Three-dimensional Surface Deformation Research Articles

Three-Dimensional Surface Deformation of the 2022 Mw 6.6 Menyuan Earthquake from InSAR and GF-7 Stereo Satellite Images

Three-Dimensional Surface Deformation of the 2022 Mw 6.6 Menyuan Earthquake from InSAR and GF-7 Stereo Satellite Images

Factors influencing the effectiveness of SM-VCE method in solving 3D surface deformation

The recovery of coseismic 3-dimensional (3D) surface deformation field plays a crucial role in studying seismic source characteristics and earthquake hazards. As of now, there are two main types of methods for recovering coseismic 3D surface deformations: the first type is to solve the problem directly by using the least squares method based on observations from three or more viewpoints, and the second type solves the problem by combining ascending and descending InSAR line-of-sight (LOS) observations with constraint models. The former type is mainly applicable to surface rupture earthquakes, because when an earthquake ruptures to the surface, we can usually obtain surface deformation observations from three or more views. The latter type applies to earthquakes that do not cause surface ruptures and have extensive blind faults. Currently, most research focuses on improving the above types of methods. However, some key factors in the coseismic 3D surface deformation inversion are rarely mentioned, such as the influence of window size on the inversion results in the strain model and variance component estimation method (SM-VCE), and whether the outliers in the observational data are considered. So, we developed a new chain of integrating InSAR observation and SM-VCE model to systematically assess the impacts of window size and outliers on coseismic 3D surface deformation inversions. Through simulation experiments, we observed that the selection of window size significantly impacts the accuracy of the results. Specifically, larger window sizes lead to wider residuals ranges in the fault region, resulting in the loss of extreme solution values when using a window of 15 × 15 pixels (i.e., 7.5 km × 7.5 km). Hence, we recommend utilizing windows with 7 × 7 pixels or 9 × 9 pixels for optimal accuracy, as larger window sizes diminish the significance of the outcomes. The elimination of points displaying different deformation directions helps reduce residuals and preserves near-field deformation results. Furthermore, the residuals along the 3D direction can be reduced by 10%–30% when a small set of points is selected using a method based on Euclidean distances. However, when 441 points were selected, the vertical residuals increased by 22% compared to 81 points. Integration of the SM-VCE algorithm with robust estimation techniques effectively minimizes far-field deformation errors in data, thereby marginally enhancing the near-field deformation solution.

Physics-Informed Approximation of Internal Thermal History for Surface Deformation Predictions in Wire Arc Directed Energy Deposition

Abstract This work presents a physics-informed fusion methodology for deformation detection using multi-sensor thermal data. A challenge with additive manufacturing (AM) is that abnormalities commonly occur due to rapid changes in the thermal gradient. Different non-destructive in-situ thermal sensors capture parts of the thermal history but are limited by the visible temperature spectrum and sensor field of view of the fabrication process. Various sensors mitigate problems with the loss of thermal history information; however, it brings forth challenges with integrating different data streams and the need to interpolate the internal thermal history. This study develops a thermal data-informed heat flux methodology that fills the gap in fusing numerical temperature approximation with data-driven knowledge of the surface of additive manufactured components. First, this study fuses infrared (IR) thermal data complexities during the AM process with the Goldak double ellipsoidal heat flux to model the energy input into the component. Second, a thermal physics-informed model input (PIMI) is created with thermal data-informed heat flux to capture internal thermal history. Lastly, a regression convolutional neural network (CNN) captures the relationship between the three-dimensional thermal gradient and the resulting surface deformation. The rapid thermal gradient formation and identification of deformation is a key step toward using thermal history data and machine learning to improve quality control in AM. The proposed surface deformation detection model achieved an mean squared error of 1.14 mm and an R2 of 0.89 in the case study when fabricating thin-walled structures.

