Structural Geology II: Faults, Joints, Shear Zones, Thrusts, Unconformities, Superposed Folds, Maps and Stereographic Projection

This chapter completes the Part B1 heading “Structural Geology”: “Folds, faults, joints, and unconformities; Shear zones, thrusts, and superposed folding; Geological maps-interpretation, measurements, and numerical analysis; Stereographic projection.” It teaches fault geometry, classification and fault rocks, joints and their origins, ductile shear zones and thrust systems (with the Himalayan thrusts), unconformities, the patterns of superposed folds, the reading and measurement of geological maps, and stereographic projection described in words. The numericals are throw and heave, shear strain across a zone, apparent dip, thickness on sloping ground, the three-point problem and the plunge of an intersection line.

1. Faults: geometry, classification and fault rocks

A fault is a fracture with displacement. The block above an inclined fault is the hanging wall and the block below is the footwall. Net slip is the true displacement vector, and dip-slip, strike-slip and oblique-slip faults are named by its direction. In a normal fault the hanging wall moves down, in a reverse fault it moves up, and a thrust is a reverse fault dipping less than about 45°. A strike-slip fault is dextral (right-lateral) if, looking across the fault, the far block has moved to the right, and sinistral if to the left, whichever side you stand on.

Throw is the vertical, and heave the horizontal, component of displacement across the fault, measured in a section perpendicular to strike. For pure dip-slip of net slip s on a fault of dip δ, throw = s sin δ and heave = s cos δ. For s = 100 m and δ = 60° they are 86.6 m and 50 m. Separation, the apparent offset of a marker seen in outcrop or on a map, is not slip: it depends on the orientation of the bed and the plane of observation.

Fault rocks
Fault rockOriginFeatures
Fault breccia, gougeBrittle, shallow; incohesiveAngular fragments; gouge is a clay-fine matrix
CataclasiteBrittle; cohesiveCemented, grain-size-reduced fragments
PseudotachylyteFrictional melting in seismic slipDark glassy veins with injection veins and clasts
MyloniteDuctile, deeper; crystal-plastic flowFoliated, fine-grained, cohesive
⚠️ Separation is not slip
Offset on a map is not slip. Where a vertical fault cuts a vertical dyke, the dyke is shifted sideways only by strike-slip movement, but dip-slip movement also shifts the outcrop of a dipping bed sideways (and that of a vertical dyke too if the fault itself is inclined). After erosion, a dip-slip fault brings older beds to the surface on its upthrown side.

Normal faults make horsts, grabens and half-grabens; listric faults flatten with depth and give a hanging-wall rollover anticline. Strike-slip zones show Riedel shears (R at about φ/2, near 15°, to the main fault and R′ near 75°), flower structures, pull-apart basins at releasing steps and push-ups at restraining bends. Kinematic indicators on fault surfaces include slickenlines, steps and drag folds.

2. Joints and their origins

A joint is a fracture with no shear displacement, only opening (Mode I). A fault shows shear displacement, and a vein is a joint filled with minerals. Joints grow parallel to σ1 and perpendicular to σ3 when the effective σ3 turns tensile, helped by high pore-fluid pressure (hydraulic fracturing). Systematic joints are parallel and regularly spaced and form sets; two or more sets make a joint system. Joints usually stop at bedding interfaces, and their spacing increases with the thickness of the mechanical layer, so thin beds are closely jointed.

  • Tectonic joints relate to folds and faults. With a along the dip, b along the hinge and c normal to bedding, ac (cross) joints are perpendicular to the hinge and bc (longitudinal) joints parallel to it. Conjugate shear joints enclose σ1 within their acute angle.
  • Unloading (sheeting) joints run parallel to the ground surface as erosion removes load, as in granite domes. Cooling joints form columnar prisms, often hexagonal, perpendicular to the cooling surface of basalt flows. Desiccation cracks form in drying mud.
  • Surface features show origin and direction: the plumose structure is a feathery pattern radiating from the point where the joint began, and arrest lines mark pauses in growth.
⚠️ Joint, fault or vein
Do not call a fracture with a visible offset a joint. Joints open; faults slip. A fracture filled with quartz or calcite is a vein, and a dyke is a joint filled by magma, so neither is a plain joint.

