The case for scales, rates, and numbers in geology

A long time ago I used to study geology in a nice city called Cluj, in the middle of that interesting part of Romania known as Transylvania. This was a place and time where and when I learned about quartz, feldspar, species of coral and foraminifera in great detail, heard about sequence stratigraphy and turbidites for the first time, and went on some great geological field trips. Not to mention the half-liter bottles of beer that would be significant components of any decent geological trip or spontaneous philosophical discussion in the evening. The less pleasant part was that many of the classes I took involved brute-force memorization of fossils, minerals, chronostratigraphic names, and formations. Although the geological vocabulary that I picked up was pretty broad and proved useful as a good set of words, terms, and definitions to play with, I forgot many of the details by now. If you asked me what was the difference between granite and granodiorite, I would have to check. I don't remember at all what fossils are characteristic of the Late Jurassic. And, despite doing some fieldwork myself over there, I cannot remember the stratigraphic nomenclature in Transylvanian Basin; I would have to look it up (probably in this paper).

After college, it took me about one year to realize with convincing clarity that there was a lot left to learn. I went on to grad school on the other side of the planet, at a well-known university. Many of the classes I took over there were - unsurprisingly - quite different; a lot more focus on laws, processes and the connections between geological things than the 'things' themselves. It was also there that I started to see the links between geology and physics and math. I picked up quite a bit of math and physics during high school, but then quickly relegated them to the status of "stuff that is rarely used in geology". At grad school, it dawned on me that numbers and mathematical laws are not only useful in geology, but are in fact necessary for doing good earth science. Maybe I am stating the obvious, but here it goes anyway: geology deals with enormous variations in scale, both in space and time; and it is not enough to say that the river was deep (how deep?), the tectonic deformation was fast (how fast?), the sea-level highstand lasted long (how long?), or the sediment gravity flows were high-energy flows (I am not even sure what that means). One of the most important things I learned was an appreciation for physical and quantitative insight in geology, that is, having at least an idea, a feel for what are the scales and rates involved in the formation of the rocks you are looking at. I cannot say it better than Chris Paola, one of the important and influential advocates of moving sedimentary geology closer to physics and math:

"For the 'modal' sedimentary-geology student, it is not sophisticated computational skills or training in advanced calculus that is lacking, but rather the routine application of basic quantitative reasoning. This means things like estimating scales and rates for key processes, knowing the magnitudes of basic physical properties, and being able to estimate the relative importance of various processes in a particular setting. Understanding scales, rates and relative magnitudes is to quantitative science what recognizing quartz and feldspar is to field geology. Neither requires years of sophisticated training, but both require repetition until they become habitual."

Developing these skills is a lot easier if one is not afraid of tinkering with simple computer programs. Want to really understand what Stokes' law is about? There is no better way than typing the equation into an Excel spreadsheet or a Matlab m-file and see how the plot of settling velocity against grain size looks like. What about settling in a fluid with different viscosity? Change the variable, and compare the result with the previous curve. High-level programming languages like Matlab or Python* are a lot easier to learn than languages closer to 'computerese' and farther from English, and they are great tools for these kinds of exercises and experiments. As somebody interested in stratigraphic architecture, I have become especially fond of creating surfaces that vaguely resemble real-world landscapes and then see how the evolution of these surfaces through time - deposition over here, erosion over there - creates stratigraphy. Complex three dimensional geometry is a lot easier to grasp if you can visualize and dissect it on the computer screen.

Of course, numbers, diagrams and images that come from computer programs are only useful if they demonstrably say something about the real world. Data collection in the field and the laboratory are equally important. But nowadays we often have more data than we wished for, and quantitative skills come handy for visualizing and analyzing large datasets - and comparing them to models.

Not everyone is excited about the growing number of earth scientists who tend to see equations 'in the rocks'. The logo of the Sedimentology Research Group at the University of Minnesota features the Exner equation carved into a pebble, allegedly as a response to the exclamation "I haven't seen yet an equation written on the rocks!" There is some concern that many geology graduates nowadays do not get to see, to map and to sample enough real rocks and sediments in the field. Although I think this unease is not entirely unsubstantiated, I wouldn't want to sound as pessimistic as Emiliano Mutti - one of the founding fathers of deepwater sedimentology - does in the last phrase of a review article:

"This approach raises a problem, and not a small one: in connection with data collection in the field, how many field geologists are being produced in these times of increasingly computerized geology; and how good are they?"

