Dear Jose,
   I'm a mining engineer and I think I can answer your question. We use kriging
variance for reserve classification. I think you know, the reserves are
classified depend on their error quantity and this quantity can be represented
using variance. If we use kriging for reserve estimation you can use kriging
variance and classified reserves as possible, probable or proved reserves.
     ----- Original Message -----
     From: José Quintín Cuador Gil
     To: ai-geostats@...
     Sent: Tuesday, March 26, 2002 8:27 PM
     Subject: AI-GEOSTATS: Ore Reserves Classification


     Dear list members

     The Kriging variance has some uses. In mining, it can be used in the Ore
Reserves Classification.
     What is the opinion about this in the Geostatistical community?
     It is possible to use the Kriging variance for ores reserves
classification?, (Yes or No).
     Thanks in advances for any opinion.

     José Quintín Cuador Gil
     Department of Informática
     University of Pinar del Río
     Cuba
     <cuador@...>


[Non-text portions of this message have been removed]

The estimate and the subsequent classification of the resources in different
classes or categories is based on different levels of risk and requires a model
able to quantify this risk for evaluation and classification of mineral
resources a long time ago.
All classification systems share some common aspects in terms of defining the
classes of resources based on distance separating samples and on the degree of
confidence or accuracy associated with the results reported. Despite of being
very clear in terms of stating sample distances, all the systems of
classification do not provide clear definitions on how confidence limits should
be calculated.
While the ordinary kriging allows a fast response to determine tonnages, the
error calculated requires a series of assumptions which in various cases are
difficult to be sustained.
Care must be taken when assigning confidence intervals with  a predetermined
distribution of the kriging errors. In practice, estimation errors are rarely
normally distributed and likewise a lognormal model is just a approximation.
Another drawback of estimation is that the interpolation algorithms tend to
smooth out details of the spatial variation of the attribute, where small values
are overestimated and large values are underestimated, don´t allowing a
realistic evaluation of the uncertainty associated with the estimate.
_________________________________________________________Luis Eduardo de Souza,
Mining Engineere-mail: esouza@..., esouzabr@...
Federal University of Rio Grande do Sul - UFRGS
Mining Engineering Department
Mineral Research and Mine Planning Laboratory
Av. Osvaldo Aranha, 99/511
Porto Alegre/RS - Brazil - CEP: 90035-190
Phones:+55 51 3316-3594 (office),+55 51 3333-8229 (home),
+55 51 9905-6587 (cellular)
home-page: http://www.lapes.ufrgs.br/Pessoal/eduardo
_________________________________________________________


[Non-text portions of this message have been removed]

Dear All

I have received a couple of emails about difficulties
with accessing the stuff in my Yahoo "briefcase".
Please accept my apologies for not reading the small
print.

Apparently Yahoo has ceased allowing public access to
briefcase files as of 25th March 2002. I am working
hard to move and update all of the files and links and
hope you will bear with me in the meantime.

They should be working by Monday 1st April. If you
find any false or broken links after that please
please let me know.

Isobel Clark
http://uk.geocities.com/drisobelclark/briefcase.html

__________________________________________________
Do You Yahoo!?
Everything you'll ever need on one web page
from News and Sport to Email and Music Charts
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List Members,

The use of the kriging variance to categorise/classify Mineral (Ore) Resources
and/or Ore Reserves is an old chestnut that periodically raises it's ugly head. 
The kriging variance is related, pure and simply, to the data configuration and
has nothing to do with the sample grades/variables being used for interpolation.
As an example say a grade was being interpolated into a block which has been
sampled on each corner, regardless of what the individual sample grades are, the
kriging variance for that block is going to be the same.  Example: if all four
samples have the same grade of (say) 2.35g/t Au you will get the same kriging
variance as the case where the four samples grades are (say) 0.01, 102.9, 0.88
and 3.60 g/t Au.  Naturally I would have more confidence in the interpolated
grade in the former scenario than the latter; thus the use of the kriging
variance to determine confidence (or classification) of an estimate is
misleading.

One method of obtaining some feel for the possible error range would be to run a
large number of grade simulations into the block, the variance of all simulated
grades would give an indication of error - again in the example given above, the
variance of the simulated grades using the former case would be much smaller
than in the latter case.

Of course classification of Mineral (Ore) Resources and/or Ore Reserves needs to
take into account a lot more items  (as expounded by the JORC (1999) code) -
than just some objective measure of estimation error, it needs to take into
consideration, amongst other things, data quality - if you have poor quality
data (eg biased/inaccurate), regardless of how good any statistical measure of
the estimation error is, you will always have poor estimate.

REFERENCES
JORC; 1999: Australasian code for reporting of mineral resources and ore
reserves (the JORC Code). Prepared by the Joint Ore Reserves Committee of the
Australasian Institute of Mining and Metallurgy, Australian Institute of
Geoscientists and Minerals Council of Australia (JORC).

Richard Hague
Hellman & Schofield Pty Ltd
Brisbane Office
p&f: +61 (0)7 3217 7355
e: richardh@...
w: http://www.hellscho.com.au


   ----- Original Message -----
   From: José Quintín Cuador Gil
   To: ai-geostats@...
   Sent: Wednesday, March 27, 2002 4:27 AM
   Subject: AI-GEOSTATS: Ore Reserves Classification


   Dear list members

   The Kriging variance has some uses. In mining, it can be used in the Ore
Reserves Classification.
   What is the opinion about this in the Geostatistical community?
   It is possible to use the Kriging variance for ores reserves classification?,
(Yes or No).
   Thanks in advances for any opinion.

