«LANDSLIDE DEFORMATION CHARACTER INFERRED FROM TERRESTRIAL LASER SCANNER DATA A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF ...»
We use the rule of thumb described above in section 3.1.1 to select PIV correlation parameters (WI, and WC of 3 m, and 2 m, respectively) to estimate the 3D displacement field with 1 m spatial resolution. The residual displacements of the PIV-estimated values (synthetic signal - PIV estimated) are less than 6 % relative error (Figure 3.5) in all three directions. The PIV-derived displacement field reproduces much of the character of the synthetic input field within the determination threshold of +/- ~ 0.06 m. There is no applied signal in the x-direction and therefore the estimated values in the x-direction are errors propagated from signals applied in the y and z-directions. ICP requires a larger number of data points in the matching window (Teza et al., 2007; Nissen et al., 2012) and therefore to find the best ICP window size for the data, we performed ICP estimation using different window sizes (2 to 9 meters). The root mean square error (RMSE) for different ICP window sizes (Figure 3.6) indicates that the use of a 4 m ICP window size recovers the signal best for this case. The RMSE is very large for a 2 m window size indicating that ~ 450 data points (average data points density = 110 per meter square) in an ICP window is not adequate to match the data in each window. The smallest RMSE for a 4 m ICP window size indicates that about 1800 or more data points are needed on average to match the data.
(a-c) Synthetic signals in the x, y and z-directions respectively. (d-f) PIV estimated displacements in the x, y and z-directions respectively. White speckles in (f) indicate areas where data points are not adequate to estimate vertical displacement. (g-i) residuals (signal-estimated) in the x, y and z-directions respectively.
Root mean square error (RMSE) of ICP estimation of the synthetic signal applied to a TLS data using different window sizes. RMSE is minimum at the 4 m window size.
3.3 Results from the Cleveland Corral Landslide The Cleveland Corral Landslide (CCL) is a slow-moving landslide complex along Highway 50 in California (Spittler and Wagner, 1998) (Figure 3.8). The CCL has been monitored since 1997 using repeat high-precision GPS ground surveys and in situ sensors including extensometers, geophones, rain gauges, sub-surface pressure transducers as well as repeat TLS scanning (Reid et al., 2003; Aryal et al., 2012). The landslide moves only when rainfall exceeds the mean annual precipitation and is otherwise dormant. It has moved episodically since the mid-1990’s, and a neighboring slide with similar characteristics failed catastrophically (Reid and LaHusen, 1998).
Therefore, the landslide may provide an opportunity to understand the transition from slowmoving slide to a catastrophic flow. Measured surface displacements at the CCL vary in space and time from millimeters to several meters per year (Reid et al., 2003; Aryal et al., 2012).
(a-c) Synthetic signals in the x, y and z-directions respectively. (d-f) ICP estimated (4 m window size when the RMSE is minimum as shown in the Figure (3.6) displacements in the x, y and zdirections respectively. (g-i) residuals (signal-estimated) in the x, y and z-directions respectively.
We scanned the CCL using an Optech Ilris-3D scanner (Figure 3.8a) and acquired six TLS datasets on 15 Jan 2010, 03 May 2010, 21 Jun 2010, 09 Feb 2011, 09 May 2011 and 24 Apr
2012. During this time, there were episodic movements at the toe portion and a portion near the head of the slide. TLS surveys were conducted from an elevated vantage point across the valley from the slide (ranging 500 – 700 m) in order to have a synoptic view of the entire slide. In each scan, point-cloud spot-spacing ranged from 6 to 15 cm. The initial scan was georeferenced to a
0.5 m DEM in a UTM coordinate system (NAD83) derived from aerial photographs acquired in
2007. Subsequent scans were aligned to the georeferenced scan masking out the data points from the active part of the landslide.
(a) Photograph showing the field scanning of the Cleveland Corral landslide in the Sierra Nevada Mountains, California with the location of the landslide (inset). Black lines mark an approximate (hand-drawn) landslide boundary (b) Shaded relief map using 50 cm DEM from TLS data. No data (black) are shadows mainly from vegetation. Landslide surface boundary in blue is adapted from Reid et al. (2003) and the surface features (scarps, thrusts, and cracks) in red were mapped in 2010. Gray boxes in (a) and (b) outline the area selected for analysis.
