This follow-up is slighlty aside the subject line of the mailing list, but
as a geologist, this is the only statistically-flavoured one I am
subscribed to. Therefore :

Federico Pardo said:
> Having N samples, and then n degrees of freedom.
> One degree of freedom is used (or taken) by the mean calculation.
> Then when you calculate the variance or the standard deviation, you only
> have left n-1 degrees of freedom.

Apart a rigorous calculation I am aware of that in this very case (cf.
Peter Bossew's contribution on the same thread, that details it), gives a
proof for this rule-of-thumb, what more or less rigourous statistical
developments gives consistance to it ?

I mean, for the empirical correlation coefficient,
rhoXiYi = SUM_i=1..N( (x_i - mx).(y_i - my) / sx / sy ) / WHAT_NUMBER
Must WHAT_NUMBER be, for a kind of unbiased estimate ("a kind of" meaning
"with some eventual Fisher z-transform"...):
* N for simplicity,
* N-2 as I have most frequently seen in books that dare give this formula
(N points, minus 1 for position and 1 for dispersion ?),
* or 2N-4 -- 2N for the (x_i,y_i), minus 4 for {mx,my,sx,sy} -- as a
strict application of the rule-of-thumb seems to suggest ?

And what about, when fitting for instance a 3-parameter non-linear
function, reducing the number of degrees of freedom, to N-3 (number of
points, minus one for each function parameter ? I have never read any kind
of explanation to support it, though it seems widely

Thanks in advance for enlightments or simply tracks for other resources of
explanations.
-- Éric L.

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David Reid
-----Original Message-----
From: Colin Badenhorst [mailto:CBadenhorst@...]
Sent: Wednesday, 31 August 2005 8:58 PM
To: ai-geostats@...
Subject: [ai-geostats] Sum of Estimates

Dear List,

 

I have a rather interesting problem with my Kriged estimates for a base metal mine. I am estimating Zn, Pb and Fe, as percentage, the sum of which should total to no more than 100% total sulphides.

 

All Zn comes from sphalerite (ZnS) at 0.671 proportion. Sphalerite SG = 3.80

All Pb comes from galena (PbS) at 0.866 proportion. Galena SG = 7.40

All Fe comes from pyrite (FeS2) at 0.466 proportion. Pyrite SG = 4.80

Total Sulphides = (Zn estimate x 1.4903) + (Pb estimate x 1.1547) + (Fe x 2.1459)

 

What I have discovered is that I have areas in which the total sulphides are greater than 100% - with very few exceptions, the total is no more than 105% total sulphide.

 

My estimation domains for Zn and Pb are well constrained and validated, and the variogram models and estimation parameters are robust, and have been tested and validated to ensure they match the geological expectations. My domains for Fe are less well constrained but the variogram models are robust, as are the estimation parameters, and these also match the geological expectation. So, at the time of the estimation, there was very little I could do to improve on these. The estimation database (composited drillhole samples) have upper data value limits (or cut-offs if you wish to use that terminology) imposed on them such that :

 

Zn > 40% is never used to estimate a block

Pb > 10% is never used to estimate a block

Fe > 46.6% is never used to estimate a block

 

Thus, there is no combination of Zn, Pb and Fe in the estimation database that totals more than 100% total sulphide

 

The areas with the anomalous (erroneous?) total sulphide summation all correlate, without fail, to areas of thick ore with very dominant pyrite content - there are individual blocks scattered across the mine that buck this trend. This leads me to suspect that the Fe estimates may be erroneous, or simply speaking, the Fe content is being overestimated, hence the total sulphide count exceeds the theoretical limit.

 

The only solution to this problem is modifying the Fe variograms and estimation parameters, but currently, in my judgment, there is nothing I can modify that would lead to better variograms or estimation parameters. Of course there may be blocks where the total sulphide is actually underestimated, but that is impossible to determine, so the overestimates may balance the underestimates in which case there is no bias, but that needs to be tested.

 

Has anyone heard of similar issues on other base metal mines? In the absence of revisiting the estimation parameters, is there anything I can do to realistically address this issue?

 

Regards,

Colin 

 

 

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-----Original Message-----
From: seba [mailto:sebastiano.trevisani@...]
Sent: 30 August 2005 18:17
To: ai-geostats@...
Subject: [ai-geostats] natural neighbor applied to indicator transforms

Dear list members

I would like to have some comments, suggestions or critics about the following topic:
building a (preliminary) local uncertainty model of the spatial distribution of discrete (categorical) variables by means of natural neighbor interpolation method applied to indicator transforms.

From my perspective, interpolating  indicator variables (well, at the end an indicator variable is the probability of occurrence of a given class) by means of a method like natural neighbor is an easy and quick way to build a (preliminary) model of local uncertainty of the studied properties, avoiding problems of order relation violations.
In my specific case I apply natural neighbor interpolation to indicator transforms representing lithological classes in the same way in which direct indicator kriging is applied. In this way, looking at the spatial distribution of the probability of occurrence of lithologies (or at the distribution of the lithological classes, if some classification algorithm is applied) I can have a first idea of the spatial distribution of lithologies. Clearly this method is utilized only as an explorative and preliminary data analysis tool.

Thank you in advance for your replies.
 
S. Trevisani

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To answer to Gregoire's question, for some comparisons between SVM and
Indicator Kriging, here is a very basic paper (from 1999):

http://baikal-bangkok.org/~nicolas/publi/acai99-svm.pdf

and a thesis chapter (chapter 6), perhaps more interesting (from 2002):

http://baikal-bangkok.org/~nicolas/cartann/these_gilardi.pdf

My personnal feeling about the distinction between using a
classification algorithm or a regression one is the importance you put
on the boundaries.
If you look for smooth boundaries, with uncertainty estimations, etc.,
then a regression algorithm (like indicator kriging) is certainly a good
approach.
Now, if you don't care much about how the categories mix together at the
interface, or if you want clear decision boundaries, then a real
classification algorithm (like SVM) is certainly a better choice.

However, it is true that many algorithms can be used in either cases,
often with a small or no modification. The best examples are the
algorithms for density estimation (RBF, Parzen Windows...).
Algorithms of the category of SVM (i.e. large margin classifiers) are
interesting for classification because they are concentrating on finding
a separation between classes, not finding the "centre" of classes. In my
opinion, the interest of this technic for regression isn't obvious...

