Three-dimensional Surface Deformation Research Articles

Method for determining weight matrix for resolving three-dimensional surface deformation using Multi-LOS D-InSAR technology

Three-dimensional surface deformation is resolved using deformations obtained from multiple line of sight differential interferometry synthetic aperture radar (multi-LOS D-InSAR). However, the random model is susceptible to both accidental errors (such as errors due to noises) and system errors (such as orbital errors and topographic errors). To solve this problem, we present a weight-determining method based on high-precision global positioning system (GPS) observations. Specifically, the precision of multi-LOS D-InSAR deformation observations is evaluated based on high-precision GPS deformation observations from the same period. Then, by considering the influence of system errors and accidental errors on the deformation of a pixel observed by multi-LOS D-InSAR, a combined fitting model associated with the positions and elevations of a pixel is built. Finally, the precision of deformations from multi-LOS D-InSAR is evaluated pixel-by-pixel by using the built model. As a result, the weights of observations in the model for resolving three-dimensional surface deformation using multi-LOS D-InSAR can be determined. We verify the feasibility and precision of the weight-determining method through a simulation experiment and a real data experiment, respectively. The verification results show that the proposed weight-determining method based on high-precision GPS observations provides higher reliability for the resolved three-dimensional surface deformation.

Time-Series SBAS Pixel Offset Tracking Method for Monitoring Three-Dimensional Deformation in a Mining Area

The ground surface deformation caused by mining damages the ecological environment and severely hinder economic development in the mining area. The acquisition of three-dimensional ground surface deformation in a mining area helps to improve understanding of the process and mechanism of ground surface deformation caused by mining and helps to prevent and control this type of disaster. In this paper, eleven TerraSAR-X images and five Radarsat-2 images covering the 52304 working face in the Daliuta mining area were used to obtain the time-series line-of-sight (LOS) direction deformation and azimuth direction deformation based on different SAR platforms by application of the small baseline subset (SBAS) pixel offset tracking method. According to the three-dimensional solution principle of multiplatform SAR images and 72 GPS points, the accuracy of deformation in the east-west direction is 0.22 m, while the accuracy in the north-south direction is 0.21 m, with an accuracy of subsidence of 0.34 m.

Measurement of three-dimensional surface deformation of ceramic materials by digital image correlation (DIC) method

Measurement of three-dimensional surface deformation of ceramic materials by digital image correlation (DIC) method

Fusion of GPS and InSAR data to derive robust 3D deformation maps based on MRF L1-regularization

ABSTRACTTo achieve the three-dimensional surface deformation maps, interferometric synthetic aperture radar (InSAR) and global position system (GPS) data are integrated. In this letter, Markov random field-based L1 regularization is proposed to reconstruct the Gibbs energy equation for improving the previous three-dimensional optimized model. Furthermore, differential evolution algorithm is used to minimize the energy function for deriving the three optimal components of the ground motion. The new method proposed in this paper is then applied to derive the three-dimensional deformation maps of the 2016 Kumamoto earthquake. The Experimental results show that our new method achieves considerably higher performance than the more standard L2-based method. The root mean square errors for the three components of east, north and up are 1.45, 1.87 and 2.14 cm, respectively, which are smaller than the L2-based method, especially in the vertical direction.

Surface deformation analysis of collapsed lungs using model-based shape matching

PurposeTo facilitate intraoperative localization of lung nodules, this study used model-based shape matching techniques to analyze the inter-subject three-dimensional surface deformation induced by pneumothorax. Methods: Contrast- enhanced computed tomography (CT) images of the left lungs of 11 live beagle dogs were acquired at two bronchial pressures (14 and 2 cm,hbox {H}_2hbox {O}). To address shape matching problems for largely deformed lung images with pixel intensity shift, a complete Laplacian-based shape matching solution that optimizes the differential displacement field was introduced.ResultsExperiments were performed to confirm the methods’ registration accuracy using CT images of lungs. Shape similarity and target displacement errors in the registered models were improved compared with those from existing shape matching methods. Spatial displacement of the whole lung’s surface was visualized with an average error of within 5 mm.ConclusionThe proposed methods address problems with the matching of surfaces with large curvatures and deformations and achieved smaller registration errors than existing shape matching methods, even at the tip and ridge regions. The findings and inter-subject statistical representation are directly available for further research on pneumothorax deformation modeling.