   José Quintín Cuador Gil
   Department of Informática
   University of Pinar del Río
   Cuba
   <cuador@...>


[Non-text portions of this message have been removed]

Richard

Thanks for the clear exposition on the limitation of
the kriging variance as a measure of reliability for
block estimation.

It should, perhaps, be pointed out that the kriging
variance is what we minimise and hence, surely, some
measure of reliability? The whole geometry versus
variability thing has been at issue since Philips and
Watson provided their seminal (sic) paper in 1986.
Given consistent data quality and a Normal (gaussian)
distribution, geometry is what determines likely
error. Under those circumstances, 1000 simulations
will yield an average of the kriged value and a
standard deviation equal to the kriging standard
deviation.

If the data quality is not consistent and the
distribution of values is not Gaussian, then your
comments hold particular force. Since these are the
circumstances under which I labour daily, I would
appreciate any and all suggestions as to what we use
instead. Simulation is not an option when you have
hundreds of thousands of blocks and a limited time to
produce a reserve.

Isobel Clark
http://www.stokos.demon.co.uk

__________________________________________________
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from News and Sport to Email and Music Charts
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Dear list members,

I wish to make a remark on the discussion started on the kriging variance.
In my opinion the SD of the solution obtained by kriging is determined by
two effects. One is the (geometrical) distribution of the data, the other
one is the (a priori) standard deviation of the data. Richards remark is
right if the data has equal weights or standard deviations (SD). However if
the data is all weighted equally (by say 1.0) we will get a scaled 'SD'. If
you like studentized statistics, you can get a estimate for the SD of the
solution by multiplying with the a posteriori variance factor.

In our problems (cross validation of bathymetry data) we have a estimate for
the SD, which we use in the covariance function for the kriging problem. The
resulting SD of the solution will depend on the chosen a priori SD for the
samples.

  Just my 2 cents,
David.



	 Quality Positioning Services bv, Huis ter Heideweg 16, 3705 LZ
Zeist, the Netherlands
Tel +31 (0)30 6925825, Fax +31 (0)30 6923663,  Web http://www.qps.nl
<http://www.qps.nl/>


	 -----Original Message-----
From: Richard Hague [mailto:richardh@...]
Sent: woensdag 3 april 2002 6:48
To: ai-geostats@...
Subject: Re: AI-GEOSTATS: Ore Reserves Classification



List Members,

The use of the kriging variance to categorise/classify Mineral (Ore)
Resources and/or Ore Reserves is an old chestnut that periodically raises
it's ugly head.  The kriging variance is related, pure and simply, to the
data configuration and has nothing to do with the sample grades/variables
being used for interpolation.  As an example say a grade was being
interpolated into a block which has been sampled on each corner, regardless
of what the individual sample grades are, the kriging variance for that
block is going to be the same.  Example: if all four samples have the same
grade of (say) 2.35g/t Au you will get the same kriging variance as the case
where the four samples grades are (say) 0.01, 102.9, 0.88 and 3.60 g/t Au.
Naturally I would have more confidence in the interpolated grade in the
former scenario than the latter; thus the use of the kriging variance to
determine confidence (or classification) of an estimate is misleading.

One method of obtaining some feel for the possible error range would be to
run a large number of grade simulations into the block, the variance of all
simulated grades would give an indication of error - again in the example
given above, the variance of the simulated grades using the former case
would be much smaller than in the latter case.

Of course classification of Mineral (Ore) Resources and/or Ore Reserves
needs to take into account a lot more items  (as expounded by the JORC
(1999) code) - than just some objective measure of estimation error, it
needs to take into consideration, amongst other things, data quality - if
you have poor quality data (eg biased/inaccurate), regardless of how good
any statistical measure of the estimation error is, you will always have
poor estimate.

REFERENCES
JORC; 1999: Australasian code for reporting of mineral resources and ore
reserves (the JORC Code). Prepared by the Joint Ore Reserves Committee of
the Australasian Institute of Mining and Metallurgy, Australian Institute of
Geoscientists and Minerals Council of Australia (JORC).

Richard Hague
Hellman & Schofield Pty Ltd
Brisbane Office
p&f: +61 (0)7 3217 7355
e: richardh@... <mailto:richardh@...>
w: http://www.hellscho.com.au <http://www.hellscho.com.au>



----- Original Message -----
From: José  <mailto:cuador@...> Quintín Cuador Gil
To: ai-geostats@... <mailto:ai-geostats@...>
Sent: Wednesday, March 27, 2002 4:27 AM
Subject: AI-GEOSTATS: Ore Reserves Classification

Dear list members

The Kriging variance has some uses. In mining, it can be used in the Ore
Reserves Classification.
What is the opinion about this in the Geostatistical community?
It is possible to use the Kriging variance for ores reserves
classification?, (Yes or No).
Thanks in advances for any opinion.

José Quintín Cuador Gil
Department of Informática
University of Pinar del Río
Cuba
< cuador@... <mailto:cuador@...> >



[Non-text portions of this message have been removed]

Dear members,

I want to know about geostatistics inversion.
What was it ?
Can you help me ?

Best regards

Didiek Bhudy Prabowo
University of Indonesia




---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6.0.338 / Virus Database: 189 - Release Date: 14/03/02


[Non-text portions of this message have been removed]

Dear members,
could you suggest me papers about application of sequential Gaussian
simulations to soil sciences, i.e., spatial distribution of a continuous
soil attribute, gas fluxes from soil, mapping the distribution of element
concentration etc...
I am working with GSLIB for mapping gas fluxes from soils.
Best Regards,
Carlo Cardellini.

