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m) within the margin of errors (±0.45m misfit, 16% relative error; Figure 2. 3).

Figure 2. 3.

Estimated slip-surface depth using the balanced cross-section (BC) method computed for 22 longitudinal sections through the landslide over three time intervals; 2 errors are shown in gray. Depth of shearing measured by shear rods is indicated by yellow triangles.

2.5.2 Elastic Dislocation We perform a multidimensional grid search of ~13 million parameter combinations to obtain marginal probability distributions (mpd) for the dislocation parameters during the three different time periods. For all calculations, we assume a Poisson’s ratio of 0.25; our sensitivity tests show that variations in Poisson’s ratio do not significantly modify the results given the relatively shallow slip surface. Figure 2. 4 shows mpds for the parameters, depth, dip, and slip that are most pertinent to the analysis here; the entire suite of eight parameters for each of the analyzed displacement fields is shown in Figure A3. The peak marginal probabilities for the dislocation parameters range from ~2.5 to ~3 m depth and for dip from 0-1° (Figure 2. 4 a, b). Peak marginal probabilities for slip (Figure 2. 4c) is ~0.45 m for the two shorter time periods (Jan-May and May-June) and ~0.9 m for the longer period (Jan-June). For all three cases, the estimated subsurface slip is about 20 - 35% larger than the mean surface displacements (dashed lines in Figure

2. 4c). As with the BC method, the peak marginal probabilities for the dislocation parameters (Figure 2. 4) at ~3 m depth are very similar to the shear rod depths of 2.37 m and 3.18 m

2.6 Discussion Using surface displacements to infer sub-surface slip character is in its nascent stages (Booth et al., 2013) and we anticipate that the general approach will be increasingly utilized as the ability to measure spatially dense surface displacement fields with techniques such as TLS also increases. Landslide geometry and rheology can be quite variable, however. Although inverse approaches such as those presented here allow quantitative comparisons, we do not expect that one forward model can be satisfactorily chosen for any given landslide until more studies with varying model approaches are undertaken. Nonetheless our study is, to the best of our knowledge, the first that demonstrates agreement between inferred and measured slip depths.

Interestingly, this agreement occurs for both, rheologically distinct, forward models that we employ. This highlights the non-uniqueness of different model predictions. Moreover, it is not possible to unequivocally determine landslide rheology using only surface displacements, as internal stress distributions must be known as well.

Figure 2. 4.

Marginal probability distribution (scaled empirically or manually) for three dislocation slip parameters (depth, dip direction, and slip magnitude) over three time intervals. (a) Slip depth. Two dashed lines are measured slip depths using shear rods located within the landslide (see Figs. 2 and 3). (b) Dip direction relative to overall ground-surface gradient. Dashed line shows an apparent dip calculated using slip depths from the shear rods. (c) Magnitude of slip along the slip surface. Dashed lines indicate average ground surface displacements with colors corresponding to the marginal probabilities for each time interval (see Figure A3 in the appendix for mpd showing all eight parameters for all three time periods).

One reason for the agreement in depth estimates may be that deformation within the CCL, as in many other landslides, is likely neither purely incompressible nor purely elastic. If the landslide materials were purely one rheology, then using the other model to infer depth would likely lead to incorrect estimates. This can be illustrated by comparing some of the model assumptions.

Purely incompressible material deformation, as assumed in the BC method, does not produce any far-field displacement. Field exposure of shear margins and tension cracks at the CCL suggests that far-field (outside the landslide) displacement may not be significant. However, if a landslide were purely incompressible, then applying an elastic dislocation model might underestimate the slip depth because the elastic model requires far-field deformation. On the other hand, if a landslide were purely elastic, then there would be smaller volume loss at the zone of depletion as compared to the loss with an incompressible material, and applying the BC method would underestimate the slip depth. However, if landslide materials are a hybrid of the two rheologies, then both approaches might provide reasonable inferences of slip depth for dominantly translational slides.

Although the models predict similar slip depths, they differ significantly in terms of predicted sub-surface slip magnitude. Given an incompressible material, as in the BC model, the amount of slip at depth directly corresponds to average ground-surface displacement. For an elastic dislocation model, more slip occurs at depth than at the ground surface. Our results show that the magnitude of slip at depth estimated by the dislocation model is 25-35 % larger than the slip inferred by the BC method (Figure 2. 1 and 4c). Additionally, some studies (e.g., Fukao, 1995) show that landslides are better modeled using single-couple dislocation and therefore the doublecouple ED we use here might overestimate slip.

The two models also imply different displacement-depth profiles and failure propagation modes.

Field evidence to support one style of deformation over another is equivocal. Numerous studies suggest that internal deformation in a slow-moving landslide is rather small, with most deformation occurring in the slip zone (e.g., Baum et al., 1998). Some inclinometer observations in active landslides (e.g., Yufei et al., 2012) corroborate the idea that the slip at depth can exceed ground surface displacement. It must be noted, however, that some models of translational landslide creep suggest that, counter to both of the approaches presented here, displacement decreases with depth (e.g., Savage and Chleborad, 1982).

