Okay, so I've got one more fantastic geology-trip to get in for 2009. Here's a clue: it's another active volcano. So things might remain quiet here until I return in a few weeks.
Mahalo.
Tuesday, December 29, 2009
Tuesday, December 15, 2009
Continuing apace, upscaling granular interactions
One of the things sedimentologists try to do is visualize how individual grains behave. This is important for things like sediment transport and deposition - it even plays an important role in things like quicksand. In some cases, it's helpful to scale a system down so that it may be observed in a lab room, under manageable timescales. I've been working on scaling things up to look at how individual grains interact with each other. A few thousand fluorescent BBs and a blacklight help bring out the details look pretty interesting with a long-exposure photograph.
Update on fractal landscapes
I had mentioned these fractal landscapes to an old college friend, and he had this to add:
I think that's an important point. A lot of fractal geology is mere "appearance," rather than true "behavior." But I think he's got a good point about the combination of gravity and the EM force. The disjunct between scales might be bound by the ability of materials to resist gravity (displayed in such things as a mineral's hardness, etc.). On top of that, there are continental-scale behaviors of crust, which allows for things like uplift and sedimentation in the first place. The reason the Sierpinski Triangle outcrop looks like it does is due in large part to the well-partitioned sedimentary cycles within the outcrop - breaking it up into nearly perfect thirds, top to bottom.
I've been doing a lot more thinking, rather than synthesizing lately, but I think the note about the EM force and gravity is an important one. Since much of what we see on the landscape is a tug-of-war between gravity, which tends to bring things towards the center of the Earth, and the EM force, which helps resist it. There's probably a bit of influence by the Strong and Weak Nuclear forces in there too. Although, I think crustal properties such as bulk modulus are more affected by the EM force, but it might be fun to look into the combination of the EM and Weak Nuclear forces, since much of our Earth's internal heat is provided by nuclear decay.
Another way to think about it: there appears to be a minimum size to silt grains generated by impacts with larger particles. At small enough scales, gravity can't generate enough energy to knock atoms apart - so there's another scale at work when it comes to very tiny silt-type grains. And don't forget the completely different behavior of clay minerals!
Of course, this EM force and the ability of minerals to resist breaking down plays a key role in any critique of a marine origin for the Coconino Sandstone. Yes there are mica grains in the sand. Yes, mica is softer than quartz. But there are more forces at work besides Moh's fancy little scale.
With the caveat that looking *like* a fractal isn't the same as being a fractal, a fractal has organizing rules that are in a recursive relationship. So it seems to me that the two organizing rules are gravity and the electromagnetic force that holds materials together, and the 'recursion' is moving the materials around, primarily water but also wind. But I could be wrong.
I think that's an important point. A lot of fractal geology is mere "appearance," rather than true "behavior." But I think he's got a good point about the combination of gravity and the EM force. The disjunct between scales might be bound by the ability of materials to resist gravity (displayed in such things as a mineral's hardness, etc.). On top of that, there are continental-scale behaviors of crust, which allows for things like uplift and sedimentation in the first place. The reason the Sierpinski Triangle outcrop looks like it does is due in large part to the well-partitioned sedimentary cycles within the outcrop - breaking it up into nearly perfect thirds, top to bottom.
I've been doing a lot more thinking, rather than synthesizing lately, but I think the note about the EM force and gravity is an important one. Since much of what we see on the landscape is a tug-of-war between gravity, which tends to bring things towards the center of the Earth, and the EM force, which helps resist it. There's probably a bit of influence by the Strong and Weak Nuclear forces in there too. Although, I think crustal properties such as bulk modulus are more affected by the EM force, but it might be fun to look into the combination of the EM and Weak Nuclear forces, since much of our Earth's internal heat is provided by nuclear decay.
Another way to think about it: there appears to be a minimum size to silt grains generated by impacts with larger particles. At small enough scales, gravity can't generate enough energy to knock atoms apart - so there's another scale at work when it comes to very tiny silt-type grains. And don't forget the completely different behavior of clay minerals!
Of course, this EM force and the ability of minerals to resist breaking down plays a key role in any critique of a marine origin for the Coconino Sandstone. Yes there are mica grains in the sand. Yes, mica is softer than quartz. But there are more forces at work besides Moh's fancy little scale.
Thursday, December 10, 2009
Speaking of Scaling...
I've stumbled upon yet another idea I want to try out: dropping various spheres into containers filled with smaller spheres:
Next up is a more controlled setting to look at variation between dropped ball density, diameter, and substrate thickness.
Next up is a more controlled setting to look at variation between dropped ball density, diameter, and substrate thickness.
Thursday, December 03, 2009
Fractals in geology
In many ways, geology is a study of fractals. There are many geological systems that display the characteristics of fractals. Mandelbrot's famous fractal pattern resembles the coastlines of many areas of the globe.