Dr. Carlo Cardellini
Dipartimento di Scienze della Terra, Università di Perugia
Piazza Università, 06100 Perugia
ITALY
tel +39 075 5852617
Fax +39 075 5852603
e-mail geochem@...


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I would suggest:

@Article{rossi:1993,
author           = {R.E. Rossi and P.W. Borth and J.J. Tollefson},
title            = {Stochastic simulation for characterizing ecological
spatial patterns and appraising risk},
journal          = {Ecological applications},
year             = 1993,
volume           = 3,
pages            = {719-735}
}

Best regards / Venlig hilsen

Søren Lophaven
******************************************************************************
Master of Science in Engineering        |  Ph.D. student
Informatics and Mathematical Modelling  |  Building 321, Room 011
Technical University of Denmark         |  2800 kgs. Lyngby, Denmark
E-mail: snl@...                  |  http://www.imm.dtu.dk/~snl
Telephone: +45 45253419                 |
******************************************************************************

On Thu, 4 Apr 2002, Cardellini Carlo wrote:

> Dear members,
> could you suggest me papers about application of sequential Gaussian
> simulations to soil sciences, i.e., spatial distribution of a continuous
> soil attribute, gas fluxes from soil, mapping the distribution of element
> concentration etc...
> I am working with GSLIB for mapping gas fluxes from soils.
> Best Regards,
> Carlo Cardellini.
>
> Dr. Carlo Cardellini
> Dipartimento di Scienze della Terra, Università di Perugia
> Piazza Università, 06100 Perugia
> ITALY
> tel +39 075 5852617
> Fax +39 075 5852603
> e-mail geochem@...
>
>
> --
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>


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Dear Didiek,

Inversion is advanced topics in Geostatistics. There is good introduction
to inverse problems (and scale effects) in chapter 8 of J-P Chiles and
Pierre Delfiner's book titled Geostatistics: Modelling Spatial Uncertainty
(Wiley, 1999). The book also covers inverse problem in hydrogeology

Regards,

Bambang

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dear members,


Is there anyone with experiences in indicator kriging with soft data using
gslib ?

i have a continous primary variable and a continous (exhaustive) secondary
variable. I allready did "normal" indicator kriging (so i allready have a
set of transformed hard indicator data and variograms for the corresponding
thresholds) and the result looks rather plausible. my idea now is to
incorporate the secondary variable within indicator kriging to improve the
estimates in regions where sample densitiy is sparse (similar to kriging
with external drift or simple kriging with varying local means using uncoded
"raw" values).

the most straightforward method seems to be simple indicator kriging using
soft prior probabilities as described by Goovaerts (1997; pp 307) and
Deutsch & Journel (1998; pp77, i hope they mean the same by "simple kriging
with prior means" !).

some questions about that method just to be sure that i am on the right way:

1. first i have to classify my secondary (continous) soft data. how do i get
discrete classes of soft data with a "calibration scattergram". In Deutsch &
Journel 1998; pp92 i can not recognize how they decided to classify ! what
is the best way to classify - the more classes the better ?

2. i have to calculate soft prior probabilities. the calibration step is to
calculate for each class the proportions of data that do not exceed one (or
more) threshold(s) (i have 7 thresholds!).  example: i have defined 3 (or 5)
classes of soft data (question 1) so i have to calculate 3(5) different
frequencies of not exceeding one threshold. the classes of soft data are
then replaced by the calculated soft probabilities (=local prior
probabilities)  => if i have more thresholds i get 3(5) different values as
local prior probabilities for each threshold ???

3. the rest of the method is very similar to simple kriging with varying
local means. the residuals i get by substracting hard indicator data [0,1]
from local soft probabilities (0 ....1) calculated in question 3. the
residuals are used to calculate semivariograms.

4. how can i do the kriging step within wingslib? with ik3d (what about the
exhaustive data-file?) or with kt3d? at least i want to use all the
advantages of indicator kriging (maps of estimated values, probabilities,
quantiles)


p.s. i am looking for some basic references on indicator kriging (using soft
data) with gslib, especially Journel (1987): Geostatistic for the
environmental sciences, EPA project no. cr 811893. Technical report. U.S.
EPA Lab, Las Vegas, NV. it's hard to get in germany ...

regards
Lenz



Lorenz Dobler
Bayer. Geologisches Landesamt
Heßstr. 128
80797 München
Tel.: 089/9214-2766
e-mail: Lorenz.Dobler@...


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I am interested in comparing different estimators of spatial means.  Any
suggestions or approaches on how to generate a 2-D, autocorrelated, skewed
distribution that exhibits non-stationary mean and variance?

Thanks in advance for your ideas.
**************************************************
William C. Thayer, P.E.

Environmental Science Center
Syracuse Research Corporation
301 Plainfield Road, Suite 350
Syracuse, NY 13212
phone: (315) 452-8424
fax: (315) 452-8440
email: thayer@...
web: http://esc.syrres.com/
         http://esc.syrres.com/geosem/
**************************************************



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I´m doing my diploma thesis on the spatial distribution of weeds and I´m an
absolute beginner with geostatistics. Please take that into account when reading
my question.

My data are weed counts with excess zeros and fit a negative binomial
distribution. But as far as I know semivariagram modelling can only be done with
a more or less gaussian distribution. If yes, has anybody an idea how to
transform negative binomial data to get a gaussian distribution? I would be very
pleased if anybody of you could give me at least a tip how to solve this problem
or maybe you can recommend some literature.


