Atmospheric Phase Screen Research Articles

Waveform Distortion of Gaussian Beam in Atmospheric Turbulence Simulated by Phase Screen Method

The atmospheric turbulence phase screen is generated based on the power spectrum inversion method, and the multiple transmission processes are statistically averaged. The waveform distortion of the Gaussian beam in the atmospheric turbulence is analyzed; the simulation results show that the property of Gaussian beam has been destroyed after its passing through the atmospheric turbulence. When the beam waist radius is close to a certain radius, the degree of change becomes larger. When it approaches the critical value, the wave surface no longer changes sharply, and as the turbulence intensity increases, the phase fluctuation becomes more and more severe, the coherence of the beam is destroyed, and the spot may be split into several pieces. Finally, the relationship of intensity fluctuation, amplitude fluctuation, and bit error rate with distance is analyzed.

A Parametric-Model-Based Approach for Atmospheric Phase Screen Removal in Ground-Based Interferometric SAR

A Parametric-Model-Based Approach for Atmospheric Phase Screen Removal in Ground-Based Interferometric SAR

Kotrupi landslide deformation study in non-urban area using DInSAR and MTInSAR techniques on Sentinel-1 SAR data

The DInSAR (Differential Interferometric SAR) and MTInSAR (Multi-Temporal Interferometric SAR) techniques are used to examine a surface displacement in the Kotrupi Region in this paper. DInSAR and MTInSAR are capable of determining the surface deformation of a rapidly moving landslide. The Vertical Line of Sight (LOS) displacements were estimated with millimeter accuracy using a DInSAR technique followed by phase unwrapping. MTInSAR approaches using APS (Atmospheric Phase Screen) and sparse point processing, on the other hand, measure earth surface displacements and track their trends over time. DInSAR is limited by several difficulties, including phase decorrelation errors, phase unwrapping errors, and atmospheric phase disturbances, all of which reduce the quality of deformation effects. MTInSAR approaches, on the other hand, use data from several different periods within the same temporal baseline. As a result, the effect atmospheric phase disturbances and unwrapping error is greatly decreased when compared to classic DInSAR approaches. After the Kotrupi landslide of August 13, 2017, conventional DInSAR with a single pair of SLC (Single Look Complex) Sentinel-1 SAR images showed a maximum displacement value of about −60 mm to 60 mm in the Kotrupi landslide runoff region. While the advanced MTInSAR results indicate a maximum rate of velocity of about −45 mm/year for the continuous deformation happening in the Kotrupi landslide area. The coherence values along Pathankot National Highway (NH) −154 before and after the landslide were 0.857 and 0.019, respectively. Deformation studies before and after the landslide occurrence are also conducted using a DEM (Digital Elevation Model). Based on the DEM obtained, erosional and depositional deformations of −3.5 m and +3.0 m have been recorded in the Kotrupi landslide runoff area, resulting in 6–7 m change and material loss. The Root Mean Square Error (RMSE) for MTInSAR DEM 0.787 m and DInSAR DEM 1.026 m was estimated after the DEMs produced from DInSAR and MTInSAR processing were compared with TanDEM-X. MTInSAR produces much better results than DInSAR in non-urban areas.

Comparison of different atmospheric phase screen correction models in ground-based radar interferometry for landslide and open-pit mine monitoring

ABSTRACT Although the atmospheric compensation models developed to date have been generally robust and effective for InSAR, how to choose the right atmospheric correction method for ground-based InSAR is worth studying. This paper uses different methods for atmospheric phase screen (APS) compensation based on studies of ground-based radar (GBR) to zero-baseline acquisitions over the Woda landslide in Sichuan, China. This landslide has a steep topography, thick fog, turbulent rivers and strong rains. Data were acquired at the Ku-band using a GAMMA Portable Radar Interferometer II (GPRI-II) in multiple campaigns (4 July 2019–13 July 2019). In 2019, the Miyun open-pit mine was also studied; the maximum deformation reached 4.03 mm/hour. The collected data were processed within one unit based on the small baseline set (SBAS) approach. The experimental results show the following (1) For long-distance monitoring with complex atmospheric disturbances, range- and/or height-dependent models fail. (2) The iterative decomposition (ITD) method can effectively address complex atmospheric disturbances. (3) If the threshold of wavelength is set to be large, the ITD method becomes a stratified model.