3. Shear zones and thrusts

A shear zone is a tabular zone of intense, localised strain. Brittle shear zones are faults; ductile ones deform continuously with a displacement gradient, and the average shear strain is γ = D/w, for displacement D across width w. Mylonites form by crystal-plastic flow with grain-size reduction and are graded by matrix proportion: protomylonite (10 to 50%), mylonite (50 to 90%) and ultramylonite (above 90%). Shear sense is read in the XZ section, parallel to the stretching lineation and perpendicular to foliation.

  • Shear-sense indicators: S–C fabrics (oblique S foliation rotating towards the C shear planes as strain grows), C′ shear bands, σ- and δ-type porphyroclasts with asymmetric tails, mica fish and asymmetric folds. The Main Central Thrust zone of the Himalaya is a broad ductile shear zone with top-to-the-south shear.
  • A thrust is a low-angle reverse fault that normally puts older rocks over younger and repeats the stratigraphy. It runs along flats parallel to bedding in weak units and cuts up through the section as ramps; a hanging-wall fault-bend fold forms as the sheet rides over a ramp. Several thrusts make an imbricate fan or a duplex (horses between a floor and a roof thrust). In piggyback (in-sequence) thrusting the younger thrusts form towards the foreland.
  • Erosion of a thrust sheet leaves a klippe, an isolated remnant of the sheet resting on younger footwall rocks, or a fenster (window), where the footwall shows through the sheet. A large, far-travelled sheet is a nappe. From north to south the major Himalayan thrusts are the Main Central Thrust, the Main Boundary Thrust and the Main Frontal Thrust, which young southwards; the South Tibetan Detachment is a normal-sense shear zone at the top of the Greater Himalayan sequence.

4. Unconformities and superposed folding

An unconformity is a surface of erosion or non-deposition that separates younger from older rocks and represents a time gap. In an angular unconformity the older beds are tilted or folded and the younger beds lie at a different angle, so the tilting predates the younger beds. A disconformity has parallel beds with an irregular erosion surface. A paraconformity has parallel beds with no visible erosion, the gap being shown only by missing fossil zones. In a nonconformity sediments rest on igneous or metamorphic rock. Evidence includes a basal conglomerate, truncated structures, a palaeosol and a break in fossils or metamorphic grade; on a map the younger unit's contact cuts across the strike of the older units.

Superposed (refolded) folds record successive phases, D1 and D2, giving F1 and F2. Evidence includes a foliation or lineation that is itself folded, hinges that curve or vary in plunge, and folded folds. In Ramsay's scheme the outcrop pattern depends on the angle between the two fold sets: Type 1 is the dome-and-basin pattern, where F2 axes are about perpendicular to F1 axes (two upright sets crossing at right angles); Type 2 is the intermediate crescent or mushroom pattern; and Type 3 is the hook pattern, where F2 refolds F1 about roughly parallel axes (coaxial refolding).

5. Geological maps: interpretation and measurement

Outcrop patterns follow the dip. Horizontal beds follow contour lines; vertical beds cross valleys in straight lines; dipping beds make V-shapes in valleys. A bed's V points down-dip, except where the bed dips downstream more gently than the valley floor falls, when it points up-dip. Folds show older rocks in the core of an anticline with dips away from the axis, and younger rocks in the core of a syncline with dips towards the axis. A plunging anticline closes in the direction of plunge and a plunging syncline against it. Faults offset contacts, and an unconformity truncates the older units.

Apparent dip in a direction at angle β to the strike is given by tan δa = tan δ sin β. For δ = 60° and β = 45°, tan δa = 1.732 × 0.7071 = 1.2247 and δa = 50.8°. Thickness: on level ground with outcrop width w measured perpendicular to strike, t = w sin δ, so a 40 m bed dipping 30° outcrops 80 m wide. If w is measured along ground sloping at angle s against the dip, t = w sin(δ + s), and with the dip, t = w sin(δ − s). A vertical borehole of length v through the bed gives t = v cos δ. Gentler dips make wider outcrops.

Three-point problem: find the middle elevation on the line joining the highest and lowest points, join it to the middle point to draw the strike line, and then dip = tan⁻¹ (elevation difference / perpendicular distance between strike lines). Structure contours are lines of equal elevation on a bed: with interval h and horizontal spacing d, tan δ = h/d, and the dip direction is perpendicular to them, towards the lower elevation. Example: contours at 100 m and 150 m elevation lying 200 m apart horizontally give δ = tan⁻¹ (50/200) = 14.0°.