Thanks a lot in advance.

Regards,
Sibylle



[Non-text portions of this message have been removed]

Yes. Generate a Gaussian random field, add a deterministic trend
surface, and take the exponent or a power transform of the sum.
--
Edzer

William Thayer wrote:
>
> I am interested in comparing different estimators of spatial means.  Any
> suggestions or approaches on how to generate a 2-D, autocorrelated, skewed
> distribution that exhibits non-stationary mean and variance?
>

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Dear Sibylle,

I suspect your residuals will never become normal, because your data
are counts. Luckily, normality is not a requirement for variogram
calculation nor for kriging interpolation.

However, before calculating variograms it may be a good idea to
correct for non-stationarity in the variances, and work with Pearson
residuals.

See:

Gotway, C.A., Stroup, W.W. (1997) A Generalized Linear Model Approach
to Spatial Data Analysis and Prediction. Journal of Agricultural, Biological
and Environmental Statistics 2(2), pp. 157--178.

Diggle, P.J., Liang, K-Y., Zeger, S.L. (1994) Analysis of Longitudinal
Data. Oxford University Press, Oxford.

or the more advanced approach of:

Diggle, P.J., J.A. Tawn, R.A. Moyeed (1998), Model-based
geostatistics. Applied Statistics 47(3), pp 299-350.
--
Edzer

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Dear all,

We are trying to apply Universal Kriging to “High Plains” Aquifer in
Kansas (OLEA, 1999) for land surface elevation (LSE), using its 317 data
points. The purpose of this application is just for didactic ends.
Our first step was to filter a prominent 1st degree drift. The way we
did it was using Surfer 8.0 (Golden Software) and obtaining the
residuals, in such way that summing the residuals by the 1st degree
trend we obtain the original data.
Obviously the values of this new variable (residuals of LSE, i.e., RLSE)
are much lower than the original one.
Calculating the experimental variogram, modeling it and kriging the
variable is possible to obtain the RLSE (residuals of land surface
elevation) map. Summing this map to the drift (calculated in a
deterministic way) we obtain a map that we suppose that represents a map
for the original variable (LSE).
But what about the standard deviation?
We did a little test and it seems that the standard deviation map for
the residuals (RLSE) represents the std. dev. map for the original
variable (LSE).

Is this a correct conclusion and procedure? If we have less data, will
it work? If we use a 2nd degree drift the standard deviation could be
wrong?

Thanks for your attention,

Rubens

==========================
Rubens Caldeira Monteiro
# ICQ 106157533
São Paulo State University at Rio Claro  - UNESP/Rio Claro
– PhD candidate on Geosciences & Environmental Sci.
São Paulo University at Piracicaba - ESALQ-USP/Piracicaba
– Undergrad. on Environmental Management
University of North Carolina at Chapel Hill - UNC-CH
URL:  <http://www.unc.edu/~rubenscm/CASEhome.html>
http://www.unc.edu/~rubenscm/CASEhome.html



[Non-text portions of this message have been removed]

Hello,

I would like to know if there is any free softwares (for windows), "easy to
use" that can perform
spheric variogram fitting
cross-variogram
co-krigging

could you help me, please?
Thank you
Marta


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Rubens

Your approach has been long used in hydrology and
similar fields with much success.

The problem with the standard deviation is that it
does not include the the 'error' on the estimation of
the true drift. To get a composite error you would
either have to

(a) add your kriging variance to some sort of
classical regression variance to get a composite one;

(b) use a Universal Kriging (or generalised
covariance) approach to estimate the surface with the
drift included.

In our experience, your estimated surface will not
change but your kriging variances will increase
slightly.

Isobel Clark

__________________________________________________
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Alessandro

Thanks for the contribution.

If Universal Kriging is applied, there is no need for
simulation or multi-indicator approaches to get a
standard error, it comes with the solution.

Isobel

__________________________________________________
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Dear all,

I'm working with data from Lateritic Ni Deposits.
I want to know what is the exploration grid traditionally in this type of
deposits.
I ask this question because the Ni grade is extremely variable in this deposits
and I trying to find the must suitable grid to study this deposits.
Thanks in advance for any opinion.

Regards

José Quintín Cuador Gil
Departamento de Informática
Universidad de Pinar del Río
Cuba
<cuador@...>


[Non-text portions of this message have been removed]

Dear all,

in the case you send a question to the list, may I remind you to post a
summary of any useful responses ?
This good old tradition does not seem to be always respected these last
months.

Thank you for your comprehension,


Gregoire

(Moderator/Owner of the ai-geostats mailing list)


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Hi all

The answers I have received about the subject Ore Reserves Classification are
listed below:
Thanks everyone.
José Quintín

José Quintín Cuador Gil
Computer Department
University of Pinar del Río
Cuba
<cuador@...>

********************************************************************************\
**********************
Question:
Dear list members

The Kriging variance has some uses. In mining, it can be used in the Ore
Reserves Classification.
What is the opinion about this in the Geostatistical community?
It is possible to use the Kriging variance for ores reserves classification?,
(Yes or No).
Thanks in advances for any opinion.


