Kriging a Geostatistics tool

[Leosallespoli 338]

First off all, I'm not so fluent with english so please excuse me if I don't make myself clear and ask me if you don't understand what I'll say.

Okay, I'm an petroleum engineer student and I work a lot on geological simulation, only analytical simulation nothing that envolves rendering or 3d models. What that does is predict where a deposit of some sort will be, given some information about the rocks around it.

Geostatistics is different from normal statistics as it gives space a weight in the analysis. While statistics try to represents the world as a single body, geostatistics make every single place different from the other and they interact forming the world. It essencially uses histograms (frequency of samples) and variograms (a function that describes the spatial variance and gives meaning to any geological analysis).

I've seen some statistical analysis here in the forums and most of it is wrong or it doesn't mean anything other than we have 0,0001% of some sort of ore... It doesn't mean that if you dig down you wont find 0,1% of that ore, and it isn't luck that is involved in that. In the real world you can predict where a vein is and if you can predict that you can improve your "luck", that is what your propick does.

Anyways, one of the most basic tools of geostatistics is kriging, it is a model used in the mining industry, what it does is given two samples and their position in space it smoothes the space between them. Let me give you an example.

sample A=50% in Fe

samble B=30% in Fe

A - - - - - - - - B

kriging it will give you

50 48 46 44 42 40 38 36 34 32 30

For two samples it is rather easy, for some samples it can give a little more work.

So what about it? I have seen some discussion about making environments that are totally different collide, like a desert next to a tundra and for me a sedimentary rock like conglomerate next to an extrusive without any metamorfic in between.

Kriging is the simplest method, there is stochastic simulation that makes it less smooth and more random without been inacurate. I won't get into the math behind in this first post, if anyone is interested I can show some basic programing with that.

[Treyflix 277]

This is kinda above my head, I want to learn more about it!

So the gist I'm getting is you could use this "kirging" to create a better stone generation border? Or help locate ores? I'm confused... (feel free to call me stupid)

[Leosallespoli 338]

http://sgems.sourceforge.net/

Its the software I use, other than MatLab, and it is free.

You could use it to make any kind of property interpolation in space, what I mean with that is that let's say you have a 3 points non-linear in space and we are analysing the ore distribuition, so in point 1 we have 50%of the ore, point 2 we have 20% and point 3 0%. What kriging does is determine what is in the surface dermined by those 3 points, if it is 4 points it may be a space border.

So in terrafirma if you determine that above 40% you have a kind of ore and below it you don't have it so kriging just might help you smooth the distribuition of ore.

It is commonly used in mining by doing some field work to determine the input points so you can use the kringing to make a model of the ore body.

In petroleum industry we need the stochastic model and conditional simulation wich is a lot more close to reality since it randomly generates models that are fit to your input points and your variogram and we process these models so they can give you a not so random model of what is there.

I would give you an example but I don't know how to post images withou imgur... and sucks to be going to other pages and coming back

[Draco18s 46]

I wonder if kirging is possible already, given the information we can obtain with the prospector's pick.

Assign values to the various results, e.g. 10% = traces, 20% = small, etc. and plug those values, along with the X, Y, Z coordinates you're standing at at the time, and it could potentially solve the distribution curve for you

[abandoned mines 119]

o interesting i ve used this soft ware in geo technical class

one of my friend used a tweeked version to help fellow students map out core drill patterns

neat to see it suggested here

[Leosallespoli 338]

I wonder if kirging is possible already, given the information we can obtain with the prospector's pick.

Assign values to the various results, e.g. 10% = traces, 20% = small, etc. and plug those values, along with the X, Y, Z coordinates you're standing at at the time, and it could potentially solve the distribution curve for you

That is a good question... I think it could but it is like killing an ant with a bazooka, but hey... I'll try to make a model of an ore body and post it here.

one of my friend used a tweeked version to help fellow students map out core drill patterns

We have a lab iat the University that does that, they make models out of drill paterns and use softwares like dataminer to predict the best plan of approach to the orebody

[Jasnatdic 85]

-bunch of stuff-

I might have missed it, but i saw a great big explanation of what kringing is, and why your familiar with it, but didn't actually see a suggestion. Are you suggesting a new "more accurate" method for generating rock layers in world gen, or are you suggesting a high tech method for mapping rock and ore locations under ground using core samples? Or, are you suggesting something else that I totally missed?