Measurement of the three-dimensional surface deformation of the Jiaju landslide using a surface-parallel flow model

ABSTRACTSAR Interferometry (InSAR) is a powerful technique for mapping land surface deformation, but single one-dimensional (1D) InSAR line-of-sight (LOS) measurement limits its application in three-dimensional (3D) displacement retrieval. Traditional methods were developed for measuring large-scale deformation. In this paper, to retrieve the slow 3D deformation process in the Jiaju landslide, a surface-parallel flow model is applied, according to the existing geological data gained from this landslide. Nine ENVISAT ASAR images and 19 ALOS PALSAR images were collected to reconstruct the 3D deformation field. An iterative method for correcting the characteristic value (IMCCV) with maximum likelihood estimation (M-estimation) adaptively generates an accurate stochastic model. The 3D deformation measurements show that the northern part of the Jiaju landslide clearly had horizontal deformation with the largest deformation velocity exceeding 15 cm year−1, while the southern part was relatively stable. Similarly, large vertical deformation appeared in the northern part (−2 cm year−1) and little deformation occurred in the southern part (−0.5 cm year−1). Compared with GPS measurements, the standard deviation is 1.4 cm year−1 and 0.7 cm year−1 in horizontal and vertical directions, respectively. Therefore, the Jiaju landslide exhibited movements in the horizontal direction accompanied by slight settlement in the vertical direction.

Retrieval of Three-Dimensional Surface Deformation Using an Improved Differential SAR Tomography System

Conventional differential synthetic aperture radar tomography (D-TomoSAR) can only capture the scatterers’ one-dimensional (1-D) deformation information along the line of sight (LOS) of the synthetic aperture radar (SAR), which means that it cannot retrieve the three-dimensional (3-D) movements of the ground surface. To retrieve the 3-D deformation displacements, several methods have been proposed; the performance is limited due to the insufficient sensitivity for retrieving the North-South motion component. In this paper, an improved D-TomoSAR model is established by introducing the scatterers’ 3-D deformation parameters in slant range, azimuth, and elevation directions into the traditional D-TomoSAR model. The improved D-TomoSAR can be regarded as a multi-component two-dimensional (2-D) polynomial phase signal (PPS). Then, an effective algorithm is proposed to retrieve the 3-D deformation parameters of the ground surface by the 2-D product high-order ambiguity function (PHAF) with the relax (RELAX) algorithm. The estimation performance is investigated and compared with the traditional algorithm. Simulations and experimental results with semi-real data verify the effectiveness of the proposed signal model and algorithm.

Mapping three-dimensional co-seismic surface deformations associated with the 2015 MW7.2 Murghab earthquake based on InSAR and characteristics of crustal strain

Three-dimensional (3D) co-seismic surface deformations are of great importance to interpret the characteristics of co-seismic deformations and to understand the geometries and dynamics of seismogenic faults. In this paper, we propose a method for mapping 3D co-seismic deformations based on InSAR observations and crustal strain characteristics. In addition, the search strategy of correlation points is optimized by adaptive correlation distance, which greatly improves the applicability of the proposed method in restoring deformations in decorrelation areas. Results of the simulation experiment reveal that the proposed method is superior to conventional methods in both the accuracy and completeness. The proposed method is then applied to map the 3D co-seismic surface deformations associated with the 2015 M W7.2 Murghab earthquake using ascending and descending ALOS-2 PALSAR-2 images. The results show that the seismogenic fault is the Sarez-Karakul fault (SKF), which is dominated by NE-SW strike slips with an almost vertical dip angle. The north section and the south segment near the epicentre have obvious subsidence along with a southwestward motion in the northwest wall, and the southeast wall has northeast movement and surface uplift trend along the fault zone. The strain field of the earthquake is also obtained by the proposed method. It is found that the crustal block of the seismic area is obviously affected by dilatation and shear forces, which is in good agreement with the movement character of the sinistral slip.

