Dear all,

here is a summary of the answers I got to my question about the
impact of local search on kriging variance.

I got many replies showing me that my question was still
unclear or could be understood in different ways.

My point really was that the kriging variance, which is
dependent on the covariance model and the data configuration,
can not properly reflect the variance of the estimates if one uses
a local search neighborhood since the experimental semivariogram
is usually modeled for the whole data set.
When I was asking about the impact of a search neighborhood
on the kriging variance, I was more thinking in terms of the
interpretation of the kriging variance.

I can only recommend to read pages 178-180 of Pierre Goovaerts'
book "Geostatistics for Natural Resources Evaluation" for what
concerns the practice of using only the data closest to the
location where an estimation is made.

Other references suggested by Victor De Oliveira and
Mustafa Touati are given hereafter. The first two references
propose a statistically sound likelihood-based method to choose
the "neighborhoods" for doing estimation and prediction.

Vecchi (1992), A new method of prediction for spatial regression models
with correlated errors, J. of the Royal Statistical Society B, 813-830

Vecchia (1988), Estimation and model identification for continuous
spatial processes, J. of the Royal Statistical Society B, 297-312.

Poids de Krigeage ( A Ph.D. Thesis from the Paris School of Mines).
(this was done early in the 80th) by Jaques Rivoirard from the
Centre de Geostatistique


You will find here under other replies that could be interesting for
the readers:

From Edzer J. Pebesma:

Obviously, when using kriging in a small neighbourhood,
you only use (and need) the variogram function for the smaller
distances. The good thing is that for smaller distances the
variogram is easier to estimate than for longer distances,
given a single replicate (realization) of a RF. OTOH, even
for kriging with a global neighbourhood the variogram at the
smaller distances is more important than at larger distances.

For ordinary or universal kriging, all data in the neigbourhood
are used for prediction, also values beyond the correlation
distance (range): one of the things they are used for is
(re-)estimating the trend value or parameters at the kriging location.
A larger neighbourhood will therefor usually lead to smaller
kriging variances, but the effect may be small after
taking, say, the 20 or 30 nearest observations. For a pure nugget
effect things are easy to write out analytically, because
data configurations don't matter here. For other cases, I would
just try a couple of neighbourhood sizes, perhaps do some cross
validations.

Robert C Reynolds & Yetta Jager remind that the kriging variance
is affected by the number, distance, position and orientation of data
used. A limited number of nearest neighbors is frequently used so as
to keep the kriging  system of equations small. Kriging weights
become small for sample points as one move away from the location
estimated and have a negligible influence,  especially of there is a
strong spatial correlation. Points beyond the sill  contribute in no way
to the kriged estimate and so can be ignored. Ideally, points should
reside fairly evenly around  (interpolation) the point to be estimated
rather than tending off to one side (extrapolation) for best results.


Mats Soderstrom reminds that it might be more efficient in some cases
to use local variograms instead of variograms made on the whole data set
and that the VESPER software (See the Software list of AI-GEOSTATS or
directly http://www.usyd.edu.au/su/agric/acpa/vesper/vesper.html) proposes
a local approach.


Last but not least, from Dan Cornford:

"The answer depends on the range of the process and the
distance beyond which the sites are and the sites locations - i.e.
it is not particularly easy to answer. In general a small number
of surrounding sites is used in kriging for several reasons:

Computational (matrix inversion scales as n^3, where n is the
number of sites. Stability (conditioning) of matrix inversion is
also likely to be improved. Stationarity becomes less of a problem
(only local needed) - but of course this is conditional on knowing
the variogram which was estimated locally thus this is a bit of a fix!

Nowadays it is possible to invert matrices of up to about 1000
observations in one go - that is there is no need to do the local
thing - but this is not always a good idea for the reasons given
above.

Adding more observations should (I think - it is a while since I have
looked at this) alweays decrease the kriging variance, but in practice
the decrease will be tiny".


Many other replies suggested me to test it by increasing the numbers
of  points in the neighbourhood and to check the kriging variance.



Thanks a lot also to Nicla Giglioli and Andrew (Nefia ?)
for their kind replies.

Have a nice week !

Gregoire



Gregoire Dubois
Section of Earth Sciences
Institute of Mineralogy and Petrography
University of Lausanne
Switzerland

Currently detached in Italy

http://curie.ei.jrc.it/ai-geostats.htm

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Dear all,
does anybody know about articles on the spatial analysis of eye-movement
data in psychological research (using eye-movement trackers). I'll have yo
analyse such data in due time but have never heard of anybody analysing
these.
Thanks
Janine

Janine Illian
School of Computing
University of Abertay Dundee
tele + 44 (0)1382 308488
fax  + 44 (0)1382 308627
e-mail   j.illian@...