As far as I know, geological field work is still an important part of the curriculum in many departments of geology - as it clearly should be. The number one reason I have become a geologist was that I loved mountains, hiking, and being outdoors in general, way before I started formally studying geology. And I still take every opportunity to go to the field. But I cannot see the growth of "computerized geology" - and of quantitative geology in general - as a bad thing. Does dry quantification take away the beauty and poetry of geology? I don't think so. Unweaving the rainbow, unfolding a mountain, and reconstructing a turbidity current only add to our appreciation of the scale and grandeur of geology.

* I will let you know later whether this is true about Python...

** I have started writing this post for Accretionary Wedge #38, mostly because I found the call for posts quite inspiring, but haven't finished it in time. Read all the good stuff at Highly Allochthonous.

Salt and sediment: A brief history of ideas

Salty weirdness
Salt is a weird kind of rock. At first sight, it behaves like most other rocks: if you pick up a piece, it is hard, it is heavy, and it breaks if hit with a hammer. But put it under stress for thousands of years, and salt will behave like a fluid: relatively small forces can cause it to flow toward less stressful surroundings. This often means it will try to find its way to the surface.

When deposited, sand and mud have lots of pore space filled with water and have relatively low density. However, as they get buried by more sediment, much pore space is lost, both through compaction and cementation. Sediments turn into sedimentary rocks, become harder, and their density increases. In contrast, salt doesn't have much pore space to begin with; its density will stay the same, regardless of depth of burial. As both salt and sediment are buried to greater depths, an unstable condition develops: lighter salt lying under denser material. In addition, the location of the salt layer in the sediment column is not entirely random: it is in the nature of sedimentary basins to initially place salt at the bottom of the sediment pile. Extensive salt layers usually form early in a basin's lifetime, when seawaters invade for the first time shallow depressions on a continent that is about to split into two along a rift zone. The Dead Sea is an obvious example that comes to mind.

Layering salt and sediment in this unstable order is a recipe for a spectacular geological show. As salt is trying to find its way to the surface, it forms drop-shaped blobs called diapirs; but also ridges, walls, and salt sheets. Several sheets can connect laterally into a huge salt canopy, a new salt layer that is entirely out-of-place or allochtonous. Salt can also act as a lubricating layer at the base of a thick sequence of sedimentary rocks. But I am rushing ahead a little bit; salt tectonics is such a new - but rapidly growing - science that salt canopies, despite their widespread presence in the subsurface Gulf of Mexico, were not recognized and described until the 1980s.

Tectonics vs. buoyancy, Europe vs. America
Before the beginning of the twentieth century, even with the role that salt played in human history, little was known about how salt domes formed. This was an age of rampant speculation; surface data was scarce because salt does not last very long after exposed as it quickly gets dissolved and washed away by precipitation. Many geologists thought that formation of salt domes didn't require any significant salt deformation or displacement. But things have changed dramatically in 1901, with the discovery of the Spindletop oil field on top of a salt dome in southeastern Texas. The recognition that oil is often found on top of and around salt domes created a much stronger interest in understanding how exactly salt formations are put in place.

European geologists thought that the main driving force was compression, the force that causes folding and thrusting and builds mountains. In Romania, where the Eastern Carpathians take a sharp turn toward the southwest, salt was found in the cores of oil-bearing anticlines. The contacts with the surrounding rocks were clearly discordant. These are the structures that prompted Ludovic Mrazec, professor of geology at University of Bucharest, to coin the term "diapir" in 1907.

Mrazec's explanation of how salt diapirs form. From Barton (1925).

Salt in Germany and Poland also seemed to occur invariably in a compressional setting, in the cores of folds, next to folds that had no salt associated. It seemed obvious that salt was 'pushed up' by tectonic forces, and it appeared unlikely that the rise of salt itself was causing the folding.

