Static Rose Tab

Located at static_analyzer/tabs/static_rose_tab.py, the Rose Plot tab (implemented as the mixin class StaticAnglesTab) renders an equal-area, strike-frequency rose diagram — a polar histogram in which each fracture segment is binned by its trend (strike) azimuth, and the resulting frequency, optionally weighted by segment length, is displayed as a radially scaled petal. Rose diagrams have been a cornerstone visualisation in structural geology for over a century, providing an immediate quantitative impression of preferred fracture orientations, orientation clustering versus dispersion, and the presence of multiple fracture sets. Within FracSTAT, the Rose Plot tab operates purely on the geometric results table produced by the Fracture Map tab and performs no stress resolution, making it a Static Analyzer (geometry-only) tool distinct from the stress-dependent Rose tab found in the Dynamic Analyzer workspace.

1. Interface Overview

The Rose Plot tab uses a two-column layout: a fixed-width (290 px), vertically scrollable settings sidebar on the left, and an expandable polar plot canvas on the right hosting a Matplotlib polar Axes embedded via FigureCanvasTkAgg. The Figure is sized 9 × 7 inches at 100 DPI and hosts one polar Axes (static_rose_ax) plus one dedicated colorbar Axes (static_rose_cbar_ax), whose position and visibility are recomputed on every redraw according to the selected colorbar placement.

Figure 1.1 — Static Analyzer workspace showing the Rose Plot tab selected, with the settings sidebar on the left and the polar plot canvas on the right.

1.1 Sidebar Card Structure

1.2 Plot Canvas and Toolbar

A slim toolbar sits above the polar plot canvas, displaying the descriptive caption "Equal-area strike rose" and a Save Image button. Clicking Save Image invokes the shared save_plot_image() routine common to every Static Analyzer tab, writing a timestamped PNG to the project's FracSTAT_plot_exports/<project_slug> folder at the DPI configured in the application-wide Settings page (default 300 DPI), with a confirmation dialog showing the full output path.

2. Data Input

2.1 Upstream Data Sources

The Rose Plot tab does not implement its own file-loading logic. It reads directly from self.results, the shared results DataFrame maintained by the Static Analyzer workspace, which is refreshed whenever the user loads a new SVG fracture-trace file, a new Excel/CSV orientation table, or changes the profile calibration. The tab automatically reflects any such change without requiring user interaction through the workspace's refresh_all_tabs() chain.

2.2 Required Columns

If StrikeDeg is absent, the tab shows an explanatory empty-state message on the polar Axes. If StrikeDeg is present but every value is non-finite after validity filtering, a separate "No valid strike angles found" message is shown. Both conditions are handled gracefully without exceptions.

2.3 Compatible Upstream Data Sources

All four upstream data formats supported by the Static Analyzer flow into the Rose Plot tab. SVG fracture-trace maps supply strike computed geometrically from the digitised trace endpoints, corrected for the Y-axis-from-North azimuth. Excel/CSV segment-coordinate tables carry pre-computed StrikeDeg values through unchanged. Legacy fracture-plane tables (ID, Strike, Dip) supply Strike directly, with the optional Length column honoured for length weighting. Trend/Plunge pole tables are converted internally to an equivalent Strike/Dip pair before reaching the Rose Plot tab.

3. Settings and Controls, Card by Card

Unless stated otherwise, every control triggers an immediate redraw through _draw_static_rose(). Numeric entry fields commit on both the Enter keypress and loss of focus (FocusOut), matching the convention used throughout FracSTAT's Static Analyzer sidebars.

3.1 Plot Mode Card

3.2 Options Card

3.3 Display Elements Card

3.4 Statistics Card (Read-Only)

The Statistics card is a read-only panel, recomputed on every redraw by _rose_update_stats() from the raw, unbinned observations — not from the discretised histogram — so its values are independent of the chosen Number of bins.

4. Mathematical Background

4.1 Axial (Bidirectional) Orientation Data

Fracture strike is an axial quantity: a fracture trending 040° is geometrically identical to one trending 220°, since both describe the same line in the horizontal plane. Axial data of this kind are 180°-periodic and cannot be treated with ordinary linear statistics (Mardia and Jupp, 2000). The Rose Plot module respects this by folding every strike value into the half-open interval [0°, 180°) prior to any statistical operation:

This folding is applied identically in both the FracSTAT-mode and Classic-mode drawing routines and is a prerequisite for the axial circular-mean formula in Section 6.1.