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Please forward to colleagues who you think may have an interest in the
subject.

The Center for Spatially Integrated Social Science has been established
by the National Science Foundation through its program of support for
research infrastructure in the social and behavioral sciences. CSISS is
located at UCSB and its main purposes are to recognize the key role
space plays in human society and to promote research that advances
understanding of spatial patterns and processes. Cartographic
visualization, geographic information systems (GIS), pattern
recognition, spatially sensitive statistical analytic tools, and
place-based search methodologies are the tools of the spatially
integrated social science (SISS) used to integrate knowledge across
disciplines and paradigms.

The center is now identifying best practice examples from each of the
Social Science disciplines and for different problem areas. I am writing
to you to ask you please to provide leads on articles or publications
that consider a spatial approach in your discipline. The papers may be
recent or past publications, authored by you or colleagues you know from
any institution for education or research. The authors of the selected
papers may be contacted to explore their inclusion in a book on Best
Practices in Spatially Integrated Social Sciences. In addition, the
proposed papers will be considered to generate user friendly, easily
understood primer examples for the center’s website CSISS.org.

Thank you very much in advance for the references and leads you could
supply for the mentioned objective.

Center for Spatially Integrated Social Science
University of California, Santa Barbara
Tel: (805) 893-8652, Fax: (805)893-8617
email jorge@...


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Hello friends,

I am developping a program to process spatial images (Landsat, Spot,
etc.) with a
neural net program and I need libraries to do this. Please anyone that
can help me.

With regards,

Jesus Mansilla Baca
Centro Nacional de Pesquisa de Solos - Brazil



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Dear all,

you will find here under interesting comments I received from
Donald Myers (thank you very much !) to my question on kriging
variance.

Enjoy the reading,

Best regards

Gregoire

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

1. I agree that in some sense there is a discrepancy between using the whole
data set to estimate the variogram and then only using a local neighborhood
for kriging but I think that asking the question that way confuses things.

2. Since the data is not collected by "random sampling", (note that random
site selection is not quite the same thing as random sampling as the term is
customarily used in statistics), there is no theoretical connection between
the set of data locations and the region for which the modeled variogram might
be used. We often assume that there is but there is not.

3. There is also the question of the difference between a spatial average,
which is what the sample variogram is, and an ensemble (theoretical
probabilistic) average which is the way the variogram is defined. Although it
is not often mentioned, using the spatial average to estimate the ensemble
average implies the use of an ergodic property. Unlike many statistical
techniques, there are no "replicates" to get around this problem. By its
definition, the variogram is not location dependent.


4. One way to see how the variogram relates to a region that is somehow
connected with the data locations is to look at the "dual" form of the kriging
estimator.

Z*(x) = SUM{i=1,...n} Bi gamma(xi - x) + SUM {j=0,...,p}Aj Fj(x)

I have written it in the form corresponding to universal kriging, for ordinary
kriging the sum on the right only has one term, a constant. It is easy to show
that the sum of the Bi's is zero. First suppose that the variogram has a
range, then consider a region enclosing the data locations but large enough so
that for all points x in the region, xi-x is less than the range of the
variogram. Now consider points outside of that region, the variogram value for
all pairs xi-x is the same and hence the first sum on the right hand side of
the equation is zero. That means that the interpolated value is entirely
determined by the right hand sum, for ordinary kriging this means a constant
(which in fact is the arithmetic mean of the data values). If the variogram
does not have a range then the same argument still applies but we have to
consider a larger region, i.e., big enough so that although the variogram
values are not constant they are essentially the same (when x is sufficiently
far enough away from all the data locations, the magnitude of the xi-x's is
essentially the same and hence the variogram values are essentially the
same).

We might then consider the "region" described above (the one containing the
data locations) as being the region intrinsically related to that set of data
locations. Unfortunately you can't compute the kriging variance from the
coefficients in the dual form.


5. Now to return to the question at hand, although it will not happen in all
instances, generally speaking the kriging variance will increase when fewer
data locations are used for the kriging. One way to see this is to consider a
system of kriging equations which includes all the data locations but now
"force" some weights (weights at some locations) to be zero so that the
solution vector now looks as though it corresponded to a local neighborhood.

This has to be a sub-optimal solution, the estimation variance obtained from
this solution can not be greater than the estimation obtained by not including
the "zero" constraints. That is, the system of equations obtained by using the
local neighborhood is a special case of the the one using all the data
locations, special in the sense that additional constraints are imposed.