6. Stereographic projection, described in words

In stereographic projection orientations are plotted on the lower half of a reference sphere and projected onto a circle, the primitive. A plane plots as a great circle and a line as a point; a vertical plane is a straight line through the centre and a horizontal plane is the primitive itself. The pole of a plane has plunge 90° − dip and trend opposite to the dip direction (dip direction ± 180°). The equal-angle (Wulff) net preserves angles and serves constructions; the equal-area (Schmidt) net preserves areas, so it is used to contour concentrations of poles. Orientations are written as strike/dip (dip to the right of strike) or dip/dip direction.

  • Intersection of two planes is the point where their great circles cross, read as trend and plunge. Two limbs dipping 30° to the west and 30° to the south intersect in a line plunging 22.2° towards the south-west.
  • Apparent dip in a given direction is read where the vertical section line through the centre crosses the plane's great circle. The angle between two lines is measured along the great circle that contains both.
  • A π-diagram plots poles to bedding: for a cylindrical fold they lie on a great circle (the π-girdle) whose pole is the fold axis. A line lying in a plane at pitch (rake) r from the strike has plunge p with sin p = sin δ · sin r, which locates slickenlines on a fault. Rotating about the strike restores tilted beds, as in removing the tilt below an unconformity.
⚠️ Pole versus plane
Pole and plane are different points of view of one orientation. The pole trends opposite to the dip direction and plunges at 90° minus the dip, so a gently dipping plane has a steeply plunging pole near the centre. A plane dipping 30° south, striking east, has its pole at trend 000, plunge 60°.

Key takeaways

  • Throw = s sin δ and heave = s cos δ for pure dip-slip. Normal, reverse and thrust faults differ in hanging-wall motion and dip; dextral and sinistral are judged by looking across the fault. Fault rocks run from breccia and gouge through cataclasite and pseudotachylyte to mylonite.
  • Joints are opening fractures with no shear displacement, parallel to σ1; spacing grows with layer thickness. Origins: tectonic, unloading, cooling (columnar) and desiccation. Plumose structure shows origin and propagation direction.
  • Ductile shear zones have γ = D/w; mylonites grade by matrix percentage and shear sense is read in the XZ section. Thrusts use flats and ramps, form fault-bend folds, imbricate fans and duplexes; erosion leaves klippen and fensters. The Main Central, Main Boundary and Main Frontal Thrusts young southwards.
  • Unconformities are angular, disconformity, paraconformity or nonconformity, each a time gap. Superposed folds show folded foliation or lineation and curved hinges, giving dome-and-basin (Type 1), crescent-mushroom (Type 2) or hook (Type 3) patterns.
  • Map numericals: tan δa = tan δ sin β; t = w sin δ on level ground, w sin(δ ± s) on sloping ground, v cos δ in a vertical borehole; three-point and structure-contour problems give strike and dip from tan δ = h/d. The V of an outcrop points down-dip, except for a bed dipping downstream more gently than the valley floor.
  • Stereonets: planes are great circles and lines are points; the pole has plunge 90° − dip and trend opposite to dip direction. Intersections of great circles give fold axes, π-girdles locate cylindrical fold axes, and sin p = sin δ sin r gives plunge from pitch. Use equal-area nets for contouring.

Practice questions (18)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. A pure dip-slip normal fault dips at 50° and has a net slip of 120 m. Its throw, in metres to one decimal place, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 91.9

    For pure dip-slip, throw = s sin δ = 120 × sin 50° = 120 × 0.7660 = 91.9 m, and the heave is s cos δ = 77.1 m. Using the cosine, which gives the heave, is the usual slip.

