Lunar Crater volcanic field, Nevada


I was on my way to San Francisco / AGU last week when I saw these volcanoes and shot these pictures through the airplane window. It turns out that this is the Lunar Crater volcanic field in Nevada, named after the largest crater that is more than 1000 meters across and about 130 m deep. There are 95 vents that are 4.2 million to 15,000 years old. Lunar Crater is the largest feature in the image below; it is a maar; most of the other vents formed cinder cones.


Here is a map showing the Houston – San Francisco flight track and the location of the volcanic field:

Hillslope diffusion

Modeling erosion and deposition of sediment using the diffusion equation is among the important subjects that are usually omitted from sedimentary geology textbooks. Part of the reason for this is that ‘conventional’ sedimentary geology tended to only pay lip service to earth surface processes and was more interested in describing the stratigraphic record than figuring how it relates to geomorphology. Nowadays, a good discussion of stratigraphy and sedimentology cannot ignore anymore what geomorphologists have learned about landscape evolution. (One textbook that clearly recognizes this is this one.)

But let’s get back to the subject of this post. Hillslope evolution can be modeled with the diffusion equation, one of the most common differential equations in science, applied for example to describe how differences in temperature are eliminated through heat conduction. In the case of heat, the heat flux is proportional to the rate of spatial temperature change; on hillslopes, the sediment flux is proportional to the spatial rate of change in elevation. This last quantity of course is the slope itself. In other words,

q = -k*dh/dx,

or

q = -k*slope,

where q is the volumetric sediment flux per unit length, k is a constant called diffusivity, h is the elevation, and x is the horizontal coordinate.

We also know that sediment does not disappear into thin air: considering a small area of the hillslope, the amount of sediment entering and leaving this area will determine how large the change in elevation will be:

dh/dt = -dq/dx,

in other words, deposition or erosion at any location is determined by the change in sediment flux.

Combining this equation with the previous one, we arrive to the diffusion equation:

dh/dt = k*d2h/dx2.

Note that the quantity on the right side is the second derivative (or curvature) of the slope profile. Large negative curvatures result in rapid erosion; places with large positive curvature have high rates of deposition. Through time, the bumps and troughs of the hillslope are smoothed out through erosion and deposition.

The simplest possible case is the diffusion of a fault scarp. The animation below illustrates how a 1 m high fault scarp gets smoothed out through time; the evolution of slope and curvature are also shown. The dashed line indicates the original topography, at time 0. [The plots were generated using Ramon Arrowsmith’s Matlab code].

More complicated slope profiles can be modeled as well; here is an example with two fault scarps:

Note how both erosion and deposition get much slower as the gradients become more uniform.

The simplicity of the diffusion equation makes it an attractive tool in modeling landscape evolution. In addition to hillslopes and fault scarps, it has been successfully applied in modeling – for example – river terraces, deltaic clinoforms, cinder cones, fluvial systems, and foreland basin stratigraphy. However, it is important to know when and where the assumptions behind it become invalid. For example, steep slopes often have a non-linear relationship between sediment flux and slope as mass movements dramatically increase sediment flux above a critical slope value. Also, the models shown here would fail to reproduce the topography of a system where not all sediment is deposited at the toe of the steeper slope, but a significant part is carried away by a river. And that brings us closer to advection; a subject that I might take notes about at another time.

Further reading: 1) The book “Quantitative Modeling of Earth Surface Processes” by Jon Pelletier has a chapter with lots of details about the diffusion equation. 2) Analog and numerical modeling of hillslope diffusion– a nice lab exercise.

Upcoming conference on seismic geomorphology

Ever since geoscientists and engineers started using seismic waves to figure out what lies under our feet, seismic reflection technology kept improving and today most oil-rich sedimentary basins have a wide coverage of high-quality three-dimensional datasets. In addition to finding structures and locations in the subsurface that are likely to be filled with hydrocarbons, these huge data volumes can also be used to reconstruct landscapes that are long gone from the Earth’s surface. After all, stratigraphy is what is left behind from an ever-changing topography, and it is a mistake to think that stratigraphy can be understood without knowing a few things about geomorphology and landscape evolution.

