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Theoretical Stratigraphy #1: Wheeler’s baselevel

July 29, 2007

Blogging on Peer-Reviewed ResearchThis post reviews some fundamental concepts of stratigraphy that are discussed in a 1964 GSA Bulletin paper by Harry Wheeler. At the same time, it is an essay about my own quest to really understand how time is recorded in rocks.

I was introduced to this paper and its ideas in an advanced stratigraphy class I took during my master’s program a few years back (which is the best class I’ve ever taken). Wheeler’s writing style is abstract and sometimes obtuse, but also very creative and profound. He has a handful of papers in the 1950s and 60s dealing with stratigraphic theory but I think the 1964 paper discussed here is the best summary of his ideas. This is one of those papers that you will need to read over and over again to “get it”. I learn something new every time. Historically, this is an important paper; a contemporary of Wheeler (and reviewer of the paper) was Larry Sloss, who published a famous paper in 1963 dealing with unconformity-bounded stratigraphic sequences in North America. Sloss was the mentor of Peter Vail, who is credited (along with his Exxon colleagues) with spearheading what is now referred to as seismic stratigraphy or sequence stratigraphy in the 1970s. I will deal with the Sloss-Vail view of stratigraphy another time.

First, to whet your appetite….let’s start with one of my favorite passages from Wheeler’s paper:

…the constantly varying undulations of the baselevel surface relative to the ever-changing lithosphere surface may be seen as a consistent function of the ebb and flow of depositional and erosional environments in the space-time continuum.

This single statement captures Wheeler’s view of how to approach unraveling the stratigraphic record. Laying out the concept of stratigraphic baselevel, which is fundamental to this view, is the thesis of this paper.

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Review of the Baselevel Concept
John Wesley Powell first explicitly discussed base level in 1875 as the ultimate lower surface beneath which rocks cannot be eroded. He proposed this in his writings after exploring and mapping the landforms of the Colorado Plateau region. In this view, sea level is the “grand base level”. This idea is intuitive and is still an important concept in areas of geomorphology that deal with net erosion and denudation of the Earth’s surface. As Wheeler discusses in the opening paragraphs, Barrell (1917) is credited with extending the baselevel concept into the depositional realm. Here I quote Wheeler quoting Barrell:

“Thus the sediments [are] deposited with respect to a nearly horizontal controlling surface. This surface of control is baselevel [which is] of more inclusive content than the sense in which has generally been used by physiographers as a level of limiting the depth of fluvial erosion. Sedimentation as well as erosion is controlled by baselevel [which] is that surface toward which external forces strive, the surface at which neither erosion nor sedimentation takes place.” (Bracketed words are Wheeler’s.)

One of Wheeler’s contributions to the development of the baselevel concept is his challenge that it is actually a “controlling” force.

Although baselevel is indeed important, it exists as a surface only in the human mind; it controls nothing.

A statement like this could open a can of worms regarding how science in general deals with forces of nature and how best to discuss them, but let’s focus on Wheeler’s point. What he is saying is that viewing baselevel as a control is limiting. Regarding baselevel as a descriptor is much more inclusive and holistic, for lack of a better term. Wheeler argues that viewing the phase of degradation and aggradation of the Earth’s surface as having separate controls and also being split into separate scientific disciplines as misguided:

Many inadequacies of concept and practice stem from the popular notion that stratigraphy is the science of past sedimentation, to the exclusion of degradation; but if time is properly incorporated in the system, stratigraphers must concern themselves with the interpretation of degradational as well as aggradational patterns. Conversely, the geomorphologist who ignores depositional phenomena is equally delinquent.

In practice, of course, stratigraphy and geomorphology are intertwined, yet distinct disciplines. When dealing with parts of the Earth’s surface that are net depositional vs. net erosional different concepts and tools are utilized to characterize and understand them. But what Wheeler is getting at is much more fundamental.

The next major aspect of baselevel that Wheeler discusses is that it is not a horizontal surface. The figure below is straight from the paper (click on it to see a larger version and caption).


