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-----Original Message-----
From: Syed Abdul Rahman Shibli [mailto:sshibli@...]
Sent: 16 July 2004 19:23
To: Gregoire Dubois
Cc: ai-geostats@...
Subject: Re: [ai-geostats] Fractals & Semivariance

Not sure how anisotropic "fractal" spatial correlation models would fit in the whole scheme of things. You're essentially assuming a power law model (Brownian motion) to model the spatial correlation, which implicitly assumes a phenomena with an infinite capacity for dispersion, i.e. no range. The ratio of two fractal dimensions is not necessarily the same as the ratio of two ranges in the two directions of maximum and minimum continuity, which is the traditional measure of "anisotropy".

However, practically speaking you can still calculate experimental variograms for two, three, or four separate directions and derive the log-log estimate of the fractal dimension from these separate variograms. I wouldn't know what this will physically mean, except to say that I have a phenomena with different capacities for dispersion in different directions.

Cheers

Syed

Dear all,
 
at
http://www.umanitoba.ca/faculties/science/botany/labs/ecology/fractals/measuring.html
 
one can read the following
 
"The fractal dimension is estimated separately for each profile from the log-log plot of cell count against step size (D = 2 - slope, where 1 <= D <= 2). The average of these values plus one provides an estimate of the surface fractal dimension."
 
 
Burrough's method (using the slope of the log-log plot of the semivariogram to calculate the fractal dimension of 1 dimensional transect or profile) could thus be extended to a 2 D case (a surface). Has anyone references discussing the use of Burrough's method when applied to a 2 D case?
 
Unless one considers the investigated phenomenon completely isotropic, averaging the fractal dimensions derived from the slopes of directional log-log semivariograms may not provide any useful/reliable information.
 
Has someone on the list any experience with this kind of issue?
 
Thanks very much for any help.
 
Best regards,
 
Gregoire
 
PS: I know there are other techniques to calculate the fractal dimension of a surface but I'm only interested in those involving the computation of the semivariance.
 
__________________________________________
Gregoire Dubois (Ph.D.)
JRC - European Commission
IES - Emissions and Health Unit
Radioactivity Environmental Monitoring group
TP 441, Via Fermi 1
21020 Ispra (VA)
ITALY
 
Tel. +39 (0)332 78 6360
Fax. +39 (0)332 78 5466
Email: gregoire.dubois@...
WWW: http://www.ai-geostats.org
WWW: http://rem.jrc.cec.eu.int
 
 
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Hi,

I am wondering if anybody knows about any software that will
implement the new Ord-Getis O statistics for local spatial
autocorrelation identification when global spatial autocorrelation is
present.

Reference: Ord, J. K., Getis, A., 2001, Testing for local spatial
autocorrelation in the presence of global autocorrelation, J. of
Regional Science, vol. 41, no. 3, pp. 411-432

Any suggestions will be very welcome.

Thanks a lot,

Monica
Monica Palaseanu-Lovejoy
University of Manchester
School of Geography
Mansfield Cooper Bld. 3.21
Oxford Road
Manchester M13 9PL
England, UK
Tel: +44 (0) 275 8689
Email: monica.palaseanu-lovejoy@...

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Jul

The warning about kriging small blocks is about
"small" relative to the sampling density. For example,
less than about one-third of the grid spacing.

The warning is the same as the one about 'point'
kriging (mapping) The map is too smooth - or, at
least, a lot smoother than the real surface would be.
High value areas will be under-estimated and low value
areas will be over-estimated.

If your objective in kriging is to obtain general maps
of an area with an idea of where the highs and lows
are, then ordinary kriging is sufficient. The over-
and under- estimations cancel out on average.

In mining applications, where block kriging
originated, most applications require a 'cutoff',
where values below a certain value are not included in
the 'plan'. In this case, mapping or estimating small
blocks will result in an over-estimation of 'payable'
ground and an under-estimation in average value.

In pollution or environmental applications, the areas
at risk will be under-estimated as will the true
toxicity or risk factors.

There are two major ways round this problem:

(1) use a non-linear kriging approach such as
disjunctive kriging or the multivariate gaussian. Ed
Isaacs and Mohan Srivastava's book is th ebest
reference for the latter. Rivoirard's book for DK.

(2) simulation. There are lots of simulation methods
around, which allow you to 'put back the roughness'
and get an idea how bad the problem might be. GSLib is
pretty good on this.

Isobel
http://geoecosse.bizland.com/course_brochure.htm

If, as in mining, you wish to apply some sort





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Not sure how anisotropic "fractal" spatial correlation models would fit
in the whole scheme of things. You're essentially assuming a power law
model (Brownian motion) to model the spatial correlation, which
implicitly assumes a phenomena with an infinite capacity for
dispersion, i.e. no range. The ratio of two fractal dimensions is not
necessarily the same as the ratio of two ranges in the two directions
of maximum and minimum continuity, which is the traditional measure of
"anisotropy".