Seismic data confirms that the past, indeed, is not that different from the present: if you peek (that is, listen) into these volumes of rock, you see ancient meandering rivers and submarine channels, deltas, barrier islands, mouth bars, and estuaries. However, in addition to and beyond the excitement of seeing another beautiful example of a sinuous channel or other depositional and erosional features, a lot remains to be learned from the true and large-scale three-dimensionality of these datasets. For a geologist, there is no other data type that offers such a degree of three-dimensionality. Even the largest outcrops offer only random two-dimensional sections through a system; the temptation is strong to convince ourselves that we can extrapolate to get an idea about the third dimension, but more often than not we are probably wrong, at least in the details of our extrapolation. This is actually worse than the case of “The Blind Men and the Elephant“; it is more like the blind men and a random cut through the elephant (but I will stop this chain of analogies right there).

Long story short, I (re)started to blog about this subject because there is going to be an SEPM research conference in Houston, a conference that focuses on using three-dimensional seismic data to better understand how sediment moves or gets deposited on continental slopes. It should be an interesting collection of talks and papers.

The image above is from the conference website and announcement; it happens to come from a paper that I am going to present, on a shelf-edge delta and its related slope channels in the Gulf of Mexico (the higher-resolution version is coming soon…). Colors represent thickness (red is thick, blue means thin). There are two leveed channels taking sediment from the shelf-edge delta into the deep ocean.

Two gigapans from Cliffs of Moher, Ireland

I shot these gigapans recently, while we were visiting some deep-water rocks in County Clare, Ireland (see more detail on these rocks and a few photos from the trip). One afternoon we took some time off from the turbidites to do a bit of geo-tourism at the Cliffs of Moher, a series of spectacular escarpments along an 8 km long stretch of the western coast of Ireland. They are 702 feet (214 meters) high at the highest point and expose Late Carboniferous (Namurian) sandstones and shales that were mostly deposited as deltaic and fluvial sediments of the Tullig and Kilkee cyclothems.

This place is one of the most visited tourist attractions in Ireland, and for a good reason: the combination of the cliffs, the landscape, and abundant wildlife is, indeed, spectacular.

This is a view to the south (launch full screen viewer):
http://api.gigapan.org/beta/gigapans/27345/snapshots/87490,83479,83403,83402/iframe/flash.html

And this is a view to the north (from O’Brian’s Tower; launch full-screen viewer):
http://api.gigapan.org/beta/gigapans/27340/snapshots/83397,83395,83394,83392,83391/iframe/flash.html

Unfortunately, these stamp-sized windows do not do justice to the panoramas; it is a good idea to click on the “Launch full-screen viewer” links.

More reasons to conclude that coastal ‘chevrons’ are not related to mega-tsunamis

ResearchBlogging.org If there was any doubt left that coastal sand accumulations called ‘chevrons’ are *not* related to gigantic tsunamis (see previous thoughts on the subject here and here; Ole also has a recent blog post, and see a news release here), the May issue of Geology provides additional arguments to show that this is the case. Joanne Bourgeois of University of Washington and Robert Weiss of Texas A&M University, both experts in the sedimentology of tsunami deposits, present two lines of arguments. First they show that the orientation of the Madagascar chevrons is significantly different from what is predicted through modeling the tsunami. While the tsunami wave tends to hit the coast with an overall perpendicular orientation, due to wave refraction, the ‘chevrons’ are oriented at various angles to the coast, angles that are more consistent with predominant wind directions. Second, they look at the sediment transport conditions and suggest that even coarse sand must have been in suspension in flows deep enough to create the chevrons. However, dune-like bedforms cannot develop without sediment being transported as bedload; therefore, the bedforms must have a different origin than mega-tsunamis. The obvious alternative is parabolic dunes; these well-known bedforms show up when vegetation partially covers the dune’s tails and slows down sediment transport. The authors don’t hesitate to draw the conclusion that

The extraordinary claim of “chevron” genesis by mega-tsunamis cannot withstand simple but rigorous testing.

I am far from being a tsunami expert, but I find this subject fascinating. The issue of suspended load vs. bedload and stratified or laminated vs. graded bedding is equally important for deposition from tsunami waves and turbidity currents. It is worth spending a bit of time and blogspace to explore the kind of analysis of sediment transport conditions that this paper presents.