But the discovery of a multitude of salt diapirs in the Gulf of Mexico made it clear that they can occur far away from any mountains and compressive tectonic forces. The much simpler setting and relative lack of deformation in the Gulf proved informative. "The Roumanian salt-dome geologist possibly may have more to learn from the American salt domes than the American salt-dome geologist has to learn from the Roumanian domes. The occurrence of the American domes in a region of tectonic quiescence suggests that tectonic thrust cannot have the importance postulated by Mrazec" - wrote Donald Barton in 1925.

This was also the time when the density difference between salt and sediment came into discussion. Gravity measurements in the Gulf of Mexico showed anomalies above salt domes that were due to the lower density of salt. It was increasingly recognized that density inversion must play an important role in diapirism, especially where compressive tectonic forces were absent. In addition, by the 1930s geologists have reached a consensus that salt diapirs must somehow punch through the overlying sediment. They seemed to ignore the fact that, as Wade (1931) put it, you cannot drive a putty nail through a wooden board. As mentioned before, salt does behave like a fluid over geological time scales. But how can it penetrate thick layers of hardened sedimentary rock?

A brilliant idea: downbuilding
The solution to this problem came in 1933, from the same Donald Barton who was discussing the differences between European and American salt domes in 1925. He suggested that diapirs can form without much piercement of the sediment above. Instead, once a small dome is initiated, it simply can stay in place, always at or close to the surface, while sediment is deposited around it and the source salt layer subsides: "it is the sediments which move, and not the salt core. The energy requirement (...) is very much less than if there were actual upward movement of the salt."

The evolution of salt diapirs through 'downbuilding'. Salt domes are always close to the surface and diapirism goes hand-in-hand with sedimentation. From Barton (1933).

This was a key insight: it got rid of the "room problem", the need for moving huge volumes of hard rock out of the way of the rising salt. It also highlighted that salt movement can happen at the same time with sedimentation, a fact that became abundantly obvious later as high-quality seismic data became available. But the concept of 'downbuilding' was ignored for the next fifty years.

Animation showing how downbuilding works. Blue represents salt, yellow is sediment. To mimic mass balance for salt (-- what is lost from the source layer must go into the salt dome), the blue area is kept constant through the animation. Right-click image for animation controls.

The beauty of instabilities
The main reason for conveniently forgetting Barton's idea was that density inversion between two fluids could be nicely studied in the lab and described with elegant equations. In one of the papers that kicked off this fascination with Rayleigh-Taylor instabilities, Nettleton (1934) used corn syrup and less dense crude oil to visualize diapir-like blobs of fluid in a transparent cylinder and to show that gravity alone, without any help from contractional forces, was enough to generate structures similar to salt domes.

Less dense crude oil (black) forming diapir-like blobs as rising through higher-density corn syrup (yellow). Redrawn from Nettleton (1934).

One problem with this approach was that oil and syrup can be photographed during deformation, but the transient structures could not be carefully dissected and analyzed later. Materials of higher viscosity were needed for that; however, increasing the viscosity resulted in a density difference too small to get the fluids moving in the first place. The trick was to place the whole experiment in a centrifuge and use the centrifugal force to imitate a larger-than-normal gravitational force. This approach formed the basis of a productive line of research on gravity tectonics in the laboratory of the Norwegian-Swedish geologist Hans Ramberg. The results are probably more relevant to what is happening deeper in the Earth, at higher temperatures and pressures, where most rocks become more similar in behavior to salt.

Modern salt tectonics
By the late 1980s it has become quite obvious that kilometer-thick piles of sedimentary rock cannot be treated as fluids and salt-sediment interaction is more similar to placing and deforming slabs of brittle material on top of a viscous fluid. Seismic from salt-bearing sedimentary basins suggested that the history of salt movement and sedimentation were highly interconnected and Barton's downbuilding concept was strongly relevant.

Three-dimensional seismic data also showed the variety and complexity of allochtonous salt bodies in salt-rich sedimentary basins. Sandbox experiments with more realistic material properties and ongoing sedimentation during deformation were performed and the results beautifully visualized. The behavior of turbidity currents flowing over complex salt-related submarine topography was investigated. Hundreds of scientific papers were written on salt tectonics, both by industry geoscientists and researchers in the academia.

N-S cross section in the Gulf of Mexico. Large volumes of the Jurassic Louann salt have been displaced and squeezed into a salt canopy surrounded by much younger sediments. From Pilcher et al., 2011

And there is quite a bit left to explore and understand.