However, practically speaking you can still calculate experimental
variograms for two, three, or four separate directions and derive the
log-log estimate of the fractal dimension from these separate
variograms. I wouldn't know what this will physically mean, except to
say that I have a phenomena with different capacities for dispersion in
different directions.

Cheers

Syed

> Dear all,
>  
> at
>
> http://www.umanitoba.ca/faculties/science/botany/labs/ecology/
> fractals/measuring.html
>  
> one can read the following
>  
> "The fractal dimension is estimated separately for each profile from
> the log-log plot of cell count against step size (D = 2 - slope, where
> 1 <= D <= 2). The average of these values plus one provides an
> estimate of the surface fractal dimension."
>  
>  
> Burrough's method (using the slope of the log-log plot of the
> semivariogram to calculate the fractal dimension of 1 dimensional
> transect or profile) could thus be extended to a 2 D case (a surface).
> Has anyone references discussing the use of Burrough's method when
> applied to a 2 D case?
>   
> Unless one considers the investigated phenomenon completely isotropic,
> averaging the fractal dimensions derived from the slopes of
> directional log-log semivariograms may not provide any useful/reliable
> information.
>   
> Has someone on the list any experience with this kind of issue?
>  
> Thanks very much for any help.
>  
> Best regards,
>  
> Gregoire
>  
> PS: I know there are other techniques to calculate the fractal
> dimension of a surface but I'm only interested in those involving the
> computation of the semivariance.
>  
> __________________________________________
> Gregoire Dubois (Ph.D.)
> JRC - European Commission
> IES - Emissions and Health Unit
> Radioactivity Environmental Monitoring group
> TP 441, Via Fermi 1
> 21020 Ispra (VA)
> ITALY
>  
> Tel. +39 (0)332 78 6360
> Fax. +39 (0)332 78 5466
> Email: gregoire.dubois@...
> WWW: http://www.ai-geostats.org
> WWW: http://rem.jrc.cec.eu.int
>  
>  
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Journel, A. G., R. Gundeso, E. Gringarten, and T. Yao. 1998. Stochastic modelling of a fluvial reservoir: a comparative review of algorithms. Journal of Petroleum Science and Engineering 21.

Deutsch, C. V., and T. T. Tran. 2002. FLUVISIM: a program for object-based stochastic modeling of fluvial depostional systems. Computers and Geosciences 28:525-535.

Holden, L., R. Hauge, O. Skare, and A. Skorstad. 1998. Modeling of fluvial reservoirs with object models. Mathematical Geology 30:473-496.

Wich soft do you use?

Regards
 

Oriol
 
 

"Shazly, Salah DSC92" wrote:

Hi All,

I am at the beginning of modelling fluvial sand channels using subsurface well data (logs &cores). I would appreciate if you could send me some tips on the optimum way to do this using object modelling and indicator techniques. Are there any published work dealing with the geometrical parameters (e.g. thickness, width, length, amplitude etc.). Is there some cross plots relating channels body thickness measured from the well data to width?

Regards,

___________________________________________________________

Salah el-Shazly (DSC/92)

Geologist Consultant, PDO Study Centre

Petroleum Development Oman- POBox: 81, PC 113

Tel: (968) 674135; FAX: (968) 691470; Mobile: (968) 9898527

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______________________________________

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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All,

I just wondering why kriging small blocks is warned. Any literature about this subject will be appreciated.
Thanks.

Regards,

Jul

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Hi

I think the discussion below is missing some key points:
1. If the individual block estimates are to be used for actual selection at
the time of mining, then conditional bias will impact the predicted
recoveries and should be minimized.
2. However, if the block model is to be used for long term mine planning,
the preparation of production schedules etc. etc., then it is unlikely that
these same block estimates will be used for selection at the time of mining.
In this scenario, it is sufficient to know the distribution of block grades
within a mining period such as annual, semi-annual, or quarterly, etc. and
conditional bias is irrelevant.
3. Now here is the rub. One cannot accurately estimate the distribution of
block grades within a mining period without invoking conditional bias unless
each block estimate is perfect, e.g., no error!

If you read Michel Davids, "Geostatistical Ore Reserve Estimation"  you will
find that he also points out this apparent contradiction (page 313 section
11.3.2) The apparent contradiction is:
1. If the block grades are conditionally unbiased, then the distribution
(histogram) of block estimates is necessarily smoothed. Thus, the prediction
of in situ tones and grade above cutoff is inaccurate (biased)!
2. If the histogram of estimated block grades yields the correct in situ
proportions and grades above cutoff (for all cutoff grades), then the block
estimates are necessarily conditionally biased.

I often refer to this as the "kriging Oxymoron", and it appears to be very
poorly understood with in the geostat community. Even Dr. Krige wrongly
claims that conditional bias should be removed or minimized in a long term
mine planning model, when in fact it is irrelevant.


-----Original Message-----
From: Isobel Clark [mailto:drisobelclark@...]
Sent: Monday, July 19, 2004 8:50 AM
To: nicolau.barros@...
Cc: ai-geostats@...
Subject: [ai-geostats] Re: Kriging Small Blocks

Nicolau

I was talking about kriging before cutoff is applied.
If the cutoff is applied to the block estimates my
comments stand. If you aply the cutoff to your data
first and then krige, you get the opposite problem,
because you will over-estimate every value and
under-estimate the tonnage.

