InSAR bias and uncertainty due to the systematic and stochastic tropospheric delay

We quantify the bias and uncertainty of interferometric synthetic aperture radar (InSAR) displacement time series and their derivatives, the displacement velocities, by analyzing the systematic and stochastic components of the temporal variation of the tropospheric delay. The biases due to the systematic seasonal delay depend on the SAR acquisition times, whereas the uncertainties depend on the standard deviation of the random delay, the number of acquisitions, the total time span covered, and the covariance of the time series of the stochastic delay between a pixel and the reference. We study the contribution of the wet delay to the InSAR observations along the western India plate boundary using (i) Moderate Resolution Imaging Spectroradiometer precipitable water vapor, (ii) stratified tropospheric delay estimated from the ERA-I global atmospheric model, and (iii) seven Envisat InSAR swaths. Our analysis indicates that the amplitudes of the annual delay vary by up to ~10 cm in this region equivalent to a maximum displacement bias of ~24 cm in InSAR line of sight direction between two epochs (assuming Envisat IS6 beam mode). The stratified tropospheric delay correction mitigates this bias and reduces the scatter due to the stochastic delay. For ~7 years of Envisat acquisitions along the western India plate boundary, the uncertainty of the InSAR velocity field due to the residual stochastic wet delay after stratified tropospheric delay correction using the ERA-I model is in the order of ~2 mm/yr over 100 km and ~4 mm/yr over 400 km. We discuss the implication of the derived uncertainties on the full variance-covariance matrix of the InSAR data

A Network-Based Enhanced Spectral Diversity Approach for TOPS Time-Series Analysis

For multitemporal analysis of synthetic aperture radar (SAR) images acquired with a terrain observation by progressive scan (TOPS) mode, all acquisitions from a given satellite track must be coregistered to a reference coordinate system with accuracies better than 0.001 of a pixel (assuming full SAR resolution) in the azimuth direction. Such a high accuracy can be achieved through geometric coregistration, using precise satellite orbits and a digital elevation model, followed by a refinement step using a time-series analysis of coregistration errors. These errors represent the misregistration between all TOPS acquisitions relative to the reference coordinate system. We develop a workflow to estimate the time series of azimuth misregistration using a network-based enhanced spectral diversity (NESD) approach, in order to reduce the impact of temporal decorrelation on coregistration. Example time series of misregistration inferred for five tracks of Sentinel-1 TOPS acquisitions indicates a maximum relative azimuth misregistration of less than 0.01 of the full azimuth resolution between the TOPS acquisitions in the studied areas. Standard deviation of the estimated misregistration time series for different stacks varies from 1.1e-3 to 2e-3 of the azimuth resolution, equivalent to 1.6-2.8 cm orbital uncertainty in the azimuth direction. These values fall within the 1-sigma orbital uncertainty of the Sentinel-1 orbits and imply that orbital uncertainty is most likely the main source of the constant azimuth misregistration between different TOPS acquisitions. We propagate the uncertainty of individual misregistration estimated with ESD to the misregistration time series estimated with NESD and investigate the different challenges for operationalizing NESD

InSAR observations of strain accumulation and fault creep along the Chaman Fault system, Pakistan and Afghanistan

We use 2004–2011 Envisat synthetic aperture radar imagery and InSAR time series methods to estimate the contemporary rates of strain accumulation in the Chaman Fault system in Pakistan and Afghanistan. At 29 N we find long-term slip rates of 16 ± 2.3 mm/yr for the Ghazaband Fault and of 8 ± 3.1 mm/yr for the Chaman Fault. This makes the Ghazaband Fault one of the most hazardous faults of the plate boundary zone. We further identify a 340 km long segment displaying aseismic surface creep along the Chaman Fault, with maximum surface creep rate of 8.1 ± 2 mm/yr. The observation that the Chaman Fault accommodates only 30% of the relative plate motion between India and Eurasia implies that the remainder is accommodated south and east of the Katawaz block microplate

InSAR observations of strain accumulation and fault creep along the Chaman Fault system, Pakistan and Afghanistan