Spatio-temporal relationship between three-dimensional deformations of a collapsible tube and the downstream flowfield

The interactions between fluid flow and structural components of collapsible tubes are representative of those in several physiological systems. Although extensively studied, there exists a lack of characterization of the three-dimensionality in the structural deformations of the tube and its influence on the flow field. This experimental study investigates the spatio-temporal relationship between 3D tube geometry and the downstream flow field under conditions of fully open, closed, and slamming-type oscillating regimes. A methodology is implemented to simultaneously measure three-dimensional surface deformations in a collapsible tube and the corresponding downstream flow field. Stereophotogrammetry was used to measure tube deformations, and simultaneous flow field measurements included pressure and planar Particle Image Velocimetry (PIV) data downstream of the collapsible tube. The results indicate that the location of the largest collapse in the tube occurs close to the downstream end. In the oscillating regime, sections of the tube downstream of the largest mean collapse experience the largest oscillations in the entire tube that are completely coherent and in phase. At a certain streamwise distance upstream of the largest collapse, a switch in the direction of oscillations occurs with respect to those downstream. Physically, when the tube experiences constriction downstream of the location of the largest mean collapse, this causes the accumulation of fluid and build-up of pressure in the upstream regions and an expansion of these sections. Fluctuations in the downstream flow field are significantly influenced by tube fluctuations along the minor axes. The fluctuations in the downstream flowfield are influenced by the propagation of disturbances due to oscillations in tube geometry, through the advection of fluid through the tube. Further, the manifestation of the LU-type pressure fluctuations is found to be due to the variation in the propagation speed of the disturbances during the different stages within a period of oscillation of the tube.

Three-dimensional surface deformation from multi-track InSAR and oil reservoir characterization: A case study in the Liaohe Oilfield, northeast China

Oil productions can result in pore pressure drop in the reservoir, generating an increase in effective stress and leading to reservoir compaction. The compaction in the subsurface reservoir translates to the earth's surface, which is manifested as a loss of elevation (land subsidence), causing damages to oil production facilities and surface infrastructures. The Liaohe oilfield, located in Liaohe River Delta (LRD), northeast of China, is one of the most significant subsidence areas in China as a direct consequence of oil extraction from the reservoir. Previous studies carried out in this area assumed the oil production-induced displacement retrieved from Interferometric Synthetic Aperture Radar (InSAR) corresponds only to vertical deformation. In this work, for the first time, we proposed a method to retrieve the full three-dimensional (3D) displacement field over the oilfield. We retrieved the vertical and east-west displacement components by combining the multiple-geometry InSAR line-of-sight (LOS) observations and retrieved the north-south component based on the assumption of a physical relationship between the horizontal and vertical displacement. Two ascending and two descending datasets from Sentinel-1 satellite covering the area were processed by an InSAR time series analysis over the 2017 to 2021 period, providing consistent displacement rate maps and displacement time series in the LOS direction. Spatial local-scale land subsidence was found in several producing fields over the deltaic region, including Shuguang, Huanxiling, and Jinzhou oilfields. The 3D displacement decomposition was then conducted in Shuguang oilfield. The derived 3D displacement field exhibit a circular subsidence bowl with a maximum subsiding rate reaching 212 mm/year, accompanied by a centripetal pattern of horizontal displacements with maximum rates up to 50–60 mm/year moving towards the subsidence center. The retrieved 3D displacements are in good agreement with predictions from the geomechanical modeling by assuming a disk-shaped reservoir subject to a uniform reduction in pore fluid pressure. Finally, we show the importance of knowing both the vertical and horizontal displacement in characterizing the lateral boundary of the subsurface reservoir.

Coseismic Slip Distribution and Coulomb Stress Change of the 2023 MW 7.8 Pazarcik and MW 7.5 Elbistan Earthquakes in Turkey

On 6 February 2023, the MW 7.8 Pazarcik and the MW 7.5 Elbistan earthquakes occurred in southeastern Turkey, close to the Syrian border, causing many deaths and a great deal of property destruction. The Pazarcik earthquake mainly damaged the East Anatolian Fault Zone (EAFZ). The Elbistan earthquake mainly damaged the Cardak fault (CF) and the Doğanşehir fault (DF). In this study, Sentinel-1A ascending (ASC) and descending (DES) orbit image data and pixel offset tracking (POT) were used to derive surface deformation fields in the range and azimuth directions induced by the Pazarcik and Elbistan earthquakes (hereinafter referred to as the Turkey double earthquakes). Utilizing GPS coordinate sequence data, we computed the three-dimensional surface deformation resulting from the Turkey double earthquakes. The surface deformation InSAR and GPS results were combined to invert the coseismic slip distribution of the EAFZ, CF, and DF using a layered earth model. The results show that the coseismic ruptures of the Turkey double earthquakes were dominated by left-lateral strike-slips. The maximum slip was 7.76 m on the EAFZ and about 8.2 m on the CF. Both the earthquakes ruptured the surface. The Coulomb failure stress (CFS) was computed based on the fault slip distribution and the geometric parameters of all the active faults within 300 km of the MW 7.8 Pazarcik earthquake’s epicenter. The CFS change resulting from the Pazarcik earthquake suggests that the subsequent Elbistan earthquake was triggered by the Pazarcik earthquake. The Antakya fault experienced an increase in CFS of 8.4 bars during this double-earthquake event. Therefore, the MW 6.3 Uzunbağ earthquake on 20 February 2023 was jointly influenced by the Turkey double earthquakes. Through stress analysis of all the active faults within 300 km of the MW 7.8 Pazarcik earthquake’s epicenter, the Ecemis segment, Camliyayla fault, Aadag fault, Ayvali fault, and Pula segment were all found to be under stress loading. Particularly, the Ayvali fault and Pula segment exhibited conspicuous stress loading, signaling a higher risk of future seismic activity.

