«LANDSLIDE DEFORMATION CHARACTER INFERRED FROM TERRESTRIAL LASER SCANNER DATA A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF ...»
Acquiring spatially continuous ground-surface displacement fields from Terrestrial Laser Scanners (TLS) will allow better understanding of the physical processes governing landslide motion at detailed spatial and temporal scales. Problems arise, however, when estimating continuous displacement fields from TLS point-clouds because reflecting points from sequential scans of moving ground are not defined uniquely, thus repeat TLS surveys typically do not track individual reflectors. Here, we implemented the cross-correlation-based Particle Image Velocimetry (PIV) method to derive a surface deformation field using TLS point-cloud data. We estimated associated errors using the shape of the cross-correlation function and tested the method’s performance with synthetic displacements applied to a TLS point cloud. We applied the method to the toe of the episodically active Cleveland Corral Landslide in northern California using TLS data acquired in June 2005 - January 2007 and January-May 2010. Estimated displacements ranged from decimeters to several meters and they agreed well with independent measurements at better than 9% root mean squared (RMS) error. For each of the time periods, the method provided a smooth, nearly continuous displacement field that coincides with independently mapped boundaries of the slide and permits further kinematic and mechanical inference.
1.1 Introduction Measuring time-varying surface deformation in active landslides can be challenging due to their wide range of displacement rates (~mm/yr to 10 m/s) (Cruden and Varnes, 1996) and variable displacement gradients reflecting block-like to fluid rheology (Iverson, 2005). Although recent geodetic techniques such as GPS and InSAR have illuminated the behavior of some active landslides (Coe et al., 2003; Hilley et al., 2004; Schulz et al., 2009), logistical and cost issues combined with the broad variation in displacement rates and gradients have prohibited their routine application to landslide monitoring.
Most landslide monitoring emphasizes either concentrated temporal coverage at selected points or widespread spatial coverage over long time intervals. For example, in situ semicontinuous monitoring of slow-moving slides using extensometers accompanied by complimentary instrumentation (rain gauges and buried pressure transducers) has allowed the observation of environmental controls on individual displacement events and long-term deformational behavior (e.g. Baum and Reid, 1995; Reid et al., 2003; Malet et al., 2005; Schulz et al., 2009a). Using networks of points, GPS monitoring has enabled 3-D characterization of landslide displacement (Brueckl and Parotidis, 2001; Malet et al., 2005; Squarzoni et al., 2005). On the other hand, repeat photogrammetric or airborne Lidar surveys can provide spatially complete maps of landslide activity, often portraying very fine detail (Baum et al., 1998; McKean and Roering, 2004; Demoulin, 2006; Roering et al., 2009). Due to logistical and cost issues, however, the excellent temporal resolution of in situ networks comes at the expense of poor spatial coverage whereas the excellent spatial resolution of repeat-pass remotely sensed surveys is often temporally limited.
Space-based interferometric synthetic aperture radar (InSAR) has been used in measuring landslide surface displacement (Colesanti et al., 2003; Hilley et al., 2004; Bulmer et al., 2006; Delacourt et al., 2007). Additionally, use of ground-based InSAR and real-aperture radar interferometry has improved observation resolution and accuracy (~ 5 m and ~3 mm) of landslide surface motion (Tarchi et al., 2003; Antonello, 2004; Noferini et al., 2007). Notwithstanding the temporal limitations of space-based observations, these interferometric techniques are limited by geometric decorrelation that occurs when displacements are higher than about half of the radar wavelength (2.8 cm for C-band and 10 cm for L-band radar). Typical landslide displacement rates measured with these radar bands, ~2-10 cm/month, represent only a fraction of the observed displacement rates for those features. Because of the geometric limitations and potentially rapid acceleration of landslide motion, there is a clear need for a ground-based, cost-effective method that can provide both high spatial and temporal resolution measurement of landslide surface motion.