Tropospheric Correction of Sentinel-1 Synthetic Aperture Radar Interferograms Using a High-Resolution Weather Model Validated by GNSS Measurements

Synthetic Aperture Radar Interferometry (InSAR) is a space geodetic technique used for mapping deformations of the Earth’s surface. It has been developed and used increasingly during the last thirty years to measure displacements produced by earthquakes, volcanic activity and other crustal deformations. A limiting factor to this technique is the effect of the troposphere, as spatial and temporal variations in temperature, pressure, and relative humidity introduce significant phase delays in the microwave imagery, thus “masking” surface displacements due to tectonic or other geophysical processes. The use of Numerical Weather Prediction (NWP) models as a tropospheric correction method in InSAR can tackle several of the problems faced with other correction techniques (such as timing, spatial coverage and data availability issues). High-resolution tropospheric modelling is particularly useful in the case of single interferograms, where the removal of the atmospheric phase screen (and especially the highly variable turbulent component) can reveal large-amplitude deformation signals (as in the case of an earthquake). In the western Gulf of Corinth, prominent topography makes the removal of both the stratified and turbulent atmospheric phase screens a challenging task. Here, we investigate the extent to which a high-resolution WRF 1-km re-analysis can produce detailed tropospheric delay maps of the required accuracy by coupling its output (in terms of Zenith Total Delay or ZTD) with the vertical delay component in GNSS measurements. The model is operated with varying physical parameterization in order to identify the best configuration, and validated with GNSS zenithal tropospheric delays, providing a benchmark of real atmospheric conditions. We correct sixteen Sentinel-1A interferograms with differential delay maps at the line-of-sight (LOS) produced by WRF re-analysis. In most cases, corrections lead to a decrease in the phase gradient, with average root-mean-square (RMS) and standard deviation (SD) reductions in the wrapped phase of 6.0% and 19.3%, respectively. Results suggest a high potential of the model to reproduce both the long-wavelength stratified atmospheric signal and the short-wave turbulent atmospheric component which are evident in the interferograms.

Novel Model-Based Approaches for Non-Homogenous Atmospheric Compensation of GB-InSAR in the Azimuth and Horizontal Directions

Atmospheric disturbance is a main interference for deformation monitoring by GB-InSAR. Most approaches for atmospheric correction are based on the homogenous atmospheric medium assumption that usually does not hold due to complex topography and various environmental factors, leading to low atmospheric correction accuracy. This study proposes two novel model-based approaches for non-homogenous atmospheric compensation in the azimuth and horizontal directions. The conception of a coordinate system is introduced to design the model for the first time. The 2D atmospheric compensation method designed based on the polar coordinate system can address the non-homogenous atmospheric phase screen (APS) correction in the azimuth direction. The 3D atmospheric compensation method based on the rectangular coordinate system deals with the non-homogenous APS in all three directions, and can better address the non-homogenous APS in the elevation direction than the 2D method. Compared with conventional models, the 2D and 3D models consider the other non-homogenous APS conditions in their respective coordinate systems, which helps to broaden the application of model-based approaches. Experiments using different equipment over two study areas are conducted to test the efficiency of the proposed models. The results demonstrate that the proposed approaches can eliminate non-homogenous atmospheric disturbance and enhance the accuracy of GB-InSAR atmospheric compensation, leading to great improvements in slope deformation estimation.

Corrections to “Iterative Atmospheric Phase Screen Compensation for Near-Real-Time Ground-Based InSAR Measurements Over a Mountainous Slope”

Corrections to “Iterative Atmospheric Phase Screen Compensation for Near-Real-Time Ground-Based InSAR Measurements Over a Mountainous Slope”

Topography-correlated atmospheric signal mitigation for InSAR applications in the Tibetan plateau based on global atmospheric models