4.2 Weighting Scheme

Each observation i contributes a weight w_i to its assigned azimuth bin. Two modes are supported:

where L_i is the segment's real-world length (Length_m). When length weighting is requested but Length_m is missing, non-finite, or non-positive for a given row, a fallback weight of 1.0 is substituted for that row rather than discarding it. Length weighting is the recommended default for fracture-trace data, because an unweighted count of traces gives equal influence to a metre-scale joint and to a basin-scale fault and therefore describes the sampling process at least as much as the fracture fabric itself (Sanderson and Peacock, 2020).

4.3 Histogram Binning

Given B bins (clamped to [4, 180]), the bin edges form a uniform partition of the 0°–180° axial domain:

Each observation's folded strike is assigned to exactly one bin via NumPy's weighted histogram (Harris et al., 2020), producing bin totals and midpoints:

The class interval is a genuinely free parameter of the method rather than a cosmetic setting: too few bins smooth out real modes, while too many produce spurious spikes that reflect sampling noise (Wells, 2000). The 10° interval implied by the default B = 18 follows long-standing practice for two-dimensional geological orientation data (Curray, 1956), but it is advisable to inspect two or three bin counts before selecting the figure to publish.

4.4 Equal-Area (Square-Root) Radius Transform

A properly constructed rose diagram requires that the visual area of each petal — not its radial length — be proportional to the quantity it represents. Because the area of a circular sector scales with the square of its radius, FracSTAT computes the plotted radius as the square root of the weighted bin total:

This equal-area convention prevents bins with high raw frequency from visually dominating the diagram disproportionately, and ensures that comparisons of petal area between diagrams are quantitatively meaningful. The argument for the square-root radius was set out explicitly by Nemec (1988), who showed that a linear-radius rose exaggerates the dominant class because the reader's eye integrates sector area rather than sector radius; the same conclusion is reached from a perceptual standpoint by Wells (2000) and is recommended as standard practice by Sanderson and Peacock (2020). FracSTAT applies the transform unconditionally, in both plot modes, so no combination of settings can produce a linear-radius (area-distorting) rose.

4.5 Full-Circle Mirroring

Because strike is axial, a complete rose diagram must display the same frequency distribution twice — once in the 0°–180° half and once, by reflection, in the 180°–360° half. When Half rose is unchecked, the module concatenates bin midpoints and radii with a 180° angular offset:

This produces a visually symmetric diagram about the origin, matching the long-established convention for axial rose diagrams in the structural-geology literature (Curray, 1956). Note that the mirrored half contains no information that is not already in the first half; it is a display convention, and the choice between the full circle and the half rose of Section 3.2 is therefore purely presentational (see the discussion of rose-diagram conventions in Sanderson and Peacock, 2020).

4.6 Colour Mapping (FracSTAT Mode)

In strike colour mode, each petal is coloured according to its bin midpoint using a fixed linear normalisation over the full axial domain, independent of the actual data range:

Using a fixed 0°–180° normalisation (rather than normalising to the observed min/max strike) ensures the same azimuth is always rendered in the same colour across different datasets and sessions — important when visually comparing rose diagrams from multiple outcrops or wells.

4.7 Percentage Reference Circles

When enabled, three dashed reference circles are drawn at radii that are simple fractions of the maximum plotted radius r_max:

Because the plotted radius already embeds the square-root equal-area transform, the fraction of the maximum bin value represented by each circle is the square of the radial fraction:

The three default circles are therefore labelled approximately 11%, 44%, and 100% of the peak weighted bin value, giving a calibrated visual scale for judging petal size without reading exact numbers from an axis. Providing such a scale addresses a specific and frequently made criticism of published rose diagrams — that they are drawn without any indication of the magnitude the petals represent, and so cannot be read quantitatively (Sanderson and Peacock, 2020). Enabling this option, and reporting n in the title, is recommended for any rose diagram intended for publication.