Imposing the additional constraints can not decrease the kriging variance. If
the larger variance is interpreted as meaning greater uncertainty then this is
what should happen when you leave out information.

Having said all of the above paragraph I would note that sometimes a data
location should be thought of as "dis-information" rather than as
"information".


6. Nearly everyone is familiar with the injunction to not use the sample
variogram plot for distances that exceed half the largest pair distance. In
fact, of course, one often does not use the sample variogram for lags that are
even that large and hence in looking at the size of local neighborhoods one
should keep in mind the largest lag used in modeling the variogram.


An interesting reference on kriging variances and sample design is:

"The updated kriging variance and optimal sample design"
(Gao, Wang and Zhao)
Math. Geology 28, (1996) 295-314


Gregoire Dubois
Section of Earth Sciences
Institute of Mineralogy and Petrography
University of Lausanne
Switzerland

Currently detached in Italy

http://curie.ei.jrc.it/ai-geostats.htm

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Hi there,
I am very new to point pattern analysis, and don't understand the math theories
behind them.

I am trying to analyse the point patterns of the locations of dengue fever
cases. In particular, I am trying to compare the difference of these point
patterns in a small area before and after a mosquito control operation.

Does anyone have any advise on how I should go about doing it? I am using
Arcview 3.2, and have the Spatial Analyst extension.

Thanks in advance for any help offered!

Basil
Vector Control & Research Dept
Singapore
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Hi

First, my apologies for a question which is a little off-topic for this
group, but I hope that someone might have an answer!

I have a set of sites distributed across Europe, and I wish (ultimately)
to use kriging to interpolate between them. The problem is that the
coordinates that I have, are in Latitude/Longditude. I want to convert
these into a cartesian system, in order to work with them. However, as
the study area is quite large (approx 15°W-35°E 35°N-72°N), I am worried
that reprojecting them (e.g. using the Albers Equal Area proj.) will
distort the spatial relation of the sites.

My questions therefore, are:
1) Will the distortion be too great? Does anyone have experience of
working at this scale?

2) Are there alternative conversion which will better preserve the
spatial relation? Presumably this will take into account the curvature
of the earth.

3) There is a piece of software listed under the Soft-FAQS of
ai-geostats called spherekit
(http://curie.ei.jrc.it/software/spherekit.htm), which appears to be
designed to work at this scale. Has anyone managed to get it to compile
under Linux?

Thanks in advance
Simon
--
------------------------------------------------------
Simon Brewer
European Pollen Database
Place de la Republique     tel: 00 33 (0)4 90 96 18 18
13200 Arles                fax: 00 33 (0)4 90 93 98 03
France                  email: simon.brewer@...
------------------------------------------------------
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Hi Simon,

This may not be the best solution but a possible alternative:
I have just recently started working on a problem with similar issues of
coordinate conversion and distortion, although the spatial nature of my
problem is somewhat different from yours.  I am unbending a river so that
kriging is done in a domain that follows the course of the river instead
of going over land.  I have converted the coordinates (which were already
in meters and on a small scale geographically) by applying a grid
generation scheme. (Gridgen is one software that can be used).

Grid generation is widely used in the field of flow simulation in channels
or around bodies where boundary conditions apply along irregular surfaces
(hydrodynamics, aeronautics etc).

The physical boundary is defined into four segments that correspond to the
four sides of a rectangle.  An equal number of grid points are laid out
along each of the pairs of facing boundaries.  Various algorithms (Laplace
transforms to linear interpolation, depending on the problem) calculate
grid lines between the extreme grid point pairs.  The grid is generated in
the original coordinate system, so each sample has to be assigned to the
nearest grid point  within limits of resolution and coordinate precision.

In flow field simulations, the differential equations and boundary
conditions are transformed based on the mathematical relationship between
the two coordinate systems.  This is not necessary in this application, as
all grid points to be estimated are calculated before kriging.
Semivarogram calculation, modeling and kriging  takes place in the
transformed space and the results need merely be mapped to the original
coordinate points corresponding to the initial grid generation output.

An excellent book on the theory is:
Numerical grid generation : foundations and applications
by Thompson, Joe F. (1985)
Published  New York : North-Holland : Elsevier Science Pub. Co.

Gridgen is available from Pointwise for a free 90 day trial period:
www.pointwise.com


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Hello everyone,
I am a newbie to geostats (I have done a little stochastic work in
hydrogeology but not much else) community and I have a question for you
folks. I am interested in kriging a set of about 2100 borehole logs to
generate a 3D picture of the subsurface in a watershed. I have defined 19
separate classes of materials in the boreholes (sand, silt, gravel, etc.)
and am, at present, skipping making combinations of materials into a class
because I do not want to introduce any more uncertainty into the system (it
has enough already!). Anyway, I wanted to find an appropriate kriging
routine for this situation. The routine would only be allowed to use one of
the 19 defined classes for a value at any given point and can not
interpolate between defined classes. With this criteria in mind I chose
indicator kriging as the my desired method.