Wheeler argues that thinking of baselevel as a horizontal surface results in numerous baselevel surfaces that come and go in time. Moreover, either deposition or erosion could occur above or below these multiple surfaces at any one time, which further complicates the notion that there is a single, horizontal controlling surface. One argument is that the other, multiple surfaces are temporary and thus not the ultimate baselevel. Wheeler’s view of a baselevel surface, shown in lower half the figure, is that it is a non-horizontal surface that describes what the Earth’s surface, or the lithosphere surface as he calls it, is doing at that time. In other words, if degradation (erosion) is occuring, baselevel is “falling”; if the lithosphere surface is aggrading (deposition), then baselevel is “rising”. I will come back to this….for now, let’s move on.

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Law of Lithosphere Relationships
Wheeler then discusses how the differement “movements” of the lithosphere surface relate to the passage of time. This is where his ideas get interesting.

But what of stratigraphic discontinuities as manifestations of nondeposition and accompanying erosion? Here we pass into the realm of no less important but completely abstract, area-time framework, in which a discontinuity takes on ‘area-time’ configuration in the form of the lacuna, which in turn, consists of hiatus and degradation vacuity.

Here, he is emphasizing the temporal value of nondeposition and erosion. It is intuitive to think about the passage of time when looking at a vertical column of stratigraphy. And the importance of significant unconformities goes back to the very foundation of the science of geology. Wheeler is proposing a more formal subdivision of this so-called “missing” time. Of course, there is no “missing” time….it is simply recorded as a surface and not as a deposit. The entire segment of time as surface, given the fantastic name of lacuna (an empty space; missing part), is subdivided into two parts:

  • hiatus = time value of nondeposition and erosion
  • degradation vacuity = time value of previous deposits that were removed by erosion

This is important. Wheeler points out that there are three separate domains of time (nondeposition, erosion, and what has been removed) all potentially recorded in a single surface!! He then, in old-school fashion, proposes a formal law of surface relationships as:

Time as a stratigraphic dimension has meaning only to the extent that any given moment in the Earth’s history may be conceived as precisely coinciding with a corresponding worldwide lithosphere surface and all simultaneous events either occurring theoron or directly related thereto.

Wheeler brings his view of baselevel (i.e., the non-horizontal, constantly undulating surface that describes the condition of aggradation or degradation) back in terms of an equilibrium relationship:

Baselevel thus intersects the lithosphere surface at all points of equilibrium, and its momentary ‘depth’ beneath or ‘height’ above the surface at any locality depends…on the relative ‘values’ of supply and energy.

The terms supply and energy are referring to the flux of sediment and the vigor with which it is transported. In other words, environments of high “energy” are those where erosion (i.e., degradation of lithosphere surface) is more likely. And, if you go back to the figure above, the points of equilibrium are where the dashed line crosses the Earth’s surface.

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Baselevel Transit Cycle
In this section of the paper, Wheeler discusses the notion of stratigraphic cycles, a concept that has been pondered almost as long as geology has been a science, within the context of baselevel. A cycle of falling baselevel following by rising, or vice-versa, is thus termed a baselevel transit cycle:

If in an erosional environment at a given locality, the supply-energy ratio increases sufficiently to induce deposition, baselevel is forced upward across the lithosphere surface at that point at the moment deposition beings, thus initiating the first or depositional phase of a new cycle. This cyclic phase continues until the supply-energy ratio is decreased sufficiently to stop deposition and induce erosion, at which time baselevel makes its downward transit of the surface, thus beginning the second or hiatal cyclic phase.

This is getting into the realm of the stratigraphic sequence. As noted above, I will save the discussion of how Wheeler’s thinking and Sloss’s work have led to our current paradigms in stratigraphic theory. For now, I want to conclude this post with a discussion of Wheeler’s summary illustration of these ideas, which is one of my favorite figures of any geology paper.

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Area-Time Configurations of Baselevel Transit
The first part of his Figure 2, shown below, is an idealized and hypothetical stratigraphic succession.