Best regards,

Nico

Gregoire Dubois wrote:
> I recently attended a presentation about the mapping of soil properties.
> Kriging was applied and I was wondering why a regression technique was
> used instead of a classification algorithm.
> Delineating soil properties seemed to be, at first sight, a
> classification problem than a regression case. This was at first sight
> and we didn't debate much on this issue unfortunately.
> Indicator kriging (IK) is somehow a bridge between these two issues
> (regression versus classification) and its simplicity in use and concept
> makes it very attractive to solve many problems.
> Now I wonder (again) if there are some fundamental papers comparing IK
> to classification algorithms (e.g. Support Vector Machine, SVM). In the
> same way, SVM used for regression seems to be not that uncommon as well.
> So where is the borderline? When are we facing a classification problem
> and when is it a regression problem? I am not sure the borderline is
> always that obvious.
>
> I am not answering Sebastiano's mail here but would be curious to see on
> this list a debate on "regression versus classification"... I presume
> there may there some material as well regarding the issue discussed below.
>
> Best regards,
>
> Gregoire

--
Nicolas Gilardi

Particle Physics Experiment group
University of Edinburgh, JCMB
Edinburgh EH9 3JZ, United Kingdoms

tel: +44 (0)131 650 5300     ; fax: +44 (0)131 650 7189
e-mail: ngilardi@... ; web: http://baikal-bangkok.org/~nicolas

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I'm also forwarding this answer from Dr Samy Bengio who hasn't
subscribed to ai-geostats. His e-mail address is available at the end of
his e-mail.

Best regards

--
Nicolas Gilardi

Particle Physics Experiment group
University of Edinburgh, JCMB
Edinburgh EH9 3JZ, United Kingdoms

tel: +44 (0)131 650 5300     ; fax: +44 (0)131 650 7189
e-mail: ngilardi@... ; web: http://baikal-bangkok.org/~nicolas

Hello,

My own contribution to the following question:

> I recently attended a presentation about the mapping of soil properties.
> Kriging was applied and I was wondering why a regression technique was
> used instead of a classification algorithm.

It is always possible to use a regression technique to solve a classification
task, while the converse is in general much harder (although never impossible).

Now why one should use one technique instead of another is a much wider
question. First, one has to think of the criterion that is optimized by the
underlying technique and compare it to the criterion that is seeked in the
problem at hand. The better these criteria fit one to the other, the more
fitted will be the technique. For instance, using a mean-squared error criterion
when solving a classification task is not optimal, although it opens the door
to many possible techniques. For classification tasks, it is better to have
a criterion that minimizes the number of errors (if this is what is expected),
and possibly while maximizing the distance between the classes in the feature
space (the so-called margin). Hence, SVMs are a good choice for classification.

However, some regression techniques, while not minimizing the best criterion,
offers other advantages that may prove interesting for the problem at hand,
such as smoothness, stochastic training, etc.

> So where is the borderline? When are we facing a classification problem
> and when is it a regression problem? I am not sure the borderline is
> always that obvious.

The border between problems is in general obvious: is the target of
your task in N or in R ? and if in N, are the elements ordered or not? these
two simple questions decide whether it is a regression or a classification
task (although you might also have other types of tasks such as density
estimation or ranking).


> -----Original Message-----
> From: seba [mailto:sebastiano.trevisani@...]
> Sent: 30 August 2005 18:17
> To: ai-geostats@...
> Subject: [ai-geostats] natural neighbor applied to indicator transforms
>
>
> Dear list members
>
> I would like to have some comments, suggestions or critics about the
> following topic:
> building a (preliminary) local uncertainty model of the spatial
> distribution of discrete (categorical) variables by means of natural
> neighbor interpolation method applied to indicator transforms.
>
>> From my perspective, interpolating  indicator variables (well, at the
> end an indicator variable is the probability of occurrence of a given
> class) by means of a method like natural neighbor is an easy and quick
> way to build a (preliminary) model of local uncertainty of the studied
> properties, avoiding problems of order relation violations.
> In my specific case I apply natural neighbor interpolation to indicator
> transforms representing lithological classes in the same way in which
> direct indicator kriging is applied. In this way, looking at the spatial
> distribution of the probability of occurrence of lithologies (or at the
> distribution of the lithological classes, if some classification
> algorithm is applied) I can have a first idea of the spatial
> distribution of lithologies. Clearly this method is utilized only as an
> explorative and preliminary data analysis tool.
>
> Thank you in advance for your replies.
>
> S. Trevisani
>
>
>

----
Samy Bengio
Senior Researcher in Machine Learning.
IDIAP, CP 592, rue du Simplon 4, 1920 Martigny, Switzerland.
tel: +41 27 721 77 39, fax: +41 27 721 77 12.
mailto:bengio@..., http://www.idiap.ch/~bengio

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I recently attended a presentation about the mapping of soil properties. Kriging was applied and I was wondering why a regression technique was used instead of a classification algorithm.
Delineating soil properties seemed to be, at first sight, a classification problem than a regression case. This was at first sight and we didn't debate much on this issue unfortunately.
Indicator kriging (IK) is somehow a bridge between these two issues (regression versus classification) and its simplicity in use and concept makes it very attractive to solve many problems.
Now I wonder (again) if there are some fundamental papers comparing IK to classification algorithms (e.g. Support Vector Machine, SVM). In the same way, SVM used for regression seems to be not that uncommon as well. So where is the borderline? When are we facing a classification problem and when is it a regression problem? I am not sure the borderline is always that obvious.
 
I am not answering Sebastiano's mail here but would be curious to see on this list a debate on "regression versus classification"... I presume there may there some material as well regarding the issue discussed below.
 
Best regards,
 
Gregoire

-----Original Message-----

From: seba [ mailto:sebastiano.trevisani@...]

Sent: 30 August 2005 18:17

To: ai-geostats@...

Subject: [ai-geostats] natural neighbor applied to indicator transforms

Dear list members

I would like to have some comments, suggestions or critics about the following topic:

building a (preliminary) local uncertainty model of the spatial distribution of discrete (categorical) variables by means of natural neighbor interpolation method applied to indicator transforms.

