Replacing The Variogram

This week, Luke nails his sacrilegious thesis to the door - that the variogram can be replaced by quality data analysis. 

We're building a product called Hutton to do exactly what has been outlined above: If you'd like to get a sneak peak, drop Luke a line at: luke@cognitivegeology.com

To dig deeper into this week's whiteboard, click on the image below to get a fullscreen version.

TRANSCRIPTION

Replacing The Variogram

Hello. Welcome back to the Cognitive Whiteboard. My name is Luke, and today, I'm nailing my thesis on the door. I am going up against the institute to commit to geostatistical heresy by showing you that variograms are not an essential element of our geological modeling processes. In fact, I wanna show you that with careful trend analysis, you can do a better job of producing geological models that represent your geology in a much more powerful way and give you much more predictive answers.

To do this, I've built a data set - it's a complex data set, they're quite geologically realistic, some tilted horse blocks through here into which we have modeled some complex geological properties. We vary those over x and y by some unknown function. We have some very complex sequence cyclicity of fining upwards and coarsening upwards trends. And we've over printed this with a burial trend. And what we want do is see how we go about representing that with this perfectly patterned drill data set, either with trends or with variogram analyses and determine which one we think is better.

So, let's first off have a look at the variogram of the raw data set and we can see immediately some of those structures, some of those trends that we impose in the model, are showing up in our variograms. We have some obviously low sills in some of the data sets that have some structures, some correlation over distance before they flatten out into our sill. But we do have some weird cyclicity that's happening and we should wonder what's going on there. So in truth, we know that this is just the complexity of having lots of different processes creating nested variograms and various sequences of cyclicity. And all geologists that are familiar with this kind of routine will know to try to take some of these trends out.

One way we could start is by subtracting the stratigraphic trend. This isn't often done but it's very, very powerful. You could take, for example, a type log and remove that from your log, from your data set, or you could do what I've done here and essentially subtract the midpoint or the mean value from every one of your K layers and see what you get after you take that out. You're basically representing sequence cyclicity when you do this. You wanna keep that trend, this black line here, because you have to add it back into your model afterwards. But when you do it, you see a reduction in the vertical variogram, as you would expect. We have described a lot of the variation that's occurring in this direction as a function of sequence cyclicity and it's not just random. And so typically, you'll see a reduction of probably the half of the variation in the vertical sense. But it won't have any impact on the major/minor directions because the same columns exist everywhere in x and y space.

Once we take that trend out, we'll have a new property - it’ll be porosity given that trend - and we can do a trend analysis on that property. So, now we're doing it against depth. And what's interesting is as you take out trends progressively, you start to see the second and third order effects that might not have been obvious in the raw data sets. In this case, it really tightened up our observation of the depth trend. And we can subtract that next. Take that trend out because it's not random and see what it does to our variograms. Now, this one changes the major and minor variograms, not the vertical one, even though that seems counterintuitive, and it's doing that because your burial depth is varying as a function of its map position. So that's why it changes those two variograms.

And again, we can keep diving down deeper and deeper into our data sets, removing progressive trends, linking this to geological processes, and pulling it out of your data. In the end, with this perfect data set, if we had described all of those trends, you would see no structure left in your data or next to no structure. And that's because you have done a pretty good job of describing geology, not just random processes. Your nugget and your sill is almost identical. That means that the observational point has just as much information immediately as it does at some great distance. That's great, you no longer need a variogram. You have done it instead with trends.

Now, this is obviously a perfect data set with an unrealistic perfectly sampled series of wells. Let's imagine what we would do with a realistic sample set with much more sparse and biased samples. Well, most gross geological trends are obvious, even in small data, small amounts of samples. But these horizontal variograms are something that we basically never get to measure in the real world. And so, we spend our time in peer reviews often defending whatever settings we have done in these major and minor directions with no basis or outcrop that we can link that to.

So, if you want to do something in this space, you can make your models much more predictive because you can end up driving geology into it and removing the dependence upon your random seed. You can do all of this in pretty much any commercial package today, but it's not particularly easy or intuitive. So, we've gone ahead and built a product for you that will do this in a much more powerful way. We call it Hutton, named after the father of geology, because with these small observations, we can make interpretations that can change our understanding of the world.

Hutton comes to the market in March 2017. It will help guide you through this trend analysis process, it even has some intelligence that can help you automate that. And if you're interested in finding out how to throw away the variogram and bring geology back into your geological models, please drop me an email, and I'll happily show it to you. But for now, in the meanwhile, that's all from us, and I'll see you next time at the Cognitive Whiteboard.

p.s email me on luke@cognitivegeology.com and I'll get back to you.