Correction: Lei et al. Three-Dimensional Surface Deformation Characteristics Based on Time Series InSAR and GPS Technologies in Beijing, China. Remote Sens. 2021, 13, 3964

In the published article [...]

Deriving 3-D Surface Deformation Time Series with Strain Model and Kalman Filter from GNSS and InSAR Data

This study proposes a new set of processing procedures based on the strain model and the Kalman filter (SM-Kalman) to obtain high-precision three-dimensional surface deformation time series from interferometric synthetic aperture radar (InSAR) and global navigation satellite system (GNSS) data. Implementing the Kalman filter requires the establishment of state and observation equations. In the time domain, the state equation is generated by fitting the pre-existing deformation time series based on a deformation model containing linear and seasonal terms. In the space domain, the observation equation is established with the assistance of the strain model to realize the spatial combination of InSAR and GNSS observation data at each moment. Benefiting from the application of the Kalman filter, InSAR and GNSS data at different moments can be synchronized. The time and measurement update steps are performed dynamically to generate a 3-D deformation time series with high precision and a high resolution in the temporal and spatial domains. Sentinel-1 SAR and GNSS datasets in the Los Angeles area are used to verify the effectiveness of the proposed method. The datasets include twenty-seven ascending track SAR images, thirty-four descending track SAR images and the daily time series of forty-eight GNSS stations from January 2016 to November 2018. The experimental result demonstrates that the proposed SM-Kalman method can produce high-precision deformation results at the millimeter level and provide two types of 3-D deformation time series with the same temporal resolution as InSAR or GNSS observations according to the needs of users. The new method achieves a high degree of temporal and spatial fusion of GNSS and InSAR data.

Three-dimensional shear angle determination with application to shear-frame test

The shear frame test is very often used in the context of plastics engineering to examine only the fiber construction for its deformability. Here, it is common to assume a homogeneous deformation, which apparently exists as a global deformation due to the shear frame. This results in the assumption of a constant overall shear angle. In this paper, we compare two analytical approaches to describe the deformation and the resulting strains in detail, particularly, the local shear angle calculation. As a second step, the extension of the shear angle computation based on curvilinear, three-dimensional surface deformations is applied to optical results of the experimental deformation behavior. For this purpose, a three-dimensional image correlation system is drawn on to determine the local, tangential shear angle even for folded fabrics. This requires an approach which is different to the classical digital image correlation method since the speckle varnish influences the deformation of the very compliant fiber bundles. In a third step, the same procedure is applied to the results of three-dimensional finite element computations since the programs do not provide the shear angle measure. The shear angle determination is discussed at various examples. As a side result of the investigations, the material parameters for orthotropic elasticity are determined using a representative volume element approach exploiting μ-CT data. Although the wrinkling prediction calculations depend on the pre-deformation, finite element discretization, and uncertainties of the specimens, calculation results might be used as an indicator to improve the specimen geometries.

