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.

Morphology of a forced regression

'Forced regression' is an important concept in sequence stratigraphy - it occurs when relative sea level falls and the shoreline shifts in a seaward direction, regardless of how much sediment is delivered to the sea. This is in contrast with 'normal' regressions, which take place when relative sea level doesn't change or it is rising, but rivers bring lots of sediment to the coast and are able to push the shoreline seaward. These concepts are commonly illustrated with simple cartoons (like the ones on the SEPM sequence stratigraphy website), showing how beach deposits stack in a dip direction, and how their tops are eroded by rivers as sea level continues to fall.

Unless you live in a horizontally challenged flatland (vertical-land? 2D seismic-land?), real regressions happen in three dimensions, and their morphology is much more complicated, more interesting, and more beautiful than what one can dream up with a few lines in a single cross section. The example below is an airborne lidar image from Finland. The original data has a horizontal resolution of 2 meters and a vertical resolution of 30 centimeters.

Airborne lidar image of uplifted coastal plain in Finland
Image courtesy of Jouko Vanne, Geological Survey of Finland

The two dominant morphologies and deposit types clearly visible in the image are (1) ancient coastlines, formed as sand brought to the sea by rivers was reworked by waves into beach ridges; and (2) an incised river valley that cuts through these shoreline deposits. Note how the river seems to be incising and migrating laterally at the same time, generating a scalloped valley edge. The reason for this forced regression during a time of global sea-level rise is the isostatic rebound of the Scandinavian Peninsula after the retreat of the ice sheet.

Looking at this crystal-clear morphology, it is tempting to think that this area must look very interesting in Google Earth as well. It turns out that it doesn't; this is actually a pretty heavily vegetated land, not too spectacular on conventional satellite imagery (see figure below). The laser rays of the lidar are able to see through the non-geomorphological 'noise' and show stunning geomorphological detail.

Comparison of satellite image from Google Earth with detail of lidar topography

To explore a higher resolution version of this image, and for additional lidar visualizations of similar beauty, check out Jouko Vanne's Flickr site. The National Land Survey of Finland has started collecting this kind of data in 2008 and they are planning to cover the whole country with high-resolution DEMs within a few years.

A great way to spend taxpayer money, as far as I am concerned.

Einstein, tea leaves, meandering rivers, and beer

If you make your tea the old-fashioned way, ending up with a few tea leaves at the bottom of the teacup, and you start stirring the tea, you would expect the leaves to move outward, due to the push of the centrifugal force. Instead the leaves follow a spiral trajectory toward the center the cup. The physical processes that result in this 'tea leaf paradox' are essentially the same as the ones responsible for building point bars in meandering rivers. It turns out that the first scientist to make this connection and analogy was none other than Albert Einstein.

In a paper published in 1926 (English translation here), Einstein first explains how the velocity of the fluid tea flow is smaller at the bottom of the cup than higher up, due to friction at the wall. [The velocity has to decrease to zero at the wall, a constraint called 'no-slip condition' in fluid mechanics.] To Einstein it is obvious that "the result of this will be a circular movement of the liquid" in the vertical plane, with the liquid moving toward the center at the bottom of the cup and outward at the surface (see the figure below). For us, it is probably useful to think things out in a bit more detail.

Einstein's illustration of secondary flow in a teacup

A smaller velocity at the bottom means a reduced centrifugal force as well. But overall, the tea is being pushed toward the sidewalls of the cup, and this results in the water surface being higher at the sidewalls than at the center. The pressure gradient that is created this way is constant throughout the whole water tea column, and overall it balances the centrifugal force (unless you stir so hard that the tea spills over the lips). This means that the centrifugal force wins at the top, creating a velocity component that points outward, but loses at the bottom, creating a so-called secondary flow that is pointing inward. The overall movement of the liquid has a helical pattern; in fact, those components of the velocity that act in a direction perpendicular to the main rotational direction are usually an order of magnitude smaller than the primary flow.

Einstein goes on to suggest that the "same sort of thing happens with a curving stream". He also points out that, even if the river is straight, the strength of the Coriolis force resulting from the rotation of the Earth will be different at the bottom and at the surface, and this induces a helical flow pattern similar to that observed in meandering rivers. [This force and its effects on sedimentation and erosion are much smaller than the 'normal' helical flow in rivers.] In addition, the largest velocities will develop toward the outer bank of the river, where "erosion is necessarily stronger" than on the inner bank.

