Fractal Nature of Structural Geology

The Fractal Nature of Structural Geology During the Late Paleozoic Alleghanian Orogeny in the Mid-Atlantic Region 
When a figure is fractal it means that regardless of the scale of observation, no matter how much we enlarge the feature and look more closely, detail will continue to emerge. This "fractal" concept not only applies to our artistic depiction of the rock record, but, more importantly, is observed within the actual rock record, both structurally and stratigraphically. 
Notice on the cross-section the five numbered boxes. Scroll down to the box numbers below to see more detail about the outlined areas.  Do not expect the different drawings to match up well with each other; they were drawn for different purposes and present some degree of speculation.
Box One. 
Box One is a more detailed view of the structures in the western portion of the main cross-section. If you compare the two you will see the similarities. The main difference is that Box One has many more faults depicted, and they are more detailed in their depiction. We have drawn over in red the fault lines common to both drawings, although there is some speculation about which faults are which. Note how many faults are missing from the main cross-section, and how much subtler the folds are drawn in the main cross section.

Gathright and Frischmann VDMR Pub. 60, 1986

The major difference between these examples is that the main cross-section was drawn to make a point about foreland basins in the Taconic Orogeny, and so just the main faults were important. But the Box One cross section was drawn specifically to highlight the structural geology in the region, and since structure was most important the authors strove to be as complete and accurate as they could, showing the most detail.
Box Two.
Box Two is an enlargement of the eastern part of the Main Cross-Section. Notice in the main cross-section that the portion labeled Blue Ridge Overthrust just looks like one big sheet of rock that had moved west along a fault. The Blue Ridge and Piedmont provinces are filled with faults or zones of weakness, of all ages, including those that are Grenville, Taconic, and Alleghanian age. 

Based on the faults alone, it is not possible to distinguish between the Piedmont and Blue Ridge Provinces. We distinguish these provinces because the rocks that make them up are very different, but structurally there is little reason to separate them. They all verge westward, and were all produced during the Alleghanian orogeny.

Box Three. 
Note the Blue Ridge Mountains (province) in the distance, and Page Valley (Valley and Ridge province) in the foreground (photo right). The Blue Ridge fault runs at the base of the Blue Ridge Mountains, that is, at the boundary between the provinces, as seen in this Cross Section
We have implied that the Blue Ridge fault is a single, long, continuous fault, however, it is a series of faults, sometimes splitting and coming together, and sometimes running separate from each other. 
The closer we examine the fault, the more detail we include, the more complex the fault becomes. As displayed from Box Two it should be clear that the Blue Ridge fault is also just one in a very large complex of faults, all related in one way or another. In fractal images this is usually the case, it is hard to determine what is most important since all the features are related in some fashion. The large scale reflects the details, and the details construct the large scale. 
Box Four.
Box Four lies west of the Blue Ridge. It is in a small quarry along the Shenandoah river, about half a mile from Rt. 211. The exposure shows a recumbent fold, i.e., a fold on its side with a near horizontal axial plane. 
For such a fold to develop, horizontal rocks must be arched up into an anticline, and then folded over until the whole arch is laying down flat on its side. The process is seen in the drawings below. To the right is the anticline; the vertical blue line is the axial plane that divides the fold into two more or less equal halves. Notice as the drawings go from right to left the axial plane lays over more and more until it is horizontal - this defines a recumbent fold, as in the quarry picture above right. The overturned nature can be best seen on the right side of the quarry, but the axial plain runs horizontally across the middle of the quarry.
Box Four lies within the southeast limb of the Massanutten Syncline, and there is little hint of other folds in that drawing, but there actually are. Two things stand out from this. One is that there are folds within folds. This is the very nature of a fractal image. The second thing is that if this small recumbent fold is there, exposed within the larger syncline, there are likely many other complex folds associated with the syncline that we cannot see.

Box Five.
The structure is located along Rt 211 on the eastern side of Massanutten Mountain, where Rt 340 and Rt 211 join. Notice in the picture that the rocks from the southeast limb of the syncline are dipping toward the left, which is west. This would make sense in a syncline; rocks on the two flanks dip toward the center. The diagrammatic cross-section of Massanutten mountain below shows how rocks dip toward the center. Looking northward, down the axis of the syncline the right side dips toward the west, the left side dips toward the east.
The two photos below were taken about half way up the outcrop, near the center of the exposure. Both photos contain alternating sandstone and shale beds. These are the individual depositional units. Notice that there are diagonal lineations running through the beds. These diagonal lineations are not part of the original sedimentary rock. They represent a shear structure called cleavage (small-scale closely spaced aligned fractures) that developed when the rock folded to form the Massanutten Syncline during the Alleghanian orogeny.

To see how this works examine the drawings below. In the top drawing are two sandstone beds, in yellow, above and below a brown shale. When the rocks are folded, stress causes one side to move in one direction while the opposite side moves in the other direction as shown by the red arrows. The large scale folding in which this takes place can be seen in the middle drawing where a stack of sandstone and shale has been folded into a syncline. This kind of shear behavior is seen if you bend a stack of paper, or a magazine. Sheets of paper that originally had their edges lined up get shifted so they no longer line up. 
When folding forces rock to move in this manner, the rock itself absorbs the shear, indicated by diagonal cleavage running at an angle to the bedding. This is shown in the lower right drawing where the lines representing cleavage that were originally at right angles to the bedding have become diagonal lines running through the beds. The real cleavage lines can be see in the rocks in the photographs above. 

1. The rock record is fractal, meaning there are structures, within structures, within structures, from the microscopic to the mega scopic.
2.  All of these structures are intimately related, the small structure is contained within the large structure, and the large structure is implied in the small structure. This means they are likely all be the result of processes operating under the same stress regime. 
3.  Small structures, like those in a quarry or roadcut, they are generally part of a much larger structure, even if one cannot see the larger structure. 
Contributed by Lynn Fichter 
Thursday, August 14, 2014
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