Despite their differences and general simplifications, the approach of using both rheologically distinct models allows us to place varying degrees of constraint on some fundamental metrics of a landslide. For the CCL, the disagreement in predicted slip magnitude suggests that more model refining is necessary, whereas the agreement for slip depth, suggests that this is a wellconstrained parameter. Moreover, although it is out of the scope of this paper, there may be other, rheologically distinct models that also satisfy the observed surface and sub-surface displacements. In the absence of prior information about a particular landslide or type of landslides’ material properties, we suggest an approach of comparing multiple viable forward models that relate surface and sub-surface displacement. This approach should become easier to implement as computational power increases and it will allow both the range of estimated parameters (e.g. slip depth and magnitude) and the appropriateness of distinct models to be better evaluated.

Acknowledgements We thank Dianne Brien for her assistance with field measurements and Neil Frazer for his insight into the grid search method we use here. We thank the USGS internal reviewers Ole Kaven and Jonathan Stock for their insightful comments.

–  –  –

Aryal, A., Brooks, B.A., Reid, M.E., Bawden, G.W., and Pawlak, G.R., 2012, Displacement

fields from point cloud data: Application of particle imaging velocimetry to landslide geodesy:

Journal of Geophysical Research-Earth Surface, v. 117, p. 15.

Baum, R.L., Messerich, J., and Fleming, R.W., 1998, Surface deformation as a guide to

kinematics and three-dimensional shape of slow-moving, clay-rich landslides, Honolulu, Hawaii:

Environmental & Engineering Geoscience, v. 4, p. 283-306.

Bishop, K.M., 1999, Determination of translational landslide slip surface depth using balanced cross sections: Environmental & Engineering Geoscience, v. 5, p. 147-156.

Booth, A.M., Lamb, M.P., Avouac, J.-P., and Delacourt, C., 2013, Landslide velocity, thickness, and rheology from remote sensing: La Clapière landslide, France: Geophysical Research Letters, v. 40, p. 4299-4304.

Brooks, B.A., and Frazer, L.N., 2005, Importance reweighting reduces dependence on

temperature in Gibbs samplers: an application to the coseismic geodetic inverse problem:

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Reid, M., Brien, D., Lahusen, R., Roering, J., de la Fuente, J., and Ellen, S., 2003, Debris-flow initiation from large, slow-moving landslides, in Rickenmann, D., and Chen, C., eds., DebrisFlow Hazards Mitigation: Mechanics, Prediction and Assessment: Rotterdam, Millpress, p. 155Roering, J., 2012, Tectonic geomorphology: Landslides limit mountain relief: Nature Geoscience, v. 5, p. 446-447.

Savage, W.Z., and Chleborad, A.F., 1982, A model for creeping flow in landslides: Bulletin of the Association of Engineering Geologists, v. 19, p. 333-338.

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We use the Particle Image Velocimetry (PIV) method adapted to point cloud data (Aryal et al., 2012) to estimate horizontal displacement fields and extend the 2D method to estimate a complete 3D displacement field. All the data processing steps and parameters to estimate 2D horizontal displacements are described in Aryal et al. (2012). To obtain vertical displacement, we translate the ground surface according to the PIV-estimated 2D horizontal displacement and then differenced the elevations (Figure A1).

Figure A1. Conceptual sketch showing components of landslide displacement at surface of a sliding block.

Ground surface displacement of G to G' consists of horizontal components uX and uY and a vertical component uZ. The vertical component uZ is the difference in elevation from G to G'. Elevation is available everywhere from TLS DEMs. Displaced location G' of grid G is located using PIV-TLS estimated uX and uY.

Many TLS data-derived vertical displacement in the literature (e.g., Baldo et al., 2009; McCoy et al.,

2010) are pixel-based differencing of gridded data. This scalar measure along the vertical axis is appropriate when the expected motion is primarily in one direction; a rare case in terms of most geologic phenomena. Any horizontal components of displacement or error in georeferencing can introduce large errors in the vertical component. In addition, artifacts such as trees or poles can cause high frequency noises in the estimated displacement. To minimize such noise, our approach finds the corresponding horizontal point location from one scan to another using the TSL-PIV-derived horizontal displacement and therefore estimates vertical displacement more accurately.


Figure A2. January to June displacement field Figure A3. Marginal probability distributions for eight slip parameters.

References cited in appendix Aryal, A., Brooks, B.A., Reid, M.E., Bawden, G.W., and Pawlak, G.R., 2012, Displacement fields from point cloud data: Application of particle imaging velocimetry to landslide geodesy: Journal of Geophysical ResearchEarth Surface, v. 117, p. 15.

Baldo, M., Bicocchi, C., Chiocchini, U., Giordan, D., and Lollino, G., 2009, LIDAR monitoring of mass wasting processes: The Radicofani landslide, Province of Siena, Central Italy: Geomorphology, v. 105, p. 193-201.

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