5. Algorithms

5.1 Mode Dispatch

The top-level redraw entry point _draw_static_rose() is a two-way dispatcher that inspects static_rose_mode_var and routes to one of two independent drawing algorithms. If the Style string begins with "Classic", control passes to _draw_classic_rose(); otherwise it passes to _draw_fracSTAT_rose(). Both routines share an identical outer skeleton — clear axes, validate data, compute the weighted histogram, apply the equal-area transform, render petals, format the polar grid, set the title, configure the colorbar, update the statistics panel, and request a canvas redraw — but differ in how petal colour is derived.

5.2 FracSTAT-Mode Rendering Algorithm

5.3 Classic-Mode Rendering Algorithm

The Classic-mode algorithm mirrors steps 1–6 and 8–14 of the table above exactly, but omits the colormap resolution and per-bin colour-array step. Every petal is rendered with the single solid colour held in static_rose_color_var, a 90% opacity, and a petal angular width of 0.92 × the full bin width to leave a visible gap between adjacent petals — a more traditional discretised rose-diagram appearance. Because Classic mode carries no data-dependent colour mapping, the colorbar Axes is always suppressed regardless of the selected Colorbar position, and the polar Axes expands to fill the reclaimed space.

5.4 Shared Polar Grid Formatting

5.5 Colorbar Placement Algorithm

Given the selected Colorbar position, _setup_rose_colorbar() computes two rectangles in Figure-fraction coordinates: one for the colorbar Axes and one for the repositioned polar Axes, so that the polar plot never overlaps the legend. Horizontal placements (Bottom/Top) receive tick marks every 20°; vertical placements (Left/Right) receive tick marks every 30°, reflecting the differing available label space. Selecting "None", or being in Classic mode, hides the colorbar Axes entirely and expands the polar Axes to an enlarged default footprint.

def _pct_reference_circles(ax, max_r, palette, n_circles=3):
    """Draw dashed percentage reference circles on a polar axis."""
    if max_r <= 0:
        return
    theta_ring = np.linspace(0, 2 * np.pi, 361)
    for k in range(1, n_circles + 1):
        r_k = max_r * k / n_circles
        pct = int(round(100.0 * (k / n_circles) ** 2))
        ax.plot(theta_ring, np.full_like(theta_ring, r_k),
                color=palette["spine"], linewidth=0.7, linestyle="--",
                zorder=1, alpha=0.55)
        ax.text(np.deg2rad(180), r_k, f"{pct}%",
                color=palette["muted"], fontsize=8,
                ha="center", va="bottom", zorder=2)

Module-level helper function _pct_reference_circles() defined at module scope outside the class, so it requires no instance state and remains independently testable.

6. Statistical Methods

6.1 Weighted Axial (Circular) Mean

Ordinary arithmetic averaging is invalid for orientation data because of wrap-around discontinuities — for example, the arithmetic mean of 179° and 1° is 90°, which is geometrically nonsensical for near-parallel fractures straddling the 0°/180° boundary. The correct treatment is to average the observations as unit vectors and take the direction of the resultant (Fisher, 1993). For axial (180°-periodic) data such as strike, the standard device is to double each angle before forming the resultant and halve the result afterwards — the doubling transform of Mardia and Jupp (2000, §2.3.2), introduced for two-dimensional geological orientation data by Krumbein (1939) and Curray (1956). FracSTAT implements exactly this in _static_axial_mean(strikes, weights):

Doubling each angle maps the 180°-periodic axial domain onto the standard 360°-periodic circular domain, where conventional vector-resultant averaging is valid; halving the resultant direction maps the answer back onto the physically meaningful 0°–180° range. The mean is always computed from the raw, unbinned observations — not the discretised histogram — so its value is independent of the chosen Number of bins. The same weights w_i defined in Section 4.2 are used, so the reported mean is a length-weighted mean whenever length weighting is active.

6.2 Dominant Bin

The dominant (modal) orientation is reported as the midpoint of whichever histogram bin carries the largest weighted total: argmax_k(V_k). Unlike the axial mean, this statistic is sensitive to the chosen bin count and edge alignment, and should be interpreted as a discretised estimate of the peak of the underlying orientation distribution rather than an exact value. Its resolution is bounded below by the class interval itself, 180°/B — 10° at the default setting — and for a peak that straddles a bin boundary the reported value can jump by one full interval in response to a change of a single bin (Wells, 2000). Where a bin-independent estimate of the modal orientation is required, a kernel-density or parametric-distribution approach on the unbinned angles is appropriate (Fisher, 1993, §2.4); neither is implemented in this tab.