  2. A vertical, north–south striking fault cuts a vertical, east–west striking dyke. The part of the dyke east of the fault lies 200 m north of the part west of the fault. The sense of slip on the fault is:

    1. dextral (right-lateral), because the eastern block has moved northwards, which is towards the top of the map and so to the right
    2. normal dip-slip, because the dyke has a different position on the two sides of the fault
    3. sinistral (left-lateral), because looking across the fault from either side the far block has moved to the left
    4. reverse dip-slip, because the offset of a vertical marker always indicates that one block has been raised
    Show answer

    Answer: C — sinistral (left-lateral), because looking across the fault from either side the far block has moved to the left

    Standing on the west block and looking east, the far (east) block has moved north, which is to the left, so the fault is sinistral; standing on the east block and looking west, the far block has moved south, again to the left. The sense is the same from both sides. Dextral is the tempting answer if north on the map is mistaken for right, and a horizontal offset of a vertical dyke by a vertical fault is strike-slip, not dip-slip.

  3. Which of the following statements about joints are correct?

    1. Plumose structure, a feathery pattern radiating from a point, shows where a joint began and the direction in which it spread
    2. Columnar joints in a basalt flow form perpendicular to the cooling surface of the flow
    3. A joint is defined by a measurable shear displacement of the rock on either side, parallel to its surface
    4. Sheeting joints parallel to the ground surface form as erosion removes the overlying rock and unloads the rock below
    Show answer

    Answer: A — Plumose structure, a feathery pattern radiating from a point, shows where a joint began and the direction in which it spread; B — Columnar joints in a basalt flow form perpendicular to the cooling surface of the flow; D — Sheeting joints parallel to the ground surface form as erosion removes the overlying rock and unloads the rock below

    Plumose structure records the origin and direction of propagation, columnar joints grow perpendicular to the cooling surface, and sheeting joints form by unloading, so those three are correct. A joint shows opening but no shear displacement; a fracture with shear displacement is a fault, so the statement that defines a joint by shear displacement is wrong.

  4. In a sandstone sequence under one uniform tectonic stress, a 0.2 m bed and a 2 m bed are both jointed by strata-bound joints. How do the joint spacings compare?

    1. They are the same, because the spacing is set by the stress and not by the thickness of the bed
    2. The spacing is smaller in the thicker bed, because a thick bed stores more strain energy that is released by more fractures
    3. The spacing in the 2 m bed cannot be compared with the thin bed, because only a bed of the same thickness has comparable joints
    4. The spacing is larger in the thicker bed, because joint spacing increases with the thickness of the mechanical layer
    Show answer

    Answer: D — The spacing is larger in the thicker bed, because joint spacing increases with the thickness of the mechanical layer

    Joint spacing scales with the thickness of the mechanical layer, so the 2 m bed has much wider spacing than the 0.2 m bed. Stress alone does not set the spacing, which is why the equal-spacing answer is wrong, and a thick bed carries its load over a longer distance between fractures, not shorter.

  5. A ductile shear zone of uniform width 120 m accommodates a total displacement of 1.8 km across it, distributed uniformly. The average shear strain γ across the zone is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 15

    The average shear strain is displacement divided by width, γ = D/w, with both in the same unit: 1800 m / 120 m = 15. Forgetting to convert 1.8 km to 1800 m gives 0.015, which is the usual slip.

  6. Which section of a mylonite is the best one in which to determine the sense of shear from S–C fabrics and asymmetric porphyroclasts?

    1. A section parallel to the stretching lineation and perpendicular to the foliation (the XZ section)
    2. A section perpendicular to the stretching lineation and perpendicular to the foliation (the YZ section)
    3. A section parallel to the foliation itself, looking down on the foliation surface (the XY section)
    4. Any section, because the asymmetry of the fabrics is the same in all orientations through the rock
    Show answer

    Answer: A — A section parallel to the stretching lineation and perpendicular to the foliation (the XZ section)

    The shear direction lies parallel to the stretching lineation (X) and perpendicular to the foliation (Z), so the clearest asymmetry is in the XZ section. In the YZ section, perpendicular to the lineation, the fabrics look nearly symmetric, and a foliation-parallel view cannot show the rotation of S towards C. The asymmetry is not the same in all sections.

  7. Which sequence lists the principal Himalayan thrusts from north (older) to south (younger)?

    1. Main Frontal Thrust, Main Boundary Thrust, Main Central Thrust
    2. Main Central Thrust, Main Boundary Thrust, Main Frontal Thrust
    3. Main Boundary Thrust, Main Central Thrust, Main Frontal Thrust
    4. Main Central Thrust, Main Frontal Thrust, Main Boundary Thrust
    Show answer

    Answer: B — Main Central Thrust, Main Boundary Thrust, Main Frontal Thrust

    The Himalayan thrusts propagated southwards towards the foreland, so from north to south they are the Main Central Thrust (oldest), the Main Boundary Thrust and the Main Frontal Thrust (youngest). The reverse order places the youngest structure in the hinterland, which contradicts in-sequence piggyback thrusting.