My point (1) is that, if you wish to avoid conditional
bias in your kriging, you could consider using a
non-linear kriging method such as those mentioned. I
have no experience with either, since I follow a
different route in the correction of conditional bias
in mineral resource estimation.

Isobel
http://geoecosse.bizland.com/whatsnew.htm



--- nicolau.barros@... wrote: > Isobel,
>
> So for mining purposes can't we just krige before
> applying the cut-off
> criteria? I mean, for most mining applications one
> will prefer to have a
> more realistic geologic block model and will always
> have the chance to
> evaluate his/her panels under the appropriate
> cut-off criteria, but applying
> that criteria after estimating small blocks, right?
>
> Could you please explain your point in solution (1)
> below? Thanks for
> indicating the literature.
>
> Thanks
>
> Nicolau Barros
> Engineer
> Mine Planning and Production Control Department
> Mineração Rio do Norte S.A.
> nicolau.barros@...
> +55 (93) 549 8215
>
> Confidencialidade
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> -----Mensagem original-----
> De: Isobel Clark [mailto:drisobelclark@...]
> Enviada em: segunda-feira, 19 de julho de 2004 05:23
> Para: Julhendra_Solin@...
> Cc: ai-geostats@...
> Assunto: [ai-geostats] Re: Kriging Small Blocks
>
> Jul
>
> The warning about kriging small blocks is about
> "small" relative to the sampling density. For
> example,
> less than about one-third of the grid spacing.
>
> The warning is the same as the one about 'point'
> kriging (mapping) The map is too smooth - or, at
> least, a lot smoother than the real surface would
> be.
> High value areas will be under-estimated and low
> value
> areas will be over-estimated.
>
> If your objective in kriging is to obtain general
> maps
> of an area with an idea of where the highs and lows
> are, then ordinary kriging is sufficient. The over-
> and under- estimations cancel out on average.
>
> In mining applications, where block kriging
> originated, most applications require a 'cutoff',
> where values below a certain value are not included
> in
> the 'plan'. In this case, mapping or estimating
> small
> blocks will result in an over-estimation of
> 'payable'
> ground and an under-estimation in average value.
>
> In pollution or environmental applications, the
> areas
> at risk will be under-estimated as will the true
> toxicity or risk factors.
>
> There are two major ways round this problem:
>
> (1) use a non-linear kriging approach such as
> disjunctive kriging or the multivariate gaussian. Ed
> Isaacs and Mohan Srivastava's book is th ebest
> reference for the latter. Rivoirard's book for DK.
>
> (2) simulation. There are lots of simulation methods
> around, which allow you to 'put back the roughness'
> and get an idea how bad the problem might be. GSLib
> is
> pretty good on this.
>
> Isobel
> http://geoecosse.bizland.com/course_brochure.htm
>
> If, as in mining, you wish to apply some sort
>
>
>
>
>
>
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>





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Hi, Dear List:

 

I am trying to use Gstat to do Gaussian Conditional Simulation on my soil C content data. I got 3 questions as following:

 

1. If I use "set nsim=100" to do 100 times simulation, does the simulations follow a single random path or they will follow 100 different random paths? What should I do if I want to let them follow different random paths.

 

2. Is it possible for me to write all the results of 100 simulations to one single file? How?

 

3. Gstat needs gnuplot to do the plot, but I could not get gnuplot compiled and start in windows, could you please tell me how to do it if you have experience on this.

 

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Ed

I would differ from your explanation on one point.

If you are merely declaring a mineral resource, i.e.
mineral in the ground, then the conditional bias may
not be relevant at the "pre feasibility" stage.

However, as soon as you introduce any economic or
technical parameters which entail selection, the
conditional bias makes its appearance.

In every project I have worked on, from
pre-feasibility onwards, I have been asked for a
grade/tonnage calculation - no matter how hand-waving
it may be. The grade/tonnage curve will be affected by
the conditional bias. By how much has to be assessed
at the time. Most of Chapter 3 in Practical
Geostatistics 1979 is devoted to working out what the
(theoretical) global grade tonnage curve looks like
when you adjust for the variance reduction. Even this
will differ from the curve derived from the kriged
estimates, no matter what size the block.

The problem is even greater for environmental
applications, especially toxic level risks. A 'global
view' - i.e. a map - will not identify the true peaks
because of the conditional bias. The fact that the
overall average is unbiassed is irrelevant when trying
to identify an area which is likely to be lethal.

So, there is no contradiction. Conditional bias is
unimportant (or irrelevant) until you apply some
selection criterion. Yes, we agree. However, selection
criteria can be relevant at very early stages of a
project. It depends on your objective.

Isobel
http://uk.geocities.com/drisobelclark/practica.htm for
free downloads of Practical Geostatistics 1979

PS: sorry I mis-spelled your name, I know it drives me
nuts when people call me 'Clarke' ;-)





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Dear Mike.