6.3 Summary of Reported Statistics

Total Length is computed over every row of the results table, including rows whose strike was discarded as non-finite, so it reports the total mapped trace length of the dataset rather than the sum of the plotted weights. It is therefore not equal to ΣV_k in general, and does not change with the weighting mode.

7. Visualization & Figure Components

7.1 Polar Petal Bars

Petals are rendered with a single vectorised ax.bar() call in polar coordinates. Bar centre angles equal the (possibly mirrored) bin midpoints in radians; bar heights equal the equal-area radii r_k; bar bottoms are fixed at zero. In FracSTAT mode the bar width equals the full bin angular width so adjacent petals visually abut one another (as in a continuous histogram). In Classic mode a 0.92 width factor introduces a visible inter-petal gap for a more traditional, discretised rose-diagram appearance.

Figure 7.1 — Full-circle FracSTAT-mode rose diagram with a Viridis colormap, bottom colour bar, cardinal labels, and percentage reference circles enabled.

Figure 7.2 — Half-circle Classic-mode rose diagram with a solid blue petal colour and visible inter-petal gaps.

7.2 Colour Legend / Colour Bar

In FracSTAT mode, a ScalarMappable sharing the same colormap and fixed 0°–180° Normalize instance used for the petals is passed to Matplotlib's fig.colorbar(), producing a legend labelled "Segment strike, degrees". Its position (Bottom / Top / Left / Right / None) is fully reconfigurable, and the polar Axes' bounding box is recomputed on every change to avoid overlap. The colour bar is intentionally omitted in Classic mode, since a single solid petal colour carries no scale to legend.

7.3 Cardinal and Angular Labelling

Angular tick marks are placed every 30° around the full or half circle. When cardinal labelling is enabled, the four principal directions are rendered as N / E / S / W in place of 0° / 90° / 180° / 270°, while all remaining ticks continue to show numeric degree values — a hybrid convention familiar from paper-based structural fabric diagrams.

7.4 Reference Circles and Crosshairs

Two independent optional overlays aid quantitative reading of the diagram: the percentage reference circles (Section 4.7), which calibrate petal size against the peak bin value, and the N-S/E-W crosshair spokes, which provide a lightweight visual reference grid without the density of a full polar grid. Both can be enabled or disabled independently via their respective checkboxes in the Options card.

7.5 Empty-State Handling

Three distinct conditions each trigger a dedicated styled empty-state message rendered directly on the polar Axes via _static_rose_empty_state(), rather than an uncaught exception or a blank canvas: no data loaded / StrikeDeg column absent ("Load SVG or Excel fracture data"); all strike values non-finite ("No valid strike angles found"); histogram sum is zero, for example all weights filtered out ("No plottable rose values"). In all three cases the Statistics card fields are reset to a placeholder dash.

8. Step-by-Step Example Workflows

8.1 Example 1 — Quick-Look Orientation Screening

1. Load an SVG trace map (or Excel/CSV) via the workspace header's Load SVG or Load Excel button; the Fracture Map, Rose Plot, and all other tabs populate automatically.
2. Open the Rose Plot tab. With default settings (18 bins, Length weighting, FracSTAT strike-colour mode, full circle) the diagram immediately reveals one or more dominant petal directions.
3. Read the Statistics card: Mean Strike gives the length-weighted average trend; Dominant Bin gives the single most frequent azimuth class, useful for checking whether the mean is being pulled between two conjugate sets.
4. Toggle Show % reference circles to gauge, at a glance, what fraction of the dominant petal's weighted length the secondary petals represent.

8.2 Example 2 — Comparing Count-Based and Length-Weighted Fabrics

Switching Weight petals by from Length to Count on the same loaded dataset can reveal a different dominant orientation. Count weighting treats every fracture equally regardless of length; Length weighting emphasises the orientations carrying the greatest total trace length. Running both modes and comparing the resulting Dominant Bin and Mean Strike values is a standard diagnostic for distinguishing "many small" versus "few large" fracture populations — a meaningful distinction for flow-model permeability anisotropy inputs (Odling, 1997). Because fracture length distributions in rock are typically heavy-tailed, often approximately power-law (Bonnet et al., 2001), a small number of long traces can carry a large fraction of the total length, and the two weighting modes can legitimately identify different dominant sets in the same dataset.

