Measurement of Surface Displacement and Deformation of Mass Movements Using Least Squares Matching of Repeat High Resolution Satellite and Aerial Images
<p>Deformation of a template and transformation of its parameters from easting-northing to longitudinal-transverse axis.</p> ">
<p>A section of the aerial photographic image (400 m × 600 m) over part of the Muragl rockglacier taken on 7 September 1981, North to the top.</p> ">
<p>A section of the aerial photographic image (1,233 m × 1,233 m) over part of the Nigardsbreen taken on 19 August 2001, North to the top.</p> ">
<p>A section of the QuickBird panchromatic satellite image (1,600 m × 2,430 m) over the La Clapière landslide taken on 06 September 2003, North to the top.</p> ">
<p>Velocity (ma<sup>−1</sup>) maps and vectors of (<b>a</b>) the Muragl rockglacier, (<b>b</b>) the Nigardsbreen glacier and (<b>c</b>) the La Clapière landslide computed using the LSM.</p> ">
<p>The longitudinal <span class="html-italic">ɛ̇<sub>L</sub></span> (<b>a</b>), transverse <span class="html-italic">ɛ̇<sub>T</sub></span> (<b>b</b>), and shear <span class="html-italic">ɛ̇<sub>LT</sub></span> (<b>c</b>) strain rates and the rotation rate φ̇ (<b>d</b>) for the Muragl rockglacier.</p> ">
<p>The negative sum of the horizontal strain rates (assumed to be equal to the vertical strain rate for an incompressible medium) for the Muragl rockglacier.</p> ">
<p>The negative sum of the horizontal strain rates (assumed to be equal to the vertical strain rate) of the Nigardsbreen glacier.</p> ">
<p>The longitudinal <span class="html-italic">ɛ̇<sub>L</sub></span> (<b>a</b>), transverse <span class="html-italic">ɛ̇<sub>T</sub></span> (<b>b</b>), and shear <span class="html-italic">ɛ̇<sub>LT</sub></span> (<b>c</b>) strain rates and the rotation rate φ̇ (<b>d</b>) for the La Clapière landslide.</p> ">
<p>The longitudinal <span class="html-italic">ɛ̇<sub>L</sub></span> (<b>a</b>), transverse <span class="html-italic">ɛ̇<sub>T</sub></span> (<b>b</b>), and shear <span class="html-italic">ɛ̇<sub>LT</sub></span> (<b>c</b>) strain rates and the rotation rate φ̇ (<b>d</b>) for the La Clapière landslide.</p> ">
Abstract
:1. Introduction
2. The Least Squares Matching Algorithm and Its Significance in Mass Movement Analysis
2.1. The Least Squares Matching Algorithm
2.2. The Least Squares Matching in Mass Movement Analysis
3. Methods
3.1. Image Datasets
3.2. Image Matching
3.2.1. Estimation of Initial Parameters
3.2.2. Least Squares Iteration
3.3. Computation of Displacement and Deformation
3.3.1. Horizontal Surface Displacement
3.3.2. Surface Strain and Rotation Rates
3.4. Performance Evaluation
4. Results
4.1. Horizontal Surface Displacements
4.2. Precision and Validity of the Displacement Data
4.3. Surface Strain and Rotation Rates
4.3.1. The Muragl Rockglacier
4.3.2. The Nigardsbreen Glacier
4.3.3. The La Clapière Landslide
4.4. Precision and Validity of the Deformation Data
5. Discussion
5.1. Computed Displacements and Deformations
5.2. On the Precision of the Algorithm and Sources of Error
6. Conclusions and Outlook
Acknowledgments
References
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Transformation Parameters of Equations (3) and (4) | Deformation Type Quantified | Visual Example | Significance in Mass Movement |
---|---|---|---|
p1 and p4 | Translation | | Quantifies shift, creep, slip, and slide. Change in position disregarding shape and size. |