José Quintín Cuador Gil
Computer Department
University of Pinar del Río
Cuba
<cuador@...>


Answers:
********************************************************************************\
**********************
Form Joao Felipe

yes, have a look at APCOM 2002 proceedings and you'll find a couple a papers in
the subject including one I'm a senior authors. If you don't have access to the
proceedings I'll be glad to send you an electronic copy

regards

--------------------------------------------------------------------------------\
------------------------
Joao Felipe Coimbra Leite Costa, Mining Engineer, MSc, PhD
Mining Engineering Department
Federal University of Rio Grande do Sul
Av. Osvaldo Aranha 99/504 90035-190
Porto Alegre, Brazil
+55 +51 33163357
Fax +55 +51 32864343
Home +55 +51 32229321
--------------------------------------------------------------------------------\
-----------------------

********************************************************************************\
**********************
From Marcelo Godoy

Hi José,

Yes, it is possible! But you have to keep in mind the fact that
estimation variance is just a function of sample density. It does
not reflect spatial variability at all. In the latest edition of
the APCOM Symposium several papers have been presented that explore
the issue of Ore Reserve Classification.

Cheers,

Marcelo

-----------------------------------------------------------------
Marcelo C. Godoy, MSc, PhD candidate
University of Queensland                    Tel:  +61 7 3365 1674
W.H. Bryan Mining Geology Research Centre   Fax : +61 7 3365 7028
Brisbane, Qld 4072, Australia               Home: +61 7 3870 7069
E-mail: m.godoy@...
http://www.minmet.uq.edu.au/~bryan/staff/marcelo.html
-----------------------------------------------------------------

********************************************************************************\
**********************
Form Turkan Kaynak <turkan@...>

Dear Jose,
I'm a mining engineer and I think I can answer your question. We use kriging
variance for reserve classification. I think you know, the reserves are
classified depend on their error quantity and this quantity can be represented
using variance. If we use kriging for reserve estimation you can use kriging
variance and classified reserves as possible, probable or proved reserves

********************************************************************************\
**********************
Form Mark Burnett Deelkraal <MBurnett@...>

Dear Jose
Isobel Clarke will probably also comment on this question, however I would
suggest you have a look in the archives at the ai-geostats home page. This
question is generally raised at least once a year.

My personal experience is that using the krige slope of regression (0.6)
works well for ordinary kriging on a Witwatersrand ore body (as long as you
are not trying to estimates more than 10 to 20m ahead of your data. Simple
krige with varying local area means would need a more laborious process,
however here I have found that the Kvar does work.

It still boils down to the quality of your data and a solid understanding of
your ore body.

Hope this helps

Mark

M. Burnett

Ore Reserve Manager
Elandskraal
Production Unit 1 (Deelkraal)
Tel. 018 785 6625

www.Harmony.co.za

********************************************************************************\
**********************
Form Luis Eduardo de Souza <esouza@...>

The estimate and the subsequent classification of the resources in different
classes or categories is based on different levels of risk and requires a model
able to quantify this risk for evaluation and classification of mineral
resources a long time ago.
All classification systems share some common aspects in terms of defining the
classes of resources based on distance separating samples and on the degree of
confidence or accuracy associated with the results reported. Despite of being
very clear in terms of stating sample distances, all the systems of
classification do not provide clear definitions on how confidence limits should
be calculated.
While the ordinary kriging allows a fast response to determine tonnages, the
error calculated requires a series of assumptions which in various cases are
difficult to be sustained.
Care must be taken when assigning confidence intervals with  a predetermined
distribution of the kriging errors. In practice, estimation errors are rarely
normally distributed and likewise a lognormal model is just a approximation.
Another drawback of estimation is that the interpolation algorithms tend to
smooth out details of the spatial variation of the attribute, where small values
are overestimated and large values are underestimated, don´t allowing a
realistic evaluation of the uncertainty associated with the estimate.

_________________________________________________________
Luis Eduardo de Souza, Mining Engineer
e-mail: esouza@..., esouzabr@...
Federal University of Rio Grande do Sul - UFRGS
Mining Engineering Department
Mineral Research and Mine Planning Laboratory
Av. Osvaldo Aranha, 99/511
Porto Alegre/RS - Brazil - CEP: 90035-190
Phones:+55 51 3316-3594 (office),+55 51 3333-8229 (home),
+55 51 9905-6587 (cellular)
home-page: http://www.lapes.ufrgs.br/Pessoal/eduardo
_________________________________________________________

********************************************************************************\
**********************
Form Richard Hague <richardh@...>

List Members,

The use of the kriging variance to categorise/classify Mineral (Ore) Resources
and/or Ore Reserves is an old chestnut that periodically raises it's ugly head. 
The kriging variance is related, pure and simply, to the data configuration and
has nothing to do with the sample grades/variables being used for interpolation.
As an example say a grade was being interpolated into a block which has been
sampled on each corner, regardless of what the individual sample grades are, the
kriging variance for that block is going to be the same.  Example: if all four
samples have the same grade of (say) 2.35g/t Au you will get the same kriging
variance as the case where the four samples grades are (say) 0.01, 102.9, 0.88
and 3.60 g/t Au.  Naturally I would have more confidence in the interpolated
grade in the former scenario than the latter; thus the use of the kriging
variance to determine confidence (or classification) of an estimate is
misleading.

One method of obtaining some feel for the possible error range would be to run a
large number of grade simulations into the block, the variance of all simulated
grades would give an indication of error - again in the example given above, the
variance of the simulated grades using the former case would be much smaller
than in the latter case.

Of course classification of Mineral (Ore) Resources and/or Ore Reserves needs to
take into account a lot more items  (as expounded by the JORC (1999) code) -
than just some objective measure of estimation error, it needs to take into
consideration, amongst other things, data quality - if you have poor quality
data (eg biased/inaccurate), regardless of how good any statistical measure of
the estimation error is, you will always have poor estimate.