Although I see no reasons to disagree with the paper’s conclusions (as it could be predicted from my previous posts on the subject), at first reading I didn’t fully understand the line of reasoning about suspended load vs. bedload. So here goes my attempt to understand it.

The argument goes as follows. The Rouse number is the ratio between the settling velocity of a certain grain size and the shear velocity of the flow, multiplied by von Karman’s constant (which is ~0.4): Ro = ws/k*u_shear. For a grain of a given size, if the Rouse number is larger than 2.5, the grain’s settling velocity is much larger than the upward-directed component of the turbulence, and the grain tends to stay close to the bottom, in the bedload. [This is equivalent to saying that the settling velocity has to be larger or equal to the shear velocity, a condition also known as the suspension criterion]. If the Rouse number is less than 0.8, the flow is turbulent enough to keep the grain fully suspended. In between these values, there is a zone of transitional behavior. For the flows that might have deposited the chevrons, the Rouse number is always less than 2.5, regardless of how the other parameters like the Froude number, grain diameter, and roughness length are varied. Although the authors state that the flows must have been deeper than 8 m (because most chevrons are higher than 4 m, and the flow must be at least twice as high as the bedform), there seems to be no other constraint on tsunami behavior [note that I did not have access – yet – to the supplementary web material].

So the question is: doesn’t this reasoning apply to other types of flows as well? For example, the Mississippi River is certainly deeper than 8 m in many places — does this mean that it is able to suspend very coarse (2 mm diameter) sand? In other words, what is the difference between flow in a tsunami run-up and the Mississippi River? The answers might be obvious to many, but they are certainly not obvious to me.

One thing we can do is to create a different kind of plot: instead of plotting the Rouse number against flow depth, let’s plot velocity vs. depth. I have a better feeling for what are reasonable velocities for different kind of flows than I do for Rouse numbers. The Rouse number would form the third dimension of the plot; one can visualize that as a contour map of Rouse numbers as a function of flow depth and velocity:


The Rouse numbers shown in this plot are valid for a grain diameter of 2 mm and roughness length of 1 m (using the same equations for settling velocity and shear velocity as in Bourgeois & Weiss 2009). Anything coarser than this cannot be called sand any more. So if this grain size doesn’t stay in the bedload, there is no chance for finer sediment either. It is obvious from the plot that, for flows deeper than 8-10 m, very coarse sand will be part of the bedload unless flow velocity is larger than ~5 m/s. The Mississippi River at New Orleans has velocities on the scale 1.5 m/s, so 1-2 mm sand should definitely stay close to the bottom, and in fact it does.

We know however that tsunamis are not exactly tranquil flows like the big old Mississippi at New Orleans. The larger ones are fast and furious and Google Earth might need massive updates after they rearrange entire coastal landscapes. [Don’t get me wrong, I am not trying to diminish the power and destructive force of the Mississippi.] In other words, the Froude number of a tsunami run-up is larger than the Froude number of the Mississippi River. The Mississippi is relatively slow and deep; the tsunami is fast and relatively shallow. The Froude number is the ratio between velocity and the square root of gravity multiplied by flow depth:

Fr = u/√(g*d)

This number for the Mississippi is much less than one (these flows are called subcritical flows). On the other hand, tsunamis are waves of very large wavelengths, and they behave even in the open ocean as shallow water waves (wavelength 20 times larger than water depth). For these kinds of waves, the velocity is solely a function of water depth:

u = √(g*d)

If we assume that the tsunami run-up has a comparable velocity to that of the tsunami wave in the nearshore zone, we find that the Froude number of the run-up must be around 1. This is obviously a very back-of-the-envelope argument, but the point is that these flows must have in general relatively large Froude numbers. If we plot the lines for Fr = 1 and Fr =1.5 on the depth-velocity diagram (see above), we can see how different likely tsunami behavior is from that of large rivers. It also becomes evident that even coarse sand would not be part of the bedload in these flows, especially not in flows deep enough to build the ‘chevrons’. Which means that sandy tsunami deposits are likely to be largely unstructured or poorly structured sand sheets rather than several m thick accumulations of cross-bedded sand.