Now here is my questions/problems.
1) I would like to know if indicator kriging is the approach I should take.
2) I have a copy of the book GSLIB (1st edition) which has an indicator
kriging routine in it but it is a 2-parameter routine. I am wondering if
anyone knows where I can get my hands on a n-parameter indicator kriging
routine (preferably for free because I am just a poor humble PhD student)?


Thanks in advance for your help,

Jon Paul Jones
University of Waterloo
Department of Earth Sciences
Waterloo, Ontario, Canada N2L-3G1
Phone: 519-888-4567 ext. 2984
Fax:   519-746-7484
"Just because you are paranoid does not mean that they are not all out to
get you."

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A message I have been asked to forward which may be of interest.

A free forum to learn - contribute - inquire about sensitivity analysis
is now available.

If you are interested in this new expanding discipline, please give a
look to it at: http://sensitivity-analysis.jrc.cec.eu.int/ The forum is
organised in rooms, with experts identified for the various topics. You
may upload-download articles, references, links, announcements
etc. etc.
You need to register to make uploads, but there is no filtering a-
priori.
Anonymous mails are allowed. Thank you for re-posting this
message to other lists, offering us your feedback, flagging bugs,
contributing in any way to this initiative. Yours

Andrea  Saltelli,
Institute for Systems, Informatics and Safety,
The European Commission, Joint Research Centre  TP 361, 21020
ISPRA(VA)
ITALY Tel: +39 0 332 78 9686 Fax: +39 0 332-78 5733 E-mail
SMTP:
andrea.saltelli@... http://www.jrc.cec.eu.int/uasa

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Hello Jon,

if you are not familiar with geometrical  a n d  geostatistical 3D-modelling
then I would emphatically recommend to look for an alternative approach to
your problem, i.e. correspondig to the scientific problem which you would like
to
analyse, e.g.

1. is it possible to reduce to 2D
2. can you transform classes of materials into hydro-geological relevant
     parameters (porosity, permeability or K-values) so that you can
     work with a single parameter in 3D space (which is difficult enough)
3.? etc

If you want to get  a picture of the subsurface only then the relation
of scientific result/expenditure tends to zero.

Regards,

Heinz Burger


Jon Jones schrieb:

> Hello everyone,
> I am a newbie to geostats (I have done a little stochastic work in
> hydrogeology but not much else) community and I have a question for you
> folks. I am interested in kriging a set of about 2100 borehole logs to
> generate a 3D picture of the subsurface in a watershed. I have defined 19
> separate classes of materials in the boreholes (sand, silt, gravel, etc.)
> and am, at present, skipping making combinations of materials into a class
> because I do not want to introduce any more uncertainty into the system (it
> has enough already!). Anyway, I wanted to find an appropriate kriging
> routine for this situation. The routine would only be allowed to use one of
> the 19 defined classes for a value at any given point and can not
> interpolate between defined classes. With this criteria in mind I chose
> indicator kriging as the my desired method.
>
> Now here is my questions/problems.
> 1) I would like to know if indicator kriging is the approach I should take.
> 2) I have a copy of the book GSLIB (1st edition) which has an indicator
> kriging routine in it but it is a 2-parameter routine. I am wondering if
> anyone knows where I can get my hands on a n-parameter indicator kriging
> routine (preferably for free because I am just a poor humble PhD student)?
>
> Thanks in advance for your help,
>
> Jon Paul Jones
> University of Waterloo
> Department of Earth Sciences
> Waterloo, Ontario, Canada N2L-3G1
> Phone: 519-888-4567 ext. 2984
> Fax:   519-746-7484
> "Just because you are paranoid does not mean that they are not all out to
> get you."
>
> --
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--
*****************************************************
Dr. Heinz Burger
Freie Universitaet Berlin
- Geoinformatik -
Malteserstr. 74-100
12249 BERLIN, Germany
Tel. (49) 30-838-70561 Fax: (49) 30-775-2075
e-mail: hburger@...
Web-Seite: http://userpage.fu-berlin.de/~hburger
****************************************************


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Hello again,
This is just a note to thank everyone who responded to my inquiry w.r.t.
indicator kriging. I received many replies and have been given many avenues
to explore, all of which look promising.