ABSTRACT Atmospheric heterogeneity mainly exposes itself as tropospheric-phase delay in Satellite Interferometric Synthetic Aperture radar (InSAR) observations, which smears or even overshadows the deformation component of InSAR measurements. In this study, we estimated the performance of four Global Atmospheric Models (GAMs), i.e. European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5), ERA-Interim (ERA-I), Modern-Era Retrospective analysis for Research and Applications v2 (MERRA2) and Generic Atmospheric Correction Online Service for InSAR (GACOS), for tropospheric-phase delay reduction in InSAR applications in the Tibetan plateau, of which ERA5 is the latest GAM released by ECMWF. We demonstrated the effectiveness of Atmospheric Phase Screen (APS) correction using the four GAMs for more than 700 Sentinel-1 Terrain Observation by Progressive Scans interferograms covering two study areas in the southern (R1) and northwest margins (R2) of the Tibetan plateau. Topography-correlated signals have been widely observed in these interferograms, which are most likely due to the APS effects. We calculated the Standard Deviations (SD) and Pearson’s Correlation Coefficients (r) between InSAR Line of Sight measurements and topography before and after applying APS correction. The results show that the SDs of non-deformation areas from the GAMs decrease to approximately 4 mm from around 10 mm and 12 mm originally on average for R1 and R2, respectively, and the r after the APS correction are reduced below 0.4 from around 0.8 for the selected interferometric pairs. In addition, as the newly released GAM, ERA5 has similar performance with GACOS products and outperforms other models generally. This suggests that GAMs, particularly ERA5, have great potential in the APS correction for InSAR applications in the Tibetan plateau.

Deriving Centimeter-Level Coseismic Deformation and Fault Geometries of Small-To-Moderate Earthquakes From Time-Series Sentinel-1 SAR Images

Small-to-moderate earthquakes (e.g. ≤Mw5.5) occur much more frequently than large ones (e.g. >Mw6.0), yet are difficult to study with InSAR due to their weak surface deformation that are severely contaminated by atmospheric delays. Here we propose a stacking method using time-series SAR images that can effectively suppress atmospheric phase screens and extract weak coseismic deformation in centimeter to sub-centimeter level. Using this method, we successfully derive coseismic surface deformations for three small-to-moderate (Mw∼5) earthquakes in Tibet Plateau and Tienshan region from time-series Sentinel-1 SAR images, with peak line-of-sight deformation ranging from 5–6 mm to 13 mm. We also propose a strategy to downsample interferograms with weak deformation signal based on quadtree mesh obtained from preliminary slip model. With the downsampled datasets, we invert for the centroid locations, fault geometries and slips of these events. Our results demonstrate the potential of using time-series InSAR images to enrich earthquake catalog with geodetic observations for further study of earthquake cycle and active tectonics.

Efficient Approach for Atmospheric Phase Screen Mitigation in Time Series of Terrestrial Radar Interferometry Data Applied to Measure Glacier Velocity

The accuracy of surface displacements measured by differential radar interferometry is significantly degraded by the atmospheric phase screen (APS). This article presents a practical and efficient approach for APS mitigation based on the coherent pixels technique (CPT) displacement velocity estimation algorithm. In the proposed approach, all motionless coherent pixels closest to the moving area are defined as seeds surrounding the moving area at the integration step of the CPT. This arrangement consequently minimizes the integration path and the APS effect in the final velocity result. It is designed for terrestrial radar interferometry (TRI) applications. A piecewise processing chain is further introduced as a continuous operational mode processing framework to derive arbitrary temporal displacement patterns in this work. Three-day datasets measured by Ku-band TRI over a mountainous region in the canton of Valais, Switzerland, were used for validation. Through this validation, a comparative study of five algorithms was carried out. This evaluation showed the efficiency of the proposed approach. The proposed approach does not require phase unwrapping, kriging interpolation, and spatio-temporal covariance inference for APS mitigation, which is appropriate for continuous TRI operation.