And that ends my Saturday exercise in Fluid Mechanics 101.

Reference
Bourgeois, J., & Weiss, R. (2009). “Chevrons” are not mega-tsunami deposits–A sedimentologic assessment Geology, 37 (5), 403-406 DOI: 10.1130/G25246A.1

Links to this post:
Scientia Pro Publica #4

Normal grading

In sedimentology, the word ‘grading’ has nothing to do with exams and assignments. Instead, it refers to a regularly decreasing or increasing grain size within one sedimentary layer. Because it is much more common than the other alternative, upward decreasing grain size is called ‘normal grading’. Grains that consistently increase in size toward the top of the bed are responsible for ‘inverse grading’. Upward fining and coarsening are related terms that are often used to describe grain-size trends in not one, but multiple beds.

Normal grading in a turbidite from the Talara Basin, Peru

The simplest way to generate normal grading is to put some poorly sorted sand and water in a container, shake it up, and then let it settle. The larger grains will settle faster than the smaller ones (as Stokes’ law tells us) and most of the large grains will end up at the bottom of the deposit. [Note that some fine grains will be at the bottom as well – the ones that were already close to the bottom at the beginning of sedimentation.] This kind of static suspension settling is not how most sediment is deposited on a river bed or a beach; even if a grain is part of the suspended load, it usually goes through a phase of bedload transport, that is, a phase of jumping and rolling and bouncing on the bed, before it comes to rest. The resulting deposit usually has lots of thin layers, laminations, and there are no obvious and gradual upward changes in grain size.

What is needed is a sediment-rich flow that suddenly slows down or spreads out and looses its power to carry most of its sediment load. Grains are getting to the bottom so fast that there is not much time for the flow to keep them rolling and bouncing around; instead they quickly get buried by the other grains that are ready to take a geological break. While this is still quite different from static suspension settling (because the flow did not come to a full stop), it can be thought of as a modified version of static settling: all is needed is a horizontal velocity component, in addition to the vertical one. Of course, the segregation of the coarser grains to the bottom of the flow may have started much earlier. Typically, they never made it to the top in the first place.

Conglomerate bed in the Cretaceous Cerro Toro Formation, Torres del Paine National Park, Southern Chile. There is some inverse grading at the base of this bed, before the size of the clasts starts decreasing

Such large, sediment-laden flows are not very common, certainly not on a human timescale. When they do occur, they tend to show up in the news, especially if human artifacts, or humans themselves, become part of the normally graded deposits. Deposits of snow avalanches, volcanic ash-laden pyroclastic flows, subaerial debris flows, tsunamis, submarine turbidity currents can all show normal grading. The images shown here all come from deposits of large submarine gravity flows. Some of them (like the one below) have a muddy matrix, but the grading is still obvious (the two large clasts at the top of the bed have lower densities).

Normally graded conglomerate layer with a muddy matrix, Cerro Toro Formation, Chile

In recent years, some questions have been raised about the common presence of normal grading, especially in turbidites. The fact is that normal grading is often seen in rocks of all ages, and, in a simple view, it is a reflection of larger grains getting quickly to the bottom.

Normal grading is normal, after all.

Description does not suffice for an explanation

On February 3, 1967, J. R. L. Allen gave the fifth “Geologists’ Association Special Lecture”, entitled “Some Recent Advances in the Physics of Sedimentation”. This is from the introduction:

“Two stages can generally be recognised in the historical growth of a reasonably advanced scientific discipline. There is an early, descriptive stage in which with little guide from theory, an attempt is made to collect, define and analyse phenomena. In the later, explanatory stage we see that efforts are concentrated on the production of generalisations and on the explanation of the reduced phenomena in terms of general laws. Of course, there is never a single point in time at which there is change over the entire scope of a discipline from the descriptive to the explanatory stage. The change is, rather, uneven, taking place earlier in some branches than in others, and more gradually in one branch than in another.