REFERENCES
JORC; 1999: Australasian code for reporting of mineral resources and ore
reserves (the JORC Code). Prepared by the Joint Ore Reserves Committee of the
Australasian Institute of Mining and Metallurgy, Australian Institute of
Geoscientists and Minerals Council of Australia (JORC).

Richard Hague
Hellman & Schofield Pty Ltd
Brisbane Office
p&f: +61 (0)7 3217 7355
e: richardh@...
w: http://www.hellscho.com.au

********************************************************************************\
**********************
From Isobel Clark <drisobelclark@...>

Richard

Thanks for the clear exposition on the limitation of
the kriging variance as a measure of reliability for
block estimation.

It should, perhaps, be pointed out that the kriging
variance is what we minimise and hence, surely, some
measure of reliability? The whole geometry versus
variability thing has been at issue since Philips and
Watson provided their seminal (sic) paper in 1986.
Given consistent data quality and a Normal (gaussian)
distribution, geometry is what determines likely
error. Under those circumstances, 1000 simulations
will yield an average of the kriged value and a
standard deviation equal to the kriging standard
deviation.

If the data quality is not consistent and the
distribution of values is not Gaussian, then your
comments hold particular force. Since these are the
circumstances under which I labour daily, I would
appreciate any and all suggestions as to what we use
instead. Simulation is not an option when you have
hundreds of thousands of blocks and a limited time to
produce a reserve.

Isobel Clark
http://www.stokos.demon.co.uk




[Non-text portions of this message have been removed]

Dear list members

My question is as follows:

In my exercise,  semivariance value is at near zero
high at first lag, then in second lag jumps to the
highest semivariance value, and then decreases
gradually to global variance and fluactuates around
it. These data is logtransformed form of a data with a
skewness of 3.9. Variogram is omnidirectional. Data is
composed of 34 samples.

Where is the problem? How to solve this?

Regards
Ercan

__________________________________________________
Do You Yahoo!?
Yahoo! Tax Center - online filing with TurboTax
http://taxes.yahoo.com/

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** Reply Requested When Convenient **

Dear colleagues,

I don't have much experience with geostatistics, but from now on I will use it
in my PhD-study on spatial variability in soil physical properties and
hydrological processes. I've been looking for the "ultimate" software for some
time now, and I've tried GS+ from Gamma Designs and Genstat5 from the Numerical
Algorithms Group Ltd. I also have access to Arcview spatial analyst (ESRI). My
newest data typically show significant spatial trends, and some data exhibit
very distinct periodicity. I'd be very greatful to get some advice on what
software to choose (unfortunately I'm not very good at programming...), and also
some comments on your experiences with the already mentioned programs.

Thanks!

Best regards,
Sigrun


Sigrun H. Kværnø
Centre for Soil and Environmental Research
Frederik A. Dahls vei 20
N-1432 Ås
NORWAY


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Ercan,

There might be two problems in your data set.
(1) The sample number is too small.
(2) The are some high value outliers in your data set.

I understand that it is hard for you to improve the first problem. However,
the second problem can be partly solved by (1) excluding the outliers in the
variogram calculation; (2) a better transformation (e.g., Box-Cox); (3) use
of median values instead of the average in the variogram calculation. The
highest value at the first lag is caused by some pairs of significant
variance at very short distances (one of the values in these pairs should be
regarded as a spatial outlier).

Good luck.

Chaosheng Zhang
=================================================
Dr. Chaosheng Zhang
Lecturer in GIS
Department of Geography
National University of Ireland
Galway
IRELAND

Tel: +353-91-524411 ext. 2375
Fax: +353-91-525700
Email: Chaosheng.Zhang@...
        ChaoshengZhang@...
Web: http://www.nuigalway.ie/geography/zhang.html
=================================================

----- Original Message -----
From: "Ercan Yesilirmak" <ercanyesilirmak@...>
To: <ai-geostats@...>
Sent: Monday, April 15, 2002 8:59 AM
Subject: AI-GEOSTATS: relatively high semivariances at first lags


> Dear list members
>
> My question is as follows:
>
> In my exercise,  semivariance value is at near zero
> high at first lag, then in second lag jumps to the
> highest semivariance value, and then decreases
> gradually to global variance and fluactuates around
> it. These data is logtransformed form of a data with a
> skewness of 3.9. Variogram is omnidirectional. Data is
> composed of 34 samples.
>
> Where is the problem? How to solve this?
>
> Regards
> Ercan
>
> __________________________________________________
> Do You Yahoo!?
> Yahoo! Tax Center - online filing with TurboTax
> http://taxes.yahoo.com/
>
> --
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> * As a general service to the users, please remember to post a summary of
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"unsubscribe ai-geostats" followed by "end" on the next line in the message
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The replies I received to my request appear below, along with the original
request for help.  Thanks to those who replied.

Original request:
I am interested in comparing different estimators of spatial means.  Any
suggestions or approaches on how to generate a 2-D, autocorrelated, skewed
distribution that exhibits non-stationary mean and variance?

Replies:
How about using sasim.f in GSLIB to generate several non-conditional
realizations of a property using simulated annealing? You can
specify:

1. a user-defined histogram, which may be as skewed as you wish, and
2. a non-stationary power law variogram (fractional Brownian motion)
to approximate a variable with a drift component.

Hope this helps.

