How to Read a Stereonet

Imagine a plane — a bedding surface, a joint, a fault — passing through the centre of a hollow sphere. It intersects the sphere in a circle, and because the top half of that circle mirrors the bottom half, nothing is lost by discarding one. Geologists keep the lower hemisphere, leaving a half-circle of intersection on the inside of a bowl.

The stereonet is that bowl viewed from directly above, every point projected onto the flat disc you are looking at. A plane becomes an arc across the disc: a great circle. A line — a fold axis, a lineation, a borehole trajectory — pierces the hemisphere at one spot, so it becomes a single point.

Two rules follow, and they are what make a net readable at a glance. North is at the top and azimuths increase clockwise, exactly as on a map. And the centre of the disc is vertical, the rim is horizontal: a horizontal plane projects to the rim, a vertical plane to a straight line through the centre. So a shallow plane plots as a lazy arc hugging the rim and a steep one as a tight arc near the centre — and once that is internalised you can estimate a dip to within about five degrees by eye.

There are two ways to do the projection, and they are not interchangeable. They look almost identical at a glance, which is precisely the problem.

The equal-area net — the Schmidt net, or Lambert azimuthal equal-area projection — distorts shapes but preserves area. A patch covering 1% of the hemisphere covers 1% of the disc wherever it sits, so point density on the plot is a true measure of point density on the sphere. That is the only condition under which contouring, mean orientations and "which joint set is dominant" mean anything.

The equal-angle net, the Wulff net or stereographic projection, preserves angles instead. Circles on the sphere stay circles on paper, which makes hand constructions with a compass straightforward and is why crystallographers use it. The cost is that area is stretched towards the rim, so a cluster near the edge looks more spread out than the same cluster near the centre.

The most literal way to plot a plane is as its great circle. Below are 50 measurements from a folded sequence: 25 bedding planes, two steep joint sets, and 10 intersection lineations as points.

Read individual planes off this and it works well. A strike and dip pair fixes one arc: its two endpoints on the rim give the strike line, and its closest approach to the centre gives the dip. Intersections are just as direct — the point where two great circles cross is their line of intersection, which is how you get the trend and plunge of a fold hinge from two limbs, or of a wedge from two joint sets in a slope stability analysis.

What great circles do badly is population. There are 40 planes on that figure, and the bedding arcs cross so many times that no statistical impression survives. Beyond roughly ten planes a great-circle plot stops being a dataset and becomes a scribble.

The fix is to plot each plane not as its trace but as its pole — the line perpendicular to it, which pierces the lower hemisphere at one point. A pole carries the same information as its great circle in one dot, and the geometry inverts in a way that takes getting used to: a shallow plane has a steep pole and plots near the centre, while a vertical plane has a horizontal pole and plots on the rim.

Here is the identical dataset as poles, with density contours underneath.

Everything the great-circle plot buried is now legible. Two joint sets are two spots; the bedding poles trace a band; and the ten lineations sit in a cluster whose mean vector is 040/25 — the same orientation, to the degree, as the fold axis recovered from the bedding poles. That agreement between two independent measurements is what a net shows you and a table does not.

Past about fifty poles even the dots overlap, and the eye is a poor judge of which of two clumps is denser. Contouring answers that properly: a counting circle of fixed area is swept across the net, the poles inside it counted at each position, and the resulting surface contoured.

The standard method is Kamb contouring, and its virtue is that it sizes the counting circle from the sample size rather than from habit. The circle is chosen so that a uniform distribution of n points would put a set number inside it, and contours are labelled in units of σ above what a uniform distribution would give — so a 2σ contour encloses density two standard deviations above random. On the figure above, 40 poles give a 35.3° counting circle, an expected count of 7.3 ± 2.45, and a peak 5.6σ above uniform: a real cluster, not a lucky pile.

The older 1% area method counts within a circle covering 1% of the hemisphere instead. It is serviceable, but its circle is a fixed size regardless of n, so it over-smooths small datasets and under-smooths large ones.

Three arrangements cover most of what you will see, and each one is a geological statement.

The eigenvalue statistics printed under a net put numbers on that impression. Three eigenvalues S₁ ≥ S₂ ≥ S₃ summing to 1 describe the shape of the point cloud: one large value and two small ones is a cluster, two comparable values and one near zero is a girdle. Woodcock's K condenses that into a single number — above 1 is cluster-like, below 1 is girdle-like. The bedding above scores K = 0.01 with eigenvalues 0.52 / 0.48 / 0, about as pure a girdle as field data produces; joint set J2 scores K = 22.2, an unambiguous cluster.