 913-1098
Fax: (734) 913-2201

http://home.comcast.net/~goovaerts/

-----Original Message-----
From: Recep kantarci [mailto:recep_kantarci_1978@...]
Sent: Thu 6/30/2005 9:38 AM
To: ai-geostats@...
Cc:
Subject: [ai-geostats] modelling trend and kriging type

Dear ai-geostats members

When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal kriging, kriging with a trend, regression kriging etc).
If this is the case, does one should use the same type of kriging or different depending on modeling the trend using coordinates of target variable or using other (namely, secondary or auxillary) variables such as elevation or topography ? That is , are there a dinstinction depending on the type of variables to model the trend while kriging?

Best regards
Recep

_____

Yahoo! kullaniyor musunuz?
http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>
• Dear AI-list, in which context KED is mostly used? I have found examples of this methodology in the context of soil science and climatology: Bourennane, H.,
Message 5 of 10 , Jul 1, 2005
Dear AI-list,

in which context KED is mostly used? I have found examples of this methodology in the context of soil science and climatology:

Bourennane, H., King, D. and Couturier, A., 2000. Comparison of kriging with external drift and simple linear regression for predicting soil horizon thickness with different sample densities: Geoderma, v. 97, p. 255-271.

Bourennane, H. and King, D., 2003. Using multiple external drifts to estimate a soil variable: Geoderma, v. 114, p. 1-18.

Goovaerts, P., 1999. Using elevation to aid the geostatistical mapping of rainfall erosivity: Catena, v. 34, p. 227-242.

Hudson, G. and Wackernagel, H., 1994. Mapping temperature using kriging with external drift: theory and an example from Scotland: International Journal of Climatology, v. 14, p. 77-91.

Martinez-Cob, A. and Cuenca, R.H., 1992. Influence of elevation on regional evapotranspiration using multivariate geostatistics for various climatic regimes in Oregon. Journal of Hydrology 136, 353–380.

Are there other interesting references for this methodology in the same or other application fields?

Best wishes,
___________________________________________________

Els Verfaillie, PhD student
Renard Centre of Marine Geology - Ghent University
Krijgslaan 281-S8
B-9000 Gent - Belgium
tel: +32-9-2644573 fax: +32-9-2644967
e-mail: Els.Verfaillie@...
http://www.rcmg.ugent.be/
___________________________________________________

-----Original Message-----
From: Pierre Goovaerts [mailto:Goovaerts@...]
Sent: donderdag 30 juni 2005 16:54
To: Recep kantarci; ai-geostats@...
Subject: RE: [ai-geostats] modelling trend and kriging type

1. Universal kriging = kriging with a trend. The second terminology has been proposed by Andre
Journel who felt that the term "universal" was vague and misleadingly "ambitious".

2. Kriging with an external drift (KED) is mathematically the same as universal kriging (UK). Secondary variables
are simply replacing the spatial coordinates used in UK.

3. Regression kriging denotes all the techniques where the trend is modeled outside the kriging algorithm.
There are various methods that can be used to model that trend, ranging from linear regression
to neural networks. Kriging is used to interpolate the residuals. In practice these techniques have more
flexibility than universal kriging in term of modeling the trend: multiple variables either categorical or
continuous can be incorporated easily and many sofwtare are available for this trend modeling.
The only limitation is that the trend is modeled globally (i.e. the regression coefficients are constant
in space) while in KED the coefficients are reestimated within each search window.

Cheers,

Pierre

Pierre Goovaerts

Chief Scientist at Biomedware

516 North State Street

Ann Arbor, MI 48104

Voice: (734) 913-1098
Fax: (734) 913-2201

http://home.comcast.net/~goovaerts/

-----Original Message-----
From: Recep kantarci [mailto:recep_kantarci_1978@...]
Sent: Thu 6/30/2005 9:38 AM
To: ai-geostats@...
Cc:
Subject: [ai-geostats] modelling trend and kriging type

Dear ai-geostats members

When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal kriging, kriging with a trend, regression kriging etc).
If this is the case, does one should use the same type of kriging or different depending on modeling the trend using coordinates of target variable or using other (namely, secondary or auxillary) variables such as elevation or topography ? That is , are there a dinstinction depending on the type of variables to model the trend while kriging?