8.3 Example 3 — Publication-Quality Figure Preparation

The steps below assemble a figure that carries the information a reader needs in order to interpret it — sample size, class interval, weighting mode, and a magnitude scale — which is what distinguishes a usable rose diagram from a decorative one (Sanderson and Peacock, 2020; Rougier et al., 2014).

1. Set Colorbar position to "Bottom" and choose a colour-blind-friendly colormap such as Viridis or Cividis (see Section 4.6).
2. Disable Show grid lines for a cleaner appearance, but enable Show cardinal labels and Show % reference circles for quantitative legibility.
3. Enter a descriptive Custom title (e.g., "Joint set orientations, Outcrop A, n = 214"). Note that a custom title replaces the automatic one, which is where n would otherwise appear — so include n in the text you type.
4. Increase Border Width slightly (e.g., to 1.4) for improved visibility at reduced print size.
5. State the bin count and the weighting mode in the figure caption; neither is rendered on the plot itself.
6. Click Save Image to export a high-resolution PNG to the project's plot-exports folder.

Figure 8.1 — Example workflow: Half-circle rose diagram prepared for publication with Cividis colormap, bottom colour bar, and percentage reference circles enabled.

9. Geological Interpretation

9.1 Reading a Rose Diagram

A single sharply peaked petal (or symmetric petal pair in the full-circle presentation) indicates a strongly unimodal fracture fabric, consistent with a single dominant regional stress orientation acting during fracture formation — such as joints formed perpendicular to a uniaxial extension direction or systematic joints related to a single tectonic episode. Two petals separated by an acute angle (commonly 40°–70°) are the classic signature of a conjugate shear-fracture pair, and their angular bisector approximates the orientation of the maximum principal compressive stress (σ₁) at the time of formation (Anderson, 1951), following the Andersonian/Coulomb faulting framework used in FracSTAT's Dynamic Analyzer. Multiple broadly distributed petals of comparable magnitude suggest a polymodal or polyphase fracture history.

9.2 Significance of Length Weighting

Length-weighted rose diagrams better represent the orientation distribution of throughgoing, hydraulically or mechanically significant fractures, since long fractures typically dominate bulk rock-mass permeability and mechanical anisotropy (Odling, 1997). Count-based diagrams better represent the orientation distribution of fracture initiation events and can be more sensitive to sampling bias toward short, easily digitised features. The two diagrams together provide a complementary picture of the fracture population, and reporting both is recommended practice (Sanderson and Peacock, 2020).

9.3 The Mean Strike as a Design Parameter

The reported Mean Strike is frequently used as an input for downstream engineering workflows — for example, orienting a horizontal wellbore trajectory to intersect the dominant fracture set at a favourable angle for stimulation, or orienting a slope-stability kinematic analysis with respect to the governing discontinuity set (Priest, 1993). Because the statistic uses the doubled-angle axial-mean method, it remains geometrically valid even when the underlying distribution straddles the 0°/180° boundary — a common pitfall when analysts instead average raw azimuths arithmetically (Mardia and Jupp, 2000). It remains a summary of a single mode, however, and the caution in Section 6.1 applies before the value is carried into a design calculation.

9.4 Caution Regarding Sampling Bias

As with any orientation-frequency analysis derived from a two-dimensional trace map or outcrop pavement, the rose diagram is subject to orientation sampling bias: fractures whose strike is sub-parallel to a linear exposure, scanline, or window edge are systematically under-sampled relative to fractures oriented perpendicular to it. The standard correction is the weighting scheme of Terzaghi (1965), in which each observation is weighted by the reciprocal of the sine of the angle between the fracture and the sampling line or surface; censoring of long traces at the boundaries of a finite window biases length-weighted diagrams in addition (Priest and Hudson, 1981; Mauldon, 1998).

10. Performance Optimization

10.1 Vectorised Histogram and Colour Computation

All per-observation operations — modulo folding, weight resolution, and the weighted histogram itself — are performed with NumPy array operations (np.histogram, boolean masking, np.where) rather than per-row Python loops (Harris et al., 2020), giving effectively linear-time performance in the number of fracture segments, which routinely numbers in the thousands to tens of thousands for digitised trace maps.

