Flame structures

Flame structures are sedimentary structures that usually consist of upward-pointing flame-shaped finer-grained sediment tongues that protrude into coarser sediment (like sand). Almost invariably, the ‘flames’ are inclined in a downslope direction (in a paleogeographic sense, of course) — like in these two images from the Precambrian Windermere Group in the Canadian Caribou Mountains.

Flame structures are often interpreted as load structures: the overall higher-density sand sinks into the lower-density underlying shale. That would put flame structures into the category of Rayleigh-Taylor instabilities, which result from density inversion. In geology, one of the most important types of Rayleigh-Taylor instability is related to salt: if buried deep enough, the density of the compacting overlying sediment exceeds the density of salt, and the latter starts flowing upward, giving rise to salt diapirs. Salt diapirs often have mushroom shapes, typical of Rayleigh-Taylor instabilities.

The shapes of the flame structures above actually remind me more of the Kelvin-Helmholtz instability, which is related to shear (that is, different velocities) across a fluid interface, and can occur even if the densities are not inverted. K-H instabilities in the atmosphere can result in elegant clouds. K-H billows are common at the tops of turbidity currents, due to the shear between the static water column above and the moving sediment-laden current below. There is no reason why the instability could not occur at the base of the current as well, if the underlying sediment is still fluid enough, and the current itself is not too erosive.

Here is the classic picture of K-H billows at the top of a density current, from Van Dyke’s Album of Fluid Motion.

Clastic Detritus has more on flame structures.

A day in a delta’s life

I did some hiking recently in the Canadian Rockies. There is some stunning mountain scenery over there, with glaciers, lakes of out-of-this-world colors, icecap-covered humongous peaks, abundant wildlife, and so on. But some of the most exciting finds for a sedimentologist/geologist like myself must be the beautifully developed deltas that enter the glacial lakes. ‘Enter’ is actually an euphemism here, because the rivers are slowly, but surely filling with sediment these magnificent bodies of water, and it is only a matter of a few hundred or thousand years before most of the average size lakes become relatively uninteresting flatlands.

The delta at the updip end of the well-known (and somewhat overrated) Lake Louise is one of these lacustrine deltas. However, the one that really caught my attention is feeding into Peyto Lake. We got to the Peyto Lake overview area relatively early in the morning, when there was no wind, and the lake’s turquoise surface was perfectly smooth. Stunning view from high above, but most of my excitement evaporated (<– euphemism) when a busload of noisy (<– euphemism) tourists arrived and the viewing area suddenly felt like a Houston shopping mall on a weekend (<– exaggeration). So we started our descent toward the lake, on the trail that ultimately, if you are brave enough and rough enough (we were neither of these, but that is a different story), leads to Caldron Lake, above Peyto Glacier.

After only a couple of hundreds of meters, the population density dropped to zero, and my excitement not only went back to its previous levels, but exponentially grew as the lakehead delta started to take shape beyond the trees below us. You could see very well the active distributary channels sending slightly muddy or silty plumes into the lake. Because it was relatively cold, the glacier up in the valley was not melting too fast, and the discharge was small, so the plumes themselves seemed nice, but were barely noticeable.

This has changed during the day: as temperatures rose, the river that enters the lake became larger and larger, and by the time we got back to the lakehead delta in the afternoon, the plumes became much larger and much more evident.

The discharge of the river coming from the Peyto Glacier increases during the day and sends larger plumes into the lake in the afternoon

What is even more interesting is the fact that these plumes terminate relatively abruptly and it is very likely that they form density underflows in the lake. In other words, the sediment-rich water descends toward the lake bottom and flows down the slope as an underwater extension of the river, until it reaches the deepest parts of the lake. That is where it slows down and lets all of the sediment settle out, probably forming a graded layer, similar to the graded turbidites well known from marine sediments and rocks.

Such underflows often form in lakes when the sediment concentration in the river entering the lake is relatively high. In addition to the sediment concentration, the density excess can be enhanced by lower temperatures of the river. However, if the river is entering a sea or the ocean, it is much more difficult to form such underflows (that are often called hyperpycnal flows — just to make it a bit more confusing ūüôā ), because seawater has a lot of salt in it and therefore is denser than the river’s water. In this case, the sediment concentration of the river must be much higher to overcome the density of the seawater.

River, minibasin, delta, lake

As you walk up from the lakeshore toward the apex of the delta (which, by the way, has a classic triangular textbook delta shape), the size of the clasts on the delta’s surface slowly increases (statistically speaking). Further up, the valley gets narrow and then widens up again, giving place to a small minibasin. This minibasin probably was a lake some time ago, a lake that was completely filled.