Syed

Bill, just a quick idea.  Build a variogram with a trend in it, no sill, and
use it in a Gaussian simulator (e.g., sgsim).  Make the simulation in
standard normal space and then use the GSLIB trans program to transform it
to any raw-space skewed distribution you want.  The transformation is
quantile preserving so should not change the autocorrelation, but I would
double-check the results.  This process will certainly generate a correlated
field with a skewed distribution and non-stationary mean.  I'm not exactly
sure how you want the variance to be non-stationary and that may be harder
to do.  Non-linear transforms can produce a prorportional effect (variance
is a function of the simulated value), but they generally don't preserve the
variogram.

good luck

Sean

Without giving it too much thought, I wonder if just generating a
stationary autocorrelated normal field, Zn and "back-transforming" it to
produce a lognormal field, Zl wouldn't work?  Because the kriging variance
comes into both the mean and variance of the back-transformed variable, it
should
be non-stationary.

Yetta


Yes. Generate a Gaussian random field, add a deterministic trend
surface, and take the exponent or a power transform of the sum.

Edzer
**************************************************
William C. Thayer, P.E.

Environmental Science Center
Syracuse Research Corporation
301 Plainfield Road, Suite 350
Syracuse, NY 13212
phone: (315) 452-8424
fax: (315) 452-8440
email: thayer@...
web: http://esc.syrres.com/
        http://esc.syrres.com/geosem/
**************************************************



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Hi!

Please find below my original message and the list of answers to my question
concering the transformation of negative binomial data deriving from weed
counts. Thanks everybody for your effort!

Sibylle

--------------------------------------------------------------------------------


I´m doing my diploma thesis on the spatial distribution of weeds and I´m an
absolute beginner with geostatistics. Please take that into account when reading
my question.

My data are weed counts with excess zeros and fit a negative binomial
distribution. But as far as I know semivariagram modelling can only be done with
a more or less gaussian distribution. If yes, has anybody an idea how to
transform negative binomial data to get a gaussian distribution? I would be very
pleased if anybody of you could give me at least a tip how to solve this problem
or maybe you can recommend some literature.


Thanks a lot in advance.

Regards,
Sibylle

--------------------------------------------------------------------------------

I suggest you may want to transform the data in a different way, namely by
recording as a rate per something such as area, i.e. to make the data look like
averages over cells. Presumably your counts already represent something like
this but the problem with pure counts is that they don't "add" right. The
variogram corresponds to "point" data and the theory provides a way to
"regularize" the variogram when the support changes, pure counts will likely not
behave properly in that respect.

With respect to transforming a negative binomial to a normal, strictly speaking
that can't be done since the negative binomial is discrete and the normal is
continuous. You might want to look at some of the literature relating to
geostatistics and entomology, see for example papers by Liebhold and Hohn.

Donald E. Myers
http://www.u.arizona.edu/~donaldm


--------------------------------------------------------------------------------


Hi,

just a quick suggestion. If you have enough data you could use a non-parametric
indicator kriging technique. Often when there are many zeros this works well to
delineate the regions of presence and absence.

Ben

Benjamin Warr

Research Associate
Centre for the Management of Environmental Resource(CMER)
INSEAD
Boulevard de Constance,
77305 Fontainebleau Cedex,
France

Tel: 33 (0)1 60 72 4456
Fax: 33 (0)1 60 74 55 64
e-mail: benjamin.warr@...
http://www.insead.fr/CMER



--------------------------------------------------------------------------------


Sibylle,

I am rather new on geostats too, and I went through the same problem when I
started.  I work with soybean cyst nematode, so I also have count data with
a negative binomial distribution.
What I did with my data is a log 10(counts+1) transformation.  Then you do
the semivariogram and if it is not stationary, try to remove a linear or a
quadratic trend.  If that solves the non-stationarity problem, then apply
universal krigging.
It is pretty simple to do with Surfer.

Good luck!
Felicitas


--------------------------------------------------------------------------------




Hy Sibylle

You can fit variogram models for any kind of distribution. Gaussian
distributions are required just on some
simulation algorithms, but gaussian transformation (or gaussian anamorphosis) is
a useful
tool to use and transform a raw variable in a gaussian variable, with mean = 0
and variance = 1,
making structures more clear on variography.

For that you can use gslib (normal score transformation or nscore.par) or
gaussian anamorphosis
at Isatis Software (Geovariances).


Alessandro Henrique Medeiros Silva
Geologist - Anglogold Brasil
alessandro@...

+55-31-3589-1687
+55-31-9953-0759


--------------------------------------------------------------------------------


Dear Sibylle,

I suspect your residuals will never become normal, because your data
are counts. Luckily, normality is not a requirement for variogram
calculation nor for kriging interpolation.

However, before calculating variograms it may be a good idea to
correct for non-stationarity in the variances, and work with Pearson
residuals.

See:

Gotway, C.A., Stroup, W.W. (1997) A Generalized Linear Model Approach
to Spatial Data Analysis and Prediction. Journal of Agricultural, Biological
and Environmental Statistics 2(2), pp. 157--178.

Diggle, P.J., Liang, K-Y., Zeger, S.L. (1994) Analysis of Longitudinal
Data. Oxford University Press, Oxford.

or the more advanced approach of:

Diggle, P.J., J.A. Tawn, R.A. Moyeed (1998), Model-based
geostatistics. Applied Statistics 47(3), pp 299-350.
--
Edzer


--------------------------------------------------------------------------------


Just as a complement to Edzer's email:

The package geoRglm (www.maths.lancs.ac.uk/~christen)
does the analysis based on the Poison/Binomial  models
suggested in his last reference.

geoRglm in an add-on (package) to the R software (www.r-project.org)

Cheers
P.J.