Best regards
Recep

_____

Yahoo! kullaniyor musunuz?
http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>

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No virus found in this incoming message.
Checked by AVG Anti-Virus.
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• Dear Els A good reference on geostats in the oil industry is the excelent book from Olivier Dubrule Geostatistics for Seismic Data Integration in Earth
Message 6 of 10 , Jul 1, 2005
Dear Els

A good reference on geostats in the oil industry is the excelent book from
Olivier Dubrule "Geostatistics for Seismic Data Integration in Earth
Models", where you will also find KDE aplications.

Actually, it is the reference book of a 1 day course offered by SEG (Society
of Exploration GEophysicists)/EAGE (European Association og Geoscientists
and Engineers).
Opendivs=s13,s15

Sincerely

Carlos Eduardo ABreu

-----Message d'origine-----
De : Els Verfaillie [mailto:els.verfaillie@...]
Envoyé : vendredi 1 juillet 2005 10:55
À : Pierre Goovaerts; Recep kantarci; ai-geostats@...
Objet : RE: [ai-geostats] modelling trend and kriging type

Dear AI-list,

in which context KED is mostly used? I have found examples of this
methodology in the context of soil science and climatology:

Bourennane, H., King, D. and Couturier, A., 2000. Comparison of kriging with
external drift and simple linear regression for predicting soil horizon
thickness with different sample densities: Geoderma, v. 97, p. 255-271.

Bourennane, H. and King, D., 2003. Using multiple external drifts to
estimate a soil variable: Geoderma, v. 114, p. 1-18.

Goovaerts, P., 1999. Using elevation to aid the geostatistical mapping of
rainfall erosivity: Catena, v. 34, p. 227-242.

Hudson, G. and Wackernagel, H., 1994. Mapping temperature using kriging with
external drift: theory and an example from Scotland: International Journal
of Climatology, v. 14, p. 77-91.

Martinez-Cob, A. and Cuenca, R.H., 1992. Influence of elevation on regional
evapotranspiration using multivariate geostatistics for various climatic
regimes in Oregon. Journal of Hydrology 136, 353–380.

Are there other interesting references for this methodology in the same or
other application fields?

Best wishes,
___________________________________________________

Els Verfaillie, PhD student
Renard Centre of Marine Geology - Ghent University
Krijgslaan 281-S8
B-9000 Gent - Belgium
tel: +32-9-2644573 fax: +32-9-2644967
e-mail: Els.Verfaillie@...
http://www.rcmg.ugent.be/
___________________________________________________

-----Original Message-----
From: Pierre Goovaerts [mailto:Goovaerts@...]
Sent: donderdag 30 juni 2005 16:54
To: Recep kantarci; ai-geostats@...
Subject: RE: [ai-geostats] modelling trend and kriging type

1. Universal kriging = kriging with a trend. The second terminology has been
proposed by Andre
Journel who felt that the term "universal" was vague and misleadingly
"ambitious".

2. Kriging with an external drift (KED) is mathematically the same as
universal kriging (UK). Secondary variables
are simply replacing the spatial coordinates used in UK.

3. Regression kriging denotes all the techniques where the trend is modeled
outside the kriging algorithm.
There are various methods that can be used to model that trend, ranging from
linear regression
to neural networks. Kriging is used to interpolate the residuals. In
practice these techniques have more
flexibility than universal kriging in term of modeling the trend: multiple
variables either categorical or
continuous can be incorporated easily and many sofwtare are available for
this trend modeling.
The only limitation is that the trend is modeled globally (i.e. the
regression coefficients are constant
in space) while in KED the coefficients are reestimated within each search
window.