From my perspective, interpolating  indicator variables (well, at the end an indicator variable is the probability of occurrence of a given class) by means of a method like natural neighbor is an easy and quick way to build a (preliminary) model of local uncertainty of the studied properties, avoiding problems of order relation violations.

In my specific case I apply natural neighbor interpolation to indicator transforms representing lithological classes in the same way in which direct indicator kriging is applied. In this way, looking at the spatial distribution of the probability of occurrence of lithologies (or at the distribution of the lithological classes, if some classification algorithm is applied) I can have a first idea of the spatial distribution of lithologies. Clearly this method is utilized only as an explorative and preliminary data analysis tool.

Thank you in advance for your replies.

 

S. Trevisani

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Hello list

I am a PhD student looking at developing a statistical model to predict
the size-distribution of an area's oil and gas fields.

It is clear that previous investigators prefer either a Pareto power law
or a lognormal distribution to approximate field-size distributions.

The data I am using does not look like it comes from a Pareto distribution
- which I explain as being a result of undersampling - which previous
investigators have reported - that undersampling occurs because the small
fields are not sampled or recoded.  However by using basin-modelling
software to simulate oil and gas fields (for the same basin that my
discovered empirical data comes from) I notice that this sample is also
undersampled - that is fields under a certain size are not being simulated
- which is probably due to the resolution of my input data but what is
interesting is that the undersampling actually occurs throughout all the
size ranges - including the medium to larger sizes - which I would not
have expected.  Like the discovery dataset (n = 25)  the simulated dataset
(n = 140) looks like it is more from a lognormal distribution than a
Pareto distribution.

My conclusion is that without being able to say that a Pareto is better
than a lognormal and vise-versa it appears only logical to use both
distributions.

Geologically there does not seems to be a reason why a modal size (greater
than what is detectable by exploration methods) of fields should exist  -
which would be the case if the data was from a  lognormal distribution -
except if the distribution is highly right skewed (at the small field
size) and the mode is actually just below the detection of size.

Geologically there does seem reason for fields to become so small that
they become entities (that trap oil and gas)  - and this relationship may
be better approximated by a Pareto.


The Pareto and lognormal form is similar but maybe one is better to
approximate field sizes than the other.
My question is do you think a Pareto distribution better approximates an
oil and gas size distribution than a  lognormal (or vise-versa) and if so
why.


I am currently working on goodness of fit test to throw some more light on
this - but if anyone has any thing to say I'd appreciate some comments.

Thank you,

Kind regards

Beatrice

Geological and Nuclear Sciences
New Zealand
www.gns.cri.nz

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This follow-up is slighlty aside the subject line of the mailing list, but
as a geologist, this is the only statistically-flavoured one I am
subscribed to. Therefore :

Federico Pardo <federico.pardo@...> said:
> Having N samples, and then n degrees of freedom.
> One degree of freedom is used (or taken)  by the mean calculation.
> Then when you calculate the variance or the standard deviation, you only
> have left n-1 degrees of freedom.

Apart a rigorous calculation I am aware of that in this very case (cf.
Peter Bossew's contribution on the same thread, that details it), gives a
proof for this rule-of-thumb, what more or less rigourous statistical
developments gives consistance to it ?

I mean, for the empirical correlation coefficient,
   rhoXiYi = SUM_i=1..N( (x_i - mx).(y_i - my) / sx / sy ) / WHAT_NUMBER
Must WHAT_NUMBER be, for a kind of unbiased estimate ("a kind of" meaning
"with some eventual Fisher z-transform"...):
  * N for simplicity,
  * N-2 as I have most frequently seen in books that dare give this formula
(N points, minus 1 for position and 1 for dispersion ?),
  * or 2N-4 -- 2N for the (x_i,y_i), minus 4 for {mx,my,sx,sy} -- as a
strict application of the rule-of-thumb seems to suggest ?

And what about, when fitting for instance a 3-parameter non-linear
function, reducing the number of degrees of freedom, to N-3 (number of
points, minus one for each function parameter ? I have never read any kind
of explanation to support it, though it seems widely

Thanks in advance for enlightments or simply tracks for other resources of
explanations.
-- Éric L.

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I'm intruding into foreign territory here, since I don't have
experience in exploring for gas fields etc., (though I have had
to deal with patches of contamination, which is the same sort
of thing on a small scale). So apologies if I blunder around
and tread on toes!

Be that as it may, a point which has occurred to me in reading
this thread is that the distribution being observed is the
distribution of size conditional on being discovered, and the
probability of being discovered may be expected to increase
with size.

So the frequency f(x) of occurrence of a size x in nature is
attenuated by a factor equal to the probability that an item
of size x will be discovered -- g(x) say. The frequency of x
in the observed data is f(x | D), say, and so

   f(x | D) = f(x)*g(x)

from which f(x) = f(x | D)/g(x). From this point, provided
there is a reasonaboly justifiable model for g(x) (to within
a constant of proportionality, e.g. simply g(x) = x), you can
"demodulate" the observed data to infer the "wild" data.

There has for many decades been a similar problem in classical
geometrical probability (the ancestor of spatial statistics
and morphometry), namely to infer the distribution of (e.g.)
areas of cells given the observed distribution of the sizes
of transects by lines, or of counts of sampling points intersecting
them, leading to an integral equation.

Maybe all this is old hat in the areas you are investigating,
but since it did not seem to be even implicit in the discussion
so far I thought I would bring it to the surface.

Best wishes to all,
Ted.