River systems, such as the "Driftless Area" in southwestern Wisconsin display a beautiful fractal geometry:
A shaded elevation map of of the Upper Mississippi River region (white is higher elevation). The Mississippi River is the thick black area running diagonally through the image. The white square shows the zoomed-in area for the next image.
Zoom in 50% - more fine-scale details appear, but they are remarkably similar to the larger-scale ones.
Zoom in another 50%
And another 50%. We're looking at 12.5% of the original image. My starting resolution was a little rough, so the digital artifacts of the raster image is getting in the way. But you get the gist - in ArcGIS, one can adjust the color ramp, which produces patterns amazingly similar to mathematical fractal patterns. I've been searching for some more technical analysis of the Driftless Area and its fractal geometry, but so far I've come up short. If any of you are aware of some good landscape geo studies, feel free to share.
Finally, another type of fractal pattern can be seen in near-vertical exposures of rock. Small parts resemble the larger outcrop, even down to individual piles of debris.
Triassic (chinle equivalent from the Bighorn Basin - the name eludes me right now) redbeds. This is a pretty darn good representation of the Sierpinski Triangle. Oh, and I got an interesting comment from a young-earther related to this photo. I'll have to share that sometime...
There are plenty of examples of other landscape fractal patterns. One thing that strikes me, however, is that - despite this self-similarity - there are breaks in the "scaling." Take a mountain range - from far enough away, it looks relatively smooth and small. Zooming in, reveals topographic changes that start to look self-similar, down to a certain smaller scale. Then, the characteristics of the individual rocks take over. Phenocrysts, ground mass, local variations begin to render one outcrop different than another. But, zoom in further, so that an individual phenocryst has the apparent size of a mountain, and this self-similarity shows up again. It begins resembling, at least in part, the larger mountain range at big scales. You jump down to the microscopic, molecular level, and the characteristics of the individual mineral take over yet again. Zipping into sub-atomic scales, we see vast empty spaces, filled with electrons, protons, then quarks and gluons and all sorts of Dr. Suess-like particles and physical interactions. Interestingly, this sub-atomic scale, superficially at least, resembles a super-duper-macro-scale view of the solar system and universe.
So, do these "jumps" in scaling represent some kind of "boundary condition" within which the fractal system must operate? Or is the idea of "self-similarity" in the landscape incorrect? Is it something different - a rough approximation, but not really the most useful concept for describing and exploring the natural world?
River systems, such as the "Driftless Area" in southwestern Wisconsin display a beautiful fractal geometry:
A shaded elevation map of of the Upper Mississippi River region (white is higher elevation). The Mississippi River is the thick black area running diagonally through the image. The white square shows the zoomed-in area for the next image.
Zoom in 50% - more fine-scale details appear, but they are remarkably similar to the larger-scale ones.
Zoom in another 50%
And another 50%. We're looking at 12.5% of the original image. My starting resolution was a little rough, so the digital artifacts of the raster image is getting in the way. But you get the gist - in ArcGIS, one can adjust the color ramp, which produces patterns amazingly similar to mathematical fractal patterns. I've been searching for some more technical analysis of the Driftless Area and its fractal geometry, but so far I've come up short. If any of you are aware of some good landscape geo studies, feel free to share.
Finally, another type of fractal pattern can be seen in near-vertical exposures of rock. Small parts resemble the larger outcrop, even down to individual piles of debris.
Triassic (chinle equivalent from the Bighorn Basin - the name eludes me right now) redbeds. This is a pretty darn good representation of the Sierpinski Triangle. Oh, and I got an interesting comment from a young-earther related to this photo. I'll have to share that sometime...
There are plenty of examples of other landscape fractal patterns. One thing that strikes me, however, is that - despite this self-similarity - there are breaks in the "scaling." Take a mountain range - from far enough away, it looks relatively smooth and small. Zooming in, reveals topographic changes that start to look self-similar, down to a certain smaller scale. Then, the characteristics of the individual rocks take over. Phenocrysts, ground mass, local variations begin to render one outcrop different than another. But, zoom in further, so that an individual phenocryst has the apparent size of a mountain, and this self-similarity shows up again. It begins resembling, at least in part, the larger mountain range at big scales. You jump down to the microscopic, molecular level, and the characteristics of the individual mineral take over yet again. Zipping into sub-atomic scales, we see vast empty spaces, filled with electrons, protons, then quarks and gluons and all sorts of Dr. Suess-like particles and physical interactions. Interestingly, this sub-atomic scale, superficially at least, resembles a super-duper-macro-scale view of the solar system and universe.
So, do these "jumps" in scaling represent some kind of "boundary condition" within which the fractal system must operate? Or is the idea of "self-similarity" in the landscape incorrect? Is it something different - a rough approximation, but not really the most useful concept for describing and exploring the natural world?