[Leosallespoli 338]

http://imgur.com/0xiXJ

This should be a little ore body, given that i've tested on an already exploitated sphalerite mine i had so the samples were only medium. The white dots are the points of research with the propick. I did 0.1 for traces, 0.2 for small and 0.3 for medium, in red is 0.3 or more, so there is a good chance the ore is there.

Also just to be clear the blocks are 0.5 of width while minecraft blocks are 1, I did that just to give resolution to the analysis.

I did made some suggestions, it could improve world gen and block mapping, I don't really like it to locate ore since it would be over analysis, but yes you could do that.

[Jasnatdic 85]

Ahh, so new world gen algorithms, I don't thing its really necessary. However, that is up to Bioxx of course so if he wants to incorporate this for a more natural feel to the world gen i wont argue against it.

However, world gen is completely different in 49 than it was before, and i haven't don't allot of exploring but deserts and taigas for example shouldn't be next to each other. Check out the notes for all the changes in build 49.

[Leosallespoli 338]

However, world gen is completely different in 49 than it was before, and i haven't don't allot of exploring but deserts and taigas for example shouldn't be next to each other. Check out the notes for all the changes in build 49.

I know, z difference to make the biome allocations. Its simple and solves the problem, but you could be even more precise. But in my opinion rock layers is the best approach with a model like kriging, so you have that overlapping to be smooth and precise.

[Draco18s 46]

http://imgur.com/0xiXJ

This should be a little ore body, given that i've tested on an already exploitated sphalerite mine i had so the samples were only medium. The white dots are the points of research with the propick. I did 0.1 for traces, 0.2 for small and 0.3 for medium, in red is 0.3 or more, so there is a good chance the ore is there.

Also just to be clear the blocks are 0.5 of width while minecraft blocks are 1, I did that just to give resolution to the analysis.

I did made some suggestions, it could improve world gen and block mapping, I don't really like it to locate ore since it would be over analysis, but yes you could do that.

That, right there, is really cool.

It might be a nuke for a flyswatter, but hey.

http://sgems.sourceforge.net/

I decided to poke at the software myself and I can't figure out how to input data. :

[Leosallespoli 338]

What i've found with that model:

0.1 for traces 0.2 for small and 0.3 for medium is not the right scale but it is close to that. But there is a big discordance to how the propick works to how the kriging does its model, the propick search a volume of 25x25x13 while the kriging search on an ellipsoid, so there may have some problems in that.

To give an exact model you have to take a lot of samples to be absolutely sure. I don't think that searching for ores would be a good way to use kriging, not in this case.

[Draco18s 46]

It's probably closer to .16 for traces, .33 for small, etc.

In any case, I still haven't figured out how to enter data.

[Leosallespoli 338]

Make a .txt:

Title

number of properties

name of property 1(like position x)

" " " 2

" " " 3

...

last property

Table of properties, each collumn is meant for a single property for the all samples and must be spaced by TAB.

Example:

teste

4

X

Y

Z

Esfalerita

-340 136 -9636 0.1

-345 134 -9636 0.1

-355 135 -9637 0.3

-353 136 -9630 0.1

-354 138 -9642 0.3

-369 137 -9646 0.3

-355 129 -9651 0.1

-346 136 -9647 0.1

-357 128 -9640 0.3

-364 129 -9637 0.3

-353 129 -9638 0.2

-355 140 -9639 0.3

-343 134 -9641 0.1

-356 134 -9641 0.3

why the heck tab doesn't work on these forums?

then you drag and drop the .txt to the workspace and make it a pointset

[Draco18s 46]

Ah, thanks!

*Fiddles*

...and how do you generate the heat map?

[Leosallespoli 338]

Heat map?

[bsb23 303]

He is referring to the picture you posted earlier that looks similar to an infrared picture.