The river is a Serious River

Where the delta meets the lake, you can easily get close to the distributary channels and their termination points. The coarser sediment tends to be deposited here from the flow, because the flow expands as it enters the lake and its velocity drops. Lower velocity means (1) lower shear stress at the bottom, and therefore fewer grains carried along the bottom, and (2) lower turbulence in the water column, which translates to less sediment carried in suspension. The enhanced deposition right in front of the channel mouth gives rise to a so-called distributary mouth bar, that tends to split the flow into two branches. With time, the mouth bar becomes an island, and the channel splits into two lower-order and simultaneously active distributary channels.

One of the distributary channels, with a nice mouth bar that splits the flow into two

It turns out, of course, that I am not the first to note how superb this little sedimentary system is — there are a number of studies that looked at the density underflows of Peyto Lake. This article tells us that Peyto Lake has a 7 m high sill in the middle, which splits the lake into two subbasins. Underflows (or turbidity currents) fill with sediment-rich water the updip subbasin to the spillpoint, and then the underflow spills over into the other subbasin. As far as I know, this is the only documented example of a truly ponded turbidity current. It has also been calculated that 61% of the sediment deposited in the lake comes from the underflows (most of the rest of the deposition is due to delta progradation).

Detailed view of the sediment-rich distributary mouths and their plumes

The sad news is that, with sedimentation rates similar to those observed today, Peyto Lake will be completely filled within less than 600 years. You should go and witness this jawdropping place before that happens.

* * *

PS: As Brian points out, the Peyto delta is remarkably similar to some of the experimental deltas generated at St. Anthony Falls Laboratory. See for example the image above — it is *not* a lake in the Canadian Rockies!

A TarkŇĎi HomokkŇĎ a Sedimentology bor√≠t√≥j√°n

Az agusztusi Sedimentology bor√≠t√≥j√°n l√°that√≥ fot√≥ a Bodza v√∂lgy√©ben k√©sz√ľlt, m√©g akkoriban, amikor alul√≠rott arrafele m√©ricsk√©lte a homokk√∂veket. Mint sok z√∂ldf√ľlŇĪ doktorandusz, nem igaz√°n tudtam akkor, hogy mire is lesz majd j√≥ a sok r√©tegtani szelv√©ny, de ut√≥lag tal√°ltam a v√°laszra k√©rd√©st, √©s most ford√≠tott sorrendben a k√©rd√©s √©s a v√°lasz is benne vannak ugyanabban a Sedimentology sz√°mban.

Ha valakit esetleg √©rdekel — a cikk l√©nyege az, hogy a bodza-v√∂lgyi r√©tegvastags√°gokat legjobban a lognorm√°lis eloszl√°ssal lehet jellemezni, annak ellen√©re, hogy egyesek szerint a hatv√°nyf√ľggv√©ny-eloszl√°s (vagy frakt√°leloszl√°s) a domin√°ns a turbiditekn√©l. A frakt√°leloszl√°s val√≥ban izgalmas, de csak akkor, ha van r√° j√≥ bizony√≠t√©k — de sok esetben a bizony√≠t√©k hi√°nyzik, √©s egy egyszerŇĪ log-log grafikon alapj√°n egyesek hajlamosak frakt√°lnak ny√≠lv√°n√≠tani mindent.

A TarkŇĎi HomokkŇĎ – √©s az olaszorsz√°gi Marnoso-Arenacea Form√°ci√≥ – eset√©n vil√°gosan kimutathat√≥, hogy a lognorm√°lis eloszl√°s jellemzi a vastagon √©s a v√©konyan r√©tegzett turbiditeket egyar√°nt. √Čs nem csak a statisztikai elemz√©s mutatja ezt, hanem valahogy filozof√°lgat√≥ szinten is szimpatikusabb nekem ez a “megold√°s”, mint ak√°r a frakt√°leloszl√°s, ak√°r az exponenci√°lis eloszl√°s, m√©g akkor is, ha ez ut√≥bbiak izgalmas spekul√°lgat√°sokra adnak okot, sk√°la-f√ľggetlen fizik√°r√≥l, Poisson folyamatokr√≥l, meg √∂nszervezŇĎdŇĎ kritikalit√°sr√≥l (angol “self-organized criticality”).

Na, ez kezd nagyon posztmodern√ľl hangzani, √ļgyhogy jobb, ha abbahagyom.

If you talk about power laws, read this paper:

A. Clauset, C. R. Shalizi and M. E. J. Newman, “Power-law distributions in empirical data”, arxiv:0706.1062. Let me just repeat three key points that Shalizi summarizes on his blog:

Lots of distributions give you straight-ish lines on a log-log plot. True, a Gaussian or a Poisson won’t, but lots of other things will. Don’t even begin to talk to me about log-log plots which you claim are “piecewise linear”.


