Structural domains: when to pool orientation data

A mean direction, a concentration, a confidence cone: none of them mean anything if the data came from two rock volumes that were deformed differently. Turner and Weiss made identifying homogeneous structural domains the first operation of structural analysis for exactly this reason, and it is the step most often skipped.

Skipping it is easy because nothing goes wrong visibly. Pooled data produce a perfectly well formed mean with a reassuringly narrow confidence interval. The number is simply about nothing. This dataset is large enough and spread widely enough to make that failure obvious.

One park, two hundred kilometres

The National Park Service compiled eight U.S. Geological Survey quadrangle maps by Billingsley and co-authors, published between 2000 and 2013, into one geodatabase for Grand Canyon. Pull out the joints and you get 1,042 of them, every one recorded as vertical, spread over roughly 217 kilometres east to west and 123 north to south.

Nobody would consciously assume a single fracture population spans that distance. The assumption gets made anyway, every time a file is loaded and a mean computed.

The pooled answer is no answer

Plot all 1,042 strikes on one rose and the mean resultant length comes out at 0.10. For practical purposes that is indistinguishable from a uniform distribution. Read literally, the Grand Canyon has no preferred joint orientation.

Set detection does slightly better and fails more informatively. It finds two broad modes, near 067° and 153°, but leaves 368 measurements, 35 per cent of the dataset, in no set at all. That fraction is the diagnostic. A two-set model that cannot account for more than a third of the data is not a description of a fracture network. It is what is left when several networks are averaged together.

Cutting domains by hand

The traditional fix is to draw domains on the map and analyse each one separately, and drawing them by eye is a perfectly respectable method. The domains you can defend are the ones that correspond to something on the ground, a fault block, a monocline, a change of structural style, and the map is where that correspondence is visible. A stereonet cannot show it to you.

Lasso a cluster of stations on the map and turn the selection into its own analysis set. Repeat for each cluster you can justify. Three to five domains is enough for a first pass.

Then open a rose for each domain and compare them side by side. One caution if you do this: do not link the panes together. Linked views share which data is checked, which is precisely what you do not want when the whole point is to show two domains at once. Copy the plot settings between them instead, so the styling matches while the data does not.

What domaining recovers

This dataset carries the source quadrangle on every record, which gives a ready-made partition to check the hand-drawn one against. Running the same detection inside each sheet separately produces a very different picture from the pooled one.

Two things change at once. The unassigned fraction drops from 35 per cent to somewhere between 3 and 24, and the set azimuths move: the north-easterly set ranges over more than fifty degrees between domains and the north-westerly set over more than forty. The pooled two-set model is an average of all of these, and it describes no domain in particular.

The obvious objection

An alert reader should push back here. Those eight domains coincide exactly with eight separately published maps, by different author teams, thirteen years apart at the extremes, at two different scales. A difference between maps need not be a difference between rock volumes. It may just record which fractures each mapper thought worth drawing.

The objection is a good one, and the dataset can answer it. Take the largest sheet on its own, where author, scale and publication year are all constant, and cut it into three latitude bands.

The southern third of that single sheet carries a north-south set holding 62 joints that the sheet-wide model does not contain at all, and a three-set model accounts for 92 per cent of it. Same mapper, same scale, same year. Whatever else is going on, the variation is not only cartographic.

Cutting the park into longitude thirds and ignoring the map boundaries entirely points the same way: two sets in the west, two rather different ones in the centre, and three in the east.

How to report this

The output of a domain analysis is not a mean. It is a domain map, a set model for each domain, and a plain statement of what was pooled and what was not. Three habits make that reportable, and none of them costs anything.

Publish the detection parameters. Every model above used the same smoothing, minimum separation and window width, and a set model quoted without them cannot be reproduced. Publish the unassigned fraction, which is the cheapest available measure of whether the model fits and the number that moved most in this analysis. And distinguish geological boundaries from procedural ones: where your domains coincide with map sheets, survey campaigns or operators, say so, and test inside one of them before you claim a structural boundary. Compiled datasets, which is what most open orientation data are, carry the history of their own compilation.

None of this establishes what the sets mean in the Grand Canyon. That needs field measurement, cross-cutting relations and an argument about timing. What it settles is the prior question of whether the 1,042 measurements may be treated as one population. They may not, and you can see that in a single number before any interpretation starts.

Data and sources

The extract is a single CSV of 1,042 records with strike, dip, latitude, longitude, mapped unit, geologic period, source quadrangle and publication scale. It imports into Stereogram Pro with the quadrangle carried through as a category you can group and filter by.