References and further reading
Barton, D. C. (1926) The American Salt-Dome Problems in the Light of the Roumanian and German Salt Domes, AAPG Bulletin, v. 9, p. 1227–1268.

Barton, D. C. (1933) Mechanics of Formation of Salt Domes with Special Reference to Gulf Coast Salt Domes of Texas and Louisiana, AAPG Bulletin, v. 17, 1025–1083.

Hudec, M., & Jackson, M. (2007) Terra infirma: Understanding salt tectonics. Earth Science Reviews, 82(1-2), 1–28.

Jackson, M. (1996) Retrospective salt tectonics, in M.P.A. Jackson, D.G. Roberts, and S. Snelson, eds., Salt tectonics: a global perspective: AAPG Memoir 65, p. 1–28. [great summary of the history of salt tectonics]

Mrazec, L. (1907) Despre cute cu sȋmbure de străpungere [On folds with piercing cores]: Bul. Soc. Stiint., Romania, v. 16, p. 6–8.

Nettleton, L. L. (1934) Fluid Mechanics of Salt Domes, AAPG Bulletin, v. 18, p. 1–30.

Pilcher, R. S., Kilsdonk, B., & Trude, J. (2011) Primary basins and their boundaries in the deep-water northern Gulf of Mexico: Origin, trap types, and petroleum system implications. AAPG Bulletin, v. 95(2), p. 219–240.

Wade, A. (1931) Intrusive salt bodies in coastal Asir, south western Arabia: Institute of Petroleum Technologists Journal, v. 17, p. 321–330, 357–361.

Where on Google Earth? WoGE #296

Hindered Settling hasn't hosted a Where-on-Google-Earth in a long time, but WoGE #295 (hosted at Andiwhere's) had such a range of colors and geological features that I couldn't refrain from looking for it and, once found it, had to post the solution. So, after a short break in the game (busy week!) here is WoGE #296 -- the rules of the game are nicely described over here. I invoke the Schott rule. Posting time is July 8, 2011, 14:00 UTC.

click on image for larger view

Stretching the truth: vertical exaggeration of seismic data

If someone showed a photograph of the famous Cuernos massif (Torres del Paine National Park, Chile) like the one below, it would be - probably, hopefully - obvious to everybody that something is wrong with the picture. Our eyes and brains have seen enough mountain scenery that we intuitively know how steep is 'steep' in alpine landscapes. The peaks in this photograph just look too extreme, too high if one takes into account their lateral extent.

The Cuernos in Torres del Paine National Park, Chile, vertically exaggerated by a factor of two.

For comparison, here is the original shot:

The Cuernos, beautiful, without exaggeration.

Yet this kind of vertical stretching of images is the rule rather than the exception when displaying seismic sections, both on computer screens and in scientific papers. There are two main reasons for this: first, subsurface geometries are often more obvious when vertically stretched and slopes are larger than in real life. Second, more often than not, we have no precise knowledge of the actual vertical scale. Raw seismic reflection data is recorded in time: we are measuring how long it takes before a seismic wave propagates down to a discontinuity and comes back to the surface. This time measure is called 'two-way traveltime'; in order to convert it to depth, knowledge of the velocity of sound through the rocks is needed:

depth = seismic_velocity * two-way_traveltime / 2

The problem is that the velocity of the wave varies as it goes deeper (usually increases with depth as rocks become 'harder'); and, unless we are looking at perfect layercake stratigraphy (not that common!), it also changes laterally. So, if we want to look at the actual geological structures, without distortions due to varying velocities, we need to do a depth conversion and we need a 'velocity model' that roughly describes the spatial distribution of velocities. Precise velocity measurements often come from wells where depth is well known; less precise estimates can be backed out from the seismic recordings themselves, but the solution is often non-unique and multiple iterations are necessary to build a good velocity- and depth model. As a result, seismic reflection data is often interpreted with two-way traveltime on the vertical axis, without depth conversion; and not knowing the true vertical scale makes it easier to use vertical exaggeration with vengeance. 