10.2 Colormap Resolution Caching

Resolving a user-facing colormap display name (e.g. "Red-Yellow-Blue") to its underlying Matplotlib identifier ("RdYlBu") is performed once inside _on_rose_cmap_change() and the result is cached in the instance attribute static_rose_cmap_resolved. Subsequent redraws triggered by unrelated setting changes read the cached identifier directly rather than re-resolving the dropdown's display string on every frame.

10.3 Idle-Draw Scheduling

The canvas is repainted via FigureCanvasTkAgg.draw_idle() rather than the blocking draw(), deferring pixel-level rendering to the next Qt idle cycle. This keeps rapid successive setting changes (e.g. dragging through bin-count values or a fast sequence of colour-picker changes) from stalling the UI thread with redundant full redraws.

10.4 Shared Geometry Computation

Because the Rose Plot tab performs no independent geometry recomputation — it consumes the DataFrame already computed once by the Fracture Map tab's geometry engine — reloading data or changing the profile scale triggers only a single shared O(n) geometry pass, not a duplicated per-tab recalculation. The Rose Plot tab's own per-redraw cost is limited to the histogram, colour-mapping, and rendering steps.

11. Advanced Features

11.1 Colormap Library

The Colormap dropdown draws from the same 25-entry, application-wide colour-scale catalogue used throughout FracSTAT, spanning perceptually uniform scientific colormaps (Viridis, Plasma, Inferno, Magma, Cividis), classic scales (Turbo, Jet, Parula — a bundled MATLAB-style approximation), diverging scales (Coolwarm, Spectral, Red-Yellow-Blue), cyclic scales (HSV, Twilight, Rainbow (cyclic)) well suited to angular data, and several thematic/sequential scales (Hot, Ocean, Terrain, Earth, and others). For the reasons set out in Section 4.6, the perceptually uniform and cyclic families are preferable for quantitative figures, and the classic non-uniform rainbow scales are best reserved for exploratory work (Crameri et al., 2020).

11.2 Half-Circle vs Full-Circle Presentation

The Half rose toggle allows analysts to choose between the compact 0°–180° semicircular presentation (useful when screen or print space is limited, or when comparing several diagrams side-by-side) and the traditional full-circle mirrored presentation expected in most published structural-geology figures. Both modes use identical statistical inputs; only the angular display range and the mirroring of bins differ.

11.3 Dynamic Colorbar Repositioning

Selecting a new Colorbar position does not merely relocate the legend graphic; the polar Axes' own position rectangle is simultaneously recalculated via _setup_rose_colorbar() so that the two never overlap and the plot remains centred and appropriately sized — Bottom/Top placements reserve a horizontal strip and shrink the plot's vertical extent, while Left/Right placements reserve a vertical strip and shrink its horizontal extent.

11.4 No "Reset to Defaults" Button

Unlike the Dynamic Analyzer's Rose tab, the Static Rose tab does not provide a "Reset to Defaults" button. To restore a control to its factory value, set it manually using the defaults listed in the tables of Section 3.

11.5 Relationship to the Dynamic Analyzer's Rose Tab

A structurally analogous but functionally distinct Rose tab exists in the Dynamic Analyzer workspace (dynamic_rose_tab.py). That implementation supports colouring petals by a resolved stress attribute (slip tendency, dilation tendency, fracture susceptibility, or critical-stress state) rather than by strike itself, and additionally supports overlaying the σ₁ azimuth as a reference line. Those attributes derive from resolving a stress tensor onto each fracture plane, in the slip- and dilation-tendency framework of Morris et al. (1996) and Ferrill et al. (1999). The two modules share the equal-area square-root radius convention and the general polar-histogram construction, but the Static Rose tab documented here performs no stress resolution and requires no stress-tensor input.

12. Limitations

13. References

Sources are listed alphabetically. In-text citations throughout this page link to the corresponding entry below; the reference list is self-contained, so this page can be cited or printed independently of the rest of the documentation.