In point pattern analysis, your sample is supposed to
be a homogeneous thinning of a more global underlying
point process, and is therefore expected to share same
characteristics.

Usually Monte Carlo simulations are involved to test
null hypothesis. The less point you have the less
robust your test will be: each significant rejection
of the null hypothesis are about to be generalized to
the underlying process, whereas no conclusions have to
be made about non-significant results (since larger
sample could have lead, or not, to significant
rejection of H0).

Of this, what i understood was that no real minimum
sample size can be defined.

I found the manual of P.J. Diggle 2003 a valuable and
clear source of information about points patterns :
"Diggle, P. J. (2003). Statistical analysis of spatial
point patterns (2d edn). London, UK: Arnold."

Hope it would help.
sheers.

Joseph.

----------------------
Joseph Le Cuziat
PhD Student
IMEP - ECWP

--- Mike Saunders <mike_saunders@...> a
écrit : > I have been surfing the internet and looking
through
> a few older spatial spatistics books and could not
> find any recommendations on minimum sample size for
> point pattern analyses, specifically the Ripley's
> K(d) function.  Is there a source citing this
> somewhere?
>
> Thanks,
>
> Mike R. Saunders
> Research Associate
> Forest Ecosystem Research Program
> Department of Forest Ecosystem Sciences
> University of Maine
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=====
----------------------------------------------
Joseph LE CUZIAT

IMEP, FST St Jérôme, case 461, 13397 Marseille cedex 20, FRANCE

ECWP, Province de Boulemane, BP 47 Missour, MAROC






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Gregoire,

To be honest I have never attempted this, although as you said the
angular tolerance, bandwidth, and lag tolerance will ultimately
determine whether the directional fractal dimensions can be averaged to
give an "omnidirectional" dimension, D. I would argue that two
directional variograms each with a directional tolerance of about 45
degrees on either side of the azimuth in the two principal directions
would yield an average D similar to an omnidirectional case, but this
will not strictly be true the smaller the tolerances used.

I have used simulated annealing to generate (stochastic) fractal fields
with different dimensions in three directions X, Y, and Z in 3D space,
e.g. assumption of fractional Gussian noise vertically with high Hurst
exponent (persistence) and fractional Brownian motion laterally with
lower Hurst exponent (anti-persistence).

Cheers

Syed

> Hello Syed,
>   
> I was hoping a reply from you :)
>  
> I didn't think about the problematic of anisotropy and the potential
> use of ratios of fractal dimensions. It might be worth some further
> investigation.
>   
> The physical meaning of fractals derived from directional variograms
> is tricky indeed.
>  I was wondering if the average of all these fractal dimensions would
> be formally equal to the fractal dimension derived from
> omnidirectional variogram.
>  My first guess would be yes, but this would depend on the angular
> tolerance of the directional variograms. And would the average value
> of the fractal dimension have any reasonable physical meaning?
>  
> Any experience with this?
>  
> Thanks again for the kind help.
>  
> Gregoire
>  
> -----Original Message-----
> From: Syed Abdul Rahman Shibli [mailto:sshibli@...]
>  Sent: 16 July 2004 19:23
> To: Gregoire Dubois
> Cc: ai-geostats@...
> Subject: Re: [ai-geostats] Fractals & Semivariance
>
>
> Not sure how anisotropic "fractal" spatial correlation models would
> fit in the whole scheme of things. You're essentially assuming a power
> law model (Brownian motion) to model the spatial correlation, which
> implicitly assumes a phenomena with an infinite capacity for
> dispersion, i.e. no range. The ratio of two fractal dimensions is not
> necessarily the same as the ratio of two ranges in the two directions
> of maximum and minimum continuity, which is the traditional measure of
> "anisotropy".
>
> However, practically speaking you can still calculate experimental
> variograms for two, three, or four separate directions and derive the
> log-log estimate of the fractal dimension from these separate
> variograms. I wouldn't know what this will physically mean, except to
> say that I have a phenomena with different capacities for dispersion
> in different directions.
>
>  Cheers
>
> Syed
>
>
> Dear all,
>  
> at
> http://www.umanitoba.ca/faculties/science/botany/labs/ecology/
> fractals/measuring.html
>  
> one can read the following
>  
> "The fractal dimension is estimated separately for each profile from
> the log-log plot of cell count against step size (D = 2 - slope, where
> 1 <= D <= 2). The average of these values plus one provides an
> estimate of the surface fractal dimension."
>  
>  
> Burrough's method (using the slope of the log-log plot of the
> semivariogram to calculate the fractal dimension of 1 dimensional
> transect or profile) could thus be extended to a 2 D case (a surface).
> Has anyone references discussing the use of Burrough's method when
> applied to a 2 D case?
>  
> Unless one considers the investigated phenomenon completely isotropic,
> averaging the fractal dimensions derived from the slopes of
> directional log-log semivariograms may not provide any useful/reliable
> information.
>  
> Has someone on the list any experience with this kind of issue?
>  
> Thanks very much for any help.
>  
> Best regards,
>  
> Gregoire
>  
> PS: I know there are other techniques to calculate the fractal
> dimension of a surface but I'm only interested in those involving the
> computation of the semivariance.
>  
> __________________________________________
> Gregoire Dubois (Ph.D.)
> JRC - European Commission
> IES - Emissions and Health Unit
> Radioactivity Environmental Monitoring group
> TP 441, Via Fermi 1
> 21020 Ispra (VA)
> ITALY
>  
> Tel. +39 (0)332 78 6360
> Fax. +39 (0)332 78 5466
> Email: gregoire.dubois@...
> WWW: http://www.ai-geostats.org
> WWW: http://rem.jrc.cec.eu.int
>  
>  
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Hi Isabel