Sedimentology stands today in a period of transition. Its subject matter is sedimentary deposits, and its goal the origin and meaning of these in the context of planetary studies in general. But it is apparent, except to adherents of geological phenomenalism, that sedimentary deposits cannot be explained in terms of themselves. Already we are in possession of major generalisations about these deposits, and our chief task for some years should be to explore and ratify them in terms of general laws in order that our understanding of the sedimentary record can be made sharper. In those parts of the field where major generalisations have already been established, the provision of further descriptive data is of little value, except in so far as light is shed on the problems of particular deposits. These are validly a part of the subject, leading to a refinement of certain planetary laws. But the other and no less important laws in terms of which we should seek to frame our understanding are those of general chemistry, physics and biology. In order to achieve this framework in the case of detrital sediments, it will be necessary to set aside for a while the problems of particular deposits. This will, of course, be unacceptable to those who claim that geology, or sedimentology, is only to do with rocks as conceived in a historico-geographical manner. But they will be proved wrong, provided we keep our major goals in mind, for it is a mistake to suppose that a description will suffice for an explanation. Most of our explanations will probably turn out to be no better than qualitative, so complex are most sedimentary systems, but we should nevertheless attempt them and try to frame them as exactly as possible.”

Forty years after publication of the paper, this seems as timely as ever.

Reference:
Allen, J. R. L., 1969. Some Recent Advances in the Physics of Sedimentation. Proceedings of the Geologists’ Association 80:1-42.

Three photos from Chilean Patagonia

I was lucky to attend a few days ago a field conference in southern Chile, looking at deep-water rocks in an area that includes Torres del Paine National Park. It was good to be back in this place of unbloggable beauty. The conference was well organized (of course! – Brian was one of the conveners) and we were extremely lucky with the weather: no rain at all on the outcrops, beautiful sunshine most of the time. Although I have been to Chilean Patagonia three times before on various geological field trips and even did some field work there, I realized during this conference that it doesn’t matter how many times you have seen some rocks, there is always a chance to rethink what you thought you have already settled in your mind (see blog title). It was also good to see that these field conferences are increasingly not just about the local geology: many if not most presentations and spontaneous discussions compare the local outcrop data with sedimentary systems from other basins, and try to think about how the always-too-small outcrops would look like in seismic sections and volumes.

Brian did not have time to take a lot of photos, so here are three shots (more here). As if anybody needed more shots of the Paine Grande and the Cuernos.

Conference participants examine the turbidites of the Punta Barrosa Formation

The Paine massif (Paine Grande and Cuernos), with Rio Serrano in the foreground

Strong winds on Paine Grande

Update – here is a Gigapan:

function FlashProxy() {}
FlashProxy.callJS = function() {}

http://gigapan.org/viewer/PanoramaViewer.swf?url=http://share.gigapan.org/gigapans0/18452/tiles/&suffix=.jpg&startHideControls=0&width=42349&height=11090&nlevels=9&cleft=0&ctop=0&cright=42349.0&cbottom=11090.0Launch full screen viewer

[it is strongly recommended that you do launch the full screen viewer if you want to do justice to the Gigapan]

The science of espresso, with a dash of geology

Almost every morning, I start the day with an experiment on flow in porous media. First, I generate some fine-grained sediment with a well-defined average grain size and proper sorting; then I use that sediment to fill a little basin of sort and try to mimic compaction. Finally, I use a machine to put water under pressure and force it to flow through this miniature sedimentary basin. Then I sit down to drink the fluid which is not simple water anymore, due to its interaction with the grains; and its taste and consistency tell me whether I got the grain size and the porosity right.

That’s a geologist’s view of making espresso. Unless you have a fully automated and ultra-expensive espresso machine, creating a high-quality caffeine concoction is not trivial, because the water must have the right temperature and has to spend the right amount of time in contact with the coffee grains that have the right size. The right temperature is 85–95 °C (185–203 °F), and, at least with our simple machine, the trick is to start the brewing at the right time. Better espresso machines do not use steam to generate pressure because that makes the water too hot; instead, they have a motor-driven pump that generates the ~9 bars of pressure. The correct grain size is easily achieved with a burr grinder (as opposed to a simple blender); a good espresso grind is a fine grind, because the water spends relatively little time in contact with the grains.