Mapping three-dimensional surface deformation caused by the 2010 Haiti earthquake using advanced satellite radar interferometry.

Mapping three-dimensional (3D) surface deformation caused by an earthquake is very important for the environmental, cultural, economic and social sustainability of human beings. Synthetic aperture radar (SAR) systems made it possible to measure precise 3D deformations by combining SAR interferometry (InSAR) and multiple aperture interferometry (MAI). In this paper, we retrieve the 3D surface deformation field of the 2010 Haiti earthquake which occurred on January 12, 2010 by a magnitude 7.0 Mw by using the advanced interferometric technique that integrates InSAR and MAI data. The surface deformation has been observed by previous researchers using the InSAR and GPS method, but 3D deformation has not been measured yet due to low interferometric coherence. The combination of InSAR and MAI were applied to the ALOS PALSAR ascending and descending pairs, and were validated with the GPS in-situ measurements. The archived measurement accuracy was as little as 1.85, 5.49 and 3.08 cm in the east, north and up directions, respectively. This result indicates that the InSAR/MAI-derived 3D deformations are well matched with the GPS deformations. The 3D deformations are expected to allow us to improve estimation of the area affected by the 2010 Haiti earthquake.

Measurement of three-dimensional surface deformation by Cosmo-SkyMed X-band radar interferometry: Application to the March 2011 Kamoamoa fissure eruption, Kīlauea Volcano, Hawai'i

Abstract Three-dimensional (3D) surface deformation is retrieved for the March 6–10, 2011 (UTC dates), Kamoamoa fissure eruption along the East Rift Zone of Kīlauea Volcano, Hawai'i, through the integration of multi-temporal synthetic aperture radar (SAR) interferometry (InSAR) and multiple-aperture interferometry (MAI) measurements from the COSMO-SkyMed X-band SAR. The measurement accuracies of 1) the individual and multi-stacked MAI interferograms and 2) the 3D deformation, which is measured from COSMO-SkyMed data, are assessed using continuous GPS stations. The root-mean-square (RMS) errors of individual MAI interferograms for descending and ascending data are 2.97 ± 0.6 cm and 3.20 ± 0.62 cm, respectively. The MAI interferograms stacked from multi-temporal observations can produce better results by emphasizing surface deformation signals, with the RMS errors of 1.06 and 1.24 cm for descending and ascending data, respectively. The empirical equations for measurement uncertainties are determined with respect to interferometric coherence for individual and stacked MAI interferograms. An assessment of the 3D components of deformation was performed as well, and RMS errors of 0.75, 0.83, and 0.68 cm were estimated in the east, north, and up directions. A performance test of magma source model parameter estimations was carried out by using the InSAR and 3D measurements. From the 3D deformation field, we found that the magma chamber source at the Kīlauea caldera should be modeled by the spheroid source rather than the simple point source. The performance comparison between the InSAR and 3D modeled results showed that the 3D deformation field allows for precise model parameter estimation.

Optical microscope for three-dimensional surface displacement and shape measurements at the microscale.

We report a novel optical microscope for full-field, noncontact measurements of three-dimensional (3D) surface deformation and topography at the microscale. The microscope system is based on a seamless integration of the diffraction-assisted image correlation (DAIC) method with fluorescent microscopy. We experimentally demonstrate the microscope's capability for 3D measurements with submicrometer spatial resolution and subpixel measurement accuracy.

Notch root strain measurement of WE43-T6 magnesium alloy using electronic speckle pattern interferometry

The notch root elasto-plastic strains of circumferentially grooved round specimen of cast magnesium WE43-T6 were experimentally measured using the electronic speckle pattern interferometry (ESPI) and numerically evaluated using the finite element analysis (FEA). The specimens have notch radii of 1.6mm and 0.8mm and an opening angle of 60°. The technique of ESPI showed its accuracy in measuring three-dimensional surface deformations on large negatively curved manifolds. The measured nominal stress for rupture is well beyond the ultimate strength, suggesting the existence of significant biaxial stress at the notch root region. The ESPI-based strains on the notch tips were shown to be in agreement with those evaluated by the FEA. The FEA also showed that the maximum elastic strain is shifted away from the notch root surface as the plastic strain is predominant.