Application of a multi-smartphone measurement system in slope model tests

Physical model tests are considered to be useful tools and are widely used in landslide research. The three-dimensional (3D) surface deformation of slope models provides useful information for investigating the behaviour and mechanism of landslides. In this study, a measurement system called a multi-smartphone measurement (MSM) system was proposed and developed to measure the 3D surface deformation of slope models. This system includes nine identical smartphones, a USB hub, a control software package, and some postprocessing software. A series of high-quality images were simultaneously captured through the hardware devices and subsequently processed by using postprocessing software including 3D reconstruction and particle image velocimetry. A comparison with the results of a laser scanner was performed, and the performance of the MSM system was tested in two static models and one dynamic slope model. The system's accuracy was assessed using the root mean square error (RMSE) of the cloud-to-cloud distance. The results show that the accuracy of the MSM system for both the static and dynamic models is less than 1.1 mm. A short-period, low-cost, and easy-to-build system with millimetre accuracy has the potential to become a popular approach for measuring slope models. In addition, the performance of the MSM system is illustrated in three example applications.

Three-Dimensional Surface Deformation Characteristics Based on Time Series InSAR and GPS Technologies in Beijing, China

Excessive exploitation of the groundwater has resulted in obvious three-dimensional (3D) deformation features on the surface of the Beijing Plain. This paper, by combining Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS) technologies, has obtained time-series information of the 3D surface deformation in the Beijing Plain, analyzing its spatial distribution characteristics. On this basis, the relationship between different controlling factors with the 3D deformation of the surface has been analyzed as well. The following results are obtained: (1) From 2013 to 2018, the land subsidence, which generally showed the trend of slowing down, was mainly concentrated in the eastern, northern, and southern regions of Beijing Plain, with multiple subsidence centers. (2) Under the International Terrestrial Reference Frame 2005 (ITRF2005), the horizontal direction of all GPS points in the plain is basically the same, with the dominant movement direction being NE112.5°~NE113.8°. Under the Eurasian reference frame, the horizontal movement rate of GPS points significantly decreases. The movement rate and direction of each point are not characteristic of overall trend activity. (3) The distribution and extent of the 3D surface deformation in the Beijing Plain are controlled by the basement structure. Part of the subsided area corresponds to a Quaternary depression formed at the junction of active faults disrupting the area. Similarly, the distribution of horizontal deformation in the E-W and N-S directions of the plain is controlled by the regional basement structure comprising major faults bounding horizontal deformation. (4) Groundwater exploitation is the main cause of the 3D surface deformation in the Beijing Plain. The groundwater funnels of the second and third confined aquifer are in suitable agreement with the land subsidence. The horizontal movement in the Beijing Plain is either directed toward the center of the groundwater or the land subsidence funnel, and the deformation is directed from areas with higher to areas with lower groundwater levels.

D-InSAR Monitoring Method of Mining Subsidence Based on Boltzmann and Its Application in Building Mining Damage Assessment

Monitoring and predicting mining area subsidence caused by coal mining help effectively control geological disasters. Information regarding small surface deformations can be obtained using a differential interferometric synthetic aperture radar (D-InSAR), which exhibits high monitoring accuracy and can cover large areas; thus, D-InSAR are being applied for mining area settlement monitoring. However, mining areas are prone to large gradient deformations in short durations; obtaining information regarding such deformations is outside the scope of D-InSAR monitoring. To adapt to the characteristics of D-InSAR monitoring, this study selected a Boltzmann function model with a slow boundary convergence rate to address the problem of probabilistic integration methods exhibiting a high boundary convergence rate. The three-dimensional surface deformation of the mining area can be accurately obtained. According to the projection relationship between D-InSAR line of sight (LOS) directional deformation, subsidence, and horizontal movement, a D-InSAR monitoring equation for mining subsidence assisted by Boltzmann is derived. This equation is combined with the shuffled frog leaping algorithm (SFLA) to obtain the parameters to be estimated from the equation. The D-InSAR LOS deformation information of the 13121 working face in the Huainan mining area was obtained from July 14 to October 30, 2019. The proposed method was then used to obtain the predicted parameters of the working face under insufficient mining. The predicted parameters of mining subsidence were calculated to obtain the predicted parameters when it was fully mined. Then, the revised parameters were used to predict the subsidence and horizontal movement of the mining area and compared with the actual leveling observations. The results show that the mean square error of predicted subsidence is 97.1 mm, which is about 3.09% of the maximum subsidence value; the mean square error of predicted horizontal movement is 46.1 mm, which is about 4.1% of the maximum horizontal movement value. The predicted results of the aforementioned method were used to analyze the damage to the buildings above the working face and determine the damage level of the buildings to provide a reference for the demolition and maintenance of the Zhaimiao village.