Abusing linear regression makes the baby Gauss cry. Fitting a line to your log-log plot by least squares is a bad idea. It generally doesn’t even give you a probability distribution, and even if your data do follow a power-law distribution, it gives you a bad estimate of the parameters. You cannot use the error estimates your regression software gives you, because those formulas incorporate assumptions which directly contradict the idea that you are seeing samples from a power law. And no, you cannot claim that because the line “explains” a lot of the variance that you must have a power law, because you can get a very high R^2 from other distributions (that test has no “power”). And this is without getting into the errors caused by trying to fit a line to binned histograms.

It’s true that fitting lines on log-log graphs is what Pareto did back in the day when he started this whole power-law business, but “the day” was the 1890s. There’s a time and a place for being old school; this isn’t it.

In addition,

Use a goodness-of-fit test to check goodness of fit. In particular, if you’re looking at the goodness of fit of a distribution, use a statistic meant for distributions, not one for regression curves. This means forgetting about R^2, the fraction of variance accounted for by the curve, and using the Kolmogorov-Smirnov statistic, the maximum discrepancy between the empirical distribution and the theoretical one. If you’ve got the right theoretical distribution, KS statistic will converge to zero as you get more data (that’s the Glivenko-Cantelli theorem). The one hitch in this case is that you can’t use the usual tables/formulas for significance levels, because you’re estimating the parameters of the power law from the data. This is why God, in Her wisdom and mercy, gave us the bootstrap.

If the chance of getting data which fits the estimated distribution as badly as your data fits your power law is, oh, one in a thousand or less, you had better have some other, very compelling reason to think that you’re looking at a power law.

The good news is that, despite having been submitted for publication too soon to cite Clauset et al., this paper is largely following the advice above and is trying to convey the message to sedimentary geologists (hopefully others will look at it as well) that straightish-looking lines on log-log plots with a large R squared are not enough evidence for power-law behavior.

Related previous posts:
The fractal nature of Einstein’s and Darwin’s letter writing
My talk on bed thicknesses and power laws
On cumulative probability curves
Power laws and log-log plots II.
Power laws and log-log plots I.

No vestige of a beginning, no prospect of an end

When James Hutton saw the unconformity at Siccar Point, where only slightly tilted 345 million years old Old Red Sandstone layers are sitting on top of near-vertical beds of ~425 million years old Silurian greywackes, he realized that such structures could not have formed in only a few thousand years. First, the sediment in the older formation was deposited in horizontal layers; it got buried, compacted and became hard rock; it was tilted to an almost vertical position and lifted above sea level; was eroded by subaerial erosion; and was buried again by much younger sediment that was itself later cemented and tilted by tectonic forces. Most of these processes can be relatively well observed and tracked, especially today, and they are extremely slow compared to most of the things we are dealing with in a human lifetime: both erosion and sedimentation happens at the rate of a few millimeters to centimeters a year, that is, slower than the nail grows. Tectonic movements are not much faster either. Hutton of course had no idea of the absolute age of the rocks, and had no precise measurements of erosion, sedimentation and uplift rates available, but he clearly came to the realization that geology is happening on a timescale a few orders of magnitude larger than that of the Bible and of known human history:

“Here are three distinct successive periods of existence, and each of these is, in our measurement of time, a thing of infinite duration. …The result, therefore, of this physical inquiry is, that we find no vestige of a beginning, no prospect of an end.”

Siccar Point is impressive and one of the most important sites in the history of geology, but the unconformity of all unconformities must be the one in Grand Canyon, appropriately called the Great Unconformity. This is how it looks like from Lipan Point, on the southern rim of the canyon:

And here is another shot with a broader perspective:

The tilted reddish strata in the lower part of the first photo are the Dox Formation; the darker rocks above this belong to the Cardenas Basalt. Both of these formations are of Mesoproterozoic age; the overlying horizontal ledge of rock is the Cambrian Tapeats Sandstone. The time gap between the Cambrian and the Proterozoic is 200 million years, about three times longer than the missing time at Siccar Point. Although the unconformity lower in the stratigraphy exposed at Grand Canyon, between the crystalline basement rocks and Mesoproterozoic sediments represents an even larger gap of 475 million years, the ‘great unconformity’ is visually much more impressive.

It is ridiculous that more than two hundred years after Hutton saw no ‘vestige of a beginning’, and initiated modern geology, there are people who seriously think that the Grand Canyon was carved by the biblical flood, or that sedimentation and erosion can take place at extremely high rates so that all geologic history would fit into six thousand years.