  8. Two sets of upright folds with horizontal axes, one set perpendicular to the other, refold the same layers. The resulting outcrop pattern is:

    1. a dome-and-basin interference pattern, with closed outcrops of alternating domes and basins
    2. a hook-shaped pattern, which arises only when the two fold sets have roughly parallel axes
    3. straight, parallel outcrops, because the second set simply tilts the layers uniformly
    4. a single closed elliptical outcrop, because the two sets merge into one fold
    Show answer

    Answer: A — a dome-and-basin interference pattern, with closed outcrops of alternating domes and basins

    Orthogonal upright fold sets give Ramsay's Type 1, the dome-and-basin pattern, in which closed domes and basins alternate. The hook pattern (Type 3) belongs to coaxial refolding, with roughly parallel axes, which is the tempting alternative. Straight outcrops would need only one fold set, and two sets cannot merge into one closed elliptical fold.

  9. Which of the following are evidence that rocks have been affected by superposed (refolded) folding?

    1. A slaty cleavage that is itself crenulated and folded by later folds
    2. A lineation whose trend and plunge vary systematically around later folds
    3. A single set of folds with parallel hinges of the same trend and plunge across the whole area
    4. Closed dome-and-basin or hook-shaped outcrop patterns of the layering
    Show answer

    Answer: A — A slaty cleavage that is itself crenulated and folded by later folds; B — A lineation whose trend and plunge vary systematically around later folds; D — Closed dome-and-basin or hook-shaped outcrop patterns of the layering

    A folded earlier foliation, a lineation that is itself bent around later folds, and interference outcrop patterns (domes and basins, hooks) are the standard evidence for two fold generations. A single set of parallel, uniformly plunging hinges is what one generation of cylindrical folds looks like and so gives no sign of refolding.

  10. Two sedimentary sequences lie parallel to one another across a surface that shows no erosion or weathering, yet the fossil zones of a whole stage are missing between them. The surface is a:

    1. disconformity, because any time gap between parallel beds must be marked by an irregular surface cut by channels
    2. angular unconformity, because a missing fossil zone is only possible if the older beds were tilted before burial
    3. nonconformity, because the missing stage implies that the younger beds rest on crystalline basement
    4. paraconformity, because the beds are parallel and the gap is shown by the missing fossil zones alone
    Show answer

    Answer: D — paraconformity, because the beds are parallel and the gap is shown by the missing fossil zones alone

    A paraconformity separates parallel beds with no visible erosion, and the time gap is detected only from fossil zones. A disconformity needs an erosion surface, which the stem rules out, an angular unconformity needs tilted older beds, and a nonconformity needs igneous or metamorphic rock below the sediments.

  11. A bed has a true dip of 40°. A cliff face is cut along a direction making an angle of 30° with the strike of the bed. The apparent dip of the bed on the cliff face, in degrees to one decimal place, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 22.8

    tan δa = tan δ × sin β = tan 40° × sin 30° = 0.8391 × 0.5 = 0.4195, so δa = 22.8°. Taking the angle from the dip direction instead of from the strike, which swaps sine for cosine, would give a larger value of 36.0°.

  12. A bed dips 30° towards the east. On ground that slopes 10° down towards the west, that is against the dip, the outcrop width measured along the ground surface, perpendicular to strike, is 150 m. The true thickness of the bed, in metres to one decimal place, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 96.4

    With the ground sloping against the dip, the angle between the ground surface and the bedding is δ + s = 30° + 10° = 40°, so t = w sin 40° = 150 × 0.6428 = 96.4 m. Using δ − s (20°) is the slip for ground sloping with the dip and would give 51.3 m; using δ alone gives 75 m.

