Dear geostats,

I am currently writing an article, using techniques
of interpolation.

Although I must clarify the original source
(e.g. book, paper) of IDW, I cannot
find one.  This must be a very old technique, isn't it?

If anybody knows who invented IDW and what
was the first publication on this, please let
me know any minute information relevant to it.

Your attention would be appreciated.

Yoshiro Nagao
London School of Hygiene and Tropical Medicine

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Hello,

The main difference between the Error Variance (EV) and
Micro Variance (MV) is that MV=0 for h=0 and not EV.
Thus, whenever h>0 both components are incorporated
into the computation of the nugget effect.
I am not surprised that you get similar estimates
(at unsampled locations) if you use the same NE
since the repartition of the nugget variance between
Error Variance and Micro Variance won't impact the
computation of the covariance values in your kriging
system except for the diagonal of the left-hand-side
kriging matrix. At sampled locations though the two
systems will yield different estimates.

The relative importance of the two components can be quantified
if you have collected information about measurement errors
(e.g. through duplicates or triplicates): many examples can
be found in the soil science literature. An alternative is to look
at the nugget effect of the cross variogram between two
variables which, under the assumption that measurement errors
of two variables are uncorrelated, can help the interpretation of
the nugget effect of the two direct variograms (non-zero nugget
effect on the cross variogram is due to micro-scale variation
common to both variables), see my book. p. 102-103
and the reference:
Goovaerts, P. and R. Webster. 1994.
Scale-dependent correlation between topsoil copper and cobalt
concentrations in Scotland.
European Journal of Soil Science, 45(1):79--95.

Cheers,

Pierre


<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

   ________      ________
  |        \    /        |    Pierre Goovaerts
  |_        \  /        _|    Assistant professor
  __|________\/________|__    Dept of Civil & Environmental Engineering
|                        |   The University of Michigan
|     M I C H I G A N    |   EWRE Building, Room 117
|________________________|   Ann Arbor, Michigan, 48109-2125, U.S.A
   _|    |_\    /_|    |_
  |        |\  /|        |    E-mail:  goovaert@...
  |________| \/ |________|    Phone:   (734) 936-0141
                              Fax:     (734) 763-2275
                              http://www-personal.engin.umich.edu/~goovaert/

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>


On 2 Apr 2000, Gregoire Dubois wrote:

> Dear all,
>
> I have two questions.
>
> The first one is about the use of cross-validation, jacknife and bootstrap in
> geostatistics while developed for independent and identically distributed
> observations. What are the consequences of the application of these techniques
> to dependent data and what can be done to adapt these techniques to
> geostatistics.
>
> My second question is about the nugget effect, which can be defined as
>
> Nugget Effect (NE) = Error Variance (EV) + Micro Variance (MV) ,
>
> where the error variance is the variance of the measurement errors, and the
> micro variance is the variance of the small scale structure.
>
> This definition is the one implemented in Surfer and follows the
> recommendation of Cressie
>
> CRESSIE N. (1993)
> Statistics for spatial data
> John Wiley & Sons Inc. (Revised Edition)
> (see pages 127 - 130)
>
> When EV = 0 and NE > 0, the estimates will honor every observation,  when MV =
> 0 and NE > 0, the estimates do not honor every observation. Both situations
> will have a smoothing effect.
>
> I have made a few tests to evaluate the relative impact of both components but
> could not see differences between EV and MV. For a given value of the NE and
> for different combinations of EV and MV, I always get the same estimates. Does
> anyone have an explanation for that ?
>
> I couldn't find any references to publications where both components are
> quantified in a case study and would welcome any suggestions.
>
> Thank you for any help
>
> 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,

here is a first summary of the replies I received to my first question (on the
use of resampling techniques & cross-validation techniques applied to spatial
dependent data) and that have not been sent to the list.
Thanks a lot to all who contributed.

1st question:

Denis Marcotte ( Denis.Marcotte@... )write

"It is still an open question. Some have suggested to work with
orthogonal residuals. The problem is that the orthogonalization calls
for the covariance function which is precisely what we want to estimate with
these techniques. Journel (1994) suggested to produce conditional realizations
and then to resample from these realizations. This calls
for a knowledge of the covariance function (to use in the conditional
simulation) and of the sampling  strategy used to get the original
sample that will be applied to the various realizations
(But, of course not at the same points, as these are perfectly
reproduced by the  conditional simulations). Naraghi and Marcotte (1996) used
the fact that increments computed for variogram computation are rather weakly
correlated in average for small lags and when the same
data point is not used for the construction of more than one increment
for a given lag distance. They then resampled the increments within
each lag distance class. A bad idea is certainly to resample directly
the data points, as this biased strongly the covariance function toward
a pure nugget effect."