[Leosallespoli 338]

So let me stop smelting the copper to respond to this one.

Ok, I'll try to be clear even though that even in portuguese I may sound confusing.

1. You make the file with your log (the results that you've acquired in field)

2. you import the file by dragging and dropping it on the workspace of the program.

3. You make the grid which will contain your future model, it is made of little blocks that you can choose the size and where they are in space.

4. With all that done you can start analyzing, first of all you have to do the variogram and that is tricky, if you don't know anything about statistics you may stop here. What that does is a function that walks in a vector determining the variance between every two samples so it can give you how the samples are distributed in space. The variogram has 3 main approaches spherical variogram, gaussian variogram and exponential for what I can tell about it is if it fits then it is right, what I mean is there is no sure way to know what approach you should do for a model. Usually the spherical will do.

So you go to the variogram menu choose the variable you want to work with, next you have to choose the number of lags that the variogram will analyse, their size(separation) and tolerance(this is almost useless given that it just adds noise, so make it very tiny). Number of directions it will go, as of vectors it will analyse, usually north, east and z(azimuth 0 is north, 90 is east and dip 0 is the surface and 90 is going down), tolerance being that it will not only search the vector but the surroundings, bandwith limits this.

Now that this part is done you may finish the analysis by selecting the max,med and min -they will be the constants of the function in the variogram- that fits the curve to the data(it won't fit perfectly). By the way you have to look for the histogram of the sample for the variance as it is the sill.

Save it.

5. The last part is the estimation, select kriging, ordinary kriging. There is some different approaches to do the kriging, ordinary is the simplest and more accurate of them. Now choose the data, the grid that it will go to, and the most important the search ellipsoid. What it is is that for every given point of data it will make an ellipsoid that fills with the inner blocks of the grid by using the variogram that you will give in the other tab, so when two ellipsoids intersect their data will be a kind of interpolation between the two using the variogram. So if you make the ellipsoids too little they wont intersect and the points around each given pointset will be equal to the pointset chosen, and if you make them too big every point will interfeer with each other.

And you're done... I hope it helped

[Draco18s 46]

...Not really. :

In terms of English, I understood, but in trying to actually do I caused the program to crash (ok, this is only if I attempt to change the plot settings).

I get to the part where it shows a graph and has the mix/max sliders, but I don't have a next button at this point. So even when I have a graph that "looks good" I can't do anything with it.

(Not that I can tell if the graph is right or not...I only see a line, no data points)

[Leosallespoli 338]

1000??? really?? You've mapped that much? You know that makes for the total distance you've mapped.

And how can I post images like that?

And there is no data because it has catched no data in that vector with the specifications you've given.

[Draco18s 46]

1000??? really?? You've mapped that much? You know that makes for the total distance you've mapped.

And how can I post images like that?

And there is no data because it has catched no data in that vector with the specifications you've given.

It doesn't matter what number I put in, I can't see any data points.

As for images, the tag and http://tinypic.com/

I blindly tried a smaller value and got a heat-map. Woo. Unfortunately, depite being a 3D algorithm and renderer, it only does a heatmap on the surface of each cartesian grid face. Sadface.

[Leosallespoli 338]

First things first

you should have a grid and a point set like this:

Then off to the variogram

This is an example

number of lags * lag separation must be less then the max size of the grid.

[Leosallespoli 338]

If you still don't have any data showing maybe is because you have too little data.

This is a good "tutorial" on how it works

[Draco18s 46]

If you still don't have any data showing maybe is because you have too little data.

This is a good "tutorial" on how it works

No, I mean, it only does the surfaces of the cube.

It doesn't have any way to look at a single slice.

So I went and ran the exact same settings on a couple single-slices.

But as you should be able to see, those slices aren't accurate to the whole cube. WAY more of the dark blue along that z-axis edge.

[Leosallespoli 338]

Use the volume explorer, pick a range like .3 to .36. And may be it is, it depends on what is in the middle of the cube, for instance there can be a zone where nothing good can be in in just in the middle of the grid and at the borders it may have something worth looking at