geology · structural
Rose Diagram (Azimuth Distribution)
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Inputs
Paste one row per line — separate columns with a comma or tab: Azimuth (°), Weight (—)
⚠ Needs at least 3 valid rows to calculate — 0 so far.
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°
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Description
Builds a rose diagram — a circular histogram of strike, dip-direction, fracture/joint-trend, or paleocurrent azimuth measurements — from a pasted list of 0-360° azimuth values, each with an optional weight (e.g. exposure length, grain area, or measurement confidence). Supports both the Unidirectional (paleocurrent) convention, where each measurement plots as a single petal, and the Bidirectional/Mirrored (structural/fracture/joint) convention, where each measurement also plots its supplementary +180° direction since a strike or joint line has no inherent polarity. Reports the mean vector azimuth and vector strength (R, the mean resultant length, 0-1) alongside the diagram, using the same sine/cosine-summation circular-statistics method used throughout structural geology and sedimentology for directional data.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Petals | — | Binned Petal Frequencies |
| θ | ° | Mean Vector Azimuth |
| R | — | Vector Strength (Mean Resultant Length) |
| α | — | One row per measurement: a strike, dip-direction, fracture/joint trend, or paleocurrent azimuth in degrees (0-360, compass convention), and an optional weight (e.g. exposure length, grain area, or measurement confidence) — leave the weight cell blank, or leave off the whole second column, for a weight of 1 (every measurement counts equally, today's default behavior). Azimuth values are auto-normalized modulo 360, so a stray negative value or one slightly over 360 is still handled rather than rejected outright. A weight of 0 means that row is included in the petal counts but excluded from the mean vector/R calculation; a dataset where every weight is 0 cannot produce a meaningful mean vector at all (see this calc's own flags/limitations). |
| Mode | — | 1 = Unidirectional (paleocurrent convention) — each measurement plots as a single petal. 2 = Bidirectional (Mirrored Behaviour, structural/fracture/joint convention) — each measurement also plots its supplementary (+180°) direction, since a strike, joint, or fracture line has no inherent polarity. Per Ortolano et al. (2021), Mode 2 is intended for data spanning <=180° of true angular range; a wider-ranging dataset still renders, but a warning flag is raised. |
| Δα | ° | Angular width of each rose-diagram petal (bin). 10° is the conventional default for most structural/paleocurrent rose diagrams — finer widths show more angular detail but need more measurements per bin to stay statistically meaningful. |
| Scale | — | 0 = Frequency — the radial grid rings show raw measurement counts per petal. 1 = Percentage — the same rings show each petal's share of the total measurement count instead. This is a display-only toggle (a linear rescale by a constant factor); it does not change the petals' relative proportions, the mean vector azimuth/strength, or the sample count, only how the axis rings are labeled. |
Assumptions
- Each pasted azimuth is an independent, already-corrected (e.g. magnetic-declination-corrected) compass measurement in degrees, 0-360, compass convention (0=N, clockwise) — not a raw uncorrected field reading.
- In Bidirectional (Mirrored) mode, the underlying geological feature (strike, joint, fracture) is genuinely non-polar (axial) — a strike line and its reciprocal both describe the same physical trend, which is the entire justification for mirroring.
- Petal width (bin size) is fixed and uniform across the full 360° — an unequal or adaptive binning scheme is not supported.
Limitations
- The weight column has no per-row upper bound beyond its own range (0-1,000,000) — a single extreme outlier weight can dominate the mean vector/R far more than the same measurement would unweighted; this calculator does not detect or flag disproportionately-influential rows.
- The mean vector and R are reported for the dataset as a single population — this calculator does not perform multi-modal clustering (splitting the data into separate families/clusters first, as Ortolano et al.'s M.E.A.D. algorithm does); a visibly multi-modal rose diagram's single mean vector may not usefully represent any individual mode.
- In Bidirectional mode, the <=180°-range check is a straightforward circular-spread heuristic centered on the data's own mean direction, not a rigorous statistical test — it will not catch every case where mirroring is a poor representational choice for markedly multi-modal or highly dispersed data.
Use Cases
- → Fracture/joint-set orientation analysis: Plot a set of fracture or joint strike measurements from an outcrop or borehole image log in Bidirectional mode to identify dominant fracture-set orientations for wellbore stability, hydraulic-fracture-azimuth planning, or natural-fracture reservoir characterization.
- → Paleocurrent direction analysis: Plot cross-bed, ripple, or channel-axis paleocurrent readings in Unidirectional mode to determine a formation's dominant depositional transport direction — a classic sedimentology application of rose diagrams.
Related Calculations
Region Notes
Global
Rose-diagram convention (unidirectional vs. bidirectional/mirrored, petal-width choice) varies by sub-discipline and even by research group — always state which convention was used when presenting a rose diagram alongside other structural or sedimentological data, since a diagram plotted with the wrong convention can visually suggest a bimodal distribution where none exists (or vice versa).
References
Primary source
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