Such idiocies keep showing up over and over again, and I start to think with Hutton one more time that, unfortunately, there is no prospect of an end.

ps. Suggested readings:
Annals of the Former World by John McPhee; there is a highly readable account of Hutton’s discovery of unconformities in the first part of the book, “Basin and Range”.
Vestiges of James Hutton – a nice article about Hutton in American Scientist.

Sedimentology on Mars: wet or dry gravity flows?

Once again, the ‘water on Mars’ subject made it to the headlines: researchers claim that recent gully activity that took place in the last few years (as documented by photographs taken in 1999 and 2005) suggests that watery sediment flows (debris flows) are shaping the planet’s surface as we speak.

The problem is, of course, that it is difficult to keep water liquid in an environment where the temperature is usually way below 0 degrees Celsius and the atmospheric water vapor pressure is also very low. And, as far as I am concerned, the morphology of the gullies and of the associated deposits does not rule out deposition from dry granular flows at all. Of course, several papers have been written on the subject; here is, for example, an opinion from Allan Treiman (2003):

The salient features of the Martian gullies [Malin and Edgett, 2000, 2001] are consistent with their origin as dry flows of eolian sediment: gully deposits are fine granular material (erodable by wind); eolian sediment are available where gullies form; the distribution of gullies are consistent with deposition of sediment from wind; and the orientations of gullies are similarly consistent with wind patterns. Further, it is clear that granular materials can flow as if they were Bingham liquids, and granular flows can produce landforms with all of the geomorphic features of Martian gullies. No known data concerning the gullies (chronological, geomorphic, or geologic) falsify this hypothesis, so it is worth further investigation.

I just find it interesting that, by the time the story reaches the media, all the uncertainties disappear, and the story is unequivocal: watery flows must occur on Mars today, period.

Bedforms in Matlab – everything you wanted to know about ripple marks and cross beds

David Rubin’s bedform-generating code has been implemented in Matlab (in fact, it has been out there for a while). It is a great learning, teaching, and research tool that can be downloaded as part of an USGS open file report. Strongly recommended to anyone having some interest in sedimentary structures, bedforms, and cool Matlab graphics.

That reminds me of something else: it would be nice to have a Matlab version running on Intel Macs. I hope Mathworks will keep its promises and have something ready by early 2007. Having to reboot the iMac in Windows XP is an acceptable solution, but I could live without it [although even Windows XP looks OK on this kind of hardware ūüôā ].

On cumulative probability curves

Let’s go back to some good old science subjects and take some notes about sediments, something I am supposed to be an expert in.

One of my favorite pastimes lately is collecting examples from the geological literature in which the statistical analysis went incredibly wrong. Take for example the papers dealing with grain-size distributions that advertise cumulative probability plots as the best technique to identify subpopulations in a mixed distribution. Here is what G.S. Visher says in his 1969 paper on “Grain size distributions and depositional processes” (Journal of Sedimentary Petrology, v. 39, p. 1074-1106):

“The most important aspect in analysis of textural patterns is the recognition of straight line curve segments. In figure 3 four such segments occur on the log-probability curve, each defined by at least four control points. The interpretation of this distribution is that it represents four separate log-normal populations. Each population is truncated and joined with the next population to form a single distribution. This means that grain size distributions do not follow a single log-normal law, but are composed of several log-normal populations each with a different mean and a standard deviation. These separate populations are readily identifiable on the log-probability plot, but they are difficult to precisely define on the other two curves.” (p. 1079)

I am wondering if this tendency to see straight line segments in cumulative probability plots and to give them some special significance is a syndrome restricted only to geologists – whose abilities for pattern recognition are excellent in general – or one could find such examples from other fields as well. The fact that a certain distribution looks like a straight line on a cumulative plot does not mean that mixtures of the same type of distribution will plot as straight line segments. The excellent sedimentologist Robert Folk has pointed this out in a 1977 discussion of a paper coauthored by Visher (in which they try to prove that the Navajo Sandstone is not an eolian deposit – yeah, right):

“A general defect of the Visher method is exemplified by Kane Creek #2, which is shown as consisting of four straight line segments, implying that it is a mixture of four populations. It can be proved by anyone using probability paper and ordinary arithmetic that such kinky curves can be made by a simple mixing of two (not four) populations that are widely separated; the ‘flat’ portions represent the gaps in the distribution. Furthermore, mixing of populations on probability paper results in smoothly curving inflexions, not angularly joined straight-line segments.”

Despite this, multiple straight-line-fitting to cumulative probability plots is fashionable again, although this time it is done on log-log plots of exceedence probability of either bed thickness or fault size data. But this is going to be part of a paper that I am working on right now (in the evenings and weekends…) — so more about this later.