Thanks again,

Jon Paul Jones
University of Waterloo
Department of Earth Sciences
Waterloo, Ontario, Canada N2L-3G1
Phone: 519-888-4567 ext. 2984
Fax:   519-746-7484
"Just because you are paranoid does not mean that they are not all out to
get you."

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I would like to unsubscribe to geostats.

Thank you,

Linda Marshall

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Hi Jon,

Indicator Kriging can work with as many classes as you want. At each grid node,
it

will give the probability for each class. You would then need to extract the
most
probable
class for each node, if you are after a categorical model. For the same amount
of
modeling
efforts, Sequential Indicator Simulation can give you the categorical model by
sequential
Monte-Carlo sampling from those local probabilyties.

Both algorithms require a variogram model for each class and both are available
in
GSLIB.

Gilles

Heinz Burger wrote:

> Hello Jon,
>
> if you are not familiar with geometrical  a n d  geostatistical 3D-modelling
> then I would emphatically recommend to look for an alternative approach to
> your problem, i.e. correspondig to the scientific problem which you would like
> to
> analyse, e.g.
>
> 1. is it possible to reduce to 2D
> 2. can you transform classes of materials into hydro-geological relevant
>     parameters (porosity, permeability or K-values) so that you can
>     work with a single parameter in 3D space (which is difficult enough)
> 3.? etc
>
> If you want to get  a picture of the subsurface only then the relation
> of scientific result/expenditure tends to zero.
>
> Regards,
>
> Heinz Burger
>
> Jon Jones schrieb:
>
> > Hello everyone,
> > I am a newbie to geostats (I have done a little stochastic work in
> > hydrogeology but not much else) community and I have a question for you
> > folks. I am interested in kriging a set of about 2100 borehole logs to
> > generate a 3D picture of the subsurface in a watershed. I have defined 19
> > separate classes of materials in the boreholes (sand, silt, gravel, etc.)
> > and am, at present, skipping making combinations of materials into a class
> > because I do not want to introduce any more uncertainty into the system (it
> > has enough already!). Anyway, I wanted to find an appropriate kriging
> > routine for this situation. The routine would only be allowed to use one of
> > the 19 defined classes for a value at any given point and can not
> > interpolate between defined classes. With this criteria in mind I chose
> > indicator kriging as the my desired method.
> >
> > Now here is my questions/problems.
> > 1) I would like to know if indicator kriging is the approach I should take.
> > 2) I have a copy of the book GSLIB (1st edition) which has an indicator
> > kriging routine in it but it is a 2-parameter routine. I am wondering if
> > anyone knows where I can get my hands on a n-parameter indicator kriging
> > routine (preferably for free because I am just a poor humble PhD student)?
> >
> > Thanks in advance for your help,
> >
> > Jon Paul Jones
> > University of Waterloo
> > Department of Earth Sciences
> > Waterloo, Ontario, Canada N2L-3G1
> > Phone: 519-888-4567 ext. 2984
> > Fax:   519-746-7484
> > "Just because you are paranoid does not mean that they are not all out to
> > get you."
> >
> > --
> > *To post a message to the list, send it to ai-geostats@....
> > *As a general service to list users, please remember to post a summary
> > of any useful responses to your questions.
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> Dr. Heinz Burger
> Freie Universitaet Berlin
> - Geoinformatik -
> Malteserstr. 74-100
> 12249 BERLIN, Germany
> Tel. (49) 30-838-70561 Fax: (49) 30-775-2075
> e-mail: hburger@...
> Web-Seite: http://userpage.fu-berlin.de/~hburger
> ****************************************************
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--
**************************************************
Gilles Bourgault        RC Squared Inc.
Senior Geostatistician  9177 East Mineral Circle
E-mail: gilles@...  Suite 100
Phone: 303-749-7962     Englewood CO 80112
      /RRR  CCC\ 2       USA
     | RRR  C   |        http://www.rc2.com
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Dear all out there,

I have got 2 (maybe very basic) questions, the first one about the
requirement of stationary mean in semivariance analysis, the 2. about the
correlation dimension of fractal analysis.

1.
before performing a semivariance analysis, any secular trend must be
removed from the data in order to meet the requirement of stationarity of
the mean. Question: how do you decide at which scale fluctuations are
actually trends ? Stationarity of the empirical data means regional mean =
µ(x) = const. over x, but over which range of x the regional mean has to
be taken ?
As an example, I add (see zipped attachment <examp1.doc>) the spatial
distribution of count rates over a monazite (a radioactive mineral)
containing beach of Brazil. The dots represent the sampling locations. The
picture has been produced using 'naive' kriging with Surfer Software, i.e.
using the default settings for the variogram and assuming isotropy, just
in order to grossly visualize the distribution. I would say that there is
an obvious trend, represented by the maximum between easting 300 and 450
m; but is the maximum at ca. 160 m also part of the trend ? Doesn't the
big maximum in fact consist of 3 maxima at ca. 340, 370 and 410 m,
respectively, which should be modelled by the trend surface ? (Apart from
the problem, how to model such a trend structure.)

