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1.25 m, respectively), over the majority of the displacement field, we obtained residual values that were randomly distributed with less than 5% relative error (Figure 1.7c,d). At the margin of the field where displacement gradients are non-uniform, however, residuals are systematically negative (Figure 1.7d). Although the iterative window deformation technique we use here works well if the mean displacement gradient within the window is uniform, errors may also propagate in space within the interrogation window if the displacement gradient changes over shorter spatial scales than the interrogation window and we attribute the small bias to this effect (Figure

1.7c,d). Nonetheless, this is a minor bias (4%) and our analysis shows that the spatial density of the TLS data is sufficient to measure the principal features of the January–May 2010 displacement field and that the PIV control parameters are well-chosen.

Figure 1.7.

PIV estimation of a synthetic signal applied to January 2010 point cloud data. a) Magnitude of the synthetic signal varying smoothly to a maximum of 0.5 m in negative y direction (black dots are January 2010 point cloud). b) PIV recovered displacement magnitudes (colors) in y direction. c) Residuals in x direction with vectors showing total residuals. d) Same as c) except in y direction.

Using these PIV parameters, we then estimated a 2-D map-view displacement field for the January to May 2010 time period (Figure 1.8). The region of detected displacement is ~ 30 m wide and ~60 m long. Total displacement over the time period ranges from 0.01 to 0.54 ± 0.1 m and displacement is generally in the down-slope direction. The boundaries of the PIV-derived field agree quite well with active shear boundaries and tension cracks mapped in the field for the same time period, particularly the upslope scarp and the east lateral shear zone (Figure 1.8). Due to shadowing from tall trees in the foreground, the point cloud near the mapped toe is particularly sparse and so we do not have much confidence in the PIV solution there (Figure 1.8).

1.5.3 Validation We validated our PIV results using two independent methods: 1) repeat static GPS surveys of a suite of monuments located on the slide and on nearby stable ground that we processed with respect to a nearby base-station ( 1 km baseline) to better than ~ 3 cm horizontal accuracy, and

2) tracking of manually identified features in the TLS point clouds consisting primarily of reflections from tree trunks and shrubs. These features do not lend themselves to solid modeling because of their irregular nature, and so to quantify their motion between successive TLS data sets, we determined the centroid of the set of reflections originating from the same feature for each observational epoch (Figure 1.4c,f). Uncertainty in the centroid measurement is then the standard deviation of the mean position divided by the square root of the number of data points (Taylor, 1982).

Figure 1.8.

PIV estimated total displacement field and vectors (black) with error ellipses (95% significance) of CCL between January 2010 and May 2010. GPS horizontal-displacement vectors (red) and displacement vectors of features (eg. trees) identifiable in the point cloud data (white) plotted using the same scale as the PIV vectors. Landslide features adapted from Reid et al. (2003) are in gray and the features mapped in the field in 2010 are in red.

For the 2005-2007 data set, the PIV-estimated values, GPS, and feature-tracking estimates agree well with one another, accurately tracking the entire range of observed displacements (Figure

1.9a). The standard deviation of misfit of ~0.43 m (~8.6% relative error) with the featuretracking estimates is smaller than with the GPS estimates (~0.61 m) because of the aforementioned ~2 m georeferencing RMS error with the 2007 DEM and because of the high displacement gradients in the vicinity of the GPS monuments. As above, we use the standard deviation of the misfit associated with the feature-tracking values (~0.43 m, 8.6% relative error) to set the interpretation threshold scale for these data.

For the 2010 data set, as with the 2005-2007 data set, displacements derived from the PIV analysis and both feature tracking and GPS measurements all agree well with one another, accurately portraying the entire range of observed displacements (Figure 1.9b). The misfit between PIV and feature tracking is most likely smaller than the misfit with GPS measurements because of the aforementioned ~2 m georeferencing RMS error, although the errors associated with each GPS measurement are smaller than with each feature-tracking measurement. We consider georeferencing error to be the largest source of the misfit: for PIV estimates in the xy plane, potential vegetation change (seasonal growth/removal) errors are negligible over this time period and probably an order of magnitude smaller than errors associated with georeferencing.