On 01-Sep-05 Chris Hlavka wrote:
> Beatrice - This is a vexing problem that I've tried to deal with in
> sizes of features in satellite imagery (Hlavka, C. A. and J. L.
> Dungan, 2002.  Areal estimates of fragmented land cover - effects of
> pixel size and model-based corrections. International Journal of
> Remote Sensing23(4): 711-724.)  The affine (count versus continuous)
> nature of the digital imagery is at least part of the problem.  I've
> used probability plots to assess type of distribution.
>
> In gas field work, there is evidence that the apparent lognormality
> of field-sizes is due to lower rates of discovery of smaller fields
> than larger fields - especially for older surveys.   It has been
> noted that newer field data was closer to Pareto than older data and
> thus inferred that the actual distribution is Pareto.  -- Chris
>
>
>
>>Hello list
>>
>>I am a PhD student looking at developing a statistical model to predict
>>the size-distribution of an area's oil and gas fields.
>>
>>It is clear that previous investigators prefer either a Pareto power
>>law
>>or a lognormal distribution to approximate field-size distributions.
>>
>>The data I am using does not look like it comes from a Pareto
>>distribution
>>- which I explain as being a result of undersampling - which previous
>>investigators have reported - that undersampling occurs because the
>>small
>>fields are not sampled or recoded.  However by using basin-modelling
>>software to simulate oil and gas fields (for the same basin that my
>>discovered empirical data comes from) I notice that this sample is also
>>undersampled - that is fields under a certain size are not being
>>simulated
>>- which is probably due to the resolution of my input data but what is
>>interesting is that the undersampling actually occurs throughout all
>>the
>>size ranges - including the medium to larger sizes - which I would not
>>have expected.  Like the discovery dataset (n = 25)  the simulated
>>dataset
>>(n = 140) looks like it is more from a lognormal distribution than a
>>Pareto distribution.
>>
>>My conclusion is that without being able to say that a Pareto is better
>>than a lognormal and vise-versa it appears only logical to use both
>>distributions.
>>
>>Geologically there does not seems to be a reason why a modal size
>>(greater
>>than what is detectable by exploration methods) of fields should exist
>>-
>>which would be the case if the data was from a  lognormal distribution
>>-
>>except if the distribution is highly right skewed (at the small field
>>size) and the mode is actually just below the detection of size.
>>
>>Geologically there does seem reason for fields to become so small that
>>they become entities (that trap oil and gas)  - and this relationship
>>may
>>be better approximated by a Pareto.
>>
>>
>>The Pareto and lognormal form is similar but maybe one is better to
>>approximate field sizes than the other.
>>My question is do you think a Pareto distribution better approximates
>>an
>>oil and gas size distribution than a  lognormal (or vise-versa) and if
>>so
>>why.
>>
>>
>>I am currently working on goodness of fit test to throw some more light
>>on
>>this - but if anyone has any thing to say I'd appreciate some comments.
>>
>>Thank you,
>>
>>Kind regards
>>
>>Beatrice
>>
>>Geological and Nuclear Sciences
>>New Zealand
>>www.gns.cri.nz
>>
>>
>>* By using the ai-geostats mailing list you agree to follow its rules
>>( see http://www.ai-geostats.org/help_ai-geostats.htm )
>>
>>* To unsubscribe to ai-geostats, send the following in the subject
>>or in the body (plain text format) of an email message to
>>sympa@...
>>
>>Signoff ai-geostats
>
>
> --
> ***************************************
> Chris Hlavka
> NASA/Ames Research Center 242-4
> Moffett Field, CA 94035-1000
> (650)604-3328  FAX 604-4680
> Christine.A.Hlavka@...
> ***************************************


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding@...>
Fax-to-email: +44 (0)870 094 0861
Date: 02-Sep-05                                       Time: 09:16:02
------------------------------ XFMail ------------------------------

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Hello list

I am a PhD student looking at developing a statistical model to predict
the size-distribution of an area's oil and gas fields.

It is clear that previous investigators prefer either a Pareto power law
or a lognormal distribution to approximate field-size distributions.

The data I am using does not look like it comes from a Pareto distribution
- which I explain as being a result of undersampling - which previous
investigators have reported - that undersampling occurs because the small
fields are not sampled or recoded.  However by using basin-modelling
software to simulate oil and gas fields (for the same basin that my
discovered empirical data comes from) I notice that this sample is also
undersampled - that is fields under a certain size are not being simulated
- which is probably due to the resolution of my input data but what is
interesting is that the undersampling actually occurs throughout all the
size ranges - including the medium to larger sizes - which I would not
have expected.  Like the discovery dataset (n = 25)  the simulated dataset
(n = 140) looks like it is more from a lognormal distribution than a
Pareto distribution.

My conclusion is that without being able to say that a Pareto is better
than a lognormal and vise-versa it appears only logical to use both
distributions.

Geologically there does not seems to be a reason why a modal size (greater
than what is detectable by exploration methods) of fields should exist  -
which would be the case if the data was from a  lognormal distribution -
except if the distribution is highly right skewed (at the small field
size) and the mode is actually just below the detection of size.

Geologically there does seem reason for fields to become so small that
they become entities (that trap oil and gas)  - and this relationship may
be better approximated by a Pareto.


The Pareto and lognormal form is similar but maybe one is better to
approximate field sizes than the other.
My question is do you think a Pareto distribution better approximates an
oil and gas size distribution than a  lognormal (or vise-versa) and if so
why.


I am currently working on goodness of fit test to throw some more light on
this - but if anyone has any thing to say I'd appreciate some comments.

Thank you,

Kind regards

Beatrice

Geological and Nuclear Sciences
New Zealand
www.gns.cri.nz


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May I suggest that you look at other analogous datasets with n > 25, e.g. the
North Sea basin or Gulf of Mexico, before making some firm conclusions about
whether Pareto or Lognormal works best. A lot of this information is in the
public domain, one can browse the Websites of the UK DTI, Norwegian Petroleum
Directorate, or the Danish Energy Agency for public domain field information.
Certainly, at first blush, the log normal seems to make more sense than the
other, you have your few giant fields (Brent, Statfjord, Ekofisk, etc), lots of
middle sized fields, and many more small pimples in the North Sea that have yet
to be developed.