2.
It seems to me that the correlation dimension is quite a useful tool to
assess the topologic structure of the spatial distribution of a variable;
or could be if used properly. I use this kind of fractal dimension because
it is (as I think) the easiest to calculate: D :<=> AM(n(r)) ~ r^D, where
the left hand side denotes the number of points within distance r from a
fixed point x, averaged over all points x. D is then easily calculated by
log regression.
Now the question: there is always an 'edge effect' to D produced by the
fact that the sampling area is inevitably limited in space. An infinite
complete regular quadratic sampling grid, e.g., has D = 2, but the same
grid with finite extension has D < 2, because the points at the border
have naturally less neighbours than points within the grid and therefore
contribute to AM(n(r)) by lowering D and thus inferring a fractal
patchiness of the structure which is clearly an artefact. For this reason,
D depends heavily on the overall size (extent) of the grid (number of
sampling points), regardless of its structure, which makes this quantity
somewhat questionable, I think. Does somebody know how to deal with this
problem ?

Thank you very much & regards, PB

--------------------------------------------------------------------------------\
-----
Peter Bossew
Georg Sigl-Gasse 13/11
A-1090 Vienna, Austria
ph. +43-1-3177627
e-mail: p.bossew@...

Dear Listed Members,

I am looking for any guidelines or references on how to organize the field data
for Kriging analysis.
I have some 3D field data and would like to perform Kriging analysis.   However,
these data are
collected with variable depths for each location.  In other words, the sampling
depths are not
consistent for all of the sampling locations.  I will appreciate if you could
provide me suggestions on
how to handle this case.

Thanks.

Ying


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Hello everyone,
Here is a summary of the responses I received w.r.t. my question on
indicator kriging.

Hi Jon,

Indicator Kriging can work with as many classes as you want. At each grid
node, it

will give the probability for each class. You would then need to extract the
most
probable
class for each node, if you are after a categorical model. For the same
amount of
modeling
efforts, Sequential Indicator Simulation can give you the categorical model
by
sequential
Monte-Carlo sampling from those local probabilities.

Both algorithms require a variogram model for each class and both are
available in
GSLIB.

Gilles

Hello Jon,

if you are not familiar with geometrical  a n d  geostatistical 3D-modelling
then I would emphatically recommend to look for an alternative approach to
your problem, i.e. corresponding to the scientific problem which you would
like
to
analyze, e.g.

1. is it possible to reduce to 2D
2. can you transform classes of materials into hydro-geological relevant
     parameters (porosity, permeability or K-values) so that you can
     work with a single parameter in 3D space (which is difficult enough)
3.? etc

If you want to get  a picture of the subsurface only then the relation
of scientific result/expenditure tends to zero.

Regards,

Heinz Burger

Jon,

The GSLIB IK routines are all there is going to be (and all you need).  I'm
not sure what you mean by "2-parameter."  An indicator CAN only be one of
two values -- zero or one.  Either, you have "sand" at location x or you do
not.  What you will get out of IK is the probability of having "sand" at an
unsampled location.  You can't krige the values 1 through 19 because that
implies a numerical "sequence" to the values, whereas they really are just
arbitrary class designations: "Fred" and "Mary" would do just as well.

Obviously you can run the IK exercise 19 time, once for each class vs. "all
others", but then you're going to need to confront the issue of how you
convert all the probabilities to actual facies maps (Pr > 1/19?) and would
it be consistent.  The power of IK is that your spatial model (variogram) is
customized to the variability of the indicator in question.  You need a
variogram for each class.  The downside is that the indicator technique is
an either-or proposition.  The other plus is that IK forces you to confront
the issue of uncertainty.

Did you check out the gslib 1.2 program sisimpdf?  This is intended for
categorical variable (class) simulation.  It will generate simulated maps of
your 19 categories, but again, you've got to deal with the uncertainty
issue.  A simulation is only one of N possible alternative models, all
equally likely.  Note: sisimpdf is now incorporated within sisim in ver.
2.0.

You may need to do some thinking on what you're going to use the result for
-- if a flow model, then you may be interested only in knowing where "sand"
and "gravel" are, because that's where the water is going to flow.