A recent paper, published in Marine and Petroleum Geology, shows that vertical exaggeration of seismic data is indeed very common. Simon Stewart of Heriot-Watt University has looked through 1437 papers published between 2006-2010 and found that 75% of the papers show seismic displays with vertical exaggeration of a factor larger than 2. Only 12% are shown with roughly equal horizontal and vertical scales.

Histogram of vertical exaggerations in 1437 papers. From Stewart (2011).

One of the effects of vertical exaggeration is the strong steepening of dips. A 10 degree slope at a vertical exaggeration of 10 becomes an almost vertical drop of 60 degrees; it is hard not to think of these exaggerated slopes as steep slopes, even though they are not that abrupt in reality. Depositional geometries often have very small dips and significant vertical exaggeration is needed to illustrate the overall shapes.

The paper suggests that published seismic sections should be labeled with an estimate of the vertical exaggeration, in addition to the usual horizontal and vertical scales [I am guilty myself of not doing this as it should be done]. Even better, one can go further and create several versions of the figure with different vertical exaggerations. The cross section of a submarine lobe deposit below is a fine example of such a display. Showing only the version that was exaggerated vertically 25 times would suggest that this is a deposit at the base of a steep slope; the 1:1 figure at the top brings us back to reality and clearly shows that this morphology and stratigraphy are both extremely flat.

Dip section of a submarine lobe deposit, offshore Corsica. From Deptuck et al. (2008).

To see more about scales and vertical exaggeration in geology, check out this recent post at Highly Allochthonous; and the nice illustrations that Matt has put together over at Agile*.

References

Deptuck, M., Piper, D., Savoye, B., & Gervais, A. (2008). Dimensions and architecture of late Pleistocene submarine lobes off the northern margin of East Corsica Sedimentology, 55 (4), 869-898 DOI: 10.1111/j.1365-3091.2007.00926.x

Stewart, S. (2011). Vertical exaggeration of reflection seismic data in geoscience publications 2006–2010 Marine and Petroleum Geology, 28 (5), 959-965 DOI: 10.1016/j.marpetgeo.2010.10.003

Snorkeling and geology in Kealakekua Bay, Big Island, Hawaii

For a long time, I didn't think it was worth spending more than an hour on a beach, even the most beautiful ones, unless there were some nice cliffs nearby showing some interesting geology. My views in this regard have changed dramatically about three years ago, when I spent a week on The Big Island of Hawaii, and the hotel where we were staying offered free rental of snorkeling gear. I put on the mask and the fins, trying to remember how this was supposed to work (I did a bit of snorkeling in Baja California many years before that), and put my face into the not-too-interesting-looking waters in the front of the hotel.

Kealakekua Bay in Google Earth, with some explanations added

I was in for a surprise. The water was far from crystal clear, but I could still see fantastic coral creations lined up along the bay and lots of fish of so many colors and patterns that it felt unreal. Until then I thought that this kind of scenery was hard to see unless you were a filmmaker working for Discovery Channel or a marine biologist specializing in tropical biodiversity. The next day I spotted a couple of green turtles frolicking in the water, clearly not bothered by the nearby snorkelers, and I already knew that I needed to look into the possibility of buying a simple underwater camera.

Lots of coral, mostly belonging to the genera Lobites (lobe coral) and Pocillopora (cauliflower coral)

Three years later I went back to the Big Island with more excitement about tropical beaches, plus bigger plans and a bit more knowledge about snorkeling. After going through a few well-known snorkeling sites on the west coast, like Kahalu'u Beach in Kona and Two Step near Pu'uhonua o Honaunau park, we got on a nice boat (run by a company called Fair Wind - strongly recommended!) and did some snorkeling in Kealakekua Bay.

Visibility in Kealakekua Bay is usually very good

Old wrinkles of pahoehoe lava getting encrusted by algae and corals and chewed up by sea urchins

Kealakekua Bay is difficult to reach; there is no road and no parking lot nearby. You either have to hike in, paddle through the bay in a kayak, or take a boat. I have heard before that this was the best snorkeling spot in Hawai'i, but I think that is an understatement. Unlike all the other spots we tried during the last few years in Hawaii (and that includes several beaches on Kauai and Hanauma Bay on Oahu, the presidential snorkeling site), the water at Kealakekua Bay was calm and very clear, with fantastic visibility.

