Rockfall Inventory

Rockfall Inventory turns the change between two scans (epochs) of a slope into a list of rockfall events. Each event is a patch of significant change, with its area, volume and depth. It also fits the events' magnitude–frequency, and gives rates when you say how far apart the scans are.

Running it

1. Register the epochs. Bring the later scan onto the earlier one (or both onto a reference) with ICP; the change you measure can be no better than the registration.
2. Compare them. On one scan's menu run M3C2 against the other. This writes its M3C2 distance and M3C2 LoD95 layers (Lague et al. 2013): the change along the local surface normal, and the 95% level of detection at each point.
3. Inventory. On the same scan choose Attributes & Analysis → Rockfall Inventory... and fill in the dialog. Open a report first to get the event list and the plot in it.

Field	Description
M3C2 change layer	The M3C2 distance layer to read. Its M3C2 LoD95 layer is found by name.
Change	Losses (rockfall, erosion) or Gains (talus, deposits). Which sign is a loss follows M3C2's: a negative distance lies behind the surface along its normal.
Link distance (m)	Significant points closer than this belong to one event. Default three point spacings.
Smallest event (points)	Smaller clusters are left out. Default 10.
Days between epochs	For rates: volume and events a year. 0 gives none.
Power law above (m³)	The magnitude–frequency fit's lower cut-off; 0 lets the fit choose it.
This scan is the later epoch	Tick it when this is the scan taken after the falls (compared by M3C2 with the earlier one). M3C2's sign is then turned round — a fallen block's old surface lies in front of the later scan — and the back-analysis reads the scars (see below).

Results

• Rockfall Event layer on the scan: each point's event number, 1 the largest by volume.
• The report: the number of events and their total volume (and rates); the magnitude–frequency plot; the fit; and a table of events — points, area, volume, maximum and mean depth, and centre — the largest first (up to 200).
• The messages panel: the totals, the fit and the five largest events with where they are.

Each run is recorded in Analysis Runs, from where it can be run again.

Back-analysis

Which discontinuity sets released the falls, and did the slope stability maps see them coming? Which question it answers depends on the scan:

• On the later epoch (the box ticked), the scars are on the scan. With the scan's Dip and Azimuth layers (run Tensor Analysis on it) and project Sets, each scar's facets are matched to the nearest Set mean plane within 20°. The table gives each event's release sets (those carrying a fifth or more of its scar), and the report the share of all the scars' area, weighted by volume, on each Set.
• On the earlier epoch, the slope is as it was before the falls. If Slope Stability has been run on it, the report tests its maps against where the events then happened: for the Kinematic Mode map (any mode possible) and the Factor of Safety map (below 1), how many events lie at least half inside the flagged area, the share of the events' volume flagged, and the share of the whole slope flagged — the base rate a fall would hit by chance. The lift, volume share over base rate, above 1 says the map found where the falls happened. The table gives each event's flagged share.

This closes the loop with the slope design: the sets that released the falls, and evidence to calibrate the friction, scales and acceptance criteria the maps were made with.

Method

Significant change. A point is a loss when its M3C2 distance is below −LoD95 (a gain, above +LoD95). Without a LoD95 layer, any change counts.

Events. Significant points within the link distance of each other are joined (through a grid of cells as wide as the link distance), and each connected cluster is an event. Its area is the sum of its points' areas — for a mesh, a third of each triangle each vertex is a corner of; for a point cloud, the square of the point spacing — and its volume is the sum of each point's area times its depth of change. Its mean depth is the volume over the area.

Magnitude–frequency. Rockfall volumes typically follow a power law, N(≥ V) ∝ V^−b. The exponent is fitted by maximum likelihood (a continuous Pareto distribution),

$$b = \frac{n}{\sum_{i=1}^{n} \ln(V_i / V_\text{min})}, \qquad \sigma_b = \frac{b}{\sqrt n},$$

over the n events at or above the cut-off V_min. Unless you give it, V_min is the event volume whose fit is closest to the data by the Kolmogorov–Smirnov distance (Clauset, Shalizi & Newman 2009), so the small events that the level of detection under-counts do not bend the fit. It needs at least 10 events.

Limitations

• The events are as good as the registration and the M3C2 settings; vegetation and wet rock between epochs show as change.
• Two falls that touch between epochs are one event; one fall broken by an occluded strip is two.
• The back-analysis matches facets to each Set's mean plane only; a set with a wide spread may be under-counted. For where falls will travel, see Rockfall Trajectories.

References

1. Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review, 51, 661–703.
2. Lague, D., Brodu, N., & Leroux, J. (2013). Accurate 3D comparison of complex topography with terrestrial laser scanner: application to the Rangitikei canyon (N-Z). ISPRS Journal of Photogrammetry and Remote Sensing, 82, 10–26.

See also

• M3C2 Comparison
• Rockfall Trajectories
• Bench As-built
• Geomechanics