Andrew K. Gabriel

On the derivation of coseismic displacement fields using differential radar interferometry: The Landers earthquake

We present a map of the coseismic displacement field resulting from the Landers, California, June 28, 1992, earthquake derived using data acquired from an orbiting high-resolution radar system. We achieve results more accurate than previous space studies and similar in accuracy to those obtained by conventional field survey techniques. Data from the ERS 1 synthetic aperture radar instrument acquired in April, July, and August 1992 are used to generate a high-resolution, wide area map of the displacements. The data represent the motion in the direction of the radar line of sight to centimeter level precision of each 30-m resolution element in a 113 km by 90 km image. Our coseismic displacement contour map gives a lobed pattern consistent with theoretical models of the displacement field from the earthquake. Fine structure observed as displacement tiling in regions several kilometers from the fault appears to be the result of local surface fracturing. Comparison of these data with Global Positioning System and electronic distance measurement survey data yield a correlation of 0.96; thus the radar measurements are a means to extend the point measurements acquired by traditional techniques to an area map format. The technique we use is (1) more automatic, (2) more precise, and (3) better validated than previous similar applications of differential radar interferometry. Since we require only remotely sensed satellite data with no additional requirements for ancillary information, the technique is well suited for global seismic monitoring and analysis.

Crossed orbit interferometry: theory and experimental results from SIR-B

Abstract In a conventional imaging radar interferometer, two receiving antennas separated slightly in the cross-track direction view the same scene and altimetry information is deduced from the phase differences between the corresponding pixels in each image. It is possible to perform the same measurements with only one antenna by making two images of the scene on two separate passes; for SIR-B this involved imaging on two separate orbits. If the two orbits are parallel and separated in the cross-track direction, altitude information is derived exactly as in the two-antenna interferometer and the baseline is determined by the orbit separation. For the available SIR-B data, however, the orbits were skewed, which substantially increases the difficulty of finding altitudes. Since the orbits were not exactly parallel, the antenna on one orbit was pointed slightly forward or backward compared to the other; this was compensated for in the azimuth processing. Furthermore, the skew gave the images a cross-track d...

Crossed Orbit Interferometry

In a conventional imaging radar interferometer, two receiving antennas separated slightly in the cross track direction view the same scene, and altimetry information is deduced from the phase differences between the corresponding pixels in each image. It is possible to perform these same measurements with only one antenna by making two images of the scene on two separate passes; for the SIR-B radar this involved imaging on two separate orbits. If the two orbits are parallel and separated in the cross track direction, altitude information is derived exactly as in the two - antenna interferometer, and the baseline is determined by the orbit separation. For the available SIR-B data, however, the orbits were skewed, which substantially increases the difficulty of finding altitudes. Since the orbits were not exactly parallel, the antenna on one orbit was pointed slightly forward or backward compared to the other; this was compensated in the azimuth processing. Further, the skew gave the images a cross-track displacement that increased linearly with azimuth distance, which was removed by resampling and stretching one of the images. Because of the skewing, the baseline increased with distance from the crossing point, and theory shows that altitude variation appears as a change in the along-track position of a given pixel. This is bome out in the experimental data, which is then used to construct a coarse altitude map. Additionally, the phase difference of each overlaid pixel is related to the altitude in a complicated way. An algorithm was developed to invert this relationship, the results of which were then used to construct a more refined altitude map.

Fundamental radar properties: hidden variables in space–time

A derivation of the properties of pulsed radiative imaging systems is presented with examples drawn from conventional, synthetic aperture, and interferometric radar. A geometric construction of the space and time components of a radar observation yields a simple underlying structural equivalence among many of the properties of radar, including resolution, range ambiguity, azimuth aliasing, signal strength, speckle, layover, Doppler shifts, obliquity and slant range resolution, finite antenna size, atmospheric delays, and beam- and pulse-limited configurations. The same simple structure is shown to account for many interferometric properties of radar: height resolution, image decorrelation, surface velocity detection, and surface deformation measurement. What emerges is a simple, unified description of the complex phenomena of radar observations. The formulation comes from fundamental physical concepts in relativistic field theory, of which the essential elements are presented. In the terminology of physics, radar properties are projections of hidden variables--curved worldlines from a broken symmetry in Minkowski space-time--onto a time-serial receiver.

A simple model for SAR azimuth speckle, focusing, and interferometric decorrelation

The phenomenon of speckle in synthetic aperture radar (SAR) images is well known as a characteristic grainy appearance of radar images. Speckle is frequently a significant obstacle to visual interpretations of radar data or target identification. In addition, it is usually the dominant noise source in SAR interferometry, since it is responsible for image decorrelation that degrades interferometric fringes, places severe constraints on orbits, and limits the accuracy of height measurements. This communication deals with the geometric sources of speckle. This conventional picture is extended to the case of vertically separated scatterers, and the formulation that results is applied to the structurally similar topics of azimuth focusing, interferometric decorrelation from defocusing, and atmospheric phase delays.

Fundamental radar properties. II. Coherent phenomena in space-time

A previous publication [J. Opt. Soc. Am. A19, 946-956 (2002)] presented a general formulation of radiative systems based on special relativity, and properties of imaging radar were derived as examples. Complex and diverse properties of radar images were shown to have a simple and unified origin when viewed as lower-dimensional (temporal) projections of the space-time structure of a radar observation. A diagram was developed that could be manipulated for a simple, intuitive view of the underlying structure of radar observations and phenomena. That treatment is here extended to include coherent phenomena as they appear in the lower time dimensions of the image. Various known coherent properties of imaging radar and interferometry are derived. The formulation is shown to be a generalization of a conventional echo correlation and is extended to a second spatial dimension. From this perspective, coherent properties also have a surprisingly simple and unified structure; their observed complexity is somewhat illusory, also a consequence of projection onto the lower temporal dimension of the receiver. While this formulation and the rules governing it are quite different from the standard treatments, they have the considerable advantage of providing a much simpler, intuitive, and unified description of radiative (radar and optical) systems that is rooted in fundamental physics.