Cheers

Syed

On Wednesday, August 31, 2005, at 11:33PM, Beatrice Mare-Jones
<B.Mare-Jones@...> wrote:

>Hello list
>
>I am a PhD student looking at developing a statistical model to predict
>the size-distribution of an area's oil and gas fields.
>
>It is clear that previous investigators prefer either a Pareto power law
>or a lognormal distribution to approximate field-size distributions.
>
>The data I am using does not look like it comes from a Pareto distribution
>- which I explain as being a result of undersampling - which previous
>investigators have reported - that undersampling occurs because the small
>fields are not sampled or recoded.  However by using basin-modelling
>software to simulate oil and gas fields (for the same basin that my
>discovered empirical data comes from) I notice that this sample is also
>undersampled - that is fields under a certain size are not being simulated
>- which is probably due to the resolution of my input data but what is
>interesting is that the undersampling actually occurs throughout all the
>size ranges - including the medium to larger sizes - which I would not
>have expected.  Like the discovery dataset (n = 25)  the simulated dataset
>(n = 140) looks like it is more from a lognormal distribution than a
>Pareto distribution.
>
>My conclusion is that without being able to say that a Pareto is better
>than a lognormal and vise-versa it appears only logical to use both
>distributions.
>
>Geologically there does not seems to be a reason why a modal size (greater
>than what is detectable by exploration methods) of fields should exist  -
>which would be the case if the data was from a  lognormal distribution -
>except if the distribution is highly right skewed (at the small field
>size) and the mode is actually just below the detection of size.
>
>Geologically there does seem reason for fields to become so small that
>they become entities (that trap oil and gas)  - and this relationship may
>be better approximated by a Pareto.
>
>
>The Pareto and lognormal form is similar but maybe one is better to
>approximate field sizes than the other.
>My question is do you think a Pareto distribution better approximates an
>oil and gas size distribution than a  lognormal (or vise-versa) and if so
>why.
>
>
>I am currently working on goodness of fit test to throw some more light on
>this - but if anyone has any thing to say I'd appreciate some comments.
>
>Thank you,
>
>Kind regards
>
>Beatrice
>
>Geological and Nuclear Sciences
>New Zealand
>www.gns.cri.nz
>
>
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>
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>
>Signoff ai-geostats
>

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David Reid
-----Original Message-----
From: Colin Badenhorst [mailto:CBadenhorst@...]
Sent: Thursday, 1 September 2005 4:45 PM
To: ai-geostats@...
Subject: FW: [ai-geostats] Sum of Estimates

Hello List,

 

Ok, I have discovered the true source of the discrepancy in the total sulphide count. I was able to do this after Bob Sandfurs reply prompted me to revisit the database and look at the stoichiometry, and David Reids email confirmed Bobs suggestions.

 

Firstly, I should point out that I was incorrect about the Zn.Pb and Fe limiting values used in the estimation : these are in fact high yield limits that apply to samples that lie outside a nominated high yield search ellipsoid (different to the classic sample search ellipsoid). So, if values greater than this limit occur, and they lie inside that high yield ellipsoid, they will get used, and this is exactly what has happened.

 

Now, when examining the database, I have found that there are Fe assays that are greater than 46.6%. ALL of these assays are located in the areas where the total sulphide summation discrepancies occur. The high Fe content here is due to the occurrence of several iron oxides (note oxides) such as haematite and limonite, where the Fe content is greater than 46.6%.

 

Thus, the real problem here is the way that the total sulphides are calculated - nothing more. Remember that the the basic assumption is that all Fe comes from pyrite - it is now clear that this assumption is flawed, and I need to address it.

 

Thanks for all the help,

Colin  

 

 

-----Original Message-----
From: Colin Badenhorst [mailto:CBadenhorst@...]
Sent: 31 August 2005 12:58
To: ai-geostats@...
Subject: [ai-geostats] Sum of Estimates

Dear List,

 

I have a rather interesting problem with my Kriged estimates for a base metal mine. I am estimating Zn, Pb and Fe, as percentage, the sum of which should total to no more than 100% total sulphides.

 

All Zn comes from sphalerite (ZnS) at 0.671 proportion. Sphalerite SG = 3.80

All Pb comes from galena (PbS) at 0.866 proportion. Galena SG = 7.40

All Fe comes from pyrite (FeS2) at 0.466 proportion. Pyrite SG = 4.80

Total Sulphides = (Zn estimate x 1.4903) + (Pb estimate x 1.1547) + (Fe x 2.1459)

 

What I have discovered is that I have areas in which the total sulphides are greater than 100% - with very few exceptions, the total is no more than 105% total sulphide.

 

My estimation domains for Zn and Pb are well constrained and validated, and the variogram models and estimation parameters are robust, and have been tested and validated to ensure they match the geological expectations. My domains for Fe are less well constrained but the variogram models are robust, as are the estimation parameters, and these also match the geological expectation. So, at the time of the estimation, there was very little I could do to improve on these. The estimation database (composited drillhole samples) have upper data value limits (or cut-offs if you wish to use that terminology) imposed on them such that :

 

Zn > 40% is never used to estimate a block

Pb > 10% is never used to estimate a block

Fe > 46.6% is never used to estimate a block

 

Thus, there is no combination of Zn, Pb and Fe in the estimation database that totals more than 100% total sulphide

 

The areas with the anomalous (erroneous?) total sulphide summation all correlate, without fail, to areas of thick ore with very dominant pyrite content - there are individual blocks scattered across the mine that buck this trend. This leads me to suspect that the Fe estimates may be erroneous, or simply speaking, the Fe content is being overestimated, hence the total sulphide count exceeds the theoretical limit.

 

The only solution to this problem is modifying the Fe variograms and estimation parameters, but currently, in my judgment, there is nothing I can modify that would lead to better variograms or estimation parameters. Of course there may be blocks where the total sulphide is actually underestimated, but that is impossible to determine, so the overestimates may balance the underestimates in which case there is no bias, but that needs to be tested.

 

Has anyone heard of similar issues on other base metal mines? In the absence of revisiting the estimation parameters, is there anything I can do to realistically address this issue?

 

Regards,

Colin 

 

 

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Hi Chris

Thank you for your reply.  And thank you for your paper reference - I'll
take a look at your probability plots.

Yes the apparent lognormality of oil and gas fields which moves more to a
Pareto form with progressive and mature exploration is explained by
undersampling at the low end that eventually gets sampled as the economics
of an area and technology make smaller fields viable.

However I am surprised that my simulated oil and gas fields - based on
basin modelling - and no economic and exploration-process involvement also
produces lognormal populations of fields.  And that teh undersampling is
obvious throughout most of the size ranges - not just the small size end,

I think Syed's suggesting to use a larger dataset from a mature area is a
good way of seeing what the distribution is more like.