If you go to www.isaaks.com and click on "Otherstuff", you will find an
example where the block estimates are conditionally biased (rather
severely), but the grade tonnage curves are right on the money. Perhaps this
will help clear the confusion. Ed

-----Original Message-----
From: Isobel Clark [mailto:drisobelclark@...]
Sent: Monday, July 19, 2004 10:47 AM
To: Edward Isaaks
Cc: ai-geostats@...
Subject: [ai-geostats] Re: Kriging Small Blocks

Ed

I would differ from your explanation on one point.

If you are merely declaring a mineral resource, i.e.
mineral in the ground, then the conditional bias may
not be relevant at the "pre feasibility" stage.

However, as soon as you introduce any economic or
technical parameters which entail selection, the
conditional bias makes its appearance.

In every project I have worked on, from
pre-feasibility onwards, I have been asked for a
grade/tonnage calculation - no matter how hand-waving
it may be. The grade/tonnage curve will be affected by
the conditional bias. By how much has to be assessed
at the time. Most of Chapter 3 in Practical
Geostatistics 1979 is devoted to working out what the
(theoretical) global grade tonnage curve looks like
when you adjust for the variance reduction. Even this
will differ from the curve derived from the kriged
estimates, no matter what size the block.

The problem is even greater for environmental
applications, especially toxic level risks. A 'global
view' - i.e. a map - will not identify the true peaks
because of the conditional bias. The fact that the
overall average is unbiassed is irrelevant when trying
to identify an area which is likely to be lethal.

So, there is no contradiction. Conditional bias is
unimportant (or irrelevant) until you apply some
selection criterion. Yes, we agree. However, selection
criteria can be relevant at very early stages of a
project. It depends on your objective.

Isobel
http://uk.geocities.com/drisobelclark/practica.htm for
free downloads of Practical Geostatistics 1979

PS: sorry I mis-spelled your name, I know it drives me
nuts when people call me 'Clarke' ;-)





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Nicolau

I was talking about kriging before cutoff is applied.
If the cutoff is applied to the block estimates my
comments stand. If you aply the cutoff to your data
first and then krige, you get the opposite problem,
because you will over-estimate every value and
under-estimate the tonnage.

My point (1) is that, if you wish to avoid conditional
bias in your kriging, you could consider using a
non-linear kriging method such as those mentioned. I
have no experience with either, since I follow a
different route in the correction of conditional bias
in mineral resource estimation.

Isobel
http://geoecosse.bizland.com/whatsnew.htm



--- nicolau.barros@... wrote: > Isobel,
>
> So for mining purposes can't we just krige before
> applying the cut-off
> criteria? I mean, for most mining applications one
> will prefer to have a
> more realistic geologic block model and will always
> have the chance to
> evaluate his/her panels under the appropriate
> cut-off criteria, but applying
> that criteria after estimating small blocks, right?
>
> Could you please explain your point in solution (1)
> below? Thanks for
> indicating the literature.
>
> Thanks
>
> Nicolau Barros
> Engineer
> Mine Planning and Production Control Department
> Mineração Rio do Norte S.A.
> nicolau.barros@...
> +55 (93) 549 8215
>
> Confidencialidade
> Esse e-mail e possíveis anexos podem possuir
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> Confidentiality
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>
> -----Mensagem original-----
> De: Isobel Clark [mailto:drisobelclark@...]
> Enviada em: segunda-feira, 19 de julho de 2004 05:23
> Para: Julhendra_Solin@...
> Cc: ai-geostats@...
> Assunto: [ai-geostats] Re: Kriging Small Blocks
>
> Jul
>
> The warning about kriging small blocks is about
> "small" relative to the sampling density. For
> example,
> less than about one-third of the grid spacing.
>
> The warning is the same as the one about 'point'
> kriging (mapping) The map is too smooth - or, at
> least, a lot smoother than the real surface would
> be.
> High value areas will be under-estimated and low
> value
> areas will be over-estimated.
>
> If your objective in kriging is to obtain general
> maps
> of an area with an idea of where the highs and lows
> are, then ordinary kriging is sufficient. The over-
> and under- estimations cancel out on average.
>
> In mining applications, where block kriging
> originated, most applications require a 'cutoff',
> where values below a certain value are not included
> in
> the 'plan'. In this case, mapping or estimating
> small
> blocks will result in an over-estimation of
> 'payable'
> ground and an under-estimation in average value.
>
> In pollution or environmental applications, the
> areas
> at risk will be under-estimated as will the true
> toxicity or risk factors.
>
> There are two major ways round this problem:
>
> (1) use a non-linear kriging approach such as
> disjunctive kriging or the multivariate gaussian. Ed
> Isaacs and Mohan Srivastava's book is th ebest
> reference for the latter. Rivoirard's book for DK.
>
> (2) simulation. There are lots of simulation methods
> around, which allow you to 'put back the roughness'
> and get an idea how bad the problem might be. GSLib
> is
> pretty good on this.
>
> Isobel
> http://geoecosse.bizland.com/course_brochure.htm
>
> If, as in mining, you wish to apply some sort
>
>
>
>
>
>
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> Messenger - sooooo many all-new ways to express
> yourself
> http://uk.messenger.yahoo.com
>





