- Hi everybody

That would be a great help if experts out there shed some light on me

regarding the following questions.

Basically, I am trying to use the available tools such as GSLIB and its

manual and ... to model the variogram for my continuous elevation data

sets. Either I am reading too much from those tools or missing an

important link.

1. On page 377 of the book written by Isaaks and Srivastava, it reads:

"The most useful guideline for choosing weight coefficients is to remember

that their sum must equal the sill of the sample variogram"

The above condition is not satisfied by neither of the variogram shown on

page 27(Figure II.5) and page 28 (Figure II.6) of GSLIB manual. If these

variogram are generic, that is fine otherwise what is the cause of the

discrepancy?

2. On page 383 of the same book at the bottom of the page, it reads:

"To Summarize, the geometric anisotropy requires some foresight in

modeling the directional sample variograms. All the directional variogram

models must have identical sill values. Each nested ..........

with the same coefficient."

By the last sentence, I am assuming they mean the contribution coefficient

of each structure (i.e., cc value). First of all, why that should be the

case?

If cc should have the same value, does it mean that parameter optimization

of nested structure for the second direction should be subjected to the

values obtained in the other direction. Let me give an example.

Suppose we identify the axis of anisotropy to be x and y axis. In the

x-direction, we realized that a combination of exponential and Gaussian

structure will provide the best fit to sample variogram in that direction.

Clearly enough, we have four parameters to optimize in that direction.

As soon as we switch to y-direction, the number of parameters will drop to

two and this less degree of freedom will detoriorate the goodness of fit

dramatically in that direction while relaxing the equality of cc from one

direction to another will give rise to a comparable goodness of fit. Am I

on the right track or some normalization of range should be made at some

stage. Besides all these things, I cannot understand why the ranges for

corresponding structure should be divided by each other to define "anis"

Parameter.

3- If variogram value start to decrease after reaching the sill, what is

the physical meaning of that?

4- Is there any ERRATA being written for GSLIB manual? I need to confirm

some of the mistakes that I encounter in using the manual.

With many thanks for your time and help.

Best of luck.

Abedini

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The world is your exercise-book, the pages on which you do your sums.

You are also free to write nonsense, or lies, or to tear the pages.

Richard Bach

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of any useful responses to your questions. - Additional comments: When the variogram starts to decrease from some sill

value this is an indication of periodicities in the data. If periodic

behavior is high frequency, then you see the oscilatory behavior in the

variogram associated with a hole effect model. If the periodic behavior is

low frequency relative to your study area (sampling window) then it is seen

as just a decreasing variogram at long lags. This is a good indicator that

there are large scale trends (relative to the sampling window) in the data

which could be modeled as linear or quadratic or more complex response

surfaces with correlated residuals.

On anisotopy, Borgman and Li 1994 Math Geology give a nonparametric

technique for estimating the axes of anisotropy. The procedure allows one

to then use a linear transformation of the lag domain into a single

direction in which the model fitting is conducted. This allows the use of

all lag pairs in the model fitting procedure and ensures constant sill in

all directions and the same set of nested structures in each direction

provided you have enough data to detect multiple structures. In my

experience it takes a lot of irregularly spaced data to estimate the shape

parameters of a single structure let alone more than one structure. Good

luck, John Kern

>My 2cents worth on some of the following posted questions.

--

>

>>

>> 1. On page 377 of the book written by Isaaks and Srivastava, it reads:

>>

>> "The most useful guideline for choosing weight coefficients is to remember

>> that their sum must equal the sill of the sample variogram"

>>

>> The above condition is not satisfied by neither of the variogram shown on

>> page 27(Figure II.5) and page 28 (Figure II.6) of GSLIB manual. If these

>> variogram are generic, that is fine otherwise what is the cause of the

>> discrepancy?

>>

>

>My calculation of the sum of the weight coefficients for Fig 11.5 is

>0.22+0.53+0.25=1.00 for both the NS and EW directions. This appears

>pretty close to the sill values.

>

>For Fig. II.6 i get 0.40+0.40+0.95+0.9=2.65 for both directions. This

>matches OK the higer sill direction. I presume the question is for the

>other which has a sill around 1.7 or 1.8. The text notes that the

>last spherical structure has a range of 80K and does not practically

>contribute. Take away the weight coefficient of 0.90 and viola you

>get 1.75.

>

>> 2. On page 383 of the same book at the bottom of the page, it reads:

>>

>> "To Summarize, the geometric anisotropy requires some foresight in

>> modeling the directional sample variograms. All the directional variogram

>> models must have identical sill values. Each nested ..........

>> with the same coefficient."

>>

>> By the last sentence, I am assuming they mean the contribution coefficient

>> of each structure (i.e., cc value). First of all, why that should be the

>> case? etc etc etc [snip]

>>

>

>Your on you own there. I cheat and assume everythings nice and isotropic.

>Bad boy, I know......

>

>> 3- If variogram value start to decrease after reaching the sill, what is

>> the physical meaning of that?

>>

>

>Dont know the technical reason, but I found a similar thing when calculating

>a variogram from output from a numerical model. My dip was due to the

>boundary conditions, same constant head at two ends of an aquifer, so that

>head values at suitably large distances were magically similar and viola

>variogram value goes down.

>

>> 4- Is there any ERRATA being written for GSLIB manual? I need to confirm

>> some of the mistakes that I encounter in using the manual.

>>

>

>I hear that a new and improved manual [2nd Edn] is due to be out in January

>by Oxford Uni P for about 45 pounds.

>

>** Anyone else heard anything about the release??? **

>

>> With many thanks for your time and help.

>>

>>

>> Best of luck.

>> Abedini

>> |__|__| Mohammad J. Abedini |__|__|

>> |_____| School of Engineering |_____|

>> |_____| University of Guelph |_____|

>> |_____| Guelph Ont, N1G 2W1 |_____|

>> |__|__| Tel.:(519) 824-4120 ext. 4321 (W) |__|__|

>> |__|__| Tel.:(519) 821-1199 (H) |__|__|

>> |_____| Fax :(519) 836-0227 |_____|

>> |_____| e-mail: mabedini@... |_____|

>

>Andrew

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