Kind regards


Beatrice

Hydrocarbons Group
Institute of Geological and Nuclear Sciences Limited
69 Gracefield Road, Lower Hutt, WELLINGTON
NEW ZEALAND
64 4 570 4821
b.mare-jones@...
www.gns.cri.nz

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[Colin Badenhorst]  -----Original Message-----
From: Rajni Gaur [mailto:rajni.geophy@...]
Sent: 04 September 2005 13:01
To: ai-geostats@...
Subject: [ai-geostats] Nugget effect...

Dear list members,

I have a querry regarding the presence of nugget effect. I have brought to the notice of my seniors before that iam working on the variography of the resistivity data.

I have been monitoring the resisivity variations at a fixed point from past many months with a frequency of 7 days or sometimes 14 days. I have come across the remarkable changes in the resitivity values. Simultaneously i have been incorporating the variograms on the acquired values of resitivity. As the time is passing by the nuggest effect is decreasing witht the changes in the resistivity values. though it is not sure the resistivity increase or sometimes it decrease also but nugget effect is showing a decline in the value. Iam not able to interpret this change in the nugget effect. though it is good but in the initial value the nugget effect comes to be 1500 and then after 1 month the value reduces to 300.

It would be help to me if list suggest me some thing better for my interpretation work.

thanks in advance to all of you who consider me seriously.

regards

Rajni

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Dear,

I’m a PhD student dealing with geostatistical facies mapping,

I’m using KT3D from GSLIB (Deutsch and Journel, 1992) to make some
facies maps.
I’m working with rather large grids, and I’ve realized that the
following parameters located in the kt3d.inc file:
MAXSBX (maximum super block nodes in X direction),
MAXSBY (maximum super block nodes in Y direction),
and MAXSBZ (maximum super block nodes in Z direction),
had a huge impact on the computer time spent for interpolation. These
parameters are used to subdivide the model in super blocks in order to
speed up the searching data process.

If these parameters are set small, setting the superblock scheme is fast
but interpolation is slow, whereas if they are set large, setting the
superblock scheme is very slow whereas interpolation is faster.

I suspect that the results will be the same if independently of these
parameters. But I’m not sure if using too small numbers could lead to
inaccuracies on kriging results.

I would appreciate if anyone can provide some guidance on the correct
numbers to use.

Thank you.

Oriol


--



______________________________________

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

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

Fac. de Geologia,
Univ. de Barcelona

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HI Ted

Thanks for your reply.

Yes you are correct.  The probability that a field will be discovered is
the product of f(x) that it is from a natural abundance (of its parent
population) and as a function of its size g(x).  And yes the larger the
field is the greater the probability that it is found.

I looked at described the probability that a field will be discovered
conditional to its size for my empirical dataset as a discovery sequence -
and although there is a first order trend of decreasing size with
increasing discovery sequence there were lots of perturbations - for
example the 3rd largest field was discovered 23rd in the discovery
sequence.  therefore describing  the discovery sequence may not be a
straightforward function.  I may start off with a simplistic model  to
demodulate the observed data but may have more success with an integral as
you have mentioned for the early geometrical work.

The small dataset I have is probably  not suitable to describe the
discovery sequence theoretically  - and I will use an analogue area to
establish the discovery sequence function .

Kind regards


Beatrice


Hydrocarbons Group
Institute of Geological and Nuclear Sciences Limited
69 Gracefield Road, Lower Hutt, WELLINGTON
NEW ZEALAND
64 4 570 4821
b.mare-jones@...
www.gns.cri.nz





(Ted Harding) <Ted.Harding@...>
02/09/2005 20:56
Please respond to ted.harding


         To:     Chris Hlavka <chlavka@...>
         cc:     ai-geostats@..., Beatrice Mare-Jones
<B.Mare-Jones@...>
         Subject:        Re: [ai-geostats] Pareto vs Lognormal distribution


I'm intruding into foreign territory here, since I don't have
experience in exploring for gas fields etc., (though I have had
to deal with patches of contamination, which is the same sort
of thing on a small scale). So apologies if I blunder around
and tread on toes!

Be that as it may, a point which has occurred to me in reading
this thread is that the distribution being observed is the
distribution of size conditional on being discovered, and the
probability of being discovered may be expected to increase
with size.

So the frequency f(x) of occurrence of a size x in nature is
attenuated by a factor equal to the probability that an item
of size x will be discovered -- g(x) say. The frequency of x
in the observed data is f(x | D), say, and so

   f(x | D) = f(x)*g(x)

from which f(x) = f(x | D)/g(x). From this point, provided
there is a reasonaboly justifiable model for g(x) (to within
a constant of proportionality, e.g. simply g(x) = x), you can
"demodulate" the observed data to infer the "wild" data.

There has for many decades been a similar problem in classical
geometrical probability (the ancestor of spatial statistics
and morphometry), namely to infer the distribution of (e.g.)
areas of cells given the observed distribution of the sizes
of transects by lines, or of counts of sampling points intersecting
them, leading to an integral equation.

Maybe all this is old hat in the areas you are investigating,
but since it did not seem to be even implicit in the discussion
so far I thought I would bring it to the surface.

Best wishes to all,
Ted.

