Ophoilite, thanks for sharing your ideas. When I said uncertainty is a simple concept, I mean it. You don't need to be a geologist, or anything else for that matter, to know that uncertainty exist, and we, as scientists are trying to assess it and make predictions accordingly. It not only involves the subsurface and its properties, but also other disciplines. For example, uncertainty in climate modeling; simply weather forecast. Sometimes its correct, sometimes not. And you may never be sure whether it will rain tomorrow or not, there exist uncertainties. But we do our best to assess it and make educated predictions that there is 80% chance of rain tomorrow. Or simply in finance. There is uncertainty on how the shares are going to react and how the market changes. That's why we have the Black-Scholes model to incorporate the history and the variances (uncertainties) into a model to predict the future. This is also assessing uncertainty. The same goes for modeling catastrophic events, such as hurricane, earthquake, tsunami. There are uncertainties regarding those situations: what is a chance of earthquake in that specific region?, the possibility of a above 5 earthquake after one that is only 3? what is the possibility of a hurricane in this area?, what are the damages that may incur? These are also examples of assessing uncertainty. Other examples could be modeling the mortality and longevity, which helps insurance companies to put a price tag for your life insurance.
You see, there are many examples as in what modeling uncertainty means: some tools used for incorporating our knowledge, the physics, the geology, or any other information that we have, to generate models. They help evaluate uncertainty in the subsurface, for example what would the oil recovery be ? or whether I should drill here or not ? It could also be a simple as what is under the hood of my car. Yes, this is also assessing uncertainty. Considering what my car is, what year and model it is, and what cars generally have under the hood, I can assess what lies down there. Well, I might not have the education to list all possible parts, but it does not stop me from understanding what "assessing the uncertainty" means. There are books regarding this in general. Those books do not depend on any specific major or discipline. They are merely providing the mathematical concepts for such a case: i.e. the Bayesian approach.
And my understanding of this paper, in short, follows: You have a geological model that is describing your knowledge of the subsurface. This could have been obtained from nearby outcrop data, or geological interpretations, that for example, there are sandstone channels flowing within a specific E-W direction. You use this model to generate many more models that capture the uncertainty regarding how these channels are connected to each other, while at the same time, match all other sources of information that you have (i.e. seismic). The paper approaches this problem by the patterns (IMO, the constituents of everything around us). It is organizing the patterns (using distance-based methods and kernel mappings), and then uses these organization to simulate the phenomenon. I find it fascinating not just because of the mathematical power of such a technique (you can look into them, for example kernel methods, in computer science literature and see the applicability of such techniques in many disciplines), but because of its similarity to how humans behave. If I am given an image and would like to draw, by hand, similar looking images that also match my data, I would start looking at the image, and organizing the patterns in my mind (that's what is called "patterning" in physio-visual studies regarding our brain functionings). Also, the fact that it models the phenomenon in different scales is interesting, since as a human-being, I would have exactly done the same: by sketching a rough outline of the phenomenon (the channels for example), and then refining them until I get my final image. These are the reasons for interesting and powerful ideas. So you need to read the paper, not because of its equations, but the general idea that it conveys.