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Hello,

We're using SGSIM from GSLIB to create gaussian fields of standard
deivation = 1.
We realize that the standard deviation is always underestimated, tipical
obtianed values are betwee 0.7 and 0.9.
How can I get the correct std. dev?

Regards

--



______________________________________

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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Dear Steinar,
you can use so-called qualitative or semi-quantitative modelling
approaches. In such environments it is possible to define functions
(varibles) by means of monotonocity and thresholds. In addition,
variables are defined by means of qualitative landmarks. Regarding
the quantity spaces different variables can be constrained, as e.g.
one function may be always larger than the other. But note in such
simulations also the time is only defined in a qualitative sense.
The relevant publication is:
B. Kuipers (1994): Qualitative reasoning: Modeling and Simulation with
incomplete knowledge. MIT Press, Cambridge.
Best wishes
Juergen


Steinar Løve Ellefmo wrote:
> Hi All,
>
> I'm estimating and simulating an iron ore deposit. The decisive ore
> parameters are total iron, FeTot and iron in magnetite, FeMagn. Clearly
> FeMagn can not be larger than FeTot.
>
> FeMagn and FeTot is not correlated (coefficient of variation (CV) of
> FeMagn is much larger than the CV of FeTot). Domaining based on ore
> type is not practically possible.
>
> Is it possible to somehow "constrain" FeMagn realisations or estimations
> so that FeTot are the largest of the two?
>
> Any publications on the subject?
>
> I'm using Isatis.
>
>
> Best regards,
>
> Steinar Ellefmo
> Norwegian University of Science and Technology
> Norway
>
>
>
> ------------------------------------------------------------------------
>
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--
                          _\\|//_
                         (' O^O ')
+---------------------o00-(_)-00o------------------------+
|                   Dr. Juergen Kropp                    |
|     Potsdam Institute for Climate Impact Research      |
|          Dept. Integrated Systems Analysis             |
|       P.O.Box 60 12 03, 14412 Potsdam, Germany         |
| Office: Phone:    +49 (0) 331 288 2526                 |
|         Fax:      +49 (0) 331 288 2640                 |
|         mail:     kropp@...                 |
|--------------------------------------------------------|
| Homepage: http://www.pik-potsdam.de/~kropp/          |
| Projects: http://www.pik-potsdam.de/skalenanalyse/     |
|           http://www.pik-potsdam.de/~kropp/compromise/ |
+--------------------------------------------------------+

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Hi Steinar,

The exact same problem you have is addressed in:

"Stepwise Conditional Transformation for Simulation of Multiple Variables"
by
Oy Leuangthong and Clayton V. Deutsch, Math Geology 35(2):155-173, Feb.
2003.

What they propose is to normally transform the secondary variable
conditionally to
classes of the normally transformed primary variable. This transformation
removes
the cross-correlation at distance 0 (collocated) and often minimizes
cross-correlation
at lags different than 0, between the variables. Gaussian simulation can
then be performed
independently for each conditionally transformed variable. The simulated
values must be
back-transformed using the same "rule" created in the forward
transformation, which will
reinject any order relation they may have (such as FeTot>=FeMagn).

Hope this helps.

Julián Ortiz C., Ph. D.
Assistant Professor
Department of Mining Engineering
University of Chile

Phone: +56 2 678 4585
Fax  : +56 2 672 3504
Web  : www.ualberta.ca/~jmo1


-----Mensaje original-----
De: Steinar Løve Ellefmo [mailto:steinar.ellefmo@...]
Enviado el: martes, 20 de julio de 2004 5:49
Para: ai-geostats@...
Asunto: [ai-geostats] "Constrained" estimation / simulation


Hi All,

I'm estimating and simulating an iron ore deposit. The decisive ore
parameters are total iron, FeTot and iron in magnetite, FeMagn. Clearly
FeMagn can not be larger than FeTot.

FeMagn and FeTot is not correlated (coefficient of variation (CV) of
FeMagn is much larger than the CV of FeTot). Domaining based on ore
type is not practically possible.

Is it possible to somehow "constrain" FeMagn realisations or estimations
so that FeTot are the largest of the two?

Any publications on the subject?

I'm using Isatis.


