## Dust flux, Vostok ice core

Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

## Saturday, January 22, 2011

### Determining scale invariance in geological phenomena

One concept which is quite familiar to geologists (even though it isn't often explicitly stated) is the concept of scale invariance. The way in which this point is frequently hammered home is through the requirement of a scale in a geological photograph. The reason that a scale is required (this need not be a literal measurement--frequently it is an object of known scale, like a shoe, a person, a rock hammer, a coin, or a house) is because many geological phenomena occur across a wide range of scales.

The picture at left is a perfect example. I found it on the internet years ago, and actually now I can't remember what it is. I have no idea if this is a close-up of the beach with a field of view of under a metre, or whether it is an aerial photograph, because features that look like those at left can occur at all of those scales.

The recognition of scale invariance in natural phenomena is not new. Benford's Law, an empirical relationship first noted by Newcomb whereby the first non-zero digit of a measurement is more likely to be 1 than 9 (30% vs 4.5%) is now understood to arise as a consequence of scale invariance.

Benford's Law only holds if the size range of the features measured spans several orders of magnitude (i.e., it does not apply to human heights).

Although scale invariance is inferred from the need for scales, obtaining the actual proof that geological phenomena are scale invariant is not easy. The reason for this is that the scale of observations available to the typical geologist is very limited.

The majority of geologists deal with rocks in outcrop, or (worse) sections of rocks obtained by drilling. In some parts of Canada, we have it pretty easy, as outcrops are frequently substantial. But in many places, most of the rock is covered in swamps, lakes, talus, mud and sands, or is inaccessible for other reasons. In such places, individual outcrops might only be a few metres across. Assuming a certain amount of weathering, it may be very difficult to identify very small features. You may only be able to observe features like fractures, or folds, across one or two orders of magnitude. This is not sufficient to determine scale invariance.

The photo above shows a number of olistoliths (two are outlined in red), which are pieces of material incorporated into a landslide that happened in the past. The olistoliths and the surrounding material were all soft (mud and sand) at that time--they are rock now. Some of the olistoliths in the photo are laminated, and these lamina are deformed somewhat, testifying to the stresses that these olistoliths underwent during their emplacement. The hammer is there for a scale. Photo is of the Gowganda Formation, near Whitefish Falls, Ontario.

In the photo above, the largest olistolith is about five times bigger than the smallest observed.

Here are olistoliths observed on the split face of a piston core sample from the Nova Scotia continental slope, collected in early 1987. The sediment is unconsolidated (still mud). The scale is at the bottom of the photo, measured in cm. These olistoliths are smaller than the ones in the Gowganda Formation, but still pretty much the same order of magnitude.

Smaller features are potentially visible in core, but they can't get much larger before they get difficult to identify. If the olistolith above were about 30x bigger than the one's that are present, in the core they would look like a separate layer, rather than an olistolith. Again, it is difficult to infer the scale-invariant nature of olistoliths from only these observations.

How do we see larger features in marine sediments? We have to go to geophysical imaging methods, and the two most common are seismic profiling and sidescan sonar.

The above profile is one I worked on in the late 1980s, although it had been collected some years earlier by the Geological Survey of Canada. The image has been vertically exaggerated, so that the space beween each of the tick marks at the extreme right of the image represents 10 m, whereas the length of the image is about 4000 m. There are a few debris flows interpreted to be in the image, two of which have been labelled. They are fairly large, compared to the photographs we have of olistoliths, and it would be reasonable to presume that there are large olistoliths within these debris flows. Unfortunately olistoliths do not show up on seismic profiles, so we don't know.

Not too bad. This is something similar--a pile of material that slipped downslope (that thing that looks a little like a footprint just left of centre of the photo). From the Gaskiers Formation (of Neoproterozoic age) outcrop on Little Colinet Island, southern Newfoundland, taken in 1995. I wouldn't quite call this an olistolith, but it is close.

It would seem the only way to confirm the existence of larger olistoliths is by studying very large outcrops with excellent exposure. These are generally rare, but below we'll take a look at two of them: the Smalfjord Formation in Arctic Norway, and the Yakataga Formation in the Gulf of Alaska.

Neoproterozoic diamictites of the Smalfjord Formation, northern Norway.
The light-grey areas represent rafts of sediment carried downslope in debris flows.
The red blotch at lower left is a person crouched over taking notes.

The sedimentary blocks in the Smalfjord Formation are pretty large. The ones in this picture appear to be about 2 m thich and perhaps 10 m in length.

1500-m section of the Miocene-to-Recent Yakataga Formation near Icy
Bay, southern Alaska, taken in 1989.

Outcrop on the scale of the image above may be what the doctor (that's me) ordered.

Exposure of Yakataga Formation at Icy Bay, Alaska, showing a submarine canyon and a series of olistoliths. Overall section here is about 1500 m in height, making the largest olistolith some 200 m in length. Original photo from an N. Eyles paper (trying to figure out which one).

We can demonstrate directly that there is a wide variety of sizes of olistoliths, but we have a hard time doing it from a single outcrop.

At this point we don't know anything about the size-frequency distribution--a topic we'll come to another time.