The duration of this contact is the most difficult bit to get right. To get a good shot with lots of crema, it cannot be less or more than 20 to 30 seconds. Not just grain size, but grain sorting as well play a role. If the coffee grinder produces a poorly sorted ‘sediment’ (and that’s what a blender does), the coffee will not be porous and permeable enough. Another factor is how well the sediment is compacted; that is, how much pressure do you apply to the coffee during tamping. This affects permeability again. Finally, it matters how much coffee you put in the coffee holder; the thicker the layer that the water has to go through, the longer the trip becomes for the same amount of water.

After using the machine hundreds of times, I still manage from time to time to produce something undrinkable. The art and science of espresso making started to make more sense once I started to think of it in terms of Darcy’s Law.

Henry Darcy was a French engineer who initially had made a name for himself by designing an enclosed and gravity-driven water-supply system for the town of Dijon. Later he had time and opportunity to do experiments of his own interest. In 1855 he measured the discharge of water under variable hydraulic heads through sand columns of different heights, and found that the discharge was directly proportional with the hydraulic head and inversely related to the height of the sand column:

Q = AK(H1-H2)/L,
where A is the cross sectional area of the sand column, L is the height of the sand column, K is the hydraulic conductivity (which is constant for the same granular material and same fluid), and H1-H2 is the hydraulic head. This is Darcy’s drawing of his experimental setup:

The hydraulic conductivity depends on both the properties of the fluids and of the granular material; these properties are the viscosity and density of the fluid, and the permeability of the sediment:

K = kρg/μ,

where K = hydraulic conductivity, k = permeability, ρ = fluid density, and μ is the dynamic viscosity.

In coffee speak, the hydraulic head is given by the pressure generated by the machine, and is fixed; one cannot change the density and viscosity of water either. The most important variable is coffee permeability, which is influenced by size, sorting, and packing (compaction) of the coffee grains. Also, it helps if you get the value of L right, that is, you shouldn’t try to save coffee.

Darcy’s Law was established with some simple experiments, and it has since then been generalized and derived from the Navier-Stokes equations, but it has a huge range of applicability, from ground-water hydrology to soil physics and petroleum engineering.

Add to that list everyday espresso making.

ps. Fantastic resource on Darcy’s work and his law here.

Earth, water, wind, and fire: ‘Lava viewing’ in Hawaii

Our Christmas gift to ourselves was a little trip to the Big Island of Hawaii, something we were thinking (dreaming) about for a long time. There are many great posts about the Hawaiian volcanoes on the geoblogosphere (see for example the ones here and here); I will try to add a few notes and pictures without being too repetitive (and will try to seem less ignorant in volcanic and hard-rock matters than I actually am).

Probably the most memorable experience we had was the lava viewing at Kalapana. This is where ‘officially’ you can get relatively close to the place where the lava from Pu`u `Ō`ō enters the ocean. The USGS has a nice website with updates on what’s going on. I was so anxious to see this place that we had to go there on our first day in Hawaii, that is, on December 22. You have to drive all the way to the end of road 130; there are some big ‘No trespassing’ signs at one point, but everybody seems to ignore them, and there is an official parking lot at the end of the road, way beyond the ‘no trespassing’ signs. It is best to get there 30-60 minutes before sunset, and to stay until it’s completely dark, to see the potential show both in daylight and in nighttime darkness. Unfortunately, on December 22 we didn’t see much, apart from a beautiful sunset and a few small puffs of steam:

Sunset at the Kalapana viewing site on December 22, 2008

That was a bit of a disappointment, but I knew I had to give it another try. After talking to a ranger from Volcanoes National Park, we drove back to Kalapana five days later. This time, the show was definitely on. More than that, it was spectacular. A huge column of steam formed where the active lava tube spills the lava into the sea, and repeated explosions painted red the lower part of the column. From time to time, several tornado-like funnels formed and connected the steam cloud to the ocean.

Steam cloud with mini-tornadoes on December 27, 2008; lava-viewing boat on the left for scale

As the sun goes down, the explosions become more colorful and more obvious

S-shaped funnel between the steamy sky and cool hot ocean

This was such a uniquely beautiful scene. I wish we went there more than two times, because the whole spectacle changes as a function of the activity of lava flow, weather conditions, the direction and nature of lighting.

I have also learned that it is not easy to take good photographs of fast-moving and rapidly changing distant things in the dark. Here is the proof: