radar interferometric mapping of deformation in the year after the landers earthquake although the 1992 landers california earthquake sequence occurred in an area well sampled by geodetic networks1 3 the postseismic deformation in the months following the earthquake has been measured at only 15 geodetic stations4 another shortcoming in the geodetic coverage occurs west of the primary rupture where the existing geodetic observations suggest but cannot resolve sympathetic slip on secondary faults1 such measurements which are needed to place the landers earthquake sequence in the context of a recurring seismic cycle in california can be obtained with the dense spatial coverage provided by satellite radar interferometry5 9 here we present radar maps of the surface deformation field which reveal features that would otherwise have been poorly sampled particularly if the earthquake had occurred in a less accessible area we see triggered slip at the level of several centimetres as far as 100 km from the primary rupture and can resolve the geodetic signal of at least one small magnitude 5 aftershock the amount of surface slip following the main shock is less than a decimetre and is consistent with an exponential decay time of several months for the postseismic deformation

small scale deformations associated with the 1992 landers california earthquake mapped by synthetic aperture radar interferometry phase gradients the landers earthquake mw 7 3 occurred on june 28 1992 and ruptured nearly 100 km of previously mapped and unmapped faults in the mojave desert we use synthetic aperture radar interferometry insar to examine the cumulative surface deformation between april 24 and august 7 1992 in a 100 100 km region surrounding the northern portion of the earthquake rupture also we introduce a technique for manipulating sar interferograms to extract short wavelength displacement information this technique involves computation and subsequent combination of interferometric phase gradient maps the insar results show significant deformation signatures associated with faults fractures dry lake beds and mountainous regions within 75 100 km of the main rupture using the phase gradient method we are able to extract small scale deformation patterns near the main rupture many of the preexisting mapped faults within 50 km of the main rupture experienced triggered slip these include the old woman lenwood johnson valley west calico and calico faults the insar results also indicate right lateral offsets along secondary fractures trending n ne within the left lateral zone of shear between the main rupture and the johnson valley fault additionally there are interesting interferogram fringe signatures surrounding troy dry lake and coyote dry lake that are related to deformation of dry lake beds

surface deformation and coherence measurements of kilauea volcano hawaii from sir c radar interferometry the shuttle imaging radar c x synthetic aperture radar sir c x sar radar on board the space shuttle endeavor imaged kilauea volcano hawaii in april and october 1994 for the purpose of measuring active surface deformation by the methods of repeat pass differential radar interferometry observations at 24 cm l band and 5 6 cm c band wavelengths were reduced to interferograms showing apparent surface deformation over the 6 month interval and over a succession of 1 day intervals in october a statistically significant local phase signature in the 6 month interferogram is coincident with the pu u o o lava vent interpreted as deformation the signal implies centimeter scale deflation in an area several kilometers wide surrounding the vent peak deflation is roughly 14 cm if the deformation is purely vertical centered southward of the pu u o o caldera delays in the radar signal phase induced by atmospheric refractivity anomalies introduce spurious apparent deformation signatures at the level of 12 cm peak to peak in the radar line of sight direction though the phase observations are suggestive of the wide area deformation measured by global positioning system gps methods the atmospheric effects are large enough to limit the interpretation of the result it is difficult to characterize centimeter scale deformations spatially distributed over tens of kilometers using differential interferometry without supporting simultaneous spatially distributed measurements of refractivity along the radar line of sight studies of the interferometric correlation of images acquired at different times show that l band is far superior to c band in the vegetated areas even when the observations are separated by only 1 day these results imply longer wavelength instruments are more appropriate for studying surfaces by repeat pass observations

synthetic aperture radar for geodesy synthetic aperture radar is a technique for mapping earth9s surface that offers tremendous spatial resolution in their perspective meade and sandwell report on a recent meeting at the u s national academy of sciences in which future geodetic uses of this technique were discussed

atmospheric propagation heterogeneities revealed by ers 1 interferometry spaceborne synthetic aperture radar sar repeat pass interferometry is a technique based on the exploitation of the interference pattern of two sar images acquired in similar geometric conditions at two different dates this measure contains geometric atmospheric topographic and land deformation information in this paper we focus on the atmospheric information first we show theoretically that an adequate processing is sufficient to remove homogeneous atmospheric effects and that heterogeneities as tropospheric turbulences rain falls and ionospheric phenomena can be detected with sar interferometry then we interpret several observations and we present interferometric images of cumulus and turbulences due to relief sar interferometry could be a new remote sensing tool for the study of tropospheric turbulences at a high horizontal resolution 40 m

atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps interferogram images derived from repeat pass spaceborne synthetic aperture radar systems exhibit artifacts due to the time and space variations of atmospheric water vapor other tropospheric variations such as pressure and temperature also induce distortions but the effects are smaller in magnitude and more evenly distributed throughout the interferogram than the wet troposphere term spatial and temporal changes of 20 in relative humidity lead to 10 cm errors in deformation products and perhaps 100 m of error in derived topographic maps for those pass pairs with unfavorable baseline geometries in wet regions such as hawaii these are by far the dominant errors in the spaceborne imaging radar c and x band synthetic aperature radar sir c x sar interferometric products the unknown time delay from tropospheric distortion is independent of frequency and thus multiwavelength measurements such as those commonly used to correct radar altimeter and global positioning system gps ionospheric biases cannot be used to rectify the error in the topographic case the errors may be mitigated by choosing interferometric pairs with relatively long baselines as the error amplitude is inversely proportional to the perpendicular component of the interferometer baseline for the sir c x sar hawaii data we found that the best longest baseline pair produced a map supporting 100 m contouring whereas the poorest baseline choice yielded an extremely noisy topographic map even at this coarse contour interval in the case of deformation map errors the result is either independent of baseline parameters or else very nearly so here the only solution is averaging of independent interferograms so in order to create accurate deformation products in wet regions many multiple passes may be required rules for designing optimal data acquisition and processing sequences for interferometric analyses in nondesert parts of the world are 1 to use the longest radar wavelengths possible within ionospheric scintillation and faraday rotation limits 2 for topography maximize interferometer baseline within decorrelation limits and 3 for surface deformation use multiple observations and average the derived products following the above recipe yields accuracies of 10 m for digital elevation models and 1 cm for deformation maps even in very wet regions such as hawaii

phase gradient approach to stacking interferograms the phase gradient approach is used to construct averages and differences of interferograms without phase unwrapping our objectives for change detection are to increase fringe clarity and decrease errors due to tropospheric and ionospheric delay by averaging many interferograms the standard approach requires phase unwrapping scaling the phase according to the ratio of the perpendicular baseline and finally forming the average or difference however unique phase unwrapping is usually not possible since the phase gradient due to topography is proportional to the perpendicular baseline phase unwrapping is unnecessary prior to averaging or differencing phase unwrapping may be needed to interpret the results but it is delayed until all of the largest topographic signals are removed we demonstrate the method by averaging and differencing six interferograms having a suite of perpendicular baselines ranging from 18 to 406 m cross spectral analysis of the difference between two tandem interferograms provides estimates of spatial resolution which are used to design prestack filters a wide range of perpendicular baselines provides the best topographic recovery in terms of accuracy and coverage outside of mountainous areas the topography has a relative accuracy of better than 2 m residual interferograms single interferogram minus stack have tilts across the unwrapped phase that are typically 50 mm in both range and azimuth reflecting both orbit error and atmospheric delay smaller scale waves with amplitudes of 15 mm are interpreted as atmospheric lee waves a few global positioning system gps control points within a frame could increase the precision to 20 mm for a single interferogram further improvements may be achieved by stacking residual interferograms

measurement of ice sheet topography using satellite radar interferometry detailed digital elevation models dems do not exist for much of the greenland and antarctic ice sheets radar altimetry is at present the primary in many cases the only source of topographic data over the ice sheets but the horizontal resolution of such data is coarse satellite radar interferometry uses the phase difference between pairs of synthetic aperture radar sar images to measure both ice sheet topography and surface displacement we have applied this technique using ers 1 sar data to make detailed i e 80 m horizontal resolution maps of surface topography in a 100 km by 300 km strip in west greenland extending northward from just above jakobshavns isbrae comparison with a 76 km long line of airborne laser altimeter data shows that we have achieved a relative accuracy of 2 5m along the profile these observations provide a detailed view of dynamically supported topography near the margin of an ice sheet in the final section we compare our estimate of topography with phase contours due to motion and confirm our earlier analysis concerning vertical ice sheet motion and complexity in ers 1 sar interferograms

benchmark problems for large strain consolidation abstractmodeling of the one dimensional consolidation process for soil and other compressible porous media is important for a variety of engineering applications this paper presents solutions for two benchmark problems for large strain consolidation of a saturated soil layer that can be used to check other analytical and numerical analysis methods the solutions include effects of vertical strain soil self weight nonlinear constitutive relationships and changing material properties during the consolidation process high accuracy data are presented for each problem and include changes of settlement void ratio and excess pore pressure with time