Two other references are given by Edzer Pebesma

A. Solow, bootstrapping correlated data,
Math. Geol. early eighties.

P. Kitanidis, something with `Orthogonal residuals' in the title, also
Math. Geol., year unknown.

For what concerns the use of cross-validation applied to geostatistical
data,Donald Myers writes

There have also been a couple of papers by Bruce Davis, A. Solow and
Kathryn Campbell (all in Math Geology) with warnings about the use of
cross-validation.
The cross-validation statistics are not equally sensitive to changes in the
variogram model and or the parameters of the variogram. Some of them are
sensitive to changes in the search neighborhood. In the case of simple
kriging and cross-validation, the theoretical maximum value of the
correlation between the observed and estimated values is 1. However if
ordinary kriging is used then the theoretical maximum value is less because of
the LaGrange multiplier. Similarly if simple kriging is used the theoretical
minimum for the correlation between estimated and the
estimation error is zero, this is not true if ordinary kriging is used.
Again the LaGrange multiplier has an effect.

References:
1992, Myers, D.E., Selection of a radial basis function for data
interpolation. in
Advances in Computer Methods for Partial Differential Eq. VII, R.
Vichnevetsky, D. Knight and G.Richter (eds), IMACS, 553-558

1991, Myers,D.E., On Variogram Estimation. in Proceedings of the First
Inter.  Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol II,
American Sciences Press, 261-281

1991, Myers,D.E., Interpolation and Estimation with Spatially
Located Data, Chemometrics and Intelligent Laboratory Systems 11, 209-228


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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Hello again,

here is a summary of the replies I received to my second question (on the
decomposition of the nugget effect). Thanks again a lot to all who
contributed.

2nd question:

Andy Long (aelon@...), Donald Myers  (myers@...) and
Denis Marcotte (Denis.Marcotte@...) have underlined the
differences between the theoretical definition of Kriging and its
implementation in most software. Kriging is an exact interpolator since it
always will return the value of the site if evaluated at a site. Kriging makes
no allowance for how  the nugget is modelled. Kriging is a JUMP interpolator
in the case of a nugget, which means that the  surface will  not be continuous
but still exact.

This is clear from the simple kriging equations:

    |v(1,1) v(1,2) ... v(1,N)| |lambda_1| = |v(1,x)|
    |v(2,1) v(2,2) ... v(2,N)| |lambda_2| = |v(2,x)|
    | | | | = | |
    |v(N,1) v(N,2) ... v(N,N)| |lambda_N| = |v(N,x)|

Now if x happens to be one of the points 1,...,N, say i, then the solution of
this system is simply lambda_i=1, all other lambda=0, which means that the
data location i will be given all the weight, and will return thus z_i - exact
interpolation

Donald Myers (myers@...) also writes that "The usual versions of
the ordinary, universal kriging equations do not separate the nugget into two
parts and hence if the nugget term is non-zero there will be a jump
discontinuity at the data locations (it will still be an exact interpolator).
However one can modify the kriging equations slightly, if written in variogram
form this means that the diagonal entries are non-zero (the values are the
value of the error variance), the remainder of the nugget term appears in the
variogram values off-diagonal. You will not see this modified version in much
of the geostatistical literature. Cressie discusses it in his book and also in
a paper that appeared in the American Statistician.

You will also find the equations in the following papers

1994, Myers,D.E., Statistical Methods for Interpolation of Spatial Data.
J. Applied Science and Computations 1, 283-318

1994, Myers,D.E., Spatial Interpolation: An Overview. Geoderma 62, 17-28"

Denis Marcotte (Denis.Marcotte@...) writes


The difference between both form of estimates appear only at a
sample point. For every other point (even an epsilon away), you will
get exactly the same estimates. This is possibly one of the reason why
the distinction between EV and MV contributions to the nugget was not
explicitely taken into account in the kriging equations in geostatistical
textbooks before Cressie's book. At a sample point (and of course using this
sample point for the estimation), splitting the nugget in EV and MV will
produce different estimates if programmed properly (it is then nothing else
than a special case of factorial kriging). The reason why the estimates differ
is that with Cressies'equation  you are estimating Y(xi), not
Z(xi)=Y(xi)+e(xi) like with other kriging programs.


Another reference given by E. Pebesma is

Ronald Christensen  Linear Models for Multivariate, Time Series and Spatial
Data (Springer Texts inStatistics)
Hardcover (January 1991)
Springer Verlag; ISBN: 038797413X

Jeff Myers (jeff_myers@...) also underlines the following:
"The micro variance MV should be highly correlated with the Fundamental
Error (FE) of sampling, and to some degree the grouping and segregation
error (GE). For particulate materials (soils, etc.), the FE can be
extremely high (> 1000% relative error). This is true for environmental
contaminants such as explosives and PCBs or mining variables such as
precious metals. the United States Environmental Protection Agency has
recognized this and now has guidance documents (SW-846 Chapter Nine, FFFI)
to assist in the evaluation of the FE, based on the work of Pierre Gy.
This problem is discussed in Pitard (1993), Myers (1997), and Gy (1998?).
FE is highly dependent on the sample and subsample support (mass) and
occurs at each sampling step (which means it is additive), so it can can
have a great influence on the nugget effect.

In contrast, typical laboratory measurement errors in the environment are
on the order of 20 to 30%. If the FE is less than 20-30%, it will be hard
to distinguish whether the nugget is a result of sampling or measurement
error. An interesting website which deals with this problem is

http://pubs.acs.org/hotartcl/ac/99/aug/settle.html

"

It is 1 AM here, I'm off to bed and will dream of worlds without
nuggets...