  13. Three boreholes meet the top of a bed at points given as (east, north) in metres from borehole A: A (0, 0) at elevation 300 m, B (0, −400) at elevation 100 m and C (300, −200) at elevation 100 m. Treating the bed top as a plane, its dip, to the nearest degree, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 31

    B and C are both at 100 m, so the line BC is a strike line. Its length vector is (300, 200), of length 360.6 m, and the perpendicular distance from A to it is |300 × 400 − 200 × 0| / 360.6 = 332.8 m. A is 200 m higher, so tan δ = 200 / 332.8 = 0.601 and δ = 31°. Using the straight distance from A to B (400 m) instead of the perpendicular distance gives 27°, the usual slip.

  14. A stream flows towards the south down a valley with a gradient of 2°. A bed that crops out across the valley dips 20° towards the north, that is upstream. How does the outcrop trace cross the valley floor?

    1. As a V pointing downstream (south), because outcrop V's always point in the direction of stream flow
    2. As a V pointing upstream (north), in the direction in which the bed dips
    3. As a straight line across the valley, because only vertical beds have outcrops that ignore the topography
    4. As a line that follows the topographic contours around the valley, as horizontal beds do
    Show answer

    Answer: B — As a V pointing upstream (north), in the direction in which the bed dips

    The valley floor rises northwards while the bed sinks northwards, so the bed meets the floor farther up the valley than it meets the valley sides: the V points upstream (north), which is also the dip direction. The 'always downstream' rule is the tempting error. A straight trace would need a vertical bed, and a contour-following trace would need a horizontal bed, but this bed dips at 20°.

  15. On a geological map the youngest unit forms a U-shaped outcrop that closes towards the north, and beds on both limbs dip towards the fold axis. The fold is:

    1. an anticline plunging north, because outcrops of a plunging fold always close in the direction of the plunge
    2. an anticline plunging south, because the closure points against the plunge in every plunging fold
    3. a syncline plunging north, because younger rocks in the core and a northward closure require a northward plunge
    4. a syncline plunging south, because a plunging syncline closes against the direction of its plunge
    Show answer

    Answer: D — a syncline plunging south, because a plunging syncline closes against the direction of its plunge

    Youngest rocks in the core with dips towards the axis make a syncline. A plunging syncline closes against its plunge (an anticline closes in the direction of plunge), so a closure to the north means a plunge to the south. The anticline options fail on the age and dip evidence, and the north-plunging syncline reverses the closure rule.

  16. Two fold limbs are planar. One dips 40° towards the east and the other dips 40° towards the south. The plunge of their line of intersection, the fold axis, in degrees to one decimal place, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 30.7

    Take x east, y north and z up. The east-dipping plane is z = −x tan 40° and the south-dipping plane is z = y tan 40°, so on their intersection y = −x and the line runs towards the south-east with horizontal run √2 |x| for a drop of |x| tan 40°. Hence tan p = tan 40° / √2 = 0.8391 / 1.4142 = 0.5933 and p = 30.7°. Taking p = 40° (the dip of either limb) is the usual slip.

  17. A plane strikes 045° and dips 50° to the south-east. On a lower-hemisphere stereonet, its pole plots at (trend / plunge):

    1. 315° / 40°
    2. 135° / 50°
    3. 315° / 50°
    4. 135° / 40°
    Show answer

    Answer: A — 315° / 40°

    The dip direction is 135° (south-east), so the pole trends opposite to it, at 135° + 180° = 315°, and plunges 90° − 50° = 40°. The value 135° / 50° is the plane's own dip direction and dip, not its pole, and 315° / 50° and 135° / 40° each mix one correct number with one incorrect number.

  18. Which of the following statements about stereographic projection are correct?

    1. The equal-area net is the appropriate net for contouring the concentration of poles
    2. For a cylindrical fold the poles to bedding lie on a great circle whose own pole is the fold axis
    3. The pole to a horizontal plane plots on the primitive circle, at the edge of the net
    4. The equal-angle net preserves areas, so counts per unit area on it are unbiased
    Show answer

    Answer: A — The equal-area net is the appropriate net for contouring the concentration of poles; B — For a cylindrical fold the poles to bedding lie on a great circle whose own pole is the fold axis

    Contouring needs an area-preserving net, and the π-diagram of a cylindrical fold puts bedding poles on a great circle whose pole is the fold axis. The pole to a horizontal plane is vertical, so it plots at the centre of the net, not on the primitive; and it is the equal-area net, not the equal-angle net, that preserves areas.