Monthly Archives: March 2019

Stereographic projection – poles to planes

Facebooktwitterlinkedininstagram

great circles

This post is part of the How to… series

Stereographic projection is used in geology to decipher the complexities of deformed rock by looking at the relationships between planes and linear structures; their bearings (trends) and angular relationships one with the other. The data is plotted on a stereonet as great circles and points (Wulff and Schmidt nets). A stereonet can become pretty messy where there is a lot of data – a seemingly impenetrable maze of great circles. This is where poles-to-planes come into their own.

Instead of plotting the great circle to a planar structure like bedding, we plot its pole. Imagine this as a pole oriented at right angles to the plane. Because the pole is a linear feature, it plots as a point on our stereonet. As long as the pole is 90o to strike, it will contain all of the information in the associated great circle. We refer to this point as the pole to bedding (or any other planar feature). Poles to horizontal planes will plot at the centre of the stereonet; poles to vertically dipping planes at the perimeter. Poles to planes dipping at any other angle will plot within these bounds.

pole to bedding

In the example below the orientation of a bedding plane is plotted on an overlay as a great circle. With the great circle pinned to N, count 90 along the W-E axis passing through the centre of the stereonet; this point is the pole.

plotting poles to bedding

For cylindrical folds the poles to bedding on each limb will all plot on the same great circle (or close to it). The pole to this great circle corresponds to the β point – the fold axis, from which we can read its trend and plunge. Stereographic plots that use poles to bedding or other planes are called pi (π) plots. The utility of pi plots is illustrated in the example of an overturned anticline (the diagrams have been modified from D.M. Ragan, Structural Geology: An introduction of graphical techniques 1968, Figure 11.3).

map of overturned anticline

Dip and strike data on each fold limb are plotted as poles to bedding. We can also locate on the geological map the hinge points for each layer. The line connecting hinge points must lie on the axial surface. However, because our map view is horizontal, this line corresponds to the strike of the axial surface – another important piece of information. What we do not know about this structure is the orientation of the fold axis and the dip of the axial plane. The sequence of diagrams that follows shows the main tasks involved in solving this problem.

  • Find the great circle describing the poles to bedding by rotating a transparent overlay (make sure you mark the original N-S positions on the overlay).

stereographic poles to bedding                poles lie on a great circle

  • With the great circle pinned to North, count 90o from the circle along the east-west axis (the count must pass through the centre of the stereonet); this point is β, the fold axis.
  • Rotate the overlay counter-clockwise until β lies on the N-S axis. From North, read the fold axis trend and plunge.

stereographically determining the fold axis                 stereographic plunge and trend of fold axis

  • Plot the line representing the strike of the axial surface (N45W). The great circle containing this line must also pass through β.
  • With the second great circle pinned to North, read the dip of the axial surface.
  • Rotate the completed stereonet back to its original position.

stereographic dip of axial plane

You now have all the information you need to describe the orientation of the anticline.

Some other posts in this series:

Measuring dip and strike

Stereographic projection – the basics

Stereographic projection – unfolding folds

Using S and Z folds to decipher large-scale structures

Facebooktwitterredditlinkedin
Facebooktwitterlinkedininstagram

Using S and Z folds to decipher large-scale structures

Facebooktwitterlinkedininstagram

parasitic folds in Precambrian mudrocks

This post is part of the How to… series

A problem frequently encountered when mapping structurally deformed rocks is deciding whether the fold you see in outcrop is part of a larger structure – an anticline or syncline, overturned or recumbent, plunging? The problem is exacerbated if stratigraphic facing (younging) criteria are absent or ambiguous. Fortunately, there is a solution to the problem based on fold asymmetry.

Large folds commonly have smaller-scale folds in their limbs and crest. They are usually referred to as higher-order (2nd, 3rd order etc.) or parasitic folds. They form during flexure of layered rock where slip occurs between rock layers – a mechanism called flexural slip. Structural geology teachers frequently use a soft-cover book to demonstrate this mechanism; bend the book into a fold and watch the slip between adjacent pages that is required to accommodate extension on the outer arc of the fold and shortening on the inner arc.

 

Parasitic folds are common in deformed sedimentary rocks where slip takes place along bedding planes or between layers with contrasting strength, such as mudstone and indurated sandstone (mudrocks have abundant clays and micas that are prone to slip and shear). The example below shows an anticline (1st-order structure) and smaller 2nd-order folds developed in a relatively weak layer. The 2nd-order folds have asymmetries related to the sense of slip on each fold limb and are called S- and Z-folds. Note that the 2nd-order M-folds in the hinge are symmetrical and in this example, upright.

description of s and z folds

The difference between S- and Z-folds lies in their sense of rotation, or vergence. The long limbs of S-folds are connected by a shorter limb that implies counter-clockwise rotation or sense of displacement; the opposite applies to Z-folds. Thus, the vergence of parasitic folds is towards the hinge line (or zone)

parasitic folds in banded iron formation parasitic folds in Dalradian psammites

S- and Z-folds are three dimensional structures and will have hinge lines (or fold axes if we consider them to be cylindrical folds) and axial surfaces that can be measured. Another important property of parasitic folds is that their hinge lines (or fold axes) are parallel (or approximately so) to the hinge line of the 1st-order fold.