Finally, there are no georeferencing errors associated with the feature-tracking results, and so the

0.049 m standard deviation of the misfit estimate (8.9 % relative error) likely sets the interpretation scale for this analysis – we do not ascribe any significance to changes smaller than this value.

Figure 1.9.

Comparison of PIV-computed displacement (magnitude) of CCL with GPS measurement located in the PIV grid cell (Figure 1.6 and 1.8) and displacement from manual tracking of identifiable features’ geometric centroid. PIV errors are represented by vertical bars and GPS and feature-tracking errors are shown by horizontal error bars. Higher standard deviations (Std) of the misfit with the GPS measurement are attributable to the georeferencing error. a) June 2005 to January 2007 and b) January 2010 to May 2010.

1.6 Discussion Our results show that the PIV technique applied to TLS point cloud data collected from a series of repeated scans can provide spatially continuous, smooth, precise and accurate displacement fields. Although relatively short radar wavelengths ( a few cms for most ground-based systems) may permit a smaller motion detection threshold for radar interferometry compared to TLS approaches, interferometry must be performed along the radar’s line-of-sight (Burgmann et al., 2000), thus limiting the displacement field from each InSAR pair typically to only one component of motion. In contrast, our PIV-derived displacement fields (Figure 1.6 and 1.8) show two components and future work to extend the estimation to three components should be relatively straightforward. Additionally, the PIV method presented here accurately recovered a smooth displacement field in the presence of displacement gradients as large as ~5 m over 10’s of meters (Figure 1.6) whereas current radar interferometric techniques decorrelate in the presence of such large displacements. Nonetheless, because the rates and spatial wavelengths of landslide displacement fields vary widely, we view TLS and radar interferometry as potentially complimentary techniques.

Comparisons of repeat GPS surveys and tracking of ground features between TLS scans show that the PIV method is able to accurately detect ground-surface displacement over at least two orders of magnitude (decimeters to meters) between observational epochs (Figure 1.9). Even with irregular point cloud data (such as the 2005 and 2007 scans), PIV can accurately recover large displacements. Although the PIV method preferably requires having knowledge of displacement magnitude to constrain the parameters, the first-hand knowledge of displacement can easily be acquired from comparing positions of identifiable features over time. There are some limitations to the method, however. For instance, significant disruption of the ground surface between successive scans (as might occur during rapid movement or transition to a debris flow) would degrade correlation. Also, ground features that remain stationary (Coe et al., 2009) as a slide moves downslope through the feature (such as a spatially fixed area of ground cracking) might produce spurious results. Finally, slides with highly variable displacement patterns could be difficult to fit with a single choice of PIV parameters.

The dense coverage provided by the PIV-estimated displacement field yields new insight into the kinematics and spatial evolution of the Cleveland Corral landslide. The limits of overall landslide displacement were known from previous ground-surface mapping (Reid et al., 2003), and the limits of the 2005-2007 deformation in the downslope part of the slide coincide well with the mapped boundaries (Figure 1.6). The PIV-derived displacement vectors from the 2010 movement episode, however, reveal the birth of a new active kinematic element – essentially a new slide within the boundaries of earlier sliding (Figure 1.8). During this episode, the head of the kinematic element formed in an area of previous tensional fractures, whereas the toe and eastern margin followed pre-existing features. The new element had its largest displacement in its center, with less displacement in the headscarp region (where material was stretching) and less at the toe (where material was shortening). This pattern, of fastest motion in the middle, matches the displacement pattern observed in other large slow-moving slides (e.g. Fleming et al., 1999; Malet et al., 2002; Coe et al., 2003). In addition, some displacement vectors near the midto-lower eastern margin were rotated counter-clockwise (relative to the downslope direction) indicating that the slide material spread laterally in the toe region. During 2010, older slide material upslope and to the west of the new active kinematic element did not move.