Terrestrial Laser Scanning (TLS) is a portable ground-based laser travel-time technique capable of rapidly acquiring millions of sub-centimeter three-dimensional point locations (creating a “point cloud”) and near-infrared reflectance intensity (x,y,z,i) measurements directly from any object that reflects near-infrared laser light (Lichti and Jamtsho, 2006). Because of these characteristics there has been growing interest to use TLS data to study landslide movement (Lichti and Jamtsho, 2006; Teza et al., 2007; Collins and Sitar, 2008; Teza et al., 2008; Baldo et al., 2009). Due to small changes in either the instrument or ground surface orientation, or changes in the ground’s reflective character, repeat TLS surveys typically do not track individual reflecting points visible in sequential scans. Deriving a displacement field, therefore, by relating the point clouds acquired from distinct scans can be a computationally challenging exercise and there is no currently accepted best practice of automatically doing so.
In this paper, we present a method to derive a 2-D surface displacement field with high spatial resolution using sequential TLS scan data. We adapt a cross-correlation based Particle Image Velocimetry (PIV) method that has been well tested in fluid dynamics studies for the past several decades (Keane and Adrian, 1992; Westerweel, 1997; Meunier and Leweke, 2003; Raffel et al., 2007). First, we describe the method and test it with synthetic data. Then we apply the method to study the motion of the slow-moving Cleveland Corral landslide, California (Reid et al., 2003) using TLS data acquired at 18 and 4month intervals.
1.2 Terrestrial Laser Scanning Terrestrial laser scanning (TLS) rapidly measures two-way travel time of emitted laser pulses returning from multiple reflective objects. Typical scans acquire 3-D positions of thousands of points per second. For most commercially available instruments, the near-infrared laser (0.75-3 µm wavelength) permits sub-cm range resolution scanning to ranges of 1-2 km (Gordon and Lichti, 2007). Spot-spacing (point-spacing) or sampling interval, determined by each instrument’s acquisition scheme, is also typically mm-cm scale, as is spot-size (footprint of the beam), which is a linear function of beam width that spreads angularly with range (Lichti and Jamtsho, 2006).
TLS data collected for deformation studies need to be either independently georeferenced or the survey needs to collect sufficient data outside of the area of deformation such that common surfaces and features in each dataset can be adequately aligned to one another. In theory, alignment with the baseline scan is a simple 6-parameter (or 7-parameter if scale change is allowed) Helmert transformation (Strang and Borre, 1997). In practice, however, alignment of TLS data is non-trivial because reflective objects are not precisely preserved between observational epochs due to very small changes in the scanner’s orientation and/or changes in the reflective surface. The iterative closest point (ICP) algorithm (Besl and McKay, 1992; Chen and Medioni, 1992; Bergevin et al., 1996), based on minimizing the least-squares distance between possible corresponding points in a point cloud, is one of the more common and better performing routines for aligning scans taken at different times (Gruen and Akca, 2005). Other approaches use identifiable targets or user-deployed survey targets in the survey area (e.g spherical or cylindrical objects) as common control points (Collins et al., 2008).
The above-mentioned non-uniqueness of reflective points between observational epochs further complicates deriving displacement fields from TLS scans. A number of methods are currently employed but each is limited. Feature-tracking manually estimates displacements of objects (either passive or user-installed) identifiable in each scan (Collins et al., 2009). Although this technique can be quite precise, particularly if there are adequate identifiable features and solid modeling is used to damp measurement scatter from the reflective object, it is not automated and so derivation of a displacement field with spatial density commensurate with the acquisition resolution is time-prohibitive and user-dependent. A scalar measure of displacement along a single axis can be found by pixel-based differencing of each epoch’s gridded data (Baldo et al., 2009; McCoy et al., 2010), but this technique is appropriate for the rare case when motion in only one direction is expected. Least squares surface and curve matching (Gruen and Akca,
2005) can detect the displacement of a synthetic target located 100 m from a TLS unit with an accuracy of ± 1 cm although it is not clear that this approach would be effective for scans of natural, irregular target areas such as landslides. The piecewise alignment method (PAM) (Teza et al., 2007) uses the ICP algorithm (Besl and McKay, 1992) to match data parcels between observations and to derive a displacement field by assigning the 6-parameter (Helmert) transformation to the centroid of each parcel. PAM requires especially dense TLS data with no shadows for parcel-matching to work best and the method is well-suited for the less general case when only rigid deformation is present (Chui and Rangarajan, 2003).