On 01-Sep-05 Chris Hlavka wrote:
> Beatrice - This is a vexing problem that I've tried to deal with in
> sizes of features in satellite imagery (Hlavka, C. A. and J. L.
> Dungan, 2002.  Areal estimates of fragmented land cover - effects of
> pixel size and model-based corrections. International Journal of
> Remote Sensing23(4): 711-724.)  The affine (count versus continuous)
> nature of the digital imagery is at least part of the problem.  I've
> used probability plots to assess type of distribution.
>
> In gas field work, there is evidence that the apparent lognormality
> of field-sizes is due to lower rates of discovery of smaller fields
> than larger fields - especially for older surveys.   It has been
> noted that newer field data was closer to Pareto than older data and
> thus inferred that the actual distribution is Pareto.  -- Chris
>
>
>
>>Hello list
>>
>>I am a PhD student looking at developing a statistical model to predict
>>the size-distribution of an area's oil and gas fields.
>>
>>It is clear that previous investigators prefer either a Pareto power
>>law
>>or a lognormal distribution to approximate field-size distributions.
>>
>>The data I am using does not look like it comes from a Pareto
>>distribution
>>- which I explain as being a result of undersampling - which previous
>>investigators have reported - that undersampling occurs because the
>>small
>>fields are not sampled or recoded.  However by using basin-modelling
>>software to simulate oil and gas fields (for the same basin that my
>>discovered empirical data comes from) I notice that this sample is also
>>undersampled - that is fields under a certain size are not being
>>simulated
>>- which is probably due to the resolution of my input data but what is
>>interesting is that the undersampling actually occurs throughout all
>>the
>>size ranges - including the medium to larger sizes - which I would not
>>have expected.  Like the discovery dataset (n = 25)  the simulated
>>dataset
>>(n = 140) looks like it is more from a lognormal distribution than a
>>Pareto distribution.
>>
>>My conclusion is that without being able to say that a Pareto is better
>>than a lognormal and vise-versa it appears only logical to use both
>>distributions.
>>
>>Geologically there does not seems to be a reason why a modal size
>>(greater
>>than what is detectable by exploration methods) of fields should exist
>>-
>>which would be the case if the data was from a  lognormal distribution
>>-
>>except if the distribution is highly right skewed (at the small field
>>size) and the mode is actually just below the detection of size.
>>
>>Geologically there does seem reason for fields to become so small that
>>they become entities (that trap oil and gas)  - and this relationship
>>may
>>be better approximated by a Pareto.
>>
>>
>>The Pareto and lognormal form is similar but maybe one is better to
>>approximate field sizes than the other.
>>My question is do you think a Pareto distribution better approximates
>>an
>>oil and gas size distribution than a  lognormal (or vise-versa) and if
>>so
>>why.
>>
>>
>>I am currently working on goodness of fit test to throw some more light
>>on
>>this - but if anyone has any thing to say I'd appreciate some comments.
>>
>>Thank you,
>>
>>Kind regards
>>
>>Beatrice
>>
>>Geological and Nuclear Sciences
>>New Zealand
>>www.gns.cri.nz
>>
>>
>>* By using the ai-geostats mailing list you agree to follow its rules
>>( see http://www.ai-geostats.org/help_ai-geostats.htm )
>>
>>* To unsubscribe to ai-geostats, send the following in the subject
>>or in the body (plain text format) of an email message to
>>sympa@...
>>
>>Signoff ai-geostats
>
>
> --
> ***************************************
> Chris Hlavka
> NASA/Ames Research Center 242-4
> Moffett Field, CA 94035-1000
> (650)604-3328  FAX 604-4680
> Christine.A.Hlavka@...
> ***************************************


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding@...>
Fax-to-email: +44 (0)870 094 0861
Date: 02-Sep-05                                       Time: 09:16:02
------------------------------ XFMail ------------------------------

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Dear list members

 

When studied on a log-transformed variable and intended to construct prediction intervals, which option should be followed? Why?

 

1) construct prediction interval first, back-transform later.

 

OR

 

2) back-transform first, construct prediction interval later.

 

Thanks in advance

Recep

---

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Dear list,

I am going to fit an ellipsoid model of anisotropy.
The input are 4 ranges (scale parameters) and 4 main
directions (0, 45, 90, 135 degree) from directional
semivariogram model.

Is there anybody have experience or a reference
related to the algorithm for doing that? It is looked
simple but make me confusing. I could do it by manual,
but I want to obtain the precise ellipsoid anisotropy
by writing a small routine.

Many thanks for your attention.

Regards,

M. Nur Heriawan
http://www.mining.itb.ac.id/heriawan

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Dear list members,

I have a querry regarding the presence of nugget effect. I have brought to the notice of my seniors before that iam working on the variography of the resistivity data.

I have been monitoring the resisivity variations at a fixed point from past many months with a frequency of 7 days or sometimes 14 days. I have come across the remarkable changes in the resitivity values. Simultaneously i have been incorporating the variograms on the acquired values of resitivity. As the time is passing by the nuggest effect is decreasing witht the changes in the resistivity values. though it is not sure the resistivity increase or sometimes it decrease also but nugget effect is showing a decline in the value. Iam not able to interpret this change in the nugget effect. though it is good but in the initial value the nugget effect comes to be 1500 and then after 1 month the value reduces to 300.

It would be help to me if list suggest me some thing better for my interpretation work.

thanks in advance to all of you who consider me seriously.

regards

Rajni

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Hi,

In fact, as long as the weights are all positive and sum up to one, your
interpolated probability
will always be between 0 and 1; so you should be all right..
The approach proposed by Sebastiano is similar to median indicator kriging in
the sense
that the weights assigned to the observations will be the same across all
indicators (here instead of
a single indicator semivariogram used to compute the kriging weights, the same
weighting set
will be applied to all indicators since the data configuration, hence the size
of the Thiessen polygons,
doesn't change among indicators). Because all the weights are positive and
remain the same
for the different indicators, this approach should eliminate all order relation
deviations
(all estimated probabilities will be between 0 and 1, and at each location their
sum will be one).


Pierre

	 -----Original Message-----
	 From: Gregoire Dubois [mailto:gregoire.dubois@...]
	 Sent: Mon 9/5/2005 7:00 AM
	 To: 'seba'; ai-geostats@...
	 Cc:
	 Subject: RE: [ai-geostats] natural neighbor applied to indicator transforms


	 Ciao Sebastiano,

	 I realized nobody replied to your question (sorry for have added confusion
here).

	 I don't see any objection in applying any interpolator to probability values.
	 However, you should better use exact interpolators to avoid getting
probabilities of occurences > 1 (or smaller than 0)

	 Cheers

	 Gregoire



		 -----Original Message-----
		 From: seba [mailto:sebastiano.trevisani@...]
		 Sent: 02 September 2005 10:07
		 To: ai-geostats@...
		 Cc: ai-geostats@...; 'Nicolas Gilardi'
		 Subject: RE: [ai-geostats] natural neighbor applied to indicator transforms



		 I try to reformulate my question.....
		 When performing direct (i.e. without crossvariogram) indicator kriging,
practically we interpolate probability values by means of ordinary kriging.
These probability values could represent the probability of occurrence of some
category or the probability to overcome some threshold.
		 My question is: is there anything wrong to interpolate these probability
values with other interpolating algorithm like, for example natural neighbor (or
triangulation)?
		 In my opinion is all ok ..... considering also that we have no problem of
order relation violations.
		 Again, this technique is applied only for a preliminary data analysis

		 Then a short consideration directed about the importance of boundaries:
		 Quoting Nicolas Gilardi
		 "My personnal feeling about the distinction between using a classification
algorithm or a regression one is the importance you put on the boundaries.If you
look for smooth boundaries, with uncertainty estimations, etc., then a
regression algorithm (like indicator kriging) is certainly a good approach."