On the Definition of the Strategy to Obtain Absolute InSAR Zenith Total Delay Maps for Meteorological Applications

Atmospheric Phase Screens (APSs) derived from Interferometric Synthetic Aperture Radar (InSAR) observations contain the difference between the tropospheric water vapor induced delay of two acquisition epochs, i.e. the slave and the master (or reference) epochs. Using estimates of the atmospheric state coming from independent sources, for example numerical models and/or Global Navigation Satellite System (GNSS) observations, the APSs can be transformed into absolute maps of Tropospheric Delay (Zenith Total Delay or ZTD), related to the columnar atmospheric water vapor content. In this work, a systematic comparison between various APS and ZTD products aims to determine a convenient strategy to go from APSs to InSAR-derived absolute ZTD maps, highlighting the uncertainties and approximations introduced in the entire processing. The main problem to solve is the evaluation of a sufficiently accurate high resolution master delay map. Different sources of data and two different approaches to derive the master are validated and compared to define the most suitable strategy for meteorological applications. Maps of ZTD obtained by an iterative interpolation of a global atmospheric circulation model values result more suited than those derived from the assimilation of GNSS observations into a NWP model. A time average approach to estimate the master map is more robust than the single epoch approach with respect to the choice of the master epoch. Still the choice of a proper master epoch in the InSAR processing chain as well as that of the maps to be averaged result crucial in the estimate of the master.

Triggered afterslip on the southern Hikurangi subduction interface following the 2016 Kaikōura earthquake from InSAR time series with atmospheric corrections

The 2016 Mw 7.8 Kaikōura earthquake represents an extremely complex event involving over ten major crustal faults, altering conventional understanding of multi-fault ruptures. Although evidence for coseismic slip on the Hikurangi subduction interface is controversial, we present afterslip on the subduction zone beneath Marlborough using 13 months of Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS) observations. The spatially and temporally correlated atmospheric errors in SAR interferograms are problematic, and hence a new InSAR time series approach, combining the Generic Atmospheric Correction Online Service (GACOS) with a spatial-temporal Atmospheric Phase Screen (APS) filter to facilitate the InSAR time series analysis, is developed. For interferograms with over 250 km spatial extent, we achieve a 0.77 cm displacement RMS difference against GPS, improving 61% from the conventional InSAR time series method (TS). Comparisons between the overlapping region of two independent tracks show an RMS difference of 1.1 cm for the TS-GACOS-APS combined method, improving 54% from the TS method and 27% from using TS with an APS filter only. The APS filter reduces the short wavelength residuals substantially, but fails to remove the long wavelength error even after the ramp removal, revealing that the GACOS correction has played a key role in mitigating long wavelength atmospheric effects. The resultant InSAR displacements, together with the GPS displacements, are used to recover the time-dependent afterslip distribution on the Hikurangi subduction interface, which provides insights for reviewing the co-seismic slip sources, the present status of the subduction plate boundary and future seismic hazards.

ARU-Net: Reduction of Atmospheric Phase Screen in SAR Interferometry Using Attention-Based Deep Residual U-Net

Atmospheric phase screen (APS) is a very critical issue for the application of interferometric synthetic aperture radar (InSAR) techniques. The spatial-temporal variations of APS are the dominant error source in interferograms and may completely mask displacement signals. Many external meteorological data-based methods and phase-based methods have been developed in the past decades, but all have their inherent limitations. In this article, we propose a deep learning-based method, which is based on an attention-based deep residual U-shaped network (ARU-Net), to mitigate atmospheric artifacts. With this approach, APS patches and clean interferogram patches are sampled from InSAR interferograms to train the network. After training, the network can be used to mitigate the APS for individual interferograms. Compared with the generic atmospheric correction model (GACOS) and the advanced time-series InSAR method distributed scatterer interferometry (DSI), the key advantage of our method is that atmospheric delay can be effectively learned and removed from individual high-resolution interferometric phase itself without external data. Accuracy was validated by using individual and stacked interferograms from TerraSAR-X data over the Hong Kong International Airport (HKIA) and Hong Kong Science Park (HKSP) sites. The results showed that our method consistently delivered greater standard deviation (SD) reduction after APS correction than the GACOS method. Moreover, the time-series results were in agreement with the DSI and leveling measurements. The effectiveness of the proposed ARU-Net to remove APS effects from interferograms shows great potential for the development of a new set of deep learning-based APS reduction methods.