A note of caution; the sense of fold rotation-displacement will change if a fold is viewed from the opposite direction (i.e. S-folds will appear as Z-folds). Hence it is necessary to indicate the direction in which observations are made. Where possible, folds should be viewed down-plunge.

The geometric disposition of S- and Z-folds is extremely useful for deciphering large-scale folds, particularly when exposure is incomplete (as is commonly the case). The diagram below shows a scenario, where small folds are exposed in two outcrops.

deciphering large scale folds

Our view indicates the left outcrop is a Z-fold; the one on the right an S-fold. We can also determine the general attitude of the 1st-order fold limbs from dips and strikes on associated beds. If 1st-order fold-closure is beneath the surface, then it is a syncline (or synform if we don’t know facing direction); if above, an anticline or antiform. Both parasitic folds indicate vergence above the outcrops. If the structure was a syncline then the vergence should be in the opposite direction. The structure is therefore an antiform. If we have good facing direction data we could confirm the 1st-order structure is an overturned anticline (stratigraphy in the right outcrop is overturned).

Some other posts in this series:

Measuring dip and strike

Stereographic projection – the basics

Stereographic projection – unfolding folds

Stereographic projection – poles to planes

 

Facebooktwitterredditlinkedin
Facebooktwitterlinkedininstagram

Folded rock – some terminology

Facebooktwitterlinkedininstagram

plunging anticlines Belcher Islands

This post is part of the How to… series

Folds invoke a sense of awe, of some gargantuan, earth-bound push-and-shove. A hand bending and buckling rock with plasticine ease, like some Wallace and Grommet joke. Folds the size of your finger or entire mountains. They are windows into the forces that shape our world.

An analysis of folds is central to unravelling the structural complexities of solid Earth, the history of mountain belts, the formation and emplacement of Earth resources. And like any scientific analysis we need some terminology. Fold terminology is pragmatic; it is based primarily on what one commonly observes at the rock face or hillside. Its utility, combined with simple geometric rules, enables us to project structures beyond the immediately observable, to learn that small outcrop-scale folds formed sympathetically with much larger structures, or decipher the relative movement of fault blocks.

fold terminology

Although there are a myriad fold shapes and sizes, most can be described as variations of two basic forms: synforms which are concave upward folds, and antiforms which are convex upward. If we know the stratigraphic order of folded layers then we can use the more common names: anticline for folds that are convex in the direction of younging, and syncline for those that are concave in the direction of younging. If we do not know the younging or facing direction, a common problem in metamorphic rocks, then we must use the synform-antiform terminology.

The diagram above also shows some basic fold orientations and the inter-limb angles that determine the tightness of a fold. Have a look at the images at the bottom of this page for examples.

fold axes and axial planes

All folds have hinge points – the point (or narrow zone) of maximum curvature on a folded surface. Points of maximum curvature connected along a fold surface will define a hinge line; the hinge line may be straight or curved. However, to define the orientation of the fold uniquely, we need one other measure – the axial surface. The axial surface is defined by connecting all the hinge lines for each layer in the fold. The axial surface may be curved or planar – if it is the latter, we call it an axial plane. The orientation of an axial plane is determined by its strike and dip. Note that hinge lines also lie on the axial surface/plane.

If a hinge line is straight, it is called a fold axis (that must also lie on the axial plane). A fold axis is an imaginary straight, or nearly straight line that, when moved parallel to itself, will recreate the fold. This property distinguishes fold axes from hinge lines. The brief animation here shows diagrammatically the generation of a fold about the locus of a fold axis.

 

cylindrical folds

We can use the geometric identity of a fold axis to define two other classes of folds: cylindrical and non-cylindrical folds. All cylindrical folds have fold axes; all cylindrical folds have axial planes (non-cylindrical folds have axial surfaces). An ideal cylindrical fold is analogous to a soup can with both ends removed. Of course, real folds rarely look like cylinders – most have some degree of hinge-line curvature. But most folds can be divided into straight-line or nearly-straight line segments, such that aspects of cylindricity can be identified in each segment (as in the diagram).