We use 2004–2011 Envisat synthetic aperture radar imagery and InSAR time series methods to estimate the contemporary rates of strain accumulation in the Chaman Fault system in Pakistan and Afghanistan. At 29 N we find long-term slip rates of 16 ± 2.3 mm/yr for the Ghazaband Fault and of 8 ± 3.1 mm/yr for the Chaman Fault. This makes the Ghazaband Fault one of the most hazardous faults of the plate boundary zone. We further identify a 340 km long segment displaying aseismic surface creep along the Chaman Fault, with maximum surface creep rate of 8.1 ± 2 mm/yr. The observation that the Chaman Fault accommodates only 30% of the relative plate motion between India and Eurasia implies that the remainder is accommodated south and east of the Katawaz block microplate

Geodetic Imaging of Tectonic Deformation with InSAR

Precise measurements of ground deformation across the plate boundaries are crucial observations to evaluate the location of strain localization and to understand the pattern of strain accumulation at depth. Such information can be used to evaluate the possible location and magnitude of future earthquakes. Interferometric Synthetic Aperture Radar (InSAR) potentially can deliver small-scale (few mm/yr) ground displacement over long distances (hundreds of kilometers) across the plate boundaries and over continents. However, Given the ground displacement as our signal of interest, the InSAR observations of ground deformation are usually affected by several sources of systematic and random noises. In this dissertation I identify several sources of systematic and random noise, develop new methods to model and mitigate the systematic noise and to evaluate the uncertainty of the ground displacement measured with InSAR. I use the developed approach to characterize the tectonic deformation and evaluate the rate of strain accumulation along the Chaman fault system, the western boundary of the India with Eurasia tectonic plates. I evaluate the bias due to the topographic residuals in the InSAR range-change time-series and develope a new method to estimate the topographic residuals and mitigate the effect from the InSAR range-change time-series (Chapter 2). I develop a new method to evaluate the uncertainty of the InSAR velocity field due to the uncertainty of the satellite orbits (Chapter 3) and a new algorithm to automatically detect and correct the phase unwrapping errors in a dense network of interferograms (Chapter 4). I develop a new approach to evaluate the impact of systematic and stochastic components of the tropospheric delay on the InSAR displacement time-series and its uncertainty (Chapter 5). Using the new InSAR time-series approach developed in the previous chapters, I study the tectonic deformation across the western boundary of the India plate with Eurasia and evaluated the rate of strain accumulation along the Chaman fault system (Chapter 5). I also evaluate the co-seismic and post-seismic displacement of a moderate M5.5 earthquake on the Ghazaband fault (Chapter 6). The developed methods to mitigate the systematic noise from InSAR time-series, significantly improve the accuracy of the InSAR displacement time-series and velocity. The approaches to evaluate the effect of the stochastic components of noise in InSAR displacement time-series enable us to obtain the variance-covariance matrix of the InSAR displacement time-series and to express their uncertainties. The effect of the topographic residuals in the InSAR range-change time-series is proportional to the perpendicular baseline history of the set of SAR acquisitions. The proposed method for topographic residual correction, efficiently corrects the displacement time-series. Evaluation of the uncertainty of velocity due to the orbital errors shows that for modern SAR satellites with precise orbits such as TerraSAR-X and Sentinel-1, the uncertainty of 0.2 mm/yr per 100 km and for older satellites with less accurate orbits such as ERS and Envisat, the uncertainty of 1.5 and 0.5mm/yr per 100 km, respectively are achievable. However, the uncertainty due to the orbital errors depends on the orbital uncertainties, the number and time span of SAR acquisitions. Contribution of the tropospheric delay to the InSAR range-change time-series can be subdivided to systematic (seasonal delay) and stochastic components. The systematic component biases the displacement times-series and velocity field as a function of the acquisition time and the non-seasonal component significantly contributes to the InSAR uncertainty. Both components are spatially correlated and therefore the covariance of noise between pixels should be considered for evaluating the uncertainty due to the random tropospheric delay. The relative velocity uncertainty due to the random tropospheric delay depends on the scatter of the random tropospheric delay, and is inversely proportional to the number of acquisitions, and the total time span covered by the SAR acquisitions. InSAR observations across the Chaman fault system shows that relative motion between India and Eurasia in the western boundary is distributed among different faults. The InSAR velocity field indicates strain localization on the Chaman fault and Ghazaband fault with slip rates of ~8 and ~16 mm/yr, respectively. High rate of strain accumulation on the Ghazaband fault and lack of evidence for rupturing the fault during the 1935 Quetta earthquake indicates that enough strain has been accumulated for large (M>7) earthquake, which threatens Balochistan and the City of Quetta. Chaman fault from latitudes ~29.5 N to ~32.5 N is creeping with a maximum surface creep rate of 8 mm/yr, which indicates that Chaman fault is only partially locked and therefore moderate earthquakes (M<7) similar to what has been recorded in last 100 years are expected.</p