Typically, strike-slip shear at the lateral edges of slow-moving landslides tends to focus within a discrete zone; these zones are established during previous slide motion (e.g. Fleming and Johnson, 1989; Fleming et al., 1999). This pattern held true for the eastern margin of the new 2010 kinematic element, where the eastern lateral shear zone, based on field observations, is activated each time the slide moves. In contrast, a completely new lateral shear zone developed along the western margin of the new element, about 20 meters inboard of the western toe active in previous years (Figure 1.8). An along-slope profile of PIV-derived displacements shows that this developing margin is associated with a pattern of more broadly distributed deformation than the well-developed eastern shear zone during the time interval Jan-May 2010 (Figure 10a). This new shear zone was not readily apparent in the field when the scans were obtained; subsequent field mapping one month after the latter scan confirmed the development of this shear boundary.

Thus, it appears that the PIV displacement field captured an intermediate stage of diffuse deformation that preceded the development of a well-expressed shear zone having a combination of en echelon and through-going ground-surface cracking. These observations would be difficult without a full displacement field that recorded the transient shear formation event. In general, the limits and internal patterns of active movement may be unknown on landslide-prone hillsides, so PIV-derived displacement fields can provide a useful discriminatory tool for defining kinematic elements within a landslide, and for potentially recording the formation of new elements.

PIV-derived displacements can also provide insight into the mechanical behavior of the slide.

Mechanical analyses of slow-moving landslides often assume some viscous and/or plastic constitutive relation (e.g. Iverson, 1986; Savage and Smith, 1986; Vulliet, 2000) or use variations in frictional resistance due to fluctuations in pore-water pressure (e.g. Corominas et al., 2005;

van Asch et al., 2009) and/or soil dilatancy (e.g. Iverson, 2005; Schulz et al., 2009b) to reproduce spatial and temporal movement patterns. Complex PIV displacement fields obtained Figure 1.10.

Displacement profiles a) along-slope (at Y=110 in Figure 1.8) and b) down-slope (at X=145 in Figure 1.8). WSZ, ESZ in a) indicate the western and eastern lateral shear zones. Grey lines in b) indicate conceptual rigid displacement profile.

through repeat TLS could better constrain such analyses. For mathematical and conceptual simplicity, a slide is often approximated as a rigid sliding block with plastic deformation at its base (Lambe and Whitman, 1969). A down-slope profile of the surface displacement field for a rigid block comprises three portions: two zero-valued stable boundary segments and a single, constant-valued slide-interior segment (Figure 1.10b). For the new 2010 kinematic element, the down-slope displacement profile from the PIV displacement fields deviates from this simple form. Here, the down-slope displacement profile (Figure 1.10b) delimits positive displacement gradients in the upslope part of the element (indicating extension), and negative displacement gradients in the downslope part (indicating contraction). Both of these zones are ~20-30 m in width, centered on the maximum surface displacement value of ~0.3 m at y= ~105-120 m. The extensional zone contains both high- and lower-displacement gradient segments, likely reflecting a series of tension scarps, whereas the contractional zone has a relatively constant displacement.

Comparison with the simple rigid block model shows significant mismatch at the margins of the element as well as over the center of the slide mass (Figure 1.10b). This misfit with the rigid model, however, occurs over lengthscales of decimeters to meters. If an analysis of the displacement field were performed at lengthscales greater than 5-10 meters, the rigid block assumption might be justified.

1.7 Conclusion We have adapted the particle imaging velocity (PIV) technique from fluid mechanics to terrestrial laser scanning (TLS) point cloud data with the goal of deriving continuous displacement fields from active, slow-moving landslides. We applied the technique to TLS scans separated by 4 months and 1.5 years at the active Cleveland Corral landslide (CCL) and measured displacements ranging from decimeters to several meters. The PIV-estimated results agree with independent GPS and point cloud measurements at better than 9% RMS error of the magnitude of the maximum displacement. The smooth and nearly continuous displacement field coincides with independently mapped boundaries of the slide, and permits both the identification of a diffuse zone of displacement preceding lateral shear zone development and the demonstration of non-rigid slide behavior.

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