This example shows two sequences, A and B, that are separated by an unconformity at the left side of the diagram, and the same two sequences without a discontinuity, and thus one sequence at right (click on it for a larger view). Note the designation of time-equivalent surfaces, A1, A2, A3, etc., associated with each sequence.

The second part of this figure, shown below, takes this succession and puts it into area-time. In other words, the vertical axis is now time rather than depth/thickness. This kind of illustration of stratigraphy has become known as a Wheeler diagram.


If you’ve made it this far into this post….you should go all the way. It is worth it to look at the larger view of this figure (click on it) and study it in relation to the figure above. Remember, we are now looking at the succession in time:

Because geologists have not succeeded in developing the means for graphic portrayal of relationships in the space-time continuum, the area-time section is used.

The triangular domain that comes to a point from left to right represents the time recorded as surface, or the lacuna. As discussed above, note how the lacuna is subdivided into the hiatus and degradation vacuity. The “shape” of the lacuna changes across space … in this example its time value decreases from left to right as the unconformity transitions into a conformity. In other words, there is more “missing” time wrapped up in the unconformity at the left end of the succession. Now, when you compare this back to the corresponding area-thickness plot, you can see how this all fits together. Note how the A5 surface is truncated by the unconformity. And then when examined in the area-time plot you can see the A5 surface across the entire region, but a large portion of it is within the lacuna domain.

Wheeler notes that if we could generate accurate area-time plots such as this for any stratigraphic succession, the concept of baselevel might not be necessary. But, since we cannot, he states:

…even in time-stratigraphy it would unwise to avoid the role of baselevel, for the fact is most impressive that the constantly varying undulations of the baselevel surface relative to the ever-changing lithosphere surface may be seen as a consistent function of the ebb and flow of depositional and erosional environments in the space-time continuum.

This statement alone is why I think Wheeler’s ideas are so important to the science of stratigraphy. It is fundamental to our understanding of Earth history to view a stratigraphic succession as a continuous record. The emphasis on solely the accumulative part of the record misses much (probably most) of the history. Of course, characterizing a history that is so ambiguously represented (i.e., there is nothing there to characterize!) is difficult to impossible at any one location. The point of all this is to develop a theory about how time is recorded in rocks.

In future posts, I will try and put some of Wheeler’s concepts within the context of work that came before as well as after this paper.

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NOTE: See Theoretical Stratigraphy #2 about a 1917 paper by J. Barrell that discusses rhythms of sedimentation and how these rhythms are manifested in the stratigraphic record.

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21 Comments leave one →
  1. Chuck permalink
    July 30, 2007 4:39 am

    This is frigging cool. I don’t get half of it, but it is still cool. Got a pdf copy of that paper handy?

  2. Brian permalink
    July 30, 2007 10:13 am

    It is pretty cool…we devoted two classes to this paper and then revisited its concepts continually throughout the class.

    As I said, I still learn something every time I read it. And you definitely have to be in the mood for trying to digest his dense writing style.

    Some of the more “practical-minded” stratigraphers out there don’t see the value of reading/studying something like this…but I think they might not appreciate how it has led to what we think we know today.

  3. August 5, 2007 3:12 pm

    This is excellent stuff, Brian — I am glad I’ve found it. I have never read Wheeler’s paper; but now I have to.

    Cheers, Zoltan

  4. Brian permalink
    August 5, 2007 7:31 pm

    zoltan…you will enjoy the Wheeler paper…let me know if you want a pdf copy

  5. August 7, 2007 6:34 am

    Yes, a PDF copy would be nice… GeoScienceWorld only has the abstract.

  6. bergeron permalink
    August 21, 2007 10:21 am

    Brian, I’d love a PDF copy of the Wheeler paper as well if you have it handy. Saves a trip to the library photocopier.