There is some literature around on modeling facies distributions using
truncated gaussian simulation.  I've never done it, but the technique has
the advantage of respecting facies relationships: shale can only occur next
to limestone and never next to sandstone -- that sort of thing.  I'd
recommend cruising the SCRF web site http://ekofisk.stanford.edu/SCRF.html)
at Stanford and looking through their assortment of papers and look for
titles including "facies" or "truncated gaussian simulation".  You can also
download gslib ver. 2 from there.

Note that I'm assuming that you're modeling these lithologies as facies
rather than as discrete layers (formations).

Regards,
Chris

Hi Jon,

as I see it, your problem is primarily a problem of geometrically modeling,
and
not of estimation/prediction. Therefore, I would skip GeoStats and start
with some
interactive tool for 3d geometrical design like gOcad from ENSG Nancy,
France
(http://www.t-surf.com/).

Good luck,
Helmut Schaeben

Hello,

What do you want exactly to interpolate?
If it's just the probability of occurrence of each
of the 19 classes, IK is the way to go and in the
new Gslib version there is possibility to
perform indicator kriging of categorical variables.
Let me know if it's what you are looking
for and I could send you the source code.

Regards,










Jon Paul Jones
University of Waterloo
Department of Earth Sciences

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Dear All

Has anyone ever coded any GSLIB routines in c or c++?

If so, could you contact Dr. Nick Tate. at n.tate@...?

Many thanks

Peter
__________________________________________________________________
Dr. Peter Atkinson                      Department of Geography
Reader in Geography                     University of Southampton
Tel.        +44 (0)1703 594617          Highfield
FAX.        +44 (0)1703 593295          Southampton
E.mail.     pma@...             SO17 1BJ
__________________________________________________________________
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hi-

  I tried some years ago (about 2) using a free gcc compiler from the net and f2c
on windows; I couldn't  get the samples to work because of backspace not working
in f2c but a better f2c may be available now for your specifc platform.

Bob Sandefur
Principal Geostatistician
Pincock, Allen and Holt, Inc.
International Mineral Consultants
274 Union Blvd Suite 200
Lakewood, CO
80224
USA
303 914-4467 v
rls@...


>>> Peter Atkinson <P.M.Atkinson@...> 08/04/00 04:22AM >>>
Dear All

Has anyone ever coded any GSLIB routines in c or c++?

If so, could you contact Dr. Nick Tate. at n.tate@...?

Many thanks

Peter
__________________________________________________________________
Dr. Peter Atkinson                      Department of Geography
Reader in Geography                     University of Southampton
Tel.        +44 (0)1703 594617          Highfield
FAX.        +44 (0)1703 593295          Southampton
E.mail.     pma@...             SO17 1BJ
__________________________________________________________________
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release of an update version of the CrimeStat spatial statistics program,
distributed by the National Institute of Justice's (NIJ) Crime Mapping
Research Center.  CrimeStat is a free program for the statistical analysis
of crime and other incident locations, developed by Ned Levine & Associates
of Annandale, VA.. The program is Windows based and interfaces with most
desktop GIS programs. The aim is to provide supplemental statistical tools
to aid analysts and researchers in statistically describing the
distribution of incidents. Many of these tools are useful for geographers
(e.g., describing clusters of crime incidents; describing shifts in the
spatial distribution of shopping trips; describing the distribution of
pedestrian accidents relative to the underlying population distribution)

	 Version 1.1 is an update to the first version which was released in
November 1999 and fixes some problems associated with 1.0 (e.g., improved
performance in Windows 98), adds new database features, (e.g., the ability
to handle missing values), makes improvements to some of the existing
routines (e.g., edge corrections to Ripley's K statistic), and adds new
journey to crime calibration and estimation routines.  The latter technique
is an adaptation of location/travel behavior theory.  It could be used, for
example, to identify an optimal location to place a senior citizen center
given the distribution of seniors in a community and assumptions about
their travel behavior.

	 The program is fully documented with update notes and a new chapter on
journey to crime estimation.  There are also sample data sets
provided.  The new version can be downloaded from either NIJ's Crime
Mapping Research Center web site:

		 www.ojp.usdoj.gov/cmrc

or the web site of the NIJ archivist:

		 www.icpsr.umich.edu/NACJD/crimestat.html

Ned Levine, PhD
Ned Levine & Associates
Annandale, VA

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Hello ,

   I  am  doing  a  research about the application of spatial analysis techniques
   oriented  to relate educational and geographical variables. I started with the
   analysis of autocorrelation for some variables using lattice data.
   I  would  like  to  know  in  which  case  it  is  neccesary to standarize the
   contiguity  matrix  by rows. I obtained Moran Indexes for both cases (with and
   without standarization) and in both the results were very different.