Retrieving Three-Dimensional Large Surface Displacements in Coal Mining Areas by Combining SAR Pixel Offset Measurements with an Improved Mining Subsidence Model

Interferometric synthetic aperture radar (InSAR) technology can obtain one-dimensional surface displacements in the radar line of sight (LOS). In the field of mining subsidence, large 3D movements often occur at the same time, and hence InSAR derived one-dimensional LOS displacements can hardly reflect the actual surface motion in mining areas. To realize the monitoring of three-dimensional large surface displacements in mining areas, a method for monitoring three-dimensional large surface displacements in mining areas that combines SAR pixel offset tracking (OT) and an improved mining subsidence model is proposed in this article. First, a new functional relationship between surface subsidence and horizontal movement combined with the characteristics of the overburden rock stress and the deformation characteristics of the fractured rock mass in coal mining areas is established. Then, a three-dimensional surface deformation model is established based on the proposed relationship between surface subsidence and horizontal movement and the radar projection equation, and finally, the optimal parameters of the deformation model are inverted iteratively using LOS deformation results obtained by OT method to retrieve the three-dimensional large displacements of the surface. The significant advantage of the method proposed in this article is that it can accurately acquire the 3D large surface displacements using only two SAR amplitude images with the same imaging geometry. To verify the accuracy and reliability of the proposed algorithm, two scenes of high-resolution spotlight TerraSAR-X images are used in this paper to conduct a three-dimensional surface displacement monitoring experiment on a working panel in the Daliuta mining area in Shaanxi Province, China, based on the proposed method. Experimental monitoring results show that the maximum surface subsidence is approximately 4.5 m, and the maximum horizontal movements in the strike and dip directions are approximately 1.4 m and 1.2 m, respectively. Using GPS measurements to verify the monitoring results, the root mean square error (RMSE) of vertical subsidence is 6.8 cm, and the RMSE of horizontal movement is 7.1 cm. Compared with those in the original mining subsidence model, the accuracies of vertical subsidence and horizontal movement in the proposed model are increased by 28.2% and 37.5%, respectively, which proves the reliability and accuracy of the proposed method.

Optimization of three-dimensional multi-level surface deformation in mining areas through integration of deformation fusion model and Lagrange multiplier method based on single high resolution OTD-InSAR pair

Underground longwall mining activities usually induce three-dimensional (3-D) multi-level surface deformation, which could lead to serious natural hazards. Offset-tracking (OT) and differential interferometric synthetic aperture radar (DInSAR) technology (referred to as OTD-InSAR) can be used to observe the large-level and small-level mining deformations based on single InSAR pair, but the measured deformation is only along the radar line-of-sight (LOS) or the azimuth directions rather than in the 3-D directions. The conventional InSAR-based methods to resolve 3-D mining deformation have the strict restrictions and low south-north accuracy. In this paper, a novel methodology is proposed to utilize a multi-level deformation fusion model and the Lagrange multiplier method based on single OTD-InSAR pair (hereafter called MAOTD-InSAR) to estimate and optimize the 3-D multi-level surface deformation. The Daliuta coal mining area of China was selected to verify the feasibility and precision of the proposed method using high resolution TerraSAR-X (TSX) SAR images with six pairs. Results show that the root mean square errors (RMSEs) of MAOTD-InSAR against in-situ measured data are less than 0.2214 m, 0.1612 m and 0.1880 m in the east, north and vertical directions, respectively. The minimum RMSE in the horizontal direction could reach 0.0361 m with an improvement of about 82.6%, which particularly improve the accuracy in the south-north direction for the TSX satellite since its direction of azimuth deformation is approximately north direction, and this is also adequate for the other satellites in the near-polar orbit. In addition, an empirical model was generated with respect to the gradients of ground fissures on horizontal deformation, and this model enabled us to remove large errors caused by ground fissures. The verification results show that the proposed method provides higher precision and reliability for the resolved 3-D multi-level surface deformation, which presents 3-D mining deformation with more details from the edge to the center of the subsidence basin and will show some possibilities for new findings and interpretations in the process of coal mining.