  7. Brian permalink
    August 21, 2007 10:38 am

    go ahead and email me (address is at upper right of sidebar) and then I will reply to you with the PDF

  8. February 9, 2008 10:13 pm

    Wow, what an incredible commentary on Wheeler’s 1964 paper. I admit that I initially despised Wheeler for his dense prose, but he won me over with the Wheeler Diagram.

    The concept of the lacuna is facinating, but I struggle with how the degradational vacuity and hiatus would ever be represented in the rock record. In other words, if all that remains is a surface that represents the entire lacuna, how would we ever draw the line ‘d’ in Wheeler’s diagram? This is something that has puzzled me for a long time…

    Perhaps if I eat my Wheeler Wheaties for breakfast tomorrow I’ll be able to wrap my mind around it.

  9. February 9, 2008 10:51 pm

    Jeannette says: “…I struggle with how the degradational vacuity and hiatus would ever be represented in the rock record”

    Indeed! Since only a surface remains, the stratigrapher must look at the preserved rock above and below that surface (ideally across a large area) to gather clues about what the surface records. Admittedly, that’s not much…but that’s what we got.

  10. Richard permalink
    March 13, 2008 8:56 pm

    Can you explain why the “Migration of terminal degradation” on the Wheeler Diagram migrates from distal to proximal and young to old?.

    It seems this line and D1, D2 & D3 indicates sediment rather than time?

    How about building a rock-time-area 3D model.

  11. March 14, 2008 6:50 am

    Richard…

    A 3D Wheeler diagram would be a daunting task … it’s difficult enough to balance everything in two dimensions … but, yes, a good idea.

    As for the migration of terminal degradation, the way I see it, at least for that hypothetical diagram, is that the amount removed (i.e., degradational vacuity) expands towards the more proximal area. That is, the unconformity development removes more older material in more proximal areas.

    I’ve always been a bit confused by Wheeler’s use of the word ‘migration’ in this respect…this is not stricly temporal migration, but a ‘migration’ in area-time space, perhaps ‘trajectory’ is a less confusing word? I don’t know.

    The D1-D3 represent phases of degradation … as erosion ate into the previously-deposited strata, it started from the top (D1) and worked it’s way down (D3) … this would be a semi-continuous and incremental process, but I think Wheeler is just trying to show how that would be represented in area-time. The time that that degradation occured would be wrapped up in the Hiatus part.

  12. Richard permalink
    March 15, 2008 5:07 am

    Brian:

    Exactly. “the *amount* removed (i.e., degradational vacuity) expands towards the more proximal area” – so we are talking of rock thickness in the diagram, not time.

    Again “as erosion ate into the previously-deposited strata, it started from the top (D1) and worked it’s way down (D3)” – again, the diagram depicts strata not only time.

    May be I am being a little pedantic, but baselevel is a confusing topic. The diagram could be modified.

    I am also thinking about baselevel transit. I don’t have the full paper – is this the movement of the baselevel curve vertically & arealy throughout the source area?

    I also assume that the base level curve would extend onto the continental shelf and slope?

  13. March 15, 2008 7:35 am

    “so we are talking of rock thickness in the diagram, not time.”

    But that rock thickness took time to be deposited … so, time is being “removed” as the rock is.

    You’re right though … it is a confusing diagram … I’ve been trying to understand it for years. How might you modify it?

  14. March 15, 2008 12:52 pm

    Richard says: “…the diagram depicts strata not only time”

    Yes, exactly, that is the whole point.
    It is attempting to integrate the physical (i.e., preserved strata) with the abstract (i.e., time value of deposition, hiatus, erosion, and what was removed).

  15. August 17, 2009 12:08 pm

    I only just got the chance to read this interesting review. I would really appreciate it if you could forward along a copy of that PDF. I understand it is likely buried deep in your email or something. If it is too much of a pain, I will be happy to get it elsewhere. Thanks, Andrew

  16. Bob Schwartz permalink
    August 17, 2010 10:36 am

    Brian,

    Could you send me a pdf of the Wheeler (1964). It would be much appreciated.

    thanks,

    Bob

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