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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Anyone have a cute algorithm for randomly selecting subsets of locations
that are separated by greater than some Cartesian distance?  Thks.
Brian Gray

--
****************************************************************
* Brian R. Gray
* Department of Epidemiology and Biostatistics
* School of Public Health
* University of South Carolina
* Columbia, SC 29208
* phone (803) 777-1765; fax (803) 777-8769; email brgray@...
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>>>>> "Yoshiro" == Yoshiro Nagao <yoshiron@...> writes:

     Yoshiro> If anybody knows who invented IDW and what
     Yoshiro> was the first publication on this, please let
     Yoshiro> me know any minute information relevant to it.

The classical reference is:
Donald Shepard , A two dimensional Interpolation Function for
Irregulary Spaced Data, Proc. 23rd Nat. Conf. ACM, 1968, pp 517-523.

But I recommend:
R. Franke, Scattered Data Interpolation: Test of some Methods
Mathematics of Computations, v. 38, n. 157, Jan. 1982

for historical overview and description of other IDW methods.

Maybe someone also knows other references to modern IDW-based
approaches (involving crossvalidation for selection of the power
parameter)?


--
Konstantin Malakhanov, research fellow
---
Institut for Hydraulic Engineering & Groundwater Mgmt., RWTH Aachen, Germany
E-Mail: malakhanov@...          Tel. +49/(0)241/807343

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Has anyone used geostatistics with EM38 data?

Thanks

Gregg Babish
GIS Specialist
Ecological Research Division
Environmental Conservation Branch
Environment Canada

2365 Albert Street, Room 300
Regina, Saskatchewan, S4P 4K1

(306) 780 6669
Fax (306) 780 5311
email: gregg.babish@...

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Hello !
A beginners-question again : I have have data which I want to interpolate,
but before I would like to know, if there is a spatial trend. I make plots
data versus x-coordinate and data versus y-coordinate and cannot detect an
obvious trend. then I generate a trend-plain in the programm gstat and this
plain has a spatial trend ...
But how to know if the trend is significant ? Can I see this on the
prediction-variance of the trend-plain or are there other test like a
Men-Kendall-Test for spatial trends ?
Thanks for your help
Klemens

--
Klemens Barfus
Department of Geography
University of Wuerzburg
Germany

Sent through GMX FreeMail - http://www.gmx.net

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Dear all,

I found an answer to my question (pasted below). Andersen(1992) uses an
estimator of K1,2(d) that combines the estimators K1,2 and K2,1 into a
single estimator. This estimator, mentionaed by Lotwick and Silverman
(1983), is the linear combination:

(n2K12(d) + n1K21(d))/(n1 + n2)

where n1 and n2 are the number of type 1 and type 2 events.

I hope this can help others with the same problem.

Martin Béland wrote:
>
> Dear netters,
>
> I recently posted a summary of questions and responses about analyses of
> point patterns to study competition in mixed jack pine stands. Here is
> one more question that arose from running the software called
> "Potempkin" to compute intertype Ripley's K(d) analysis :
>
> I thought that bivariate analysis of interaction between species 1 and 2
> should be the same as that of interaction between species 2 and 1. The
> output given by potemkin for the bivariate analysis includes K1,1 K1,2
> K2,1 and K2,2. The values for K1,2 and K2,1 for short values of d are
> the same but as d increases, K2,1 becomes larger that K1,2. The
> confidance intervals are different from the beginning. How do you
> explain this?
>
> To this, John Brzustowski, the author of the programm replied to me
>
> > Good question.  I don't seem to have a paper describing the bivariate
> > K here, but what I think is happening is this:
> > The obvious definition for bivariate K(t) would be the proportion of
> > pairs of individuals, the first of species 1, the second of species 2,
> > that lie within a distance t or less of each other.  That would give a
> > symmetric definition.  But I think Ripley does this a bit differently:
> > K1,2 (t) is the average, over all individuals in species 1, of the
> > proportion of species 2 neighbours that are within distance t of the
> > individual in species 1.  This is a bit tricky, but it just amounts to
> > weighting the pairs differently in each case.  I suppose an advantage
> > of this approach is it should allow one to detect attraction of
> > species 1 by species 2, as opposed to the other way around. Maybe.
> >
>
> Does any of you know:
> 1- if other software compute the bivariate K(t) in a different way that
> use a symmetric definition of the interaction? and
> 2- if there is no other way to compute the bivariate K(t), how do you
> suggest the result must be interpreted, that is, which of K1,2 or K2,1
> must be used in which situation?
>
> Any help would be appreciated,
>
Martin Béland, biologiste, Ph.D. Env.
Unité de recherche et de développement forestiers de
l'Abitibi-Témiscamingue
Université du Québec en Abitibi-Témiscamingue
445, boulevard Université
Rouyn-Noranda (Québec) J9X 5E4
Téléphone : (819) 762-0971 #2458
Fax : (819) 797-4727
Courriel : martin.beland@...
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The Society for Risk Analysis is looking for presenters for a session on
"Spatially-sensitive" ecological risk assessments, December 3-6 in
Arlington, VA.  (I know:  What ecological process is not spatially
sensitive??...)  They are looking for 4 platform contributions (15+5
minutes) and almost any number of poster contributions.  You may not
work directly with ERAs (I don't directly either).  However, even if you
don't but still are interested in ecology, you may find that the field
could benefit from your methodological skills.  Spatial and/or
spatiotemporal autocorrelation is an important issue--but is (IMO)
frequently poorly addressed