InSAR 3-D Coseismic Displacement Field of the 2015 Mw 7.8 Nepal Earthquake: Insights into Complex Fault Kinematics during the Event

The 2015 Mw 7.8 Gorkha, Nepal, earthquake occurred in the central Himalayan collisional orogenic belt, which demonstrated complex fault kinematics and significant surface deformation. The coseismic deformation has been well documented by previous studies using Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR) data. However, due to some limitations of spatially sparse GPS stations and InSAR only-one-dimensional observation in the line-of-sight (LOS) direction, the complete distribution and detailed spatial variation of the three-dimensional surface deformation field are still not fully understood. In this study, we reconstructed the three-dimensional coseismic deformation fields using multi-view InSAR observations and investigated the refined surface deformation characteristics during this event. We firstly obtained four ascending and descending InSAR coseismic deformation maps from both Sentinel-1A/B and ALOS-2 data. Secondly, we obtained the synthetic north-south deformation field from our best-fitting slip distribution inversions. Finally, we calculated three-dimensional deformation fields, which were consistent with coseismic GPS displacements but with higher resolution. We found that the surface deformation is dominated by horizontal southward motion and vertical uplift and subsidence, with minor east-west deformation. In the north-south direction, the whole deformation area reaches at least 150 × 150 km with a maximum displacement of ~1.5 m. In the vertical direction, two areas, including uplift in the south and subsidence in the north, are mapped with a peak displacement of 1.5 and −1.0 m, respectively. East-west deformation presented a four-quadrant distribution with a maximum displacement of ~0.6 m. Complex thrusting movement occurred on the seismogenic fault; overall, there was southward push motion and wave-shaped fold motion.

Derivation of high-quality three-dimensional surface deformation velocities through multi-source point cloud fusion: Application to Kīlauea volcano

Kīlauea volcano, located in the southeast of Hawai’i, is one of the most active volcanoes in the world. Multi-source InSAR measurements acquired from ascending and descending high-resolution COSMO-SkyMed SAR imagery are used to monitor Kīlauea volcano’s deformations. In order to obtain identical observations from multi-source SAR data, the InSAR measurements acquired by different platforms are generally geocoded and resampled into a unified coordinate system. Such method is however inapplicable to the point clouds provided by high-resolution SAR data. In addition, the geocoding accuracy of high-resolution InSAR measurements would be greatly affected by external DEM error, orbit error, propagation delay, reference point parameter error. In this study, a method for estimating 3-D deformations on the basis of SAR point cloud fusion is proposed. Firstly, iterative closest point (ICP) method is introduced to fuse InSAR point clouds from ascending and descending COSMO-SkyMed datasets to reduce the influence of geocoding offsets. Then, the precise 3-D surface deformations of Kīlauea volcano are obtained by employing the homogeneous weighted observations in the local space based on the strain model. The maximum deformation rates between April 2012 and April 2013 of Kīlauea volcano are estimated as 32 mm/year and 42 mm/year in the east and up directions, respectively. The accuracies of the InSAR measurements are validated by the deformation rates obtained from the precise GNSS observations.

Search Space Reduction for Determination of Earthquake Source Parameters Using PCA andk-Means Clustering

The characteristics of an earthquake can be derived by estimating the source geometries of the earthquake using parameter inversion that minimizes the L2 norm of residuals between the measured and the synthetic displacement calculated from a dislocation model. Estimating source geometries in a dislocation model has been regarded as solving a nonlinear inverse problem. To avoid local minima and describe uncertainties, the Monte-Carlo restarts are often used to solve the problem, assuming the initial parameter search space provided by seismological studies. Since search space size significantly affects the accuracy and execution time of this procedure, faulty initial search space from seismological studies may adversely affect the accuracy of the results and the computation time. Besides, many source parameters describing physical faults lead to bad data visualization. In this paper, we propose a new machine learning-based search space reduction algorithm to overcome these challenges. This paper assumes a rectangular dislocation model, i.e., the Okada model, to calculate the surface deformation mathematically. As for the geodetic measurement of three-dimensional (3D) surface deformation, we used the stacking interferometric synthetic aperture radar (InSAR) and the multiple-aperture SAR interferometry (MAI). We define a wide initial search space and perform the Monte-Carlo restarts to collect the data points with root-mean-square error (RMSE) between measured and modeled displacement. Then, the principal component analysis (PCA) and thek-means clustering are used to project data points with low RMSE in the 2D latent space preserving the variance of original data as much as possible and extractkclusters of data with similar locations and RMSE to each other. Finally, we reduce the parameter search space using the cluster with the lowest mean RMSE. The evaluation results illustrate that our approach achieves 55.1~98.1% reductions in search space size and 60~80.5% reductions in 95% confidence interval size for all source parameters compared with the conventional method. It was also observed that the reduced search space significantly saves the computational burden of solving the nonlinear least square problem.