1.3 Particle Imaging Velocimetry Particle Image Velocimetry (PIV) is a widely-used fluid dynamics technique developed initially to derive the velocity of fluid flows seeded with particles from time-series photography (Keane and Adrian, 1992; Westerweel, 1997; Meunier and Leweke, 2003; Raffel et al., 2007). The PIV method has also been applied to measure deformation in geotechnical studies with close-range photography (White et al., 2003). Here, we adapt the PIV method for use with TLS data using the freely available DPIVsoft Matlab routines (Meunier and Leweke, 2003;
Fundamentally, PIV estimates a velocity field in a plane by cross-correlating raster images from successive observational epochs. For experimentally controlled fluids, the image plane is usually cross-sectional to the principal flow axis. For TLS data, such as from a landslide, the image plane is most likely taken to be the horizontal plane (vertical axis ‘up’). Although typical landslide motion creates a 3-D displacement field, for many landslides horizontal motion is likely to be significantly greater than vertical motion and so a 2-D treatment as developed below can provide a velocity field for motion in the dominant direction.
To adapt PIV for use with TLS data, we first grid 3-D (x,y,z) data with grid size, GR in the xyplane but we can perform it in any desired plane. The resulting image is then similar to a PIV image where the gridded 3-D data are analogous to the variable light intensity associated with the particle field in traditional PIV. Let Ik(i,j) be the z-value assigned to the ith and jth xy-grid cell of a TLS data set from the kth observation. For a given correlation window size WC, the normalized cross-correlation function ( rN ) for subsequently acquired images is
where µ and are mean and standard deviation of z values respectively for corresponding images indicated by the subscripts I1 or I2. The correlation window is shifted in both directions over the second image within an interrogation window of size WI, and rN is calculated for each grid shift (is, js) (Figure 1.1). The operation is applied for a range of shifts S (-Sx ≤ is ≤ +Sx, -Sy ≤ js ≤ +Sy) and produces a correlation matrix of size (2Sx+1) x (2Sy+1). The peak location with respect to the origin (Sx=Sy=0) in rN is a direct measurement of the displacement.
The cross correlation algorithm we adapted here (Meunier and Leweke, 2003) is advantageous for several reasons. First it allows direct cross-correlation computation as well as computation in the frequency domain via the Fast Fourier Transform (FFT) (Willert and Gharib, 1991;
Westerweel, 1997). This is particularly efficient when the size of I1 and I2 are equal. Second, because the shift ( is, js ) is an integer, there is a potential error of ±0.5GR if the correlation peak is fixed to grid nodes, therefore the algorithm uses a Gaussian fit to find the correlation peak at a precision of 1/10 to 1/20 image resolution (Raffel et al., 2007). This limits the minimum detectable motion to the order of 0.1-0.05GR. Finally, for the most realistic case where displacement within a correlation window is non-uniform, the correlation function may be broad or even have multiple peaks causing measured displacements to be less accurate or spurious. The algorithm we use here overcomes this problem by allowing iterative deformation of the correlation window (Huang et al., 1993; Meunier and Leweke, 2003; Raffel et al., 2007).
In the iterative window deformation algorithm, the computation is a multi-step process (Meunier and Leweke, 2003). The initial run estimates a coarse but relatively smooth displacement field and deformation tensor, D, which is then applied to deform the interrogation window to more precisely estimate the peak of the correlation matrix. A low-pass filter is used to smooth outliers (Meunier and Leweke, 2003). In the second run, the displacement field is re-estimated from the deformed images. In this run, the displacement gradient is smaller, therefore a unique and narrower peak in the cross-correlation matrix is more likely to appear. All incremental displacements in subsequent iterations (usually 2 or 3 are enough) are then summed with the initial estimate to yield the final result.