Cheers,

Pierre

Pierre Goovaerts

Chief Scientist at Biomedware

516 North State Street

Ann Arbor, MI 48104

Voice: (734) 913-1098
Fax: (734) 913-2201

http://home.comcast.net/~goovaerts/

-----Original Message-----
From: Recep kantarci [mailto:recep_kantarci_1978@...]
Sent: Thu 6/30/2005 9:38 AM
To: ai-geostats@...
Cc:
Subject: [ai-geostats] modelling trend and kriging type

Dear ai-geostats members

When the data used has a trend, it is needed to model trend and in
this case there exists various types of kriging to apply (universal kriging,
kriging with a trend, regression kriging etc).
If this is the case, does one should use the same type of kriging or
different depending on modeling the trend using coordinates of target
variable or using other (namely, secondary or auxillary) variables such as
elevation or topography ? That is , are there a dinstinction depending on
the type of variables to model the trend while kriging?

Best regards
Recep

_____

Yahoo! kullaniyor musunuz?
http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>

--
No virus found in this incoming message.
Checked by AVG Anti-Virus.
Version: 7.0.322 / Virus Database: 267.8.2/29 - Release Date: 27/06/2005

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• Hi all I may know this already, but what are the symptoms of data with a trend? What is the difference between a dataset with a trend and a non-stationary
Message 7 of 10 , Jul 6, 2005
RE: [ai-geostats] modelling trend and kriging type

Hi all

I may know this already, but what are the symptoms of data with a trend?  What is the difference between a dataset with a trend and a non-stationary dataset?

Cheers

Perry Collier

Senior Mine Geologist
Ernest Henry Mine
Xstrata Copper Australia
Ph (07) 4769 4527
Fx (07) 4769 4555
E-mail PCollier@...
Web http://www.xstrata.com

PO Box 527
Cloncurry QLD 4824
Australia

"Light travels faster than sound. That is why some people appear bright
until you hear them speak"

-----Original Message-----
From: Pierre Goovaerts [mailto:Goovaerts@...]
Sent: Friday, 1 July 2005 12:54 AM
To: Recep kantarci; ai-geostats@...
Subject: RE: [ai-geostats] modelling trend and kriging type

1. Universal kriging = kriging with a trend. The second terminology has been proposed by Andre
Journel who felt that the term "universal" was vague and misleadingly "ambitious".

2. Kriging with an external drift (KED) is mathematically the same as universal kriging (UK). Secondary variables
are simply replacing the spatial coordinates used in UK.

3. Regression kriging denotes all the techniques where the trend is modeled outside the kriging algorithm.
There are various methods that can be used to model that trend, ranging from linear regression
to neural networks. Kriging is used to interpolate the residuals. In practice these techniques have more
flexibility than universal kriging in term of modeling the trend: multiple variables either categorical or
continuous can be incorporated  easily and many sofwtare are available for this trend modeling.
The only limitation is that the trend is modeled globally (i.e. the regression coefficients are constant
in space) while in KED the coefficients are reestimated within each search window.

Cheers,

Pierre

Pierre Goovaerts

Chief Scientist at Biomedware

516 North State Street

Ann Arbor, MI 48104

Voice: (734) 913-1098
Fax: (734) 913-2201

http://home.comcast.net/~goovaerts/

-----Original Message-----
From: Recep kantarci [mailto:recep_kantarci_1978@...]
Sent: Thu 6/30/2005 9:38 AM
To: ai-geostats@...
Cc:
Subject: [ai-geostats] modelling trend and kriging type

Dear ai-geostats members

When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal kriging, kriging with a trend, regression kriging etc).

If this is the case, does one should use the same type of kriging or different depending on modeling the trend using coordinates of target variable or using other (namely, secondary or auxillary) variables such as elevation or topography ? That is , are there a dinstinction depending on the type of variables to model the trend while kriging?