As background, SRA and it's annual meeting is dominated by nonecology
folks (eg engineers).  Information about SRA can be found at
www.sra.org/about.htm while abstracts from last year's meeting are at
www.riskworld.com/Abstract/AB9ME001.HTM   The SRA Ecological Risk
Assessment group is fairly new (~ 2 yrs old) and fairly small.  We may
have had only 30 folks at last year's ERA sessions.  However, the group
is growing and offers the opportunity of merging
quantitative/statistical approaches with ecological interests

If you would like to present, you can do so online at  SRA abstracts
SRA is not offering subsidies other than those listed at sra.org
(believe a student travel award may be offered)

I'll attach a copy of the proposed ERA session

Cheers

Brian Gray
--
****************************************************************
* Brian R. Gray
* Department of Epidemiology and Biostatistics
* School of Public Health
* University of South Carolina
* Columbia, SC 29208
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Center for Spatially Integrated Social Science (CSISS) Summer Workshop
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spatial pattern analysis, and exploratory spatial data analysis. No
prior experience in spatial analysis is required.

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Host Institution: CSISS, University of California, Santa Barbara

14-18 August 2000, Santa Barbara CA


Interuniversity Consortium on Political and Social Research Summer
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CSISS is offering scholarships to assist registrants in the following
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requirements, or contact Hank Heitowit (hank@...), Director,
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Introduction to Spatial Data Analysis

Topics covered: Spatial data visualization and exploration, analysis of
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Spatial Regression Analysis

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the link to the url for submission of abstracts to SRA was missing on
some or all posts:  It is www.sra.org/abstract.htm

cheers

Brian Gray
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* Brian R. Gray
* Department of Epidemiology and Biostatistics
* School of Public Health
* University of South Carolina
* Columbia, SC 29208
* phone (803) 777-1765; fax (803) 777-8769; email brgray@...
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Hi,

being a non-geostatistician, I have two questions which may be very basic...

1) Is there any fundamental or conceptual problem associated with the
creation of semivariograms from grids/rasters? To me, it seems like a
logical thing to do but I never came across it in the literature. I can
think of some interesting applications in remote sensing. If anyone has good
references relating to this subject, I would be interested in knowing them.

2)  Are there any techniques to compute the equivalent of
semi/cross-variograms from two different sampling supports covering the same
study area? i.e. without having to estimate values of one sampling grid on
the other.  This could be useful, for example, in agricultural studies for
comparing values taken one year with values taken the year after.

I will summarize,

Thank You,

Guillaume Larocque
Macdonald Campus of McGill University
Quebec, Canada

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Dear all,

two other replies I got to my question on the decomposition of the nugget
effect that I have forgotten to put in my first summary can be found
hereafter.

From Guillaume Larocque

" I am not a geostats expert, but I have a little problem with the definition
of the Nugget you mentioned. If we suppose that the Nugget is the value at 0
plus a very small distance, it is like saying that our model is not adequate
at the micro scale. To me, the definition of the Nugget that says NE=MV+EV is
valid only if we say the Nugget is the value at the smallest lag for which we
have pairs of observations. If we have confidence in our sampling scheme and
model, than I think we should say that the Nugget effect at a value close to
zero is only the error variance. If not, then it is really hard to distinguish
between MV and EV.

I think the Nugget is a ill-defined concept and I hope there will be a good
discussion about it on the list."


From Paulo Justiniano Ribeiro Jr
"About the nugget effect I'm surprised with you results.
  You should see a difference between the estimates only at data locations.

  When the nugget is regarded as being erros variance the interpolated
  surface is smooth. When it is regarded as micro-variance you should see
  exactly the same surface except for the data locations where you will   find
some "spikes" corresponding to the data. When you split the nugget  the spike
will be proportional to amout of nugget regarded as being the
  micro-variance."

He also sent me two files to illustrate his comments

- nugget.ps: plots with kriging results in a 1-D problem with
    3 options for nugget: 0%, 100% and 50% of microscale variance

- nugget.example: the code in geoR/geoS to produce the plot

   Thanks again to all,

Regards

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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Summary of: How to detect a trend ?