Secondary flow in a river, the result of reduced centrifugal forces at the bottom

I find the tea-leaf analogy an excellent way to explain the development of river meanders and point bars; just like tea leaves gather in the middle of the cup, sand grains are most likely to be left behind on the inner bank of a river bend. Yet Einstein's paper is usually not mentioned in papers discussing river meandering -- an interesting omission since a reference to Einstein always lends more weight and importance to one's paper (or blog post).

A recent and very interesting exception is a paper published in Sedimentology. It is titled "Fluvial and submarine morphodynamics of laminar and near-laminar flows: a synthesis" and points out how laminar flows can generate a wide range of depositional forms and structures, like channels, ripples, dunes, antidunes, alternate bars, multiple-row bars, meandering and braiding, forms that are often considered unequivocal signs of turbulent flow. [This issue of Sedimentology is open access, so do click on the link and check out the paper!]. As they start discussing meandering rivers and point bars, Lajeunesse et al. suggest that Einstein's teacup is extremely different dynamically from the Mississippi River, yet it can teach us about how point bars form:

A flow in a teacup with a Reynolds number of the order of 10² cannot possibly satisfy Reynolds similarity with the flow in the bend of, for example, the Mississippi River, for which the Reynolds number is of the order of 10⁷. Can teacups then be used to infer river morphodynamics? 

The answer is affirmative. When dynamical similarity is rigorously satisfied, the physics of the two flows are identical. However, even when dynamical similarity is not satisfied, it is possible for a pair of flows to be simply two different manifestations of the same phenomenon, both of which are described by a shared physical framework. Any given analogy must not be overplayed because the lack of complete dynamic similarity implies that different features of a phenomenon may be manifested with different relative strengths. This shared framework nevertheless allows laminar-flow morphodynamics to shed useful light on turbulent-flow analogues.

Apart from helping understand river meandering, the tea leaf paradox has inspired a gadget that separates red blood cells from blood plasma; and helps getting rid of trub (sediment remaining after fermentation) from beer.

That explains the 'beer' part of the title. And it is time to have one.

References

Einstein, A. (1926). Die Ursache der Meanderbildung der Flusslaufe und des sogenannten Baerschen Gesetzes Die Naturwissenschaften, 14 (11), 223-224 DOI: 10.1007/BF01510300

Lajeunesse, E., Malverti, L., Lancien, P., Armstrong, L., Metivier, F., Coleman, S., Smith, C., Davies, T., Cantelli, A., & Parker, G. (2010). Fluvial and submarine morphodynamics of laminar and near-laminar flows: a synthesis Sedimentology, 57 (1), 1-26 DOI: 10.1111/j.1365-3091.2009.01109.x

Wave ripples on an eroding beach

I shot these photos in 2003, at Sea Rim State Park in east Texas, close to the border with Louisiana, a relatively remote and beautiful state park along the Gulf coast that suffered a lot of damage during both Hurricane Rita in 2005 and Hurricane Ike in 2008. On that chilly November day the light was great and the variety of shapes and patterns created by wave ripples and exposed during low tide was amazing.

Wave ripples are more symmetric than current ripples. Needless to say, wave ripples originate thanks to the back-and-forth movement of sand by waves, whereas current ripples form under unidirectional flows (like rivers and turbidity currents). Wave ripples are also more regular than current ripples, extend for much longer distances laterally, and often terminate - or continue - in 'Y'-shaped junctions. For the same wavelength, they are also taller; the L/H ratio of most wave ripples is between 4 and 10, in contrast with current ripples that have an L/H value of ~20.

Perfectly symmetrical ripples form under bidirectional currents that are perfectly symmetrical themselves; but this tends to be the exception rather than the rule, as shoaling waves create a net shore-directed movement of the water. The resulting ripples are asymmetric, with the steeper side facing the coast, but still more symmetric and more regular than pure unidirectional ripples. Weak tidal currents can cause the asymmetry as well. The photo below shows wave ripples with a significant asymmetry that makes them difficult (if not impossible) to distinguish from current ripples.

This set is also asymmetric, but to a lesser degree:

Sea Rim State Park is at a location along the Gulf coast where the beach is eroding and the coastline is retreating; it is a typical example of a transgressive coast. The erosion is the results from both sea-level rise and from lack of longshore sediment transport strong enough to nourish the beach with sand. The evidence for the transgression is quite obvious: banks of well-consolidated muds that were originally deposited in the lagoon behind the coastal barrier are being eroded by the advancing waves:

More on wave ripples at Olelog.