AI-GEOSTATS: Information about Kriging 3D and semivariogram in 3D-list of replies.
- Hi to everybody:
Regarding my recent question, I received the replies listed below. Thank you very much to all.
My question was:
Hello to everybody,
I have to build a semivariogram in 3D
and I need to know if I can use the same concepts
used for the 2D semivariogram or if the theory is
different. For example how can I consider the
distance? In one article they said that I can first
build the semivariogram in the horizontal direction
in order to find the values of sill, range, nugget
and the equation of the semivariogram. After this I
can use these information to find the range in the
vertical direction. Do you know any references that
explain exactly how to do it?
Thank you very much.
Distances and directions in 3d can be calculated very
simply just as in 2d. There is shareware (Geostat
Toolbox) and other software out there for 3d.
Calculating semi-variograms whilst pretending your
data is two dimensional can lead to extremely
misleading semi-variograms. In particular your nugget
effect will be exaggerated out of all proportion to
At the risk of offending some of our more sensitive
list members, can I suggest you try things out on our
FREE teaching software PG2000 which includes 3d
capabilities. Test data set for this is a copper dump,
which is provided in the FREE downloadable data sets.
Find all this and other free goodies at
have a look on Isaaks and Srivastava (applied geostatistics) book
you will find there a good explanation on variogram modelling
You can apply exactly the same principles in 3d that you use in 2d.
Variograms are functions to measure variability of samples by pairs using the variance as an index.
In mineral deposits what we do? We use a variogram down the hole, do define the nugget effect, that is a residual variance that you must start you variogram and must be calculated in the shortest distance that you have, after that we calculate 3 variograms to represent 3d, if you is a geologist like me, the directions are basically the azimuth, the dip and the vertical direction for the plane given by azimuth and dip.
Basic Linear Geostatistics, 1998, Armstrong, M.
Introduction to Applied Geostatistics, 1989, Isaaks & Srivastava
GSLib, 1990 Deutsch & Journel
Ciao (io no parlo italiano, io voglio parlare un dia...)
La teoria per costruire un variogramma tridimensionale e` la stessa. Se vuoi individuare rapidamente gli assi di anisotropia del modello
la cosa migliore, se hai molti dati, e` quella di studiare il variogramma di volume (il corispettivo del variogramma di superficie in due dimensioni). Comunque dipende dalla geometria di campionamento. Se non hai la possibilita` di calcolare il variogramma di volume studia il variogramma lungo diverse direzioni ed inclinazioni. Spesso si puo` studiare il variogramma solo lungo il piano e lungo la verticale. IN questo caso sei costretta ad ammettere che gli assi di anisotropia sono orientati secondo gli assi cartesiani. Ti consiglio Gstat o Gslib come software free o Isatis a pagamento. Quello che dice l'articolo non mi sembra chiaro.....a volte si fa il contrario.
Attached you can find some page write in Spanish (I hope you understand this language), in which I explain to my students the construction of the semivariograms in 2D and 3D. Be careful with the line intermittent in the last paragraph.
I hope this help you.
You can use GSLIB it's also a free soft. You can find it in ai-geostats
web page. In the corresponding book you can also find the theoretical
basis of it.
I would recommend that you look at Chapter 16 of Isaaks and
book "An introduction to Applied Geostatistics" which offers a very
description of how to model semivariograms in different directions and
up to 3 dimensions. You can also refer to the following paper:
Barabas, N., Goovaerts, P. and P. Adriaens. 2001. Geostatistical
assessment and validation of uncertainty for three-dimensional dioxin
from sediments in an estuarine river. Environmental Science &
I am studying on geostatistical 3D data, too. I am a mining engineer. I am using it in reservoir modelling. I searched material about it so much. but the information about that is very limited. Practically there are two semi-variogram plane: 1 horizontal, 2 is vertical and independent from each other. I have found a 3D variogram modelling software called "snowden" at www.sonwdentec.com.au . But I could not use the software. There are some applications at there. Have you got any material (paper, book etc.) about 3D variogram?
I guess It helps you a little.
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