postseismic rebound in fault step overs caused by pore fluid flow near field strain induced by large crustal earthquakes results in changes in pore fluid pressure that dissipate with time and produce surface deformation synthetic aperture radar sar interferometry revealed several centimeters of postseismic uplift in pull apart structures and subsidence in a compressive jog along the landers california 1992 earthquake surface rupture with a relaxation time of 270 45 days such a postseismic rebound may be explained by the transition of the poisson s ratio of the deformed volumes of rock from undrained to drained conditions as pore fluid flow allows pore pressure to return to hydrostatic equilibrium

deflation of mount etna monitored by spaceborne radar interferometry ground based measurements of volcano deformation can be used to assess eruptive hazard but require the costly and often hazardous installation and maintenance of an instrument network here we show that spaceborne radar interferometry which has already shown its utility in mapping earthquake related deformation1 can be used to monitor long term volcano deformation two families of synthetic aperture radar images acquired from ascending and descending orbits by the satellite ers 1 and looking at mount etna from opposite sides cover the time period from 17 may 1992 to 24 october 1993 and include the second half of etna s most recent eruption despite artefacts of the interferometric technique we can observe a volcano wide deflation which is an expected consequence of the eruption but which had not previously been appreciated we quantify it using a simple model based on the change of pressure in a sphere located in an elastic half space the modelled deformation increases linearly with time until the end of the eruption our results show that it will be possible to use this technique to detect the inflation of volcanic edifices that usually precedes eruptions

atmospheric limitations to repeat track radar interferometry in its recent radar imaging mission the shuttle imaging radar satellite sir c devoted three days to repeat track interferometry we have analyzed the data from a test site in the mojave desert of california although good topography 10 m on 21 m postings was obtained most of the error was caused by turbulent water vapor in the lower atmosphere spatial structure of 6 km and all smaller sizes was observed the rms one way time delay was found to be 0 24 cm essentially identical results were obtained at two wavelengths 24 and 5 7 cm

mapping small elevation changes over large areas differential radar interferometry a technique that uses synthetic aperture radar sar images to measure very small 1 cm or less surface motions with good resolution 10 m over large swaths 50 km is presented along with experimental results the method could be used for accurate measurements of many geophysical phenomena including swelling and buckling in fault zones residual displacements from seismic events and prevolcanic swelling the method is based on sar interferometry where two images are made of a scene by simultaneously flying two physically separated antennas then the phases of corresponding pixels are differenced and altitude formation is deduced from some simple computation and image rectification it is also possible to use one antenna flown twice over the same scene then if the second flight exactly duplicates the track of the first an interesting possibility occurs there would be no phase changes between the images at all unless there was a physical change in the scene such as ground swelling that would alter the distance from some resolution element to the antenna since the phase changes all occur at the short carrier wavelength the basic limitation on sensitivity is only the phase noise in the system when the two imaging passes are made from flight tracks that are separated which is the case with the seasat images used here it is no longer possible to distinguish surface changes from the parallax caused by topography however with some additional computation a third image made at some other baseline may be used to remove the topography and leave only the surface changes this method was applied using seasat data to an imaging site in imperial valley california where motion effects were observed that were ascribed to the expansion of water absorbing clays phase change images of this area are shown along with associated ground truth about the presence of water problems with the technique are explored along with a discussion of future experimental possibilities on upcoming sar missions like earth observing system eos earth resources satellite ers 1 sir c and the venus imaging radar magellan

discrimination of geophysical phenomena in satellite radar interferograms various geophysical phenomena are recorded in the interference patterns formed by differencing two synthetic aperture radar sar images the fringes generated by the topographic relief can be removed using a digital elevation model dem the remaining fringes map the change in satellite to ground range which occurred between the acquisition times of the two images by comparing different pairs of images spanning different intervals of time it is possible to discriminate between geophysical signal and interferometric artifact here we apply this pair wise logic to the area around the 1992 landers california earthquake using sar images acquired by the ers 1 satellite the range varies with time as a constant step impulsive or sloping function examples of each type include a dem error an aftershock two atmospheric perturbations and postseismic afterslip respectively their signatures are identified and separated using the pair wise logic