Best regards
Recep

_____

Yahoo! kullaniyor musunuz?
http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>

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If you receive this e-mail in error, any use, distribution or

copying of this e-mail is not permitted. You are requested to

forward unwanted e-mail and address any problems to the

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• Perry Your basic semi-variogram graph has a parabola added to it. Shoots off upwards (usually) at some distance. If the distance is large (past the range of
Message 8 of 10 , Jul 7, 2005
Perry

Your basic semi-variogram graph has a parabola added to it. Shoots off upwards (usually) at some distance. If the distance is large (past the range of influence) you can ignore it. See some of our  mid-80s papers on the Wolfcamp data which lots of people use as a teaching set now. Or read my free tutorial at http://geoecosse.bizland.com/softwares (kriging with trend).

Isobel

PCollier@... wrote:

Hi all

I may know this already, but what are the symptoms of data with a trend?  What is the difference between a dataset with a trend and a non-stationary dataset?

Cheers

Perry Collier

Senior Mine Geologist
Ernest Henry Mine
Xstrata Copper Australia
Ph (07) 4769 4527
Fx (07) 4769 4555
E-mail PCollier@...
Web http://www.xstrata.com

PO Box 527
Cloncurry QLD 4824
Australia

"Light travels faster than sound. That is why some people appear bright
until you hear them speak"

-----Original Message-----
From: Pierre Goovaerts [mailto:Goovaerts@...]
Sent: Friday, 1 July 2005 12:54 AM
To: Recep kantarci; ai-geostats@...
Subject: RE: [ai-geostats] modelling trend and kriging type

1. Universal kriging = kriging with a trend. The second terminology has been proposed by Andre
Journel who felt that the term "universal" was vague and misleadingly "ambitious".

2. Kriging with an external drift (KED) is mathematically the same as universal kriging (UK). Secondary variables
are simply replacing the spatial coordinates used in UK.

3. Regression kriging denotes all the techniques where the trend is modeled outside the kriging algorithm.
There are various methods that can be used to model that trend, ranging from linear regression
to neural networks. Kriging is used to interpolate the residuals. In practice these techniques have more
flexibility than universal kriging in term of modeling the trend: multiple variables either categorical or
continuous can be incorporated  easily and many sofwtare are available for this trend modeling.
The only limitation is that the trend is modeled globally (i.e. the regression coefficients are constant
in space) while in KED the coefficients are reestimated within each search window.

Cheers,

Pierre

Pierre Goovaerts

Chief Scientist at Biomedware

516 North State Street

Ann Arbor, MI 48104

Voice: (734) 913-1098
Fax: (734) 913-2201

http://home.comcast.net/~goovaerts/

-----Original Message-----
From: Recep kantarci [mailto:recep_kantarci_1978@...]
Sent: Thu 6/30/2005 9:38 AM
To: ai-geostats@...
Cc:
Subject: [ai-geostats] modelling trend and kriging type

Dear ai-geostats members

When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal kriging, kriging with a trend, regression kriging etc).

If this is the case, does one should use the same type of kriging or different depending on modeling the trend using coordinates of target variable or using other (namely, secondary or auxillary) variables such as elevation or topography ? That is , are there a dinstinction depending on the type of variables to model the trend while kriging?

Best regards
Recep

_____

Yahoo! kullaniyor musunuz?
http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>

**********************************************************************

The information contained in this e-mail is confidential and is

intended only for the use of the addressee(s).

If you receive this e-mail in error, any use, distribution or

copying of this e-mail is not permitted. You are requested to

forward unwanted e-mail and address any problems to the

Xstrata Queensland Support Centre.

Support Centre e-mail: supportcentre@...