p2 and p6 | Scaling | | Measures change in length due to compressive/extending motion. Measures normal strain (elongation). |
p3 and p5 | Shearing (and/or rotation) | | The slippage of orthogonal masses in relation to one another (and/or rigid rotation of the mass). Measures shear strain and/or rotation angle. |
Mass Movement | Muragl Rockglacier (ma−1) | Nigardsbreen Glacier (md−1) | La Clapière Landslide (ma−1) |
---|---|---|---|
Mean | 0.18 | 0.57 | 0.4 |
Standard deviation | 0.09 | 0.32 | 0.32 |
Maximum | 0.5 | 1.1 | 2.75 |
Image Pair | Mean Precision of the Shift Parameters (Pixels) | |
---|---|---|
X-Shift (p1) | Y-Shift (p4) | |
Muragl rockglacier creep | 0.07 | 0.06 |
Nigardsbreen glacier flow | 0.11 | 0.12 |
La Clapière landslide | 0.13 | 0.15 |
Image Pair | MAD (in pixels) | Percent MAD | |
---|---|---|---|
NCC | LSM | Reduction by LSM | |
Simulated (σ2n = 0.01) | 0.38 | 0.04 | 90 |
Simulated (σ2n = 0.1) | 0.42 | 0.2 | 52 |
Muragl rockglacier creep | 2.25 | 1.4 | 37 |
Nigardsbreen glacier flow | 0.47 | 0.34 | 27 |
La Clapière landslide | 2.5 | 2.01 | 19 |
Deformation Parameter | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|
Longitudinal strain rate (ma−1) | 0.00012 | 0.0018 | −0.0077 | 0.0085 |
Transverse strain rate (a−1) | 0.00039 | 0.0016 | −0.0061 | 0.0077 |
Shear strain rate (a−1) | 0.0015 | 0.0016 | 0 | 0.01 |
Rotation rate (degrees a−1) | 0.068 | 0.066 | 0 | 0.44 |
Deformation Parameter | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|
Longitudinal strain rate (d−1) | −0.0003 | 0.0024 | −0.01 | 0.012 |
Transverse strain rate (d−1) | −0.00067 | 0.002 | −0.01 | 0.007 |
Shear strain rate (d−1) | 0.0017 | 0.002 | 0 | 0.019 |
Rotation rate (degrees d−1) | 0.072 | 0.076 | 0 | 0.54 |
Deformation Parameter | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|
Longitudinal strain rate (a−1) | −0.0009 | 0.005 | −0.028 | 0.017 |
Transverse strain rate (a−1) | −0.0007 | 0.005 | −0.01 | 0.017 |
Shear strain rate (a−1) | 0.005 | 0.005 | 0 | 0.03 |
Rotation rate (degrees a−1) | 0.15 | 0.13 | 0 | 0.7 |
Mass Movement Type | Precision of the Parameters | |||
---|---|---|---|---|
Kp2 (p2 = 1 + εx) | Kp3 (P3 = γ1) | Kp5 (P5 = γ2) | Kp6 (P6 = 1 + εy) | |
Muragl rockglacier creep | 0.002 (0.997) | 0.002 (0.021) | 0.002 (0.022) | 0.002 (0.998) |
Nigardsbreen glacier flow | 0.003 (0.997) | 0.003 (0.013) | 0.003 (0.021) | 0.003 (0.999) |
La Clapière landslide | 0.003 (1.001) | 0.003 (0.038) | 0.003 (0.044) | 0.003 (0.098) |
Deformation Parameters | MAD | ||
---|---|---|---|
Nigardsbreen Glacier (d−1) | Muragl Rockglacier (a−1) | La Clapière Landslide (a−1) | |
ɛ̇L | 0.0001 | 0.0005 | 0.006 |
ɛ̇T | 0.0001 | 0.0006 | 0.002 |
ɛ̇LT | 0.0002 | 0.001 | 0.005 |
φ̇TL | 0.008 | 0.05 | 0.1 |
Share and Cite
Debella-Gilo, M.; Kääb, A. Measurement of Surface Displacement and Deformation of Mass Movements Using Least Squares Matching of Repeat High Resolution Satellite and Aerial Images. Remote Sens. 2012, 4, 43-67. https://doi.org/10.3390/rs4010043
Debella-Gilo M, Kääb A. Measurement of Surface Displacement and Deformation of Mass Movements Using Least Squares Matching of Repeat High Resolution Satellite and Aerial Images. Remote Sensing. 2012; 4(1):43-67. https://doi.org/10.3390/rs4010043
Chicago/Turabian StyleDebella-Gilo, Misganu, and Andreas Kääb. 2012. "Measurement of Surface Displacement and Deformation of Mass Movements Using Least Squares Matching of Repeat High Resolution Satellite and Aerial Images" Remote Sensing 4, no. 1: 43-67. https://doi.org/10.3390/rs4010043