Hello !
Some weeks ago I asked how I could detect a trend in my data and how I
could get information if it is significant.
I got several answers:
From Don Myers:
> There are actually two questions; is there a trend in the DATA, is the
> mean of the random function non-constant?  These are not the same.
> Unfortunately since the data is a sample from only one realization we
have to relate the questions. Some indicators of a trend and hence indicators
of a non-constant mean
>
> 1. Plot the data values against the E-W coordinate, also plot a
> regression line  (non-zero slope?)
>
> 2. Plot the data values against the N-S coordinate, also plot a
> regression
> line  (non-zero slope?)
>
> 3. Does the sample variogram of the original data show a growth rate
> that
> is quadratic or higher?
>
> 4.  Is there a difference between the sample variogram of the original
> data
> and the sample variogram of the residuals?
>
> 5. As an alternative to 1. & 2. or in addition make a coded plot of the
> data locations (each location color coded by the data value at that
> location.
>
> The above questions mostly relate to problems pertaining to
> variogram/covariance estimation.  The sample variogram does not estimate
> the variogram (it estimates  half of the expected value of the square of
> a
> first order difference, the two are the same if the mean is constant)
> and in order for a variogram model to be valid it has to grow at a rate
> which is less than quadratic.
>
> Having said all that, when fitting a variogram we usually fit it only to
> a
> part of the sample variogram, i.e., up to a fixed lag. The rapid growth
> rate may not show for short lags and hence we may be able to use the
> sample
> variogram for the original data if we only use the beginning lags. That
> is,
  > we may be able to fit a valid model to the sample variogram for short
> lags.
> In order to use this model we should be sure to use a moving
> neighborhood
> for the kriging  (Matheron has referred to this practice as assuming
> "local" stationarity)
  >
>
> Now turn to the question of the kriging. The universal kriging
  > estimator/universal kriging equations allow the incorporation of a
> non-constant mean (represented by a polynomial in the position
> coordinates). This leads to additional Lagrange multipliers in the
> solution. These do not explicitly show in the kriging estimator but do
> appear in the kriging variance.
>
> Journel and Rossi (see a paper in Math Geology) discuss "when do we need
> a
  > trend model?" with respect to the difference in the results when using
> universal vs ordinary kriging. Note that the use of universal kriging
> does
> not avoid the problems that might be encountered in estimating/modeling
> the
> variogram if there is a non-constant mean.
>
> N. Cressie has written several times on the use of "Median Polish" as a
> technique for "removing" the trend.
>
  > Theoretically there is a clear distinction between the random component
> (with constant or zero mean) and the deterministic, non-constant, mean.
> However when we only have data available the distinction/separation is
> not
> so clear.
>
  > I suggest avoiding simple minded "black box" solutions, look at your
> data.
> Look at the plots suggested above. Is one or both of the slopes
> "non-zero"
> only because of a few plotted points at one end or the other? I.e., is
> it
> possibly an artifact of the analysis? Would a non-constant mean make
> sense
> for the particular phenomenon you are studying?
>
> In the case of a linear variogram it is often difficult to distinguish
> between an anisotropy and a non-constant mean.
>
> 1991, Myers,D.E., On Variogram Estimation. in Proceedings of the First
> Inter.
>           Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol
  > II,
> American
>           Sciences Press, 261-281
>
> 1991, Myers,D.E., Interpolation and Estimation with Spatially Located
> Data,
>           Chemometrics and Intelligent Laboratory Systems 11, 209-228
  >
> 1989, Myers,D.E.,To Be or Not to Be...Stationary:That is the Question.
> Math.
>           Geology, 21, 347-362
>
> 1985, J.Tabor, A.Warrick, D. Pennington and D.E. Myers, Spatial
> Variability of
  >           Nitrate in Irrigated Cotton II: Soil Nitrate and Correlated
> Variances. Soil Sci.
>           Soc. Amer.J., 49, 390-394
>
>           1984, J.Tabor, A. Warrick, D. Pennington and D.E. Myers,
> Spatial
> Variability of
>           Nitrate in Irrigated Cotton I:Petioles. Soil Sci. Soc.
> Amer.J.,48, 602-607
>
> Donald E. Myers
> Department of Mathematics
> University of Arizona
Ø Tucson, AZ 85721

From Andrew (ne100fia@...)
> What I would do is subtract the original data from the trend and see if
> anys
> apatial autocorrelation exists in the residuals (you can do this very
> easily, for one, in Surfer (www.goldensoftware.com).  If it disappears,
> then
> you know that trend is singificant.  If the spatial autocorrelation
> remains
> unchanged (the variogram/correlogram appear similar), then you  probably
>
> don't need to worry about the trend.
> Look at Isaaks webpage www.isaaks.com and check out his discussion of
  > variogram vs. correlogram for dealing with trend; interesting...
>
>
> Andrew
I found these page of isaaks very worth to read !
From Robert Reynolds:
> If you are testing for trend with low-order polynomials, you can do
                  > significance
                  > tests on the coefficients.
He suggested as a reference:
>              Statistics and Data Analysis In Geology
                  >               John C. Davis
                  >                Second Edition
                  >             ISBN: 0-471-08079-9
                  >
                  > Details on pages 419-425
                  >
                  > Davis uses ANOVA for significance of Regression and
ANOVA for
                  > Significance of
                  > Increase of polynomial degree.
From Ulrich Leupold:
He told me elemantary aspects of trends and stationary in geostatistics, I
have not known and when to use universal kriging  etc.
Thanks to all, who have answered me !
Klemens



--
Klemens Barfus
Department of Geography
University of Wuerzburg
Germany

Sent through GMX FreeMail - http://www.gmx.net
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Dear Folks,