InSAR uncertainty due to orbital errors

Errors in the satellite orbits are considered to be a limitation for Interferometric Synthetic Aperture Radar (InSAR) time-series techniques to accurately measure long-wavelength (>50 km) ground displacements. Here we examine how orbital errors propagate into relative InSAR line-of-sight velocity fields and evaluate the contribution of orbital errors to the InSAR uncertainty. We express the InSAR uncertainty due to the orbital errors in terms of the standard deviations of the velocity gradients in range and azimuth directions (range and azimuth uncertainties). The range uncertainty depends on the magnitude of the orbital errors, the number and time span of acquisitions. Using reported orbital uncertainties we find range uncertainties of less than 1.5 mm yr−1 100 km−1 for ERS, less than 0.5 mm yr−1 100 km−1 for Envisat and ∼0.2 mm yr−1 100 km−1 for TerraSAR-X and Sentinel-1. Under a conservative scenario, we find azimuth uncertainties of better than 1.5 mm yr−1 100 km−1 for older satellites (ERS and Envisat) and better than 0.5 mm yr−1 100 km−1 for modern satellites (TerraSAR-X and Sentinel-1). We validate the expected uncertainties using LOS velocity fields obtained from Envisat SAR imagery. We find residual gradients of 0.8 mm yr−1 100 km−1 or less in range and of 0.95 mm yr−1 100 km−1 or less in azimuth direction, which fall within the 1σ to 2σ uncertainties. The InSAR uncertainties due to the orbital errors are significantly smaller than generally expected. This shows the potential of InSAR systems to constrain long-wavelength geodynamic processes, such as continent-scale deformation across entire plate boundary zones

DEM Error Correction in InSAR Time Series

We present a mathematical formulation for the phase due to the errors in digital elevation models (DEMs) in synthetic aperture radar (SAR) interferometry (InSAR) time series obtained by the small baseline (SB) or the small baseline subset method. We show that the effect of the DEM error in the estimated displacement is proportional to the perpendicular baseline history of the set of SAR acquisitions. This effect at a given epoch is proportional to the perpendicular baseline between the SAR acquisition at that epoch and the reference acquisition. Therefore, the DEM error can significantly affect the time-series results even if SB interferograms are used. We propose a new method for DEM error correction of InSAR time series, which operates in the time domain after inversion of the network of interferograms for the displacement time series. This is in contrast to the method of Berardino (2002) in which the DEM error is estimated in the interferogram domain. We show the effectiveness of this method using simulated InSAR data. We apply the new method to Fernandina volcano in the Galapagos Islands and show that the proposed DEM error correction improves the estimated displacement significantly.</jats:p

InSAR Time-Series Estimation of the Ionospheric Phase Delay: An Extension of the Split Range-Spectrum Technique

Repeat pass interferometric synthetic aperture radar (InSAR) observations may be significantly impacted by the propagation delay of the microwave signal through the ionosphere, which is commonly referred to as ionospheric delay. The dispersive character of the ionosphere at microwave frequencies allows one to estimate the ionospheric delay from InSAR data through a split range-spectrum technique. Here, we extend the existing split range-spectrum technique to InSAR time-series. We present an algorithm for estimating a time-series of ionospheric phase delay that is useful for correcting InSAR time-series of ground surface displacement or for evaluating the spatial and temporal variations of the ionosphere's total electron content (TEC). Experimental results from stacks of L-band SAR data acquired by the ALOS-1 Japanese satellite show significant ionospheric phase delay equivalent to 2 m of the temporal variation of InSAR time-series along 445 km in Chile, a region at low latitudes where large TEC variations are common. The observed delay is significantly smaller, with a maximum of 10 cm over 160 km, in California. The estimation and correction of ionospheric delay reduces the temporal variation of the InSAR time-series to centimeter levels in Chile. The ionospheric delay correction of the InSAR time-series reveals earthquake-induced ground displacement, which otherwise could not be detected. A comparison with independent GPS time-series demonstrates an order of magnitude reduction in the root mean square difference between GPS and InSAR after correcting for ionospheric delay. The results show that the presented algorithm significantly improves the accuracy of InSAR time-series and should become a routine component of InSAR time-series analysis