A New Model for three-dimensional Deformation Extraction with Single-track InSAR Based on Mining Subsidence Characteristics

This paper presents a new model for three-dimensional deformation extraction of single-track interferometric synthetic aperture radar (InSAR) based on mining subsidence characteristics. The model is applied to address the problem of difficult-to-obtain three-dimensional surface deformations in a mining area with high-precision using single-track InSAR. In horizontal or near horizontal coal seam mining regions, land subsidence and horizontal movement are symmetrically distributed along the strike and dip directions of the working face. The proposed method uses this characteristic to calculate the three-dimensional component of surface deformation for the mining area by performing simple addition and subtraction operations on the line-of-sight (LOS) displacement of the symmetric points. Simulations using the developed model show that the root mean square error (RMSE) of the three-dimensional deformations in the vertical, east-west, and north-south directions are 6.9, 5.5 and 8.9 mm, respectively. Experiments were processed using the Sentinel-1A images, and the results show that the vertical displacement generated by the model is consistent with the leveling data. Based on the simulation analysis, it is found that this model can solve the three-dimensional mining deformations, for situations where the strike angle of the coal seam is not perpendicular to the satellite heading.

Experimental study on free-surface deformation and forces on a finite submerged plate induced by a solitary wave

Physical experiments are conducted to study the interaction between a solitary wave and a finite horizontal plate submerged at a depth equal to 1/4 of the water depth. The spatial and temporal variation of the three-dimensional (3D) surface deformation is measured using a multi-lens stereo reconstruction system. The hydrodynamic loads are measured by underwater load cells. The plate-induced shoaling causes 3D wave focusing, leading to an increased maximum elevation along the streamwise centerline of the plate. The detailed wave focusing process and the influence of wave amplitude on focusing are presented based on the results obtained through image processing. The characteristics of the horizontal forces, vertical forces, and pitching moments are discussed. A 6-stage loading process based on the maxima of vertical wave force and pitching moment is proposed. It is coupled with the synchronous surface deformation to reveal the loading mechanism. It proves that the vertical wave force on the plate reduces apparently compared with the results from 2D experiments. The surface elevation and wave-induced load data provide an excellent benchmark for further studies on the 3D nonlinear interaction between a solitary wave and a submerged plate.

Multi-year, three-dimensional landslide surface deformation from repeat lidar and response to precipitation: Mill Gulch earthflow, California

Slow-moving landslides are often the dominant process that shapes hillslopes and delivers sediment to channels in weak lithologies. Understanding what controls their velocities is therefore essential for deciphering their role in landscape evolution and estimating hazards. In this study, we used four sequential airborne lidar data sets to derive the three-dimensional (3D), 1-m spatial resolution surface velocity field of the Mill Gulch earthflow, northern California, for three periods of time spanning a decade. Phase correlation, an image processing technique, applied to the precisely aligned lidar digital elevation models confidently resolved horizontal velocities from 0.2 to 5 m year−1. The velocity field defined three distinct kinematic zones of the landslide with different sensitivities to precipitation, such that the head moved slowly at 0.3–0.5 m year−1, the transport zone moved fastest at 2–5 m year−1, and a forked toe moved intermittently at 0–4 m year−1. Inverting the 3D surface velocity field to infer landslide thickness suggested that the head was underlain by a 6-m-deep, concave-up slip surface, while the transport zone likely had a 1–2.5-m-deep translational slip surface. We hypothesized that velocity in the head was least sensitive to changing precipitation because of its greater inferred depth, which likely dampened the amplitude of pore pressure fluctuations. A lack of major head scarp retrogressions also may have contributed to the relatively steady velocity in the head, while buttressing and debuttressing interactions between the landslide’s toes and the creek running in Mill Gulch may have contributed to the more dramatic changes in velocity in the transport zone and toes. Although predicting landslide velocity from precipitation data alone may therefore be challenging, producing detailed 3D deformation fields from repeat topographic data can be an important tool for deciphering interactions between internal controls, such as changes to landslide geometry, and external controls, such as climate, on landslide motion.