This may sound a bit contrived – actually it is – but it provides us with a sensible approach to fold analysis, particularly using stereographic projections. In the simplest case, a dip and strike measurement on each limb of a cylindrical fold will plot on a stereonet as two great circles, the intersection of which is a point that represents the trend and plunge of the hinge line, or fold axis. We can begin to make sense of more complex geometries in large-scale folds if we analyse each cylindrical fold segment in this way. The stereographic projection method of fold analysis will be described in another post.

 

Some other posts in this series:

Measuring dip and strike

Solving the three-point problem

Stereographic projection – the basics

Stereographic projection – unfolding folds

Stereographic projection – poles to planes

The Rule of Vs in geological mapping

 

Some older, but incredibly useful texts on folds and structural geology:

G.H. Davis and S.J. Reynolds. 1996 Structural geology of rocks and regions. John Wiley & Sons, Inc. New York, 776 p.

B.E. Hobbs, W.D. Means, and P.F. Williams, 1976. An outline of structural geology. John Wiley & Sons, Inc. New York, 571 p.

J.G. Ramsey, 1967. Folding and fracturing of rocks. McGraw-Hill Book Co., New York, 560 p.

J.G. Ramsey and M.I. Huber. 1987. The techniques of modern structural geology, v.2. Folds and fractures. Academic Press, London, 381 p.

Facebooktwitterredditlinkedin
Facebooktwitterlinkedininstagram

Atlas of cool-water carbonate petrology

Facebooktwitterlinkedininstagram

This is the companion Atlas to the Cool-water carbonates – outcrop images.

New Zealand cool-water carbonates are predominantly bioclastic, consisting of fauna like bivalves, calcareous bryozoa, barnacles, echinoderms, and flora such as rhodoliths (calcareous algae that encrust rock fragments and shells).  This is particularly the case on shelves with little terrigenous sediment input, such that there is a diverse epifauna. Good examples of this setting occur around New Zealand. There is no evidence in any of the Oligocene through Pleistocene stratigraphy for aragonite-producing algae like Halimeda and Penicillus.

However there is a range of bioclast compositions, ranging from low- to high magnesian calcites and aragonite, The bioclast compositional variation has a significant impact on cement types (micrite and rhomohedral calcite envelopes) calcite spar, and neomorphic replacement by calcite of original bioclast aragonite. Like cements in more tropical realms, the cement paragenesis in cool-water carbonates reflects complex histories of fluid flow and evolving fluid chemistry through sea floor cementation, burial, uplift and ingress of meteoric water. Some useful references describing the paragenesis of Pliocene cool-water carbonates from the east coast of North Island (Te Aute Group) are given below.

 

Contributors:

Vincent Caron is a lecturer in geology and researcher in carbonates based at the Université de Picardie Jules Verne in Amiens, France. He is also a member of the Basins Resources Reservoirs research group. Most of the images presented here on Te Aute limestones formed part of his PhD research at Waikato University. A short list of his publications on the Te Aute is shown below.

Cam Nelson, is one of the original adherents of the Cool Water Carbonate paradigm, who set the scene with his studies of the Oligocene Te Kuiti Group. Cam is an Emeritus Professor at Waikato University.

CS Nelson, PR Winefield, SD Hood, V. Caron, A Pallentine, and PJJ Kamp. 2003. Pliocene Te Aute limestones: Expanding concepts for cool-water shelf carbonates. New Zealand Journal of Geology and Geophysics, 46, 407-424.

V Caron, CS Nelson, and PJJ Kamp. 2004. Contrasting carbonate depositional systems for Pliocene cool-water limestones cropping out in central Hawke’s Bay, New Zealand. New Zealand Journal of Geology and Geophysics, 47, 697-717.

B.D. Ricketts , V Caron & C.S. Campbell 2004. A fluid flow perspective on the diagenesis of Te
Aute limestones. New Zealand Journal of Geology and Geophysics, 47:4, 823-838

V Caron and CS Nelson. 2009. Diversity of neomorphic fabrics in New Zealand Plio-Pleistocene limestones: Insights into aragonite alteration pathways and controls. Journal of Sedimentary Research, v. 79, p. 226-246.

 

The images:

Pliocene Te Aute Group, Hawkes Bay, New Zealand

neomorphic calcite cement neomorphic calcite cement

partial neomorphism neomorphic calcite calcite replacing aragonite calcite filling aragonite holes calcite cementscalcite cements micrite and spar cements coarse spar cement

aragonite biomoldsacicular calciteneedle cacliteacicular calcite

 

Pleistocene Pukenui Limestone, southern North Island, in plain polarized light and cathodoluminescence.

cathodoluminescence zoned cement cathodoluminescence zoned cement

 

Oligocene Potikohua Limestone near Greymouth, South Island

bryozoan limestone

 

Oligocene Orahiri and Otorohanga limestones, Te Kuiti Group. Courtesy of Cam Nelson

Facebooktwitterredditlinkedin
Facebooktwitterlinkedininstagram