surface displacement of the 17 may 1993 eureka valley california earthquake observed by sar interferometry satellite synthetic aperture radar sar interferometry shows that the magnitude 6 1 eureka valley earthquake of 17 may 1993 produced an elongated subsidence basin oriented north northwest parallel to the trend defined by the aftershock distribution whereas the source mechanism of the earthquake implies a north northeast striking normal fault the 3 millimeter accuracy of the radar observed displacement map over short spatial scales allowed identification of the main surface rupture associated with the event these observations suggest that the rupture began at depth and propagated diagonally upward and southward on a west dipping north northeast fault plane reactivating the largest escarpment in the saline range

thermally induced grain growth of calcite marbles on naxos island greece the island of naxos is composed of an elliptically shaped structural and thermal dome of miocene age peak metamorphic temperatures within the central migmatite complex exceeded 700 c decreasing to about 300 c at the most distant exposures on the island equigranular calcite marbles which outcrop together with metapelites and metabasites over the whole island show a systematic pattern of increasing grain size towards the central migmatite complex with a significant discontinuity in the pattern corresponding approximately with the 500 c isotherm the microstructures and grain size distributions in the marbles are consistent with normal grain growth the variation of grain size with peak temperature attained can be explained equally well by the assumptions that a a maximum grainsize had developed particularly at higher temperatures or that b the grain size had been frozen in by a combination of cooling and coarsening both of which combine to reduce the rate of grain growth

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

topographic mapping from interferometric synthetic aperture radar observations interferometric synthetic aperture radar observations provide a means for obtaining high resolution topographic terrain maps from data acquired simultaneously at two slightly displaced antennas calculation of the three dimensional coordinates of all the points in a radar image can be made from the combination of along track slant range and interferometer fringe measurements thus the result compensates for the layover exhibited by conventional radar maps and removes the false targets generated by multiple signal paths to a given object in the scene we have derived a topographic map of a portion of the san francisco bay area utilizing data that were recorded by a radar system mounted on a nasa cv990 aircraft and processed by a general purpose digital computer this map displays the height above sea level of a region approximately 11 km by 10 km in size sampled on an 11 m pixel grid uncertainties in the estimated height result from imprecise knowledge of the observational geometry radar bandwidth limitations and finite signal to noise ratios for our system each factor contributed approximately 3 4 m to a relative rms error of about 6 m additional global errors of the order of 10 m can result from inaccurate monitoring of aircraft attitude the statistical variation of the height measurements from the ocean portion of the map which we can presume to be quite flat is 2 10 m rms which is consistent with the theoretical estimate comparison of our results with u s geological survey contour maps indicates a high degree of correlation between the two sets of altitude data

comparison of geos 3 and seasat altimeter resolution capabilities a comparison is made between geos 3 and seasat altimeter data with regard to noise power spectral density psd derived geoid psd and short wavelength resolution at wavelengths greater than 450 km the noise psds for geos 3 and seasat are essentially the same and are attributed to mesoscale oceanographic effects at shorter wavelengths the noise spectra diverge because of the higher geos 3 instrument noise the average along track geoid psds are nearly identical between wavelengths of 4500 and 72 km the spectral coherence between repeat tracks shows that the short wavelength resolution of seasat data is 32 km and for geos 3 it is 60 km

crustal deformation measurements using repeat pass jers 1 synthetic aperture radar interferometry near the izu peninsula japan we have examined the precision of interferometric synthetic aperture radar sar measurements of surface deformation of the earth using 24 cm wavelength data acquired by the japanese earth resources satellite 1 jers 1 spacecraft over the izu peninsula japan radar images acquired from 1993 to 1994 were made into 11 independent interferograms apparent water vapor signatures with equivalent path delay up to 16 cm preclude reliable estimates of small deformation from only one interferogram averaging of interferograms improves the measurement such that residuals between precise leveling data and corresponding radar observations are less than 1 cm rms there is a clear correlation between cloud cover extent on a given day and the spectral power of the water vapor signature in an interferogram formed from the corresponding day s sar image also several water vapor features associated with local topography are consistent with accumulation of moisture on the windward side of an on shore flow analysis shows that decorrelation in mixed conifer and deciduous forest is a weak function of the time between observations imposing a roughly constant level of additional decorrelation relative to scatter stable urban areas furthermore in high relief areas correlation is high when the baseline is tens of meters but drops rapidly with increasing baseline length with strict control of the interferometric baseline length adequate correlation in interferograms over very long time periods is possible even in forested high relief regions observed inflation over ito city is consistent with a localized magma source at depth suggesting a different mechanism from the previous episode in 1989