Support Centre phone: Australia 1800 500 646

International +61 2 9034 3710

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• Hi Perry, I am curious to see how others will reply to your second question on the difference between a dataset with a trend and one that is non-stationary! My
Message 9 of 10 , Jul 7, 2005
Hi Perry,

I am curious to see how others will reply to your second question on the
difference between a dataset with a trend and one that is
non-stationary! My reply may sound provocative: you can always remove a
trend when you recognize that there is one. Moving from non-stationarity
to stationarity, on the other hand, can be infinitely more complex (e.g.
moving to non-Euclidean space)

:)

For what concerns the detection of trends, have a look at the variogram:
a quadratic/exp. increase usually means that there is a trend. Get rid
of the presumed trend and check the variogram of the residuals which
should clearly show a change of structure (if you had a trend
obviously). Quicker might be to use a moving windows strategy to plot
local averages and check if you see any structure (be careful that the
"structure" is not simply an anisotropy of your variable). You could
have a look into the old archives of AI-GEOSTATS. There have been very
nice replies from Donald Myers (see his publications) in the past on
these issues. see http://groups.yahoo.com/group/ai-geostats/

Regards

GD

-----Original Message-----
From: PCollier@... [mailto:PCollier@...]
Sent: 07 July 2005 03:49
To: ai-geostats@...
Subject: RE: [ai-geostats] modelling trend and kriging type

Hi all
I may know this already, but what are the symptoms of data with a trend?
What is the difference between a dataset with a trend and a
non-stationary dataset?
Cheers

Perry Collier
Senior Mine Geologist
Ernest Henry Mine
Xstrata Copper Australia
Ph (07) 4769 4527
Fx (07) 4769 4555
E-mail PCollier@...
Web http://www.xstrata.com

PO Box 527
Cloncurry QLD 4824
Australia

"Light travels faster than sound. That is why some people appear bright
until you hear them speak"

-----Original Message-----
From: Pierre Goovaerts [mailto:Goovaerts@...]
Sent: Friday, 1 July 2005 12:54 AM
To: Recep kantarci; ai-geostats@...
Subject: RE: [ai-geostats] modelling trend and kriging type

1. Universal kriging = kriging with a trend. The second terminology has
been proposed by Andre
Journel who felt that the term "universal" was vague and misleadingly
"ambitious".

2. Kriging with an external drift (KED) is mathematically the same as
universal kriging (UK). Secondary variables
are simply replacing the spatial coordinates used in UK.

3. Regression kriging denotes all the techniques where the trend is
modeled outside the kriging algorithm.
There are various methods that can be used to model that trend, ranging
from linear regression
to neural networks. Kriging is used to interpolate the residuals. In
practice these techniques have more
flexibility than universal kriging in term of modeling the trend:
multiple variables either categorical or
continuous can be incorporated easily and many sofwtare are available
for this trend modeling.
The only limitation is that the trend is modeled globally (i.e. the
regression coefficients are constant
in space) while in KED the coefficients are reestimated within each
search window.

Cheers,

Pierre

Pierre Goovaerts
Chief Scientist at Biomedware
516 North State Street
Ann Arbor, MI 48104
Voice: (734) 913-1098
Fax: (734) 913-2201
http://home.comcast.net/~goovaerts/
-----Original Message-----
From: Recep kantarci [mailto:recep_kantarci_1978@...]
Sent: Thu 6/30/2005 9:38 AM
To: ai-geostats@...
Cc:
Subject: [ai-geostats] modelling trend and kriging type

Dear ai-geostats members

When the data used has a trend, it is needed to model trend and
in this case there exists various types of kriging to apply (universal
kriging, kriging with a trend, regression kriging etc).
If this is the case, does one should use the same type of
kriging or different depending on modeling the trend using coordinates
of target variable or using other (namely, secondary or auxillary)
variables such as elevation or topography ? That is , are there a
dinstinction depending on the type of variables to model the trend while
kriging?