3.3.1 Displacement time series
We obtained displacement fields of the CCL using both ICP and PIV methods for four time periods when the slide was moving: Jan-May 2010, May-June 2010, Jan-Jun 2010 and Jun 2010 – Apr 2012 (Figures 3.9 and 3.10). PIV estimates for the first three time period use 1 m spatial resolution and ICP estimates all use 5 m ICP window size (average 2500 data point in a window). Estimated maximum displacements using both methods from Jan-May 2010, May-Jun 2010 and Jan-Jun 2010 are ~0.5 m, ~0.5 m and ~1 m respectively (Figures 3.9 and 3.10).
Although we found the lowest RMSE using a 4 m ICP window size in our synthetic case, because of scattered data due to vegetation and relative change of shadows over time, we needed to use a larger number of data points to better fit the ICP estimate with the GPS and feature tracking (Figure 3.11). The PIV estimated Jan-May displacement field agree with GPS and feature tracking at better than 90% of the maximum displacement (Aryal et al., 2012).
Comparison of the displacements using both methods with the GPS and feature tracking (Figure 3.11) indicate that PIV estimated displacements of the CCL match with the observations better than the ICP estimates. For example, for May-Jun 2010, standard misfit of GPS and feature tracking with PIV is 0.039 and 0.073 m respectively but for the same period of time, standard misfit of GPS and feature tracking with ICP is 0.071 and 0.09 m respectively. Comparison of the estimated ICP displacement with the ground truth suggests that the mean standard errors for JanMay, May-Jun and Jan-Jun 2010 are 0.063 m, 0.09 m and 0.18 m respectively (Figure 3.1). The relatively larger misfit for ICP estimation is likely to be due to vegetation and change in shape and size of shadows as the ICP method is sensitive to the data scattering and shadows. For the time period from Jun 2010 to Apr 2012 (Figure 3.10b-d), the estimated displacement using both methods are smaller than 3 meters compared to the GPS measurements that show displacements as large as ~5 m. In this time period, the displacements are too big to estimate accurately using both methods. Nevertheless, both PIV and ICP-estimated vectors show a similar displacement magnitude and orientation and delineate the active part of the landslide. This Jun 2010 – Apr 2012 displacement field show that the entire toe portion of the slide was active at this time period compared to only a portion of the toe active in 2010 (Figure 3.10c-d).
To summarize, although the ICP method appears to work best for our synthetic case, it has potential weaknesses that may limit the accuracy for real field data. At the CCL, PIV estimates agree better with the ground truth data. Similarly, the PIV estimates have smaller spatial resolution (PIV in 1 m compared to ICP in 5 m) and allow better characterization of a displacement field where displacement gradients are higher such as along the landslide boundaries. Therefore, we prefer using the PIV-estimated displacement field to analyze the pattern of deformation at CCL.
3.3.2 Pattern of surface deformation The estimated displacement fields can be used to acquire a dense deformation pattern which provides useful information for landslide hazard assessment and mitigation (Baum and Fleming, 1991). To characterize the surface deformation pattern, we performed a strain analysis of the estimated surface displacement fields. The strain is independent with respect to rigid body motions reflecting relative change in surface displacements only, and therefore any effects of systematic errors (e.g., due to TLS data aligning) are automatically removed. Typically, the strain field is computed via a least square interpolation of strain rates using discrete geodetic measurements. To obtain strain fields, we performed a modified least square inversion (Shen et al., 1996) on the displacements and their covariances to solve for strain rates and rotations using the Matlab tools of Teza et al. (2008).
We obtain strain maps using the PIV-estimated January-May, May-June and January-June 2010 displacement fields. All three strain maps indicate stretching (extension) in the upslope part and shortening (compression) in the downslope part of the toe portion of the landslide (Figure 3.12).