13.1 Rose Diagrams and Orientation Statistics

• Curray, J. R. (1956). The analysis of two-dimensional orientation data. The Journal of Geology, 64(2), 117–131. https://doi.org/10.1086/626329
• Fisher, N. I. (1993). Statistical Analysis of Circular Data. Cambridge University Press. https://doi.org/10.1017/CBO9780511564345
• Krumbein, W. C. (1939). Preferred orientation of pebbles in sedimentary deposits. The Journal of Geology, 47(7), 673–706. https://doi.org/10.1086/624827
• Mardia, K. V., & Jupp, P. E. (2000). Directional Statistics. John Wiley & Sons. https://doi.org/10.1002/9780470316979
• Nemec, W. (1988). The shape of the rose. Sedimentary Geology, 59(1–2), 149–152. https://doi.org/10.1016/0037-0738(88)90105-4
• Sanderson, D. J., & Peacock, D. C. P. (2020). Making rose diagrams fit-for-purpose. Earth-Science Reviews, 201, 103055. https://doi.org/10.1016/j.earscirev.2019.103055
• Wells, N. A. (2000). Are there better alternatives to standard rose diagrams? Journal of Sedimentary Research, 70(1), 37–46. https://doi.org/10.1306/2DC408FC-0E47-11D7-8643000102C1865D

13.2 Fracture Sampling, Geometry, and Interpretation

• Anderson, E. M. (1951). The Dynamics of Faulting and Dyke Formation with Applications to Britain (2nd ed.). Oliver and Boyd, Edinburgh.
• Bonnet, E., Bour, O., Odling, N. E., Davy, P., Main, I., Cowie, P., & Berkowitz, B. (2001). Scaling of fracture systems in geological media. Reviews of Geophysics, 39(3), 347–383. https://doi.org/10.1029/1999RG000074
• Ferrill, D. A., Winterle, J., Wittmeyer, G., Sims, D., Colton, S., Armstrong, A., & Morris, A. P. (1999). Stressed rock strains groundwater at Yucca Mountain, Nevada. GSA Today, 9(5), 1–8.
• Mauldon, M. (1998). Estimating mean fracture trace length and density from observations in convex windows. Rock Mechanics and Rock Engineering, 31(4), 201–216. https://doi.org/10.1007/s006030050021
• Morris, A., Ferrill, D. A., & Henderson, D. B. (1996). Slip-tendency analysis and fault reactivation. Geology, 24(3), 275–278. https://doi.org/10.1130/0091-7613(1996)024<0275:STAAFR>2.3.CO;2
• Odling, N. E. (1997). Scaling and connectivity of joint systems in sandstones from western Norway. Journal of Structural Geology, 19(10), 1257–1271. https://doi.org/10.1016/S0191-8141(97)00041-2
• Peacock, D. C. P., Nixon, C. W., Rotevatn, A., Sanderson, D. J., & Zuluaga, L. F. (2016). Glossary of fault and other fracture networks. Journal of Structural Geology, 92, 12–29. https://doi.org/10.1016/j.jsg.2016.09.008
• Priest, S. D. (1993). Discontinuity Analysis for Rock Engineering. Chapman & Hall, London. https://doi.org/10.1007/978-94-011-1498-1
• Priest, S. D., & Hudson, J. A. (1981). Estimation of discontinuity spacing and trace length using scanline surveys. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 18(3), 183–197. https://doi.org/10.1016/0148-9062(81)90973-6
• Terzaghi, R. D. (1965). Sources of error in joint surveys. Géotechnique, 15(3), 287–304. https://doi.org/10.1680/geot.1965.15.3.287

13.3 Scientific Visualization and Software

• Borland, D., & Taylor, R. M. (2007). Rainbow color map (still) considered harmful. IEEE Computer Graphics and Applications, 27(2), 14–17. https://doi.org/10.1109/MCG.2007.323435
• Crameri, F., Shephard, G. E., & Heron, P. J. (2020). The misuse of colour in science communication. Nature Communications, 11, 5444. https://doi.org/10.1038/s41467-020-19160-7
• Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., … Oliphant, T. E. (2020). Array programming with NumPy. Nature, 585(7825), 357–362. https://doi.org/10.1038/s41586-020-2649-2
• Hunter, J. D. (2007). Matplotlib: A 2D graphics environment. Computing in Science & Engineering, 9(3), 90–95. https://doi.org/10.1109/MCSE.2007.55
• Rougier, N. P., Droettboom, M., & Bourne, P. E. (2014). Ten simple rules for better figures. PLoS Computational Biology, 10(9), e1003833. https://doi.org/10.1371/journal.pcbi.1003833