Iterative Atmospheric Phase Screen Compensation for Near-Real-Time Ground-Based InSAR Measurements Over a Mountainous Slope

In this article, an atmospheric phase screen (APS) compensation algorithm for a near real-time ground-based interferometry synthetic aperture radar (GB-InSAR) over a mountainous area is investigated. A novel APS compensation scheme is proposed to compensate the fluctuated APS caused by a spatial 3-D inhomogeneous refractivity index distribution without any a priori knowledge of moving location. The proposed method simultaneously addresses to identify moving pixels by a criterion of absolute velocity estimated by the coherent pixels technique (CPT). The proposed method consists mainly of three steps: 1) the stratified APS compensation; 2) identification of moving pixel candidate; and 3) the residual APS [remained APS after 1)] compensation by Kriging interpolation. The steps mentioned above are iteratively applied in order to increase the accuracy of the whole process. In this framework, we develop the 2-D quadratic polynomial model of the refractivity index with respect to slant range and topographic height for modeling the stratified APS. Furthermore, a prediction of the residual APS is achieved by applying the intrinsic random function of order $k$ (IRF- $k$ ) Kriging interpolation, taking into account the nonstationarity of the residual APS. We evaluate the proposed method using zero-baseline GB-differential InSAR (GB-DInSAR) data over a mountainous area located in Minami-Aso, Kumamoto, Japan, through the near real-time post-landslide measurement campaign.

Neural network based synthetic aperture ladar imaging through marine atmosphere

The atmospheric turbulence can severely affect the azimuth imaging of the Synthetic Aperture Ladar (SAL). Based on a neural network, this study generates atmospheric phase screens complied with marine atmosphere spectrum. The SAL imaging results with different turbulence intensities and laser wavelengths are calculated, and the changing law of the ratio of real aperture length to atmospheric coherence diameter with turbulence intensity under different slant ranges and laser wavelengths are analyzed in this paper. The results suggest that the SAL imaging becomes worse as the turbulence intensity is stronger, and even the target is not able to be distinguished. A longer laser wavelength can be used to alleviate the defocus effect, and the phase error compensation algorithm based on marine phase screens can effectively improve the SAL imaging quality to guarantee the real–time process of echo signals of SAL in the marine atmosphere.

Atmospheric phase screen estimation for land subsidence evaluation by InSAR time series analysis in Kurdistan, Iran

Atmospheric phase screen (APS) is one of the main error sources of interferometric synthetic aperture radar (InSAR) measurements. In order to accurately retrieve displacement fields, it is necessary to use advanced methods to eliminate the tropospheric effect of interferograms. In this paper, the land subsidence in Kurdistan province of Iran is investigated using Sentinel-1A acquisitions on a single track for the period 2014–2018. The accurate and applicable 3D ray tracing technique is used to accurately estimate the APS. The ERA-I reanalysis data generated by European Centre for Medium Range Weather Forecasts (ECMWF) are used to implement the 3D ray tracing technique. In order to determine the effect of using the 3D ray tracing technique, the APSs are also determined using a traditional approach called, spatiotemporal filters method. To evaluate the capability of the two methods, the results are compared with the weather research and forecasting model (WRF) model. Finally, the interferograms are corrected using APSs from 3D ray tracing technique and traditional method and the subsidence rate in the study area is computed. Comparing the subsidence rates obtained from two APS estimation methods with piezometric data, GPS and precise levelling observations shows that the 3D ray tracing technique is significantly more accurate than traditional method in computing InSAR displacement fields.

Geostatistical Analysis and Mitigation of the Atmospheric Phase Screens in Ku-Band Terrestrial Radar Interferometric Observations of an Alpine Glacier

Terrestrial radar interferometry (TRI) can measure displacements at high temporal resolution, potentially with high accuracy. An application of this method is the observation of the surface flow velocity of steep, fast-flowing aglaciers. For these observations, the main factor limiting the accuracy of TRI observations is the spatial and temporal variabilities in the distribution of atmospheric water vapor content, causing a phase delay [atmospheric phase screen (APS)] whose magnitude is similar to the displacement phase. This contribution presents a geostatistical analysis of the spatial and temporal behaviors of the APS in Ku-Band TRI. The analysis is based on the assumption of a separable spatiotemporal covariance structure, which is tested empirically using variogram analysis. From this analysis, spatial and temporal APS statistics are estimated and used in a two-step procedure combining regression-Kriging with generalized least squares (GLS) inversion to estimate a velocity time-series. The performance of this method is evaluated by cross-validation using phase observations on stable scatterers. This analysis shows a considerable reduction in residual phase variance compared with the standard approach of combining the linear models of APS stratification and interferogram stacking.