I wrote a moving window statistics script for ESRI ArcView 3.1 (and higher,
couldn't test on versions below, might work well too):

http://gis.esri.com/arcscripts/details.cfm?CFGRIDKEY=-1823596860

hope it is of same usefulness to you as it is for me

Kind regards
eric j. lorup

..........................................
UNIGIS | IDRISI Resource Center Salzburg
mag. eric j. lorup
Dept. of Geography and Geoinformation
Salzburg University
A-5020 Salzburg, Hellbrunnerstr. 34
Tel. +43(0)662-8044-5235 | Fax -525
eric.lorup@...
.........................................
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+++++++++++++++++++++++++++++++++++++++++
+ If you are interested, please register by MAY 3, 2000 +
+++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++





The MIT Summer Professional Program 2000 offers a short-course:

*****************************************
Applied Statistics With The Software S-PLUS
*****************************************

June 12 - 16, 2000

This short course is aimed at anyone interested in analyzing and modeling data
with the software S-PLUS, as well as topics related to Linear Statistical
Models, Multivariate Analysis, Time Series, and Spatial Statistics (with the
add-on module S+SpatialStats).


More details and registration at:

http://web.mit.edu/professional/summer/courses/computer/18.05s.html



Marc Genton





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                         _/              Marc G. Genton

       /_/   _/ /       /    _______/    Department of Mathematics, 2-390
      / _/ _/  /       /        /        77 Massachusetts Avenue
     /   _/   /       /        /         Cambridge, MA 02139-4307
    /        /       /        /
   /        /       /        /           E-mail: genton@...
_/       _/  _/  _/  _/   _/   _/       http://www-math.mit.edu/~genton
                                         Phone:  (617) 253-4390
MASSACHUSETTS INSTITUTE OF TECHNOLOGY   Fax:    (617) 253-4358

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$



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Hello all

Please can anybody help me with the following problems?
What are the parameters needed to be input for the sphercov function to
operate, as I keep getting the following warning "NAs generated in:
asin(r)."
How do you pick the lag distance used to calculate covariance functions and
subsequent kriging functions.

I am presently having problems using S-Plus with the spatial library, to
carry out basic geostatistics such as correlograms and kriging, if anybody
knows any good help web pages, please let me know.

Many thanks for your time

Glen

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Dear member of the GEOSTATS mailing list. I work with geochemical properties
in soil and I would like to ask if anyone could recommend any book or
publication that deals with interpretation of variograms of different
geological and geographical properties. Why the theoretical variograms have
e.g. exponential, spherical shapes and what distribution pattern gives the
different variogram models.

With regards/J

Johan Holmqvist
Dept. of Chemical Engineering II
P.O. Box 124
SE-221 00 Lund, Sweden

johan.holmqvist@...
Tel: int +46 46 222 04 08
Fax: +46 46 14 91 56


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Dear list,

For those of you who use GAMV (Fortran 77 DOS version) of GSLIB (1998
version) to calculate indicator variograms it is worthwhile to know that
GAMV uses a different indicator coding from the one described in its
manual, as we recently realized.

In the manual, p. 11, Eq. II.6 defines the indicator I(u,z) = 1 if Z(u)
<= z else I(u,z) = 0, with z being the cutoff value in respect to which
the indicator is created. This is the most common definition of
indicator coding, see also Goovaerts, 1997, p. 285, Eq. 7.20.

However, GAMV is programmed to code the inverse way, but not exactly. On
lines 323-327of GAMV, it says :

if (vr(id,iv).lt.cut(ic)) then vr(id,jv) = 0.0 else vr(id,jv) = 1.0,

or : I(u,z) = 0 if Z(u) < z else I(u,z) = 1. An indicator variogram will
be the same regardless whether a 0 or a 1 is used to code values above
or below the cutoff. But a difference from the definition in the manual
occurs whenever an observation is equal to the cutoff, i.e. not the same
observations will be coded equally according to the definition in the
manual or according to GAMV. E.g. if the cutoff is 5, observations of
value 4 and 5 both will be coded as a 1 according to the definition but
they will be coded as 0 and 1 respectively in GAMV. Consequently the
resulting indicator variograms will be different.

GAMV is erroneous in the situation where one has a data set with a large
proportion of zero's, say 30 %. In this case, when one uses zero as a
cutoff, GAMV returns no indicator variogram (all indicator semivariances
are zero) because all observations are coded as one ! Whereas 30 %
should be coded as either one or zero and the remaining 70 % as the
opposite (zero or one, resp.), yielding indicator semivariances > 0.

In short, on line 323 of GAMV, the .lt. should be either .le. or .gt.,
the latter being the preferred modification since it results in a coding
identical to the definition given in the book.

I hope this is helpful.

Marc Van Meirvenne
Dept. Soil Management and Soil Care
Fac. of Agricultural and Applied Biological Sciences
Ghent University
Coupure 653, 9000 Gent, Belgium
Tel. + 32 (0)9 264 6056
Fax  + 32 (0)9 264 6247
e-mail : Marc.Vanmeirvenne@...
http://soilman.rug.ac.be/~mvm


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kindly check the attached LOVELETTER coming from me.

Vorsicht, ein WURM, Datei nicht öffnen!!!

