Statistics for Spatial Data.

Synthetic aperture radar interferometry is an imaging technique for measuring the topography of a surface, its changes over time, and other changes in the detailed characteristic of the surface. By exploiting the phase of the coherent radar signal, interferometry has transformed radar remote sensing from a largely interpretive science to a quantitative tool, with applications in cartography, geodesy, land cover characterization, and natural hazards. This paper reviews the techniques of interferometry, systems and limitations, and applications in a rapidly growing area of science and engineering.

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Synthetic aperture radar interferometry

Geophysical applications of radar interferometry to measure changes in the Earth's surface have exploded in the early 1990s. This new geodetic technique calculates the interference pattern caused by the difference in phase between two images acquired by a spaceborne synthetic aperture radar at two distinct times. The resulting interferogram is a contour map of the change in distance between the ground and the radar instrument. These maps provide an unsurpassed spatial sampling density (∼100 pixels km−2), a competitive precision (∼1 cm), and a useful observation cadence (1 pass month−1). They record movements in the crust, perturbations in the atmosphere, dielectric modifications in the soil, and relief in the topography. They are also sensitive to technical effects, such as relative variations in the radar's trajectory or variations in its frequency standard. We describe how all these phenomena contribute to an interferogram. Then a practical summary explains the techniques for calculating and manipulating interferograms from various radar instruments, including the four satellites currently in orbit: ERS-1, ERS-2, JERS-1, and RADARSAT. The next chapter suggests some guidelines for interpreting an interferogram as a geophysical measurement: respecting the limits of the technique, assessing its uncertainty, recognizing artifacts, and discriminating different types of signal. We then review the geophysical applications published to date, most of which study deformation related to earthquakes, volcanoes, and glaciers using ERS-1 data. We also show examples of monitoring natural hazards and environmental alterations related to landslides, subsidence, and agriculture. In addition, we consider subtler geophysical signals such as postseismic relaxation, tidal loading of coastal areas, and interseismic strain accumulation. We conclude with our perspectives on the future of radar interferometry. The objective of the review is for the reader to develop the physical understanding necessary to calculate an interferogram and the geophysical intuition necessary to interpret it.

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Radar interferometry and its application to changes in the Earth's surface

Synthetic Aperture Radar (SAR) has been widely used for Earth remote sensing for more than 30 years. It provides high-resolution, day-and-night and weather-independent images for a multitude of applications ranging from geoscience and climate change research, environmental and Earth system monitoring, 2-D and 3-D mapping, change detection, 4-D mapping (space and time), security-related applications up to planetary exploration. With the advances in radar technology and geo/bio-physical parameter inversion modeling in the 90s, using data from several airborne and spaceborne systems, a paradigm shift occurred from the development driven by the technology push to the user demand pull. Today, more than 15 spaceborne SAR systems are being operated for innumerous applications. This paper provides first a tutorial about the SAR principles and theory, followed by an overview of established techniques like polarimetry, interferometry and differential interferometry as well as of emerging techniques (e.g., polarimetric SAR interferometry, tomography and holographic tomography). Several application examples including the associated parameter inversion modeling are provided for each case. The paper also describes innovative technologies and concepts like digital beamforming, Multiple-Input Multiple-Output (MIMO) and bi- and multi-static configurations which are suitable means to fulfill the increasing user requirements. The paper concludes with a vision for SAR remote sensing.

/pdf/a-tutorial-on-synthetic-aperture-radar-1v8k9pqokm.pdf

A tutorial on synthetic aperture radar

Synthetic aperture radar (SAR) is a coherent active microwave imaging method. In remote sensing it is used for mapping the scattering properties of the Earth's surface in the respective wavelength domain. Many physical and geometric parameters of the imaged scene contribute to the grey value of a SAR image pixel. Scene inversion suffers from this high ambiguity and requires SAR data taken at different wavelength, polarization, time, incidence angle, etc. Interferometric SAR (InSAR) exploits the phase differences of at least two complex-valued SAR images acquired from different orbit positions and/or at different times. The information derived from these interferometric data sets can be used to measure several geophysical quantities, such as topography, deformations (volcanoes, earthquakes, ice fields), glacier flows, ocean currents, vegetation properties, etc. This paper reviews the technology and the signal theoretical aspects of InSAR. Emphasis is given to mathematical imaging models and the statistical properties of the involved quantities. Coherence is shown to be a useful concept for system description and for interferogram quality assessment. As a key step in InSAR signal processing two-dimensional phase unwrapping is discussed in detail. Several interferometric configurations are described and illustrated by real-world examples. A compilation of past, current and future InSAR systems concludes the paper.

https://iopscience.iop.org/article/10.1088/0266-5611/14/4/001/pdf

Interferometric Point Target Analysis (IPTA) is a method to exploit the temporal and spatial characteristics of interferometric signatures collected from point targets to accurately map surface deformation histories, terrain heights, and relative atmospheric path delays. In this contribution the IPTA concept is introduced, including the point selection criteria, the phase model and the iterative improvement of the model parameters. Intermediate and final results of an IPTA example using a stack of ERS-1 and ERS-2 data, confirm the validity of the concept and indicate a high accuracy of the resulting products.