Best regards,

Steinar Ellefmo
Norwegian University of Science and Technology
Norway

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Signoff ai-geostats

Hi All,

I'm estimating and simulating an iron ore deposit. The decisive ore
parameters are total iron, FeTot and iron in magnetite, FeMagn. Clearly
FeMagn can not be larger than FeTot.

FeMagn and FeTot is not correlated (coefficient of variation (CV) of
FeMagn is much larger than the CV of FeTot). Domaining based on ore
type is not practically possible.

Is it possible to somehow "constrain" FeMagn realisations or estimations
so that FeTot are the largest of the two?

Any publications on the subject?

I'm using Isatis.


Best regards,

Steinar Ellefmo
Norwegian University of Science and Technology
Norway

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Hello,

This may be due to conditioning data that lower the std. dev. of your
realizations.
If you want to fix this, you could use the program TRANS in GSLIB and refer
to the
paper:

"Posterior Identification of Histograms Conditional to Local Data, by A. G.
Journel and W. Xu,
Mathematical Geology, 26(3):323-359, 1994.

If you are doing unconditional simulation, the lower std. dev. may be due to
the size of your
field as compared to the range of your variogram.

Best regards,

Julián Ortiz C., Ph. D.
Profesor Asistente
Departamento de Ingeniería de Minas
Universidad de Chile

Fono: +56 2 678 4585
Fax : +56 2 672 3504
Web : www.ualberta.ca/~jmo1

-----Mensaje original-----
De: Oriol Falivene [mailto:ofaliven@...]
Enviado el: martes, 20 de julio de 2004 4:00
Para: ai-geostats@...
Asunto: [ai-geostats] std deviation when using SGSIM


Hello,

We're using SGSIM from GSLIB to create gaussian fields of standard
deivation = 1.
We realize that the standard deviation is always underestimated, tipical
obtianed values are betwee 0.7 and 0.9.
How can I get the correct std. dev?

Regards

--



______________________________________

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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Signoff ai-geostats

Thanks Julian,

I was doing unconditional simulation and the ranges were to large. I've made
some tests and each range should be at least 1/10 the grid dimensions to obtain
a good match of the standard deviation. There is any literature regarding this
issue?

Regards.

Oriol

Julián Ortiz wrote:

> Hello,
>
> This may be due to conditioning data that lower the std. dev. of your
> realizations.
> If you want to fix this, you could use the program TRANS in GSLIB and refer
> to the
> paper:
>
> "Posterior Identification of Histograms Conditional to Local Data, by A. G.
> Journel and W. Xu,
> Mathematical Geology, 26(3):323-359, 1994.
>
> If you are doing unconditional simulation, the lower std. dev. may be due to
> the size of your
> field as compared to the range of your variogram.
>
> Best regards,
>
> Julián Ortiz C., Ph. D.
> Profesor Asistente
> Departamento de Ingeniería de Minas
> Universidad de Chile
>
> Fono: +56 2 678 4585
> Fax : +56 2 672 3504
> Web : www.ualberta.ca/~jmo1
>
> -----Mensaje original-----
> De: Oriol Falivene [mailto:ofaliven@...]
> Enviado el: martes, 20 de julio de 2004 4:00
> Para: ai-geostats@...
> Asunto: [ai-geostats] std deviation when using SGSIM
>
> Hello,
>
> We're using SGSIM from GSLIB to create gaussian fields of standard
> deivation = 1.
> We realize that the standard deviation is always underestimated, tipical
> obtianed values are betwee 0.7 and 0.9.
> How can I get the correct std. dev?
>
> Regards
>
> --
>
> ______________________________________
>
> Oriol Falivene
> ofaliven@...
> http://www.ub.es/ggac
>
> tel. (+34) 93 4021373
> fax (+34) 93 4021340
>
> Fac. de Geologia,
> Univ. de Barcelona

--



______________________________________

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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Dear all,

I've been trying to use the 'jacknifing' function in GSLIB, with Ordinary
Kriging, with two data sets.  The first is a set of hard elevation points
(numbering about 283) over an area of a river valley, taken by GPS.  The second
is a set of 323 (approx) elevation points which are often very close to the hard
elevation points, and whose values are unsampled and to which I'm trying to
assign predicted elevations through the kriging process.  I've done the
variogram modelling etc, but when it comes to applying the method it all works
very well for predicting most of the 323 points, however, I am always left with
a little clustered group of about 7 points which always give a value of -999
(which means 'unestimated').  I've tried tweaking and fiddling around a bit with
the variogram model parameters, but all to no avail.  This stubborn select
little clustered group refuse to be 'predicted' and remain 'unestimated'.  I
can't see that their pattern is at all special, or that they are in anyway
'different' to other data which has kriged perfectly well.

I am wondering if anyone might know or might have a hunch as to what is
happening and what I should do to get these points to 'give in' and be
estimated.

Many thanks, in anticipation.

Best regards,

Gordon Norrie




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Hello list(s) and sorry for cross-posting,

I would like to generate random data on a grid with a given level of spatial
autocorrelation (Moran's I). Is there a method (and a software) to do it ?