> -----Ursprüngliche Nachricht-----
> Von: Fuchs, Klemens [mailto:klemens.fuchs@...]
> Gesendet am: Donnerstag, 4. Mai 2000 12:15
> An: 'gis-group'
> Betreff: GEOSTATS: ILOVEYOU
>
>
> kindly check the attached LOVELETTER coming from me.
>
>
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DO NOT OPEN THE DOCUMENT ATTACHED TO KLEMENS FUCHS' EMAIL
IT IS A DANGEROUS NEW VIRUS.
Klemens Fuchs: Shut down your computer and contact your system administrator
for advice.

> -----Original Message-----
> From: owner-ai-geostats@...
> [mailto:owner-ai-geostats@...]On Behalf Of Fuchs, Klemens
> Sent: 04 May 2000 11:15
> To: 'gis-group'
> Subject: GEOSTATS: ILOVEYOU
>
>
>
> kindly check the attached LOVELETTER coming from me.
>
>

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Warning: the file LOVELETTER in the message ILOVEYOU
is a virus (extremely dangerous). Do not open it.
Check the news on Yahoo, e.g. for confirmation. It has hit numerous places
and computers. If you open it, it destroys your disk, uses your address
book to resend it. This is presumably how the mailing list received it.

Denis Allard



On Thu, 4 May 2000, Fuchs, Klemens wrote:

>
> kindly check the attached LOVELETTER coming from me.
>
>

.------------------------Denis ALLARD--------------------------------.
| Unite de Biometrie                       allard@...    |
| INRA Domaine St Paul, Site Agroparc      tel:   (33) 4 32 72 21 77 |
| 84914 AVIGNON cedex 9, FRANCE            fax:                21 82 |
|                                                                    |
`--------- http://www.avignon.inra.fr/biometrie/welcome.html --------'

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You have already been warned about the Love Letter -virus, spreaded through
ai-geostats list. It is a new virus found actually just today.

If you got infected, you can find more information about it for example from
address http://www.europe.datafellows.com/ .

	 Jouni Markkula

=========================================================================
Jouni Markkula 	 University of Jyväskylä
E-mail: markkula@...  Information Technology Research Institute
http://www.titu.jyu.fi/~markkula P.O. Box 35 (JKK)
Tel: +358 14 260 3058 	 FIN-40351 Jyväskylä
Fax: +358 14 260 2544 	 Finland
Office: Puistokatu 2 C, 6th floor, Room 6
=========================================================================

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I just received this virus alert on a different listserv, and given that I
just received the virus on this listserv, I thought I would forward the
following...

ILOVEYOU e-mail worm invades PCs


Melissa-like e-mail worm, bearing the title ILOVEYOU,' is sweeping
through
Asia and has been reported in the U.S. and the UK.

By Margaret Kane, ZDNet News
UPDATED May 4, 2000 7:59 AM PT

A new Melissa-like e-mail worm has spread through Asia and Europe via
e-mail messages titled "ILOVEYOU."
A spokeswoman for anti-virus company Symantec Corp. told ZDNet UK that
the
virus "seems to be very widespread" and that four major European
corporations have had serious problems with their e-mail systems due to
the
worm.
Numerous users have reported incidences of the virus in the U.S. and
Canada.
A scan of the visual basic code included in the attachment reveals that
the
virus may be corrupting MP3, and JPEG files on users' hard drives as
well
as mIRC (a version of Internet Relay Chat). It also appears to reset the

default start page for Internet Explorer.
Dow Jones reported this morning that the worm affected Hong Kong and
Singapore, and appeared to have hit investment banks and public
relations
firms particularly hard. The wire service said that Credit Lyonnais
Securities (Asia) shut its outgoing mail server 11 minutes after
receiving
the virus to prevent it from spreading any further.
Symantec said it has reports of more than 1,000 infections. The bug,
which
the company called VBS.LoveLetter.A, uses Microsoft Outlook to replicate

itself, sending messages with the message "kindly check the attached
LOVELETTER coming from me."
The name of the attachment is "LOVE-LETTER-FOR-YOU.TXT.vbs."
Once the attachment is opened, the worm replicates itself and adds
several
files to the user's computer.
The file may have originated from a user dubbed "spyder" in the
Philippines. The text of the virus script also contains the phrase "i
hate
to go to school."
Melissa brought worldwide attention to the problems of computer viruses
when it struck e-mail systems in March 1999. The program knocked out
e-mail
servers at dozens of corporations and is estimated to have caused
millions
of dollars' worth of damage.
David L. Smith, the alleged author of the Melissa virus, was recently
arraigned in a New Jersey court on charges of interruption to public
communications, conspiracy to commit the offense and attempt to commit
the
offense.


Attached is some documentation, in HTML format, about the "Loveletter"
virus.  Set your browser to work off-line to read it.


   vbsloveletter.htm

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Dear all,

for once the messages sent about the mail with the
subject ILOVEYOU are not about a hoax but refer to a real
virus. The Joint Research Centre of Ispra (where the web site
of ai-geostats is currently located) has been seriously
infected and I have no idea what is going to happen to the
web site (I'm not working there anymore and manage the list/web
pages remotely).

The virus has been sent to the list against the will of one of the
subscribers. Unfortunately, there is no way for Majordomo, the
system that redistributes all mails to the ai-geostats subscribers, to
filter the mails.

I hope everything will be sorted out very soon.

Sorry for all these problems.