Heads of cauliflower coral, with yellow tangs for scale

I will not attempt to describe this whole new world; instead I will let the photographs speak for themselves (as always, more photos at Smugmug). Even better, if you go to the Big Island, make sure that you visit this place with some snorkeling gear.

Yellow tangs (Zebrasoma flavescens) often congregate in large schools and it is difficult to stop taking pictures of them

When I was at Kealakekua Bay, I didn't know much about the local geology. The big cliff bordering the bay toward the northwest, called Pali Kapu o Keoua (see image above), shows a number of layered lava flows that belong to the western flank of Mauna Loa; and I suspected that this must have been a large fault scarp, but that was the end of my geological insight. A couple of hours worth of research after I got home revealed that Pali Kapu o Keoua was a fault indeed: it is called the Kealakekua Fault and it has been mapped, along with the associated submarine geomorphological features, in the 1970s and 1980s by U.S. Geological Survey geoscientists.  It turns out that one of the shipboard scientists and key contributors to these studies was Bill Normark (see also a post about Bill at Clastic Detritus). While in California in the late 1990s, I was lucky to get to know Bill and have some truly inspiring discussions with him about turbidites, geology, and wine, so this was a doubly valuable little discovery to me.

So what is the origin of the Kealakekua Fault? The Hawaiian Islands are far away from any tectonic plate boundaries, so there is not a lot of opportunity here for inverse or strike-slip faults to develop. However, the Hawaiian volcanoes are humongous mountains and their underwater slopes are extremely steep by submarine slope standards: gradients of 15-10˚ are common. [This is in contrast by the way with the relatively gentle slopes of 3-8˚ the subaerial flanks of the volcanoes, a difference that - it just occurred to me - has to do something with the different thermal conductivities of water and air. Water is ~24 times more efficient at cooling lavas, or anything for that matter, than air, so once a volcano sticks its head out of the water, basaltic lava flows are pretty efficient at carrying volcanic material far away from the crater, thus building gently sloping shield volcanoes. The same flows are promptly solidified and stopped by the cool ocean waters as soon as they reach the coast.] Slopes that are this steep are also unstable; the underwater parts of these volcanoes tend to fail from time to time and large volumes of rock rapidly move to deeper waters as giant submarine landslides. Seafloor mapping around the islands revealed that the underwater topography is far from smooth; instead, in many places it consists of huge slide and slump blocks.

Topographic map of the Big Island. Note the location of Kealakekua Fault and the rugged seafloor to the southwest of it, marking the area affected by slides and slumps. This is a map based on higher-resolution bathymetric data collected during a collaborative effort led by JAMSTEC (Japan Marine Science and Technology Center). Source: U.S. Geological Survey Geologic Investigations Series I-2809 

Kealakekua Fault is probably part of the head scarp of one such giant landslide, called the Alika landslide. This explains the steep slopes in the bay itself: after a narrow wave-cut platform, a spectacular wall covered with coral - the continuation of the cliff that you can see onshore - dives into the deep blue of the ocean as you float away from the shore. In contrast with submarine landslides that involve well stratified sediments failing along bedding surfaces and forming relatively thin but extensive slide deposits, the Hawaiian failures affect thick stacks of poorly layered volcanic rock and, as a result, both their volumes and morphologic relief are larger (see the paper by Lipman et al, 1988). The entire volume of the Alika slide is estimated to be 1500-2000 cubic kilometers. That is about a hundred times larger than all the sediment carried by the world's rivers to the ocean in one year! The slides have moved at highway speeds and generated tsunamis. There is evidence on Lanai island for a wave that carried marine debris to 325 meters above sea level; this tsunami was likely put in motion by the Alika landslide*.

You don't want to be snorkeling in Kealakekua Bay when something like that happens. And it will happen again, it is a matter of (geological) time. Giant underwater landslides are part of the normal life of these mid-ocean, hotspot-related volcanoes.

Reference
Lipman, P., Normark, W., Moore, J., Wilson, J., Gutmacher, C., 1988, The giant submarine Alika debris slide, Mauna Loa, Hawaii. Journal of Geophysical Research, vol. 93, p. 4279-4299.

*tsunamis generated by landslides is a whole new exciting subject that we have no time now to dive or snorkel into.