   Thanks


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On Mon, 14 Aug 2000, ELSA NICKL wrote:

>
>   Hello ,
>
>   I am doing a research about the application of spatial analysis
> techniques
>   oriented to relate educational and geographical variables. I started
> with the
>   analysis of autocorrelation for some variables using lattice data.
>   I would like to know in which case it is neccesary to standarize the
>   contiguity matrix by rows. I obtained Moran Indexes for both cases
> (with and
>   without standarization) and in both the results were very different.
>
In general, standardisation gives more influence to the neighbours of
polygons with few neighbours, and less to the neighbours of polygons with
many neighbours. If all your polygons have the same number of neighbours,
the coefficients will be similar, while if some have very few neighbours
and others have very many, the results may differ - as in your case, I
guess. A reference to the key article: Tiefelsdorf M, Griffith D, Boots B
1998 A variance stabilizing coding scheme for spatial link matrices,
Environment and Planning A, 31, pp. 165-180.

Have a look at the distribution of numbers of neighbours of your polygons,
and see if there are some with many, and some with very few neighbours.

Good luck!


Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Breiviksveien 40, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93
e-mail: Roger.Bivand@...
and: Department of Geography and Regional Development, University of
Gdansk, al. Mar. J. Pilsudskiego 46, PL-81 378 Gdynia, Poland.

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Hello,

I am undertaking a Degree in GIS at Uni of South Australia and am new to
geostatistics.  I'm after information on the following subjects:
           Central Tendancy
           Inverse Areal Moment
           Naive Estimator
           Kernel Estimator
       and Nearest Neighbour analysis

If any one has any documents on these topics I'd be happy to here from you.

Cheers....Chris



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Can somebody please provide detailed document (or links) on Object
Modeling/Fluvial Simulation.
Thanks in advance,
SK

Chris Johnson wrote:

> Hello,
>
> I am undertaking a Degree in GIS at Uni of South Australia and am new to
> geostatistics.  I'm after information on the following subjects:
>           Central Tendancy
>           Inverse Areal Moment
>           Naive Estimator
>           Kernel Estimator
>       and Nearest Neighbour analysis
>
> If any one has any documents on these topics I'd be happy to here from you.
>
> Cheers....Chris
>
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Dear colleagues,

I would like to bring to your attention an interactive, map-based
internet project, Weimar Voting, concerning the electoral determinants
of the political collapse of the Weimar Republic and the Nazi Seizure of
Power. You may find this project interesting as a new way for
visualizing spatio-temporal, socio-economic data.

The URL is:
http://www.weimar-voting.de

Weimar Voting is based on an intuitive display of information in a
series of interactive, 3D maps. The maps display the socio-structural
determinants of voting for the two radical parties Nazis and Communists
against the background of the Depression.

I would appreciate your comments on the usefulness of this project for
teaching and suggestions for further improvement.

Best,
Christian Stoegbauer

--
Christian Stögbauer
Economic History
Dept. of Economics, Univ. of Munich
Ludwigstr. 33 / IV
D-80539 Munich
voice: ++49 (89) 2180-5377
fax: ++49 (89) 33 92 33
http://www.vwl.uni-muenchen.de/ls_komlos/christian.html
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least three of the topics you're interested in (central tendency, kernel
estimation, nearest neighbor analysis).  The program and documentation are
free and can be downloaded from

           http://www.icpsr.umich.edu/NACJD/crimestat.html

Ned Levine



At 02:37 PM 8/27/2000 +0930, you wrote:
>Hello,
>
>I am undertaking a Degree in GIS at Uni of South Australia and am new to
>geostatistics.  I'm after information on the following subjects:
>           Central Tendancy
>           Inverse Areal Moment
>           Naive Estimator
>           Kernel Estimator
>       and Nearest Neighbour analysis
>
>If any one has any documents on these topics I'd be happy to here from you.
>
>Cheers....Chris
>
>
>
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Ned Levine, PhD
Ned Levine & Associates
Annandale, VA

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Dear friends,

Some weeks ago, I did a question about contiguity matrix standarization. Thank
you very much Dr. Bivand for your help.
As I told you, I am doing a research about the application of spatial analysis
techniques to relate educational and geographical variables. Now I am trying to
measure the effort of children in rural areas to arrive their schools; they have
to walk one or more hours through a sloped pathway. I want to calculate the
effort they make,  and later use these results to relate the effort with other
variables (like nutritional levels, efficiency in their school, access to
communication, etc). I think I have some options: the VARCOST function of
Idrisi, to construct a regression model based in observed data, to construct a
simple model based in physics laws (considering friction and gravitational
forces).  What do you think about? Can somebody knows about some paper related
with this?.

Thanks
Elsa Nickl



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