Best regards
Recep

_____
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• Dear Perry Collier I`m interested in the second question: what is the difference between a dataset with a trend and a non-stationary dataset? Without clearly
Message 10 of 10 , Jul 8, 2005
Dear Perry Collier
I`m interested in the second question: what is the difference between a dataset
with a trend and a non-stationary dataset?
Without clearly pointing out about which kind of stationarity we are talking
(second order, intrinsic or generalized intrinsic), we need stationarity
(well !!! togheter with ergodicity) for some statistical index (in this case a
index about spatial variability) to perform inference. From my perspective the
dualism trend-residual makes possible always (or not?) to explain non
stationarity in spatial variability in term of presence of a trend: this trend
could be global as well as local: it is only a matter of scale.The point is: we
have reasons or so many data to use a complex trend model?

In particular this question makes me to think to a point. Very often people who
use Universal Kriging do this:
1) detrend data globally (same trend coefficients for all spatial domain)
2) calculate a residual variogram
3) perfom Uk with local search windows (inside which the trend coefficients are
calculated i.e. the trend is filtered locally)
This doesen`t seem to me correct: I think (maybe, if you have many data IRF-K
approach works better) that you can not
one time calculate trend globally and the other time locally: it could happen
that globally you need a quadratic trend while locally a linear trend model is

Sincerely,
Sebastiano Trevisani

At 03.48 07/07/2005, PCollier@... wrote:

Hi all

I may know this already, but what are the symptoms of data with a trend? What
is the difference between a dataset with a trend and a non-stationary dataset?

Cheers

Perry Collier

Senior Mine Geologist
Ernest Henry Mine
Xstrata Copper Australia
Ph (07) 4769 4527
Fx (07) 4769 4555
E-mail PCollier@...
Web http://www.xstrata.com

PO Box 527
Cloncurry QLD 4824
Australia

"Light travels faster than sound. That is why some people appear bright
until you hear them speak"

-----Original Message-----
From: Pierre Goovaerts [mailto:Goovaerts@...]
Sent: Friday, 1 July 2005 12:54 AM
To: Recep kantarci; ai-geostats@...
Subject: RE: [ai-geostats] modelling trend and kriging type

1. Universal kriging = kriging with a trend. The second terminology has been
proposed by Andre
Journel who felt that the term "universal" was vague and

2. Kriging with an external drift (KED) is mathematically the same as universal
kriging (UK). Secondary variables
are simply replacing the spatial coordinates used in UK.

3. Regression kriging denotes all the techniques where the trend is modeled
outside the kriging algorithm.
There are various methods that can be used to model that trend, ranging from
linear regression
to neural networks. Kriging is used to interpolate the residuals. In practice
these techniques have more
flexibility than universal kriging in term of modeling the trend: multiple
variables either categorical or
continuous can be incorporated easily and many sofwtare are available for this
trend modeling.
The only limitation is that the trend is modeled globally (i.e. the regression
coefficients are constant
in space) while in KED the coefficients are reestimated within each search
window.

Cheers,

Pierre

Pierre Goovaerts

Chief Scientist at Biomedware

516 North State Street

Ann Arbor, MI 48104

Voice: (734) 913-1098
Fax: (734) 913-2201

http://home.comcast.net/~goovaerts/

-----Original Message-----
From: Recep kantarci [mailto:recep_kantarci_1978@...]
Sent: Thu 6/30/2005 9:38 AM
To: ai-geostats@...
Cc:
Subject: [ai-geostats] modelling trend and kriging type

Dear ai-geostats members

When the data used has a trend, it is needed to model trend and in this
case there exists various types of kriging to apply (universal kriging, kriging
with a trend, regression kriging etc).

If this is the case, does one should use the same type of kriging or
different depending on modeling the trend using coordinates of target variable
or using other (namely, secondary or auxillary) variables such as elevation or
topography ? That is , are there a dinstinction depending on the type of
variables to model the trend while kriging?

Best regards
Recep

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