At the central part of this toe portion of the January-May 2010 strain map (Figure 3.12a) shows compression or shortening but the May-June 2010 strain map (Figure 3.12b) indicates extension or stretching. This suggests that there are at least two major kinematic elements in this portion that are moving at different rates over the time: the upper kinematic element moving relatively faster from January-May 2010, but the lower kinematic element moving relatively faster from May-June 2010. Overall, the January-June 2010 strain map (Figure 3.12c) shows only one major block with a relatively neutral zone in between the contrasting styles of deformation at the upslope and the downslope. This change in the strain pattern in space and time at the toe portion of the CCL also suggests non-uniform slip rates of the slide in space suggesting to us that models assuming uniform slip at a single slip plane (e.g., Aryal et al. 2013) are overly simplified.
ICP and PIV estimated displacements (horizontal and vertical) of CCL. (a-b) January – May 2010 (PIV estimation is reproduced from Aryal et al., 2012). (b-d) May – June 2010. Landslide features (black) were mapped in the field in 2010.
ICP and PIV estimated displacements (horizontal and vertical) of the landslide. Landslide features (black) were mapped in the field in 2010. (a-b) January – June 2010, and (b-d) June 2010 April
2012. Landslide features in green Reid et al. (2003) indicate that the entire toe portion of the slide was active in this period of time.
Comparison of PIV and ICP computed displacements (magnitude) of CCL with GPS measurement and displacement from manual tracking of identifiable features’ geometric centroid. STD is standard deviations of the misfit with the observation (a-b) January 2010 to May 2010 (comparison with PIV is reproduced from Aryal et al., 2012). (c-d) May 2010 to June 2010, and (e-f) January 2010 to June 2010.
3.4 Discussion Both ICP and PIV methods have been applied for more than two decades. The ICP method has been developed for point cloud data similar to TLS data. Therefore, once aligned, no other processing of the TLS data is needed to apply the ICP method. The PIV method we use is adapted from fluid dynamics and therefore the TLS data need to be pre-processed (Aryal et al.,
2012) to make images similar to PIV images. Another main advantage of ICP is that it is inherently a 3D method compared to PIV. In general PIV, 3D velocities are obtained using stereo-images (Raffel et al., 2007), but here we use PIV to estimate 2D horizontal displacement and the vertical displacement is estimated by differencing heights of corresponding points in the DEMs from different TLS scans. When finding the corresponding points in DEMs using the 2D PIV displacements, errors in the horizontal displacements can propagate to the estimated vertical displacement. This is seen in our synthetic case where the residuals in vertical displacement using PIV (Figure 3.6i) are larger compared to the ICP vertical residuals (Figure 3.8i).
The residual plots for the synthetic example (Figure 3.6 and 3.8) show that the ICP method recovers the synthetic signal better than the PIV method but the estimation resolution of ICP is coarser than the PIV resolution (Table 3.1). In contrast, PIV estimates of CCL agree better with the independent measurements (GPS and feature tracking) than the ICP estimates (Figure 3.11).
In the pixel-based PIV cross-correlation we apply here, errors in the horizontal direction propagate faster to the vertical direction. Therefore, although we do not have any synthetic displacement in the x-direction (Figure 3.6a), there are estimates as large as 0.05 m (Figure 3.6d) in the x-direction. Similarly, errors in the horizontal displacements can introduce errors in the estimated vertical displacements when finding the corresponding points, as stated above (Figure
Strain maps calculated using Jan-May, May-Jun and Jan-Jun 2010 displacement field (PIV estimated). Blue vectors represent extension and red vectors represent compression. Gray dots are location of the PIV displacement used for the strain calculations. The downslope direction is nearly parallel to South. Landslide features (black) were mapped in the field in 2010 and these periods of time, only a portion of the toe of the slide was active (see Figure 3.10c-d to compare with the entire boundary of the toe portion of the slide. The map indicates change in deformation pattern at the central part of the landslide from compression in Jan-May (a) to extension in May-Jun (b) (common boundary of two blocks highlighted in green). Overall from January - June (c), there is no deformation (neutral zone) at the central part of the landslide.