Mapping Three-Dimensional Surface Deformation by Combining Multiple-Aperture Interferometry and Conventional Interferometry: Application to the June 2007 Eruption of Kilauea Volcano, Hawaii

Surface deformation caused by an intrusion and small eruption during June 17-19, 2007, along the East Rift Zone of Kilauea Volcano, Hawaii, was three-dimensionally reconstructed from radar interferograms acquired by the Advanced Land Observing Satellite (ALOS) phased-array type L-band synthetic aperture radar (SAR) (PALSAR) instrument. To retrieve the 3-D surface deformation, a method that combines multiple-aperture interferometry (MAI) and conventional interferometric SAR (InSAR) techniques was applied to one ascending and one descending ALOS PALSAR interferometric pair. The maximum displacements as a result of the intrusion and eruption are about 0.8, 2, and 0.7 m in the east, north, and up components, respectively. The radar-measured 3-D surface deformation agrees with GPS data from 24 sites on the volcano, and the root-mean-square errors in the east, north, and up components of the displacement are 1.6, 3.6, and 2.1 cm, respectively. Since a horizontal deformation of more than 1 m was dominantly in the north-northwest-south-southeast direction, a significant improvement of the north-south component measurement was achieved by the inclusion of MAI measurements that can reach a standard deviation of 3.6 cm. A 3-D deformation reconstruction through the combination of conventional InSAR and MAI will allow for better modeling, and hence, a more comprehensive understanding, of the source geometry associated with volcanic, seismic, and other processes that are manifested by surface deformation.

Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.

Large-scale turbulence under a solitary wave: Part 2: Forms and evolution of coherent structures

The instantaneous turbulent velocity field produced by a broken solitary wave propagating on a 1 in 50 plane slope was measured in the longitudinal transverse plane in the middle part of the water column and near the bottom using a stereoscopic particle image velocimetry system. These measurements showed that large-scale turbulence first arrived in the form of a downburst of turbulent fluid. In the middle of the water column, the downbursts arrived shortly after the wave crest had passed. Each downburst was accompanied by two counter-rotating vortices. The latter grew rapidly in size to become a prominent feature of the flow field. Each vortex had a typical length scale of 1/2 to 1 water depth, and carried most of the turbulent kinetic energy in the region between the vortices. Near the bottom, the counter-rotating vortices were not as well defined and covered only a small plane area compared to the entire flow structure. The turbulent fluid descending from above diverged at the bed and the resulting flow structure developed an elongated shape as the source of down-flow travelled onshore with the broken wave. It was found that the transverse spacing between adjacent downbursts ranged from 2 to 5 times the local still water depth. Since vortices cannot end in the interior of the fluid, the counter-rotating vortices must extend to the free surface in the form of a vortex loop. It was suggested that these vortex loops were produced by bending and stretching of primary vorticity generated in the wave breaking process, possibly as a result of three-dimensional water surface deformation. The vortex loops were then carried downward by the falling water from the broken wave.

Three-dimensional deformation and strain induced by municipal pumping, Part 2: Numerical analysis

Summary Field measurements consisting of water levels from a municipal well and three-dimensional surface deformations and strains from high-precision GPS measurements at various radial distances from the well were collected as part of a 62-day controlled aquifer test at Mesquite, NV. These measurements were used as observations in several numerical models and a parameter estimation code to characterize and constrain hydraulic and mechanical properties of a 400 m thick basin-fill aquifer. A parsimonious approach was used in conceptualizing the aquifer system. Nonetheless, results from the calibrated deformation and flow models accurately reproduced the observed head and deformations during the first 20 days of pumping, the time at which a new equilibrium was achieved. Surface deformations were shown to reflect hydraulic anisotropy and direction of principal conductivity. In addition, the radius of influence and cone of depression from pumping was approximated in spite of the fact that no monitoring well data existed at the site. Sensitivity analysis indicates that cyclical head values are most sensitive to changes in horizontal hydraulic conductivity, while time-dependent vertical deformations are most sensitive to changes in skeletal specific storage. This investigation shows that GPS monitoring can be used in place of costly monitoring wells to characterize aquifers for water-management purposes where skeletal deformation tends to be elastic.