Paulo Justiniano Ribeiro Jr
Departamento de Estatistica
Universidade Federal do Parana'
Caixa Postal 19.081
CEP 81.531-990
Curitiba, PR  -  Brasil

e-mail: Paulo.Ribeiro@...
http://www.maths.lancs.ac.uk/~ribeiro (english)
http://www.est.ufpr.br/~ribeiro (portugues)


--------------------------------------------------------------------------------


Hi Sybille,

You may want to look at using an indicator transformation for your data.
I.e. split the distribution into (ordered) intervals (say 5 ore more..but it
will depend on your data)...and code your variable as 1 if it is less than
the interval-threshold, 0 if it is not. So you get a 'categorical' data set.
Zero could be one of the thresholds.
You would then use indicator kriging to interpolate.
This is usually more flexible and does not use a gaussian model.

I hope it helps,

Alessandro Gimona
Fisheries Research Services
Aberdeen
Scotland UK






[Non-text portions of this message have been removed]

Either use Gstat (www.gstat.org) or/and gslib (www.gslib.com).

Both maybe not as user friendly in the sense of nice GUIs as the software
you used so far. but they are very powerful and provide lots of methods
and oportunities to solve spatial stats problems. It is worth using them.
And they are free :-)

there are also quite a number of possibilities in R (S-Plus clone)
(www.r-project.org). But I do not know much about the modules. But R is
worth using anyway because it is a quite powerful statistics software,
maybe the most powerful at the moment. And it is free again.

Regards, Ulrich

On Mon, 15 Apr 2002, Sigrun Kværnø wrote:

> ** Reply Requested When Convenient **
>
> Dear colleagues,
>
> I don't have much experience with geostatistics, but from now on I will use it
in my PhD-study on spatial variability in soil physical properties and
hydrological processes. I've been looking for the "ultimate" software for some
time now, and I've tried GS+ from Gamma Designs and Genstat5 from the Numerical
Algorithms Group Ltd. I also have access to Arcview spatial analyst (ESRI). My
newest data typically show significant spatial trends, and some data exhibit
very distinct periodicity. I'd be very greatful to get some advice on what
software to choose (unfortunately I'm not very good at programming...), and also
some comments on your experiences with the already mentioned programs.
>
> Thanks!
>
> Best regards,
> Sigrun
>
>
> Sigrun H. Kværnø
> Centre for Soil and Environmental Research
> Frederik A. Dahls vei 20
> N-1432 Ås
> NORWAY
>
>
> --
> * To post a message to the list, send it to ai-geostats@...
> * As a general service to the users, please remember to post a summary of any
useful responses to your questions.
> * To unsubscribe, send an email to majordomo@... with no subject and
"unsubscribe ai-geostats" followed by "end" on the next line in the message
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>

--
__________________________________________________

Ulrich Leopold MSc.

Department of Physical Geography
Institute for Biodiversity and Ecosystem Dynamics
Faculty of Science
University of Amsterdam
Nieuwe Achtergracht 166
NL-1018WV Amsterdam

Phone: +31-(0)20-525-7456 (7451 Secretary)
Fax:   +31-(0)20-525-7431
Email: uleopold@...
http://www.frw.uva.nl/soil/Welcome.html

Check us also out at:
Netherlands Centre for Geo-ecological Research
http://www.frw.uva.nl/icg




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Hi Sibylle:

Sorry this is so late, but I have just been working on generating a negative
binomial as described by Pielou, Cressie and others (e.g., Diggle,
Ripley).  Apparently it can be derived in two ways, one of which is a
Poisson distribution of clusters (of weeds) and a gamma distribution
describing the number of individual weeds per cluster.

You don't say what your objective is -- if you are interested in kriging,
do you want to interpolate to find weed patches that you missed during
sampling, generate other possible realizations, or you just want to find an
index of autocorrelation?
Because you are focusing on the semivariogram, I'm assuming its the latter
you want.  The ratio of the variance to the mean (counts/quadrat) and
Ripley's K are two indices of contagion used to describe point processes.
The semivariogram is not the best tool to analyze your data with. I would
look in Cressie's book, Chapter 8 on Spatial point patterns.  If you want
to generate alternative realizations or describe your distribution, one (or
more) of these can be fitted to your data.

Good luck.

Yetta

At 09:07 AM 4/16/2002 +0200, you wrote:
>Hi!
>
>Please find below my original message and the list of answers to my
>question concering the transformation of negative binomial data deriving
>from weed counts. Thanks everybody for your effort!
>
>Sibylle
>
>----------
>
>I´m doing my diploma thesis on the spatial distribution of weeds and I´m
>an absolute beginner with geostatistics. Please take that into account
>when reading my question.
>
>My data are weed counts with excess zeros and fit a negative binomial
>distribution. But as far as I know semivariagram modelling can only be
>done with a more or less gaussian distribution. If yes, has anybody an
>idea how to transform negative binomial data to get a gaussian
>distribution? I would be very pleased if anybody of you could give me at
>least a tip how to solve this problem or maybe you can recommend some
>literature.
>
>Thanks a lot in advance.
>
>Regards,
>Sibylle
>
>----------


[Non-text portions of this message have been removed]

Dear Stuart.

I good reference paper is:

Geostatistical Simulations of regio0nalized Pore-Size Distributions Using
Min?Max Autocorrelation Factors.
A. J. Desbarats and R. Dimitrakopoulos
Mathematical Geology Vol. 32, N 8 2000
p 919-942


Cheers

Márcio Bastos Fonseca


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