Introduction: other chill things to do with clustered deposits
Last time we went through the process of trying to identify clusters of deposits with similar geochemical anomalies. We were kind of successful, in that there appears to some correspondence between some “type deposits” and the clusters.
Well, now we’ve got these clusters, so what are we actually going to do with them? How can that kind of information help with exploration targeting? We talked about two things:
1) Try to relate clusters to deposit shape
2) Try to discover concepts related to clusters using text data – to help build up a conceptual model ie: what pieces to include in our targeting
Today, we will talk about deposit shape.
Deposit shape
What do I mean by deposit shape?
I don’t really care all that much about 3D at this scale. What I want to know is what drilling pattern was eventually used at these deposits, for better or for worse. Of course we can expect a pretty linear looking pattern in general as most mineral deposits and particularly gold deposits end up like that. But are there variations within that? Are some more or less continuous? Wavy? What do they look like?
The best way to summarize that is to actually look at an image of them. We are going to make a picture where each cell represents the drilling density for each deposit in our set. We’ll keep them to a standard scale for simplicity but that in and of itself is cool because how big the hotspots are might be neat too.
So we’ve got a strategy now: we are going to make this cluster data useful by doing some transformation to it to make a derived product, and then finally we are going to say what values of the derived product are good and bad for exploration.
And after that, yes this will be hard to hear, we can move on and ignore the geochemistry data, at least at this stage. Why? Because we’ve captured its significance to exploration. It was a long and winding road but this is it. It doesn’t do anything else, despite our best wishes. So let’s wrap it up.
There are many powerful ways to consider images programmatically, but amongst the best is the scikit-image library. Yes, yes, there is deep learning too, but as we will see that perhaps may be overkill for what is at best a tenuous relationship. But let’s find out.
The plan
First things first, we need to associate drilling data, gold or otherwise, with each declustered example deposit. We only care about our aggregated deposits from last time too.
1) Associate drilling to deposits
2) Convert vector points to an image of standard size
3) Characterize the images
4) Learn something
Processing
We will spatial join the drillholes to the aggregated deposits with a distance of 5 km to start. Then we will define a square 10 km a side, centered on each deposit cluster.
Then we can clip out just the drillholes falling within each square.
Then we make an image showing the density of drilling for each cell in a grid.
Sweet. Now what can we say about this image that would be helpful for exploration?
There is a trend, which isn’t too much of a shocker but still that’s interesting. The direction of the trend won’t generally be helpful because that will vary everywhere, but perhaps the degree of trendiness? That to me would be the deviation from a straight line, or the axis ratio of an ellipse covering the blobs, and/or the length of the shape vs its area.
There are spots of high density and low. What is their average spacing? How big are the spots? For that matter how big are the continuous bodies of higher density at some kind of cutoff?
Maybe one more thing is the average number of spots in the square. Are there multiple big bodies or just one with hot spots?
That’s a pretty good to-do list, so let’s get started.
Analysis
Todo
Trend
🔲 size of the continuous bodies of higher density at some kind of cutoff
🔲 average number of trends in the square
🔲 deviation of overall trend from a straight line,
🔲 the ratio of an ellipse covering the trend
🔲 the length of the shape vs its area
Hot spots
🔲 average spacing of hot spots
🔲 size of hot spots
🔲 average number of hot spots
Both
🔲 multiple big bodies or just one with hot spots
Implementation
So we need a way to define something called a trend, which is a continuous body of elevated drilling density. And then within that trend, or outside of it too, we need to define hot spots which are smaller, possibly rounder, and of much higher density.
We will use scikit-image to first identify the trends in each square. Then we can summarize some information for each one: the eccentricity (ratio of long axis of ellipse to short axis), the solidity (the ratio of hot to cold cells within the trend), the area, and the orientation. See more detail here on the “regionprops” as they are called in scikit-image.
For hot spots, we will identify local peaks (individual high cells), count them, and assign them to a trend so we can measure the spacing particular to each trend. Here is what putting it all together looks like as an image:
We got there! Let’s check that to-do list again.
Trend
✅ size of the continuous bodies of higher density at some kind of cutoff (area)
✅ average number of trends in the square (count of trends per square)
✅ deviation of overall trend from a straight line (solidity)
✅ the ratio of an ellipse covering the trend (eccentricity)
❌ the length of the shape vs its area (kind of capture by solidity and eccentricity)
Hot spots
✅ average spacing of hot spots
❌ size of hot spots (they are one cell due to using local maxima)
✅ average number of hot spots
Both
✅ multiple big bodies or just one with hot spots (ratio of biggest area to total trend area)
OK, now we will run it for all the examples.
Looking at the data
Now we can consider the number of trends, their variability, etc. per cluster. I’ll save you the statistics, but overall, there wasn’t a significant variability in the solidity, eccentricity, or hot spot spacing between the clusters based on the Kruskal-Wallis test. The frequency of trends vs no trends made it look like cluster 2 tends to form more trends, but not enough to reject the hypothesis that the clusters are all equally likely to form trends.
The plots, as always, are a little more provocative. Let’s look at some type examples.
Cluster 0
Most images of cluster 0 are pretty boring. I think in general these represent the majority of isolated deposits with a small amount of drilling nearby, so they don’t form trends as often.
Cluster 1
Cluster 1 has more interesting plots than 0, but overall it’s a pretty similar story.
Cluster 2
Cluster 2 has more trends than the other two on average. It also has the highest circular variance of orientation, meaning more varied orientations. Again, these relationships aren’t really strongly statistically supported, but it’s interesting.
Outcomes
Based on the shape analysis of drilling associated with each cluster, there was not a significant variation in overall shape per cluster. So short answer, it looks like we couldn’t easily tell something about deposit shape using just geochemistry. I think that we must be able to, at least if we are will to zoom out further than just one part of the world, so I would speculate that is due to the nature of the experiment and particularly the decimation of examples due to the declustering. Something to change next time.
That being said, however, there are some qualitative relationships that are interesting. Cluster 2 (the intrusion-y cluster) tends to form trends more often, and they are bigger with more hotspots. They are also more variable in orientation within a given area. A new prospect with geochemistry belonging to cluster 2 could have a higher chance of being part of a larger series of trends, and they are more likely to take irregular orientations. Conversely, relatively “normal” geochemistry from cluster 0 or 1 would be more indicative of either isolated hot spots or a single, fairly regular trend. The explorer in cluster 0 or 1 might wan to identify the trend and stick with it. In cluster 2, however, exploration further into a single showing’s relative hanging wall and footwall rocks might be a good idea, with the identification of irregular, possibly intrusive bodies using geophysical data a high priority.