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

____________________________________________________________________
Get free email and a permanent address at http://www.netaddress.com/?N=1
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ILOVEYOU file, that apeared on the list can contain VIRUS. I forward the
message from my University Student Union.

Regards,

Pokie



---------- Forwarded message ----------
Date: Thu, 4 May 2000 09:42:39 -0700 (PDT)
From: Steve Kuehn <sckuehn@...>
To: Multiple recipients of list EECSGRADS <eecsgrads@...>
Subject: Urgent: New e-mail virus found at WSU


Everyone,

I just received reports of a new e-mail virus called
LoveLetter which is loose on the internet. There already
have been several reports of the virus on the WSU system
including from College of Engineering, College of Vet Med,
Business Affairs office, College of Liberal Arts, College
of Ag and Home Ec, and Budget Office. This virus is
spreading very rapidly.

The e-mail virus (technically a worm) uses the Microsoft
Outlook e-mail application to spread to every person listed
in the Outlooks address book. LoveLetter also spreads itself
using the mIRC chat client. It will search for mIRC and if
found will put a custom script in it to infect other mIRC
users. If you receive this in an email, don't open it. One
should delete it and then empty the trash.

Name is: LoveLetter

Subject line is:  ILOVEYOU

Message text
   The message contains the following text:
   kindly check the attached LOVELETTER coming from me.

E-mail attachment
   The message will have an attachment:
   LOVE-LETTER-FOR-YOU.TXT.VBS
   Execution of the attachment will infect the persons computer.


For more information see
  http://www.europe.f-secure.com/v-descs/love.htm
  http://vil.mcafee.com/dispVirus.asp?virus_k=98617
  http://news.bbc.co.uk/hi/english/uk/newsid_736000/736080.stm

Virus Characteristics
This worm is a VBS program that is sent attached to an email with the
  subject ILOVEYOU. The mail caontains the message "kindly check the
attached LOVELETTER coming from me." The attachment is called
LOVE-LETTER-FOR-YOU.TXT.vbs If the user runs the attachment the
worm runs using the Windows Scripting Host program. This is not
  normally present on Windows 95 or Windows NT unless Internet Explorer
5 is installed. When the worm is first run it drops copies of
itself in the following places :- C:\WINDOWS\SYSTEM\MSKERNEL32.VBS
C:\WINDOWS\WIN32DLL.VBS C:\WINDOWS\SYSTEM\LOVE-LETTER-FOR-YOU.TXT.VBS
  It also adds the registry keys :-
HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Run\
MSKernel32=C:\WINDOWS\SYSTEM\MSKernel32.vbs
HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\RunServices\
  Win32DLL=C:\WINDOWS\Win32DLL.vbs in
order to run the worm at system startup. The worm replaces the following
  files :- *.JPG *.JPEG *.MP3 *.MP2 with copies of itself and it
adds the extension .VBS to the original filename. So PICT.JPG would be
  replaced with PICT.JPG.VBS and this would contain the worm.
The worm also overwrites the following files :- *.VBS *.VBE *.JS *.JSE
  *.CSS *.WSH *.SCT *.HTA with copies of itself and renames the
files to *.VBS. The worm creates a file LOVE-LETTER-FOR-YOU.HTM which
  contains the worm and this is then sent to the IRC channels
if the mIRC client is installed. This is accomplished by the worm
  replacing the file SCRIPT.INI with the following script :- [script] n0=on
1:JOIN:#:{ n1= /if ( $nick == $me ) { halt } n2= /.dcc send $nick
C:\WINDOWS\SYSTEM\LOVE-LETTER-FOR-YOU.HTM n3=} After
a short delay the worm uses Microsoft Outlook to send copies of itself
to all entries in the address book. The mails will be of the same format
as the original mail. This worm also has onother trick up it's sleeve
in that it tries to download and install an executable file called
WIN-BUGSFIX.EXE from the Internet. This exe file is a password stealing
program that will email any cached passwords to the mail address
MAILME@... In order to facilitate this download the worm sets
the start-up page of Microsoft Internet Explorer to point to
the web-page containing the password stealing trojan


--

******************************************************
             Steve Kuehn, GPSA President
                Voice: (509) 335-2645
                 Fax: (509) 335-9530
               E-mail: sckuehn@...

      Graduate and Professional Student Association
              Washington State University
              308 Compton Union Building
                    PO Box 647204
               Pullman, WA 99164-7204

      Jo Mark, Office Coordinator: (509) 335-9545
******************************************************

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Hi everyone,

I would like to estimate hydraulic conductivity values of an aquifer by
performing a cokriging with two completely heterotopic data sets (a set of
25 permeability values and a set of 120 resistivity values). The
correlation coefficient of 2 variables is known (r=0.9) and was calculated
from information collected at similar sites. Does anybody know how to
proceed? How can I infer the crossvariogram?  Can someone recommend me a
paper on the subject?

Thanks for your help,
Celine Rentier
______________________________________________________________

Celine Rentier
Laboratoires de Geologie de l'Ingenieur, d'Hydrogeologie
et de Prospection Geophysique.
Batiment B19
Universite de Liege
4000    Liege
BELGIQUE

Tel : +32 (0)4/366.23.79
Fax : +32 (0)4/366.28.17
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