		 Well, if you use fuzzy classification the boundaries become continuos...fuzzy.

		 Bye

		 S. Trevisani

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Dear Pierre and Gregorie

Thank you for your help .....
Concluding (considering that natural neighbor method should be a convex and
an exact interpolator) it seems that the approach has not side effects !!!!!!

Sincerely
Sebastiano

At 17.19 05/09/2005, you wrote:
>Content-Class: urn:content-classes:message
>Content-Type: text/plain;
>         charset="utf-8"
>
>Hi,
>
>In fact, as long as the weights are all positive and sum up to one, your
>interpolated probability
>will always be between 0 and 1; so you should be all right..
>The approach proposed by Sebastiano is similar to median indicator kriging
>in the sense
>that the weights assigned to the observations will be the same across all
>indicators (here instead of
>a single indicator semivariogram used to compute the kriging weights, the
>same weighting set
>will be applied to all indicators since the data configuration, hence the
>size of the Thiessen polygons,
>doesn't change among indicators). Because all the weights are positive and
>remain the same
>for the different indicators, this approach should eliminate all order
>relation deviations
>(all estimated probabilities will be between 0 and 1, and at each location
>their sum will be one).
>
>
>Pierre
>
>         -----Original Message-----
>         From: Gregoire Dubois [mailto:gregoire.dubois@...]
>         Sent: Mon 9/5/2005 7:00 AM
>         To: 'seba'; ai-geostats@...
>         Cc:
>         Subject: RE: [ai-geostats] natural neighbor applied to indicator
> transforms
>
>
>         Ciao Sebastiano,
>
>         I realized nobody replied to your question (sorry for have added
> confusion here).
>
>         I don't see any objection in applying any interpolator to
> probability values.
>         However, you should better use exact interpolators to avoid
> getting probabilities of occurences > 1 (or smaller than 0)
>
>         Cheers
>
>         Gregoire
>
>
>
>                 -----Original Message-----
>                 From: seba [mailto:sebastiano.trevisani@...]
>                 Sent: 02 September 2005 10:07
>                 To: ai-geostats@...
>                 Cc: ai-geostats@...; 'Nicolas Gilardi'
>                 Subject: RE: [ai-geostats] natural neighbor applied to
> indicator transforms
>
>
>
>                 I try to reformulate my question.....
>                 When performing direct (i.e. without crossvariogram)
> indicator kriging, practically we interpolate probability values by means
> of ordinary kriging. These probability values could represent the
> probability of occurrence of some category or the probability to overcome
> some threshold.
>                 My question is: is there anything wrong to interpolate
> these probability values with other interpolating algorithm like, for
> example natural neighbor (or triangulation)?
>                 In my opinion is all ok ..... considering also that we
> have no problem of order relation violations.
>                 Again, this technique is applied only for a preliminary
> data analysis
>
>                 Then a short consideration directed about the importance
> of boundaries:
>                 Quoting Nicolas Gilardi
>                 "My personnal feeling about the distinction between using
> a classification algorithm or a regression one is the importance you put
> on the boundaries.If you look for smooth boundaries, with uncertainty
> estimations, etc., then a regression algorithm (like indicator kriging)
> is certainly a good approach."
>
>                 Well, if you use fuzzy classification the boundaries
> become continuos...fuzzy.
>
>                 Bye
>
>                 S. Trevisani
>
>* By using the ai-geostats mailing list you agree to follow its rules
>( see http://www.ai-geostats.org/help_ai-geostats.htm )
>
>* To unsubscribe to ai-geostats, send the following in the subject or in
>the body (plain text format) of an email message to sympa@...
>
>Signoff ai-geostats

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-----Original Message-----
From: seba [mailto:sebastiano.trevisani@...]
Sent: 02 September 2005 10:07
To: ai-geostats@...
Cc: ai-geostats@...; 'Nicolas Gilardi'
Subject: RE: [ai-geostats] natural neighbor applied to indicator transforms

I try to reformulate my question.....
When performing direct (i.e. without crossvariogram) indicator kriging, practically we interpolate probability values by means of ordinary kriging. These probability values could represent the probability of occurrence of some category or the probability to overcome some threshold.
My question is: is there anything wrong to interpolate these probability values with other interpolating algorithm like, for example natural neighbor (or triangulation)?
In my opinion is all ok ..... considering also that we have no problem of order relation violations.
Again, this technique is applied only for a preliminary data analysis

Then a short consideration directed about the importance of boundaries:
Quoting Nicolas Gilardi
"My personnal feeling about the distinction between using a classification algorithm or a regression one is the importance you put on the boundaries.If you look for smooth boundaries, with uncertainty estimations, etc., then a regression algorithm (like indicator kriging) is certainly a good approach."

Well, if you use fuzzy classification the boundaries become continuos...fuzzy.

Bye

S. Trevisani

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( see http://www.ai-geostats.org/help_ai-geostats.htm )

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----- Original Message -----

From: Rajni Gaur

To: ai-geostats@...

Sent: Sunday, September 04, 2005 2:01 PM

Subject: [ai-geostats] Nugget effect...

Dear list members,

I have a querry regarding the presence of nugget effect. I have brought to the notice of my seniors before that iam working on the variography of the resistivity data.

I have been monitoring the resisivity variations at a fixed point from past many months with a frequency of 7 days or sometimes 14 days. I have come across the remarkable changes in the resitivity values. Simultaneously i have been incorporating the variograms on the acquired values of resitivity. As the time is passing by the nuggest effect is decreasing witht the changes in the resistivity values. though it is not sure the resistivity increase or sometimes it decrease also but nugget effect is showing a decline in the value. Iam not able to interpret this change in the nugget effect. though it is good but in the initial value the nugget effect comes to be 1500 and then after 1 month the value reduces to 300.

It would be help to me if list suggest me some thing better for my interpretation work.

thanks in advance to all of you who consider me seriously.

regards

Rajni

---

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