Thanks in advance,
Sincerely.


Stephane DRAY

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Hello list members,

1. Does there any concepts or ideas concerning the comparability of time
series and spatial data exist ?
I deal with cloud top heights measured from satellite as a field and
measured by radar as a time series.
If I assume, that the clouds are advected / transported over the radar, then
I can assume a wind speed and with this wind speed I get the horizontal
extend of the time series. Now I can calculate spectrum, mean and variance
and can compare this to the same data from the satellite field. But are
there any other concepts to compare / link time series data with field /
spatial data.
2. When I get the information about the spectrum of the time series I assume
isotropy to project these spectrum on a two dimensional field.
But when there is a co-located radar nearby,  I assume the same wind
direction for both radars and transform the time series to space like
described above, are there any concepts to infer information about isotropy
and anisotropy of the underlying field from these two 'line located' data ?

Thanks for your help, inputs, and ideas in advance !

Klemens

--------
Klemens Barfus
Institute for Hydrology and Meteorology
Technical University of Dresden
Germany


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-----Original Message-----
From: Norrie, Gordon
Sent: 21 July 2004 21:24
To: ai-geostats@...
Subject: Jacknifing in GSLIB and stubborn data points

Dear all,

 

I've been trying to use the 'jacknifing' function in GSLIB, with Ordinary Kriging, with two data sets.  The first is a set of hard elevation points (numbering about 283) over an area of a river valley, taken by GPS.  The second is a set of 323 (approx) elevation points which are often very close to the hard elevation points, and whose values are unsampled and to which I'm trying to assign predicted elevations through the kriging process.  I've done the variogram modelling etc, but when it comes to applying the method it all works very well for predicting most of the 323 points, however, I am always left with a little clustered group of about 7 points which always give a value of -999 (which means 'unestimated').  I've tried tweaking and fiddling around a bit with the variogram model parameters, but all to no avail.  This stubborn select little clustered group refuse to be 'predicted' and remain 'unestimated'.  I can't see that their pattern is at all special, or that they are in anyway 'different' to other data which has kriged perfectly well.

 

I am wondering if anyone might know or might have a hunch as to what is happening and what I should do to get these points to 'give in' and be estimated.

 

Many thanks, in anticipation.

 

Best regards,

 

Gordon Norrie

 

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Hello list members,
when I posted my questions this morning -printed below- I have not
emphasized enough the question on the transformation from time to space
domain. The assumptions I have described below are just crude assumptions,
because there can be a change in cloud top height, during the advection
process. Advection can not be described as easy as I have done, because wind
direction and speed changes with altitude etc.
So the assumptions below and the resulting time-space-transformation can
describe the data very well and is therefore widely used, but the results
depend on the atmospheric conditions (wind speed etc.) described above.
Because of these uncertainties, I asked for other concepts.
One interesting concept for example is described in
http://www.bom.gov.au/bmrc/wefor/staff/cnj/Papers/jakob_etal_jgr2004.pdf
Next question refers to the radars nearby: when I use the transformation
above, I get two parallel lines with data. From these lines I can get
information for my variogram for other directions than the direction of the
lines. But these data are very sparse and there are always just particular
leg distances for every direction.
When thinking about this problem I was inspired by the article
J.R.Key (1993) Estimating the area fraction of geophysical fields from
measurements along a transect. Geoscience and Remote Sensing, IEEE
Transactions on  ,Volume: 31 , Issue: 5 Pages:1099 - 1102, though Key deals
just with indicator variables and isotropic fields but gives an insight how
many transsects are necessary to describe the underlying field.

Ok, sorry for this huge amount of text !

And thanks for your suggestions in advance !

Klemens

--------
Klemens Barfus
Institute for Hydrology and Meteorology
Technical University of Dresden
Germany


>
>
> >Hello list members,
> >
> >1. Does there any concepts or ideas concerning the comparability of time
> >series and spatial data exist ?
> >
> >I deal with cloud top heights measured from satellite as a field and
> >measured by radar as a time series.
> >If I assume, that the clouds are advected / transported over the radar,
> then
> >I can assume a wind speed and with this wind speed I get the horizontal
> >extend of the time series.
> >

> > Now I can calculate spectrum, mean and variance
> >and can compare this to the same data from the satellite field. But are
> >there any other concepts to compare / link time series data with field /
> >spatial data.
> >2. When I get the information about the spectrum of the time series I
> assume
> >isotropy to project these spectrum on a two dimensional field.
> >But when there is a co-located radar nearby,  I assume the same wind
> >direction for both radars and transform the time series to space like
> >described above, are there any concepts to infer information about
> isotropy
> >and anisotropy of the underlying field from these two 'line located' data
> ?
> >
> >
> >Thanks for your help, inputs, and ideas in advance !
> >
> >Klemens
> >
> >--------
> >Klemens Barfus
> >Institute for Hydrology and Meteorology
> >Technical University of Dresden
> >Germany
> >
> >
> >
> >
> >------------------------------------------------------------------------
> >
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