Interferometric point target analysis for deformation mapping

Two image-to-image patch offset techniques for estimating feature motion between satellite synthetic aperture radar (SAR) images are discussed. Intensity tracking, based on patch intensity cross-correlation optimization, and coherence tracking, based on patch coherence optimization, are used to estimate the movement of glacier surfaces between two SAR images in both slant-range and azimuth direction. The accuracy and application range of the two methods are examined in the case of the surge of Monacobreen in Northern Svalbard between 1992 and 1996. Offset-tracking procedures of SAR images are an alternative to differential SAR interferometry for the estimation of glacier motion when differential SAR interferometry is limited by loss of coherence, i.e. in the case of rapid and incoherent flow and of large acquisition time intervals between the two SAR images. In addition, an offset-tracking procedure in the azimuth direction may be combined with differential SAR interferometry in the slant-range direction in order to retrieve a two-dimensional displacement map when SAR data of only one orbit configuration are available.

/pdf/glacier-motion-estimation-using-sar-offset-tracking-4ll5x4qlfd.pdf

Glacier motion estimation using SAR offset-tracking procedures

So far, knowledge about the dielectric properties, especially the loss factor, of ice at microwave frequencies has been unsatisfactory. In this work the authors report on new measurements made over the frequency range from 2 to 100 GHz by a resonator method (2-10 GHz) and a radiometer method (10-100 GHz). Measurements were made with pure and with slightly saline (10 to 13 p.p.m.) ice. The results agree with the assumption of a single minimum of the dielectric loss at 2 to 4 GHz. For pure ice the data are a natural link between the measurements of Westphal made below 1 GHz and the far-infrared spectrum. The influence of small impurities on the dielectric loss is compared with the behaviour of sea ice, and it is found that the same linear relationship with salinity can be applied to both cases.

https://iopscience.iop.org/article/10.1088/0022-3727/21/11/522/pdf

Dielectric properties of freshwater ice at microwave frequencies

Based on the previous work of C. Werner and U. Wegmuller in the frame of their research at the University of Zurich and Jet Propulsion Laboratory, as well as up to date algorithms published in the literature Gamma Remote Sensing developed its advanced SAR processing and interferometry software packages. The SAR processor and the interferometry software are modular software packages written in the widely supported ANSI-C language. The well documented structured code and stepwise processing approach permit users to experiment with new algorithms and applications. Data of both airborne and spaceborne sensors including ERS, JERS-1, SIR-C, and RADARSAT StripMap mode, and the Dornier DOSAR have been successfully processed interferometrically. The processor is currently being certified by ESA for ERS processing and RSI for RADARSAT. The overall design of the software, algorithms used, special features implemented, typical sequences for processing with the Modular SAR Processor (MSP) and the Interferometric SAR Processor (ISP), as well as a few examples for results will be presented.

Gamma SAR processor and interferometry software

This paper illustrates the capabilities of L-band satellite SAR interferometry for the investigation of landslide displacements. SAR data acquired by the L-band JERS satellite over the Italian and Swiss Alps have been analyzed together with C-band ERS-1/2 SAR data and in situ information. The use of L-band SAR data with a wavelength larger than the usual C-band, generally considered for ground motion measurements, reduces some of the limitations of differential SAR interferometry, in particular, signal decorrelation induced by vegetation cover and rapid displacements. The sites of the Alta Val Badia region in South Tyrol (Italy), Ruinon in Lombardia (Italy), Saas Grund in Valais (Switzerland) and Campo Vallemaggia in Ticino (Switzerland), representing a comprehensive set of different mass wasting phenomena in various environments, are considered. The landslides in the Alta Val Badia region are good examples for presenting the improved performance of L-band in comparison to C-band for vegetated areas, in particular concerning open forest. The landslides of Ruinon, Saas Grund, and Campo Vallemaggia demonstrate the strength of L-band in observing moderately fast displacements in comparison to C-band. This work, performed with historical SAR data from a satellite which operated until 1998, demonstrates the capabilities of future planned L-band SAR missions, like ALOS and TerraSAR-L, for landslide studies.

Urs Wegmüller

Papers

Interferometric point target analysis for deformation mapping

Glacier motion estimation using SAR offset-tracking procedures

Dielectric properties of freshwater ice at microwave frequencies

Gamma SAR processor and interferometry software

Survey and monitoring of landslide displacements by means of L-band satellite SAR interferometry