Speckle interferometry: a novel method to map three-dimensional surface deformations of small bone samples

Speckle interferometry: a novel method to map three-dimensional surface deformations of small bone samples

Three-dimensional deformation and strain induced by municipal pumping, part 1: Analysis of field data

A 62-day controlled aquifer test was performed at the site of a new municipal well that penetrates a thick sequence of compressible basin-fill deposits in Mesquite, Nevada. Observation data were acquired from a high precision Global Positioning System (GPS) network to accompany the water-level data from the pumped well and a nearby observation well. The purpose of the investigation was to quantify and characterize three-dimensional surface deformation and strain associated with cyclic pumping and to evaluate aquifer properties on the basis of these data. Results indicate that both horizontal (<8 mm total displacement with 0.2 mm precision) and vertical deformation (<12 mm total displacement with 2 mm precision) were measured within the first 22 days of pumping with a slowly migrating outward wave of compressional strain in spite of the fact that an 83-m brittle unsaturated zone resided over the dynamically active aquifer. The hydraulic head and strain data indicate that steady-state pumping conditions were likely reached after 35–40 days. Results also indicate that vertical mechanical rebound occurs after about 35 days even though the rate of pumping remains unchanged. Strain analyses indicate that this result is due to the changing shape in the pore structure of the pumped aquifer as an elongation occurs in the horizontal direction to more than accommodate a small compressional strain in the vertical direction. Uniaxial specific storage was estimated from time-subsidence data to be 2.8×10 −6 /m. GPS-observed deformations reveal a mechanical and hydraulic anisotropy field that increases in rotation toward the northwest and in magnitude from west to east at the study site. This represents the first investigation where the magnitude and direction of the hydraulic conductivity tensor of the aquifer is estimated without using well data.

Runup and rundown generated by three-dimensional sliding masses

To study the waves and runup/rundown generated by a sliding mass, a numerical simulation model, based on the large-eddy-simulation (LES) approach, was developed. The Smagorinsky subgrid scale model was employed to provide turbulence dissipation and the volume of fluid (VOF) method was used to track the free surface and shoreline movements. A numerical algorithm for describing the motion of the sliding mass was also implemented. To validate the numerical model, we conducted a set of large-scale experiments in a wave tank of 104m long, 3.7m wide and 4.6m deep with a plane slope (1:2) located at one end of the tank. A freely sliding wedge with two orientations and a hemisphere were used to represent landslides. Their initial positions ranged from totally aerial to fully submerged, and the slide mass was also varied over a wide range. The slides were instrumented to provide position and velocity time histories. The time-histories of water surface and the runup at a number of locations were measured. Comparisons between the numerical results and experimental data are presented only for wedge shape slides. Very good agreement is shown for the time histories of runup and generated waves. The detailed three-dimensional complex flow patterns, free surface and shoreline deformations are further illustrated by the numerical results. The maximum runup heights are presented as a function of the initial elevation and the specific weight of the slide. The effects of the wave tank width on the maximum runup are also discussed.

Advances in light microscope stereo vision

The increasing research focus on small-scale mechanical systems has generated a need for deformation and strain measurement systems for microscale applications. Optical measurement systems, such as digital image correlation, present an obvious choice due to their non-contacting nature. However, the transfer of measurement technology developed for macroscale applications to the microscale presents unique challenges due to the differences in the required highmagnification optics. In this paper we illustrate the problems involved in calibrating a stereo microscope using traditional techniques and present a novel methodology for acquiring accurate, three-dimensional surface shape and deformation data on small-scale specimens.