Characteristic analysis of orbital angular momentum of vortex beam propagating in atmospheric turbulent

Starting from the expression of Laguerre-Gaussian vortex beam and based on Rayleigh diffraction theory, the variation of rotating coherence function of vortex beam propagating in atmospheric turbulence is studied. The crosstalk between the angular momentum of each orbital angular momentum when the vortex beam propagates in atmospheric turbulence is summarized. The topological charge detection probability is used to describe the crosstalk law, and the analytical expression of the topological charge detection probability is derived. The distribution of topological charge number of vortex beam passing through turbulence is studied, and the results are compared with the numerical simulation results of vortex beam passing through atmospheric random phase screen. The relationship between the detection probability of the theoretical and simulated topological charge numbers with the turbulence intensity and the topological charge number of the initial vortex beam is compared, and the correctness of the analytical expression of the topological charge number detection probability is verified. Through this expression, the interaction between atmospheric turbulence and vortex beam can be further studied, which can affect the essence of angular momentum scattering of vortex beam, and the suitable topological charge number interval can be selected for the space optical communication of vortex beam. It also provides a theoretical basis for selecting the appropriate beam waist size under different turbulence intensities to reduce the bit error rate (BER) caused by crosstalk.

The Multiple Aperture SAR Interferometry (MAI) Technique for the Detection of Large Ground Displacement Dynamics: An Overview

This work presents an overview of the multiple aperture synthetic aperture radar interferometric (MAI) technique, which is primarily used to measure the along-track components of the Earth’s surface deformation, by investigating its capabilities and potential applications. Such a method is widely used to monitor the time evolution of ground surface changes in areas with large deformations (e.g., due to glaciers movements or seismic episodes), permitting one to discriminate the three-dimensional (up–down, east–west, north–south) components of the Earth’s surface displacements. The MAI technique relies on the spectral diversity (SD) method, which consists of splitting the azimuth (range) Synthetic Aperture RADAR (SAR) signal spectrum into separate sub-bands to get an estimate of the surface displacement along the azimuth (sensor line-of-sight (LOS)) direction. Moreover, the SD techniques are also used to correct the atmospheric phase screen (APS) artefacts (e.g., the ionospheric and water vapor phase distortion effects) that corrupt surface displacement time-series obtained by currently available multi-temporal InSAR (MT-InSAR) tools. More recently, the SD methods have also been exploited for the fine co-registration of SAR data acquired with the Terrain Observation with Progressive Scans (TOPS) mode. This work is primarily devoted to illustrating the underlying rationale and effectiveness of the MAI and SD techniques as well as their applications. In addition, we present an innovative method to combine complementary information of the ground deformation collected from multi-orbit/multi-track satellite observations. In particular, the presented technique complements the recently developed Minimum Acceleration combination (MinA) method with MAI-driven azimuthal ground deformation measurements to obtain the time-series of the 3-D components of the deformation in areas affected by large deformation episodes. Experimental results encompass several case studies. The validity and relevance of the presented approaches are clearly demonstrated in the context of geospatial analyses.

Computational phase correction algorithms for multi-aperture systems.

Aperture cophasing can increase the resolution of a multi-aperture array while reducing optical system size and accounting for phase errors from hardware misalignments and atmospheric turbulence. Remapping apertures using an anamorphic pupil relay can separate the spatial frequency spectrum of a previously continuous modulation transfer function to facilitate a posteriori piston corrections between apertures [J. Opt. Soc. Am. A34, A47 (2017)JOAOD60740-323210.1364/JOSAA.34.000A47]. This study expands this method from two apertures to six using maximum likelihood estimation to calculate piston phase errors and least squares for tip and tilt. Perturbed test targets were generated for specific turbulence and noise values, providing random realizations of pistons, tips, tilts, and atmospheric phase screens. Results show improved Strehl ratios for corrected images in the presence of noise and atmospheric turbulence.