A rigid and weathered ice shell on Titan.

Several lines of evidence suggest that Saturn's largest moon, Titan, has a global subsurface ocean beneath an outer ice shell 50 to 200 kilometres thick. If convection is occurring, the rigid portion of the shell is expected to be thin; similarly, a weak, isostatically compensated shell has been proposed to explain the observed topography. Here we report a strong inverse correlation between gravity and topography at long wavelengths that are not dominated by tides and rotation. We argue that negative gravity anomalies (mass deficits) produced by crustal thickening at the base of the ice shell overwhelm positive gravity anomalies (mass excesses) produced by the small surface topography, giving rise to this inverse correlation. We show that this situation requires a substantially rigid ice shell with an elastic thickness exceeding 40 kilometres, and hundreds of metres of surface erosion and deposition, consistent with recent estimates from local features. Our results are therefore not compatible with a geologically active, low-rigidity ice shell. After extrapolating to wavelengths that are controlled by tides and rotation, we suggest that Titan's moment of inertia may be even higher (that is, Titan may be even less centrally condensed) than is currently thought.

The lakes of Titan.

The surface of Saturn's haze-shrouded moon Titan has long been proposed to have oceans or lakes, on the basis of the stability of liquid methane at the surface. Initial visible and radar imaging failed to find any evidence of an ocean, although abundant evidence was found that flowing liquids have existed on the surface. Here we provide definitive evidence for the presence of lakes on the surface of Titan, obtained during the Cassini Radar flyby of Titan on 22 July 2006 (T16). The radar imaging polewards of 70 degrees north shows more than 75 circular to irregular radar-dark patches, in a region where liquid methane and ethane are expected to be abundant and stable on the surface. The radar-dark patches are interpreted as lakes on the basis of their very low radar reflectivity and morphological similarities to lakes, including associated channels and location in topographic depressions. Some of the lakes do not completely fill the depressions in which they lie, and apparently dry depressions are present. We interpret this to indicate that lakes are present in a number of states, including partly dry and liquid-filled. These northern-hemisphere lakes constitute the strongest evidence yet that a condensable-liquid hydrological cycle is active in Titan's surface and atmosphere, in which the lakes are filled through rainfall and/or intersection with the subsurface 'liquid methane' table.

Titan Radar Mapper observations from Cassini's T3 fly-by.

Cassini's Titan Radar Mapper imaged the surface of Saturn's moon Titan on its February 2005 fly-by (denoted T3), collecting high-resolution synthetic-aperture radar and larger-scale radiometry and scatterometry data. These data provide the first definitive identification of impact craters on the surface of Titan, networks of fluvial channels and surficial dark streaks that may be longitudinal dunes. Here we describe this great diversity of landforms. We conclude that much of the surface thus far imaged by radar of the haze-shrouded Titan is very young, with persistent geologic activity.

The sand seas of Titan: Cassini RADAR observations of longitudinal dunes.

The most recent Cassini RADAR images of Titan show widespread regions (up to 1500 kilometers by 200 kilometers) of near-parallel radar-dark linear features that appear to be seas of longitudinal dunes similar to those seen in the Namib desert on Earth. The Ku-band (2.17-centimeter wavelength) images show approximately 100-meter ridges consistent with duneforms and reveal flow interactions with underlying hills. The distribution and orientation of the dunes support a model of fluctuating surface winds of approximately 0.5 meter per second resulting from the combination of an eastward flow with a variable tidal wind. The existence of dunes also requires geological processes that create sand-sized (100- to 300-micrometer) particulates and a lack of persistent equatorial surface liquids to act as sand traps.

Cassini radar views the surface of Titan.

The Cassini Titan Radar Mapper imaged about 1% of Titan's surface at a resolution of approximately 0.5 kilometer, and larger areas of the globe in lower resolution modes. The images reveal a complex surface, with areas of low relief and a variety of geologic features suggestive of dome-like volcanic constructs, flows, and sinuous channels. The surface appears to be young, with few impact craters. Scattering and dielectric properties are consistent with porous ice or organics. Dark patches in the radar images show high brightness temperatures and high emissivity and are consistent with frozen hydrocarbons.

Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization.

Interferometric radar techniques often necessitate two-dimensional (2-D) phase unwrapping, defined here as the estimation of unambiguous phase data from a 2-D array known only modulo 2pi rad. We develop a maximum a posteriori probability (MAP) estimation approach for this problem, and we derive an algorithm that approximately maximizes the conditional probability of its phase-unwrapped solution given observable quantities such as wrapped phase, image intensity, and interferogram coherence. Examining topographic and differential interferometry separately, we derive simple, working models for the joint statistics of the estimated and the observed signals. We use generalized, nonlinear cost functions to reflect these probability relationships, and we employ nonlinear network-flow techniques to approximate MAP solutions. We apply our algorithm both to a topographic interferogram exhibiting rough terrain and layover and to a differential interferogram measuring the deformation from a large earthquake. The MAP solutions are complete and are more accurate than those of other tested algorithms.

Widespread uplift and 'trapdoor' faulting on Galápagos volcanoes observed with radar interferometry.

Volcanic uplift, caused by the accumulation of magma in subsurface reservoirs, is a common precursor to eruptions. But, for some volcanoes, uplift of metres or more has not yet led to an eruption. Here we present displacement maps of volcanoes in the Galápagos Islands, constructed using satellite radar interferometry, that might help explain this dichotomy. We show that all but one of the seven volcanoes on the islands of Isabela and Fernandina deformed during 1992-99. Cerro Azul and Fernandina erupted during the observation period and show evidence of inflation, co-eruptive deflation and shallow dyke intrusion. In contrast, the largest volcano, Sierra Negra, has not erupted, yet exhibits spatially and temporally variable deformation, with a maximum uplift of 2.7 m between 1992 and 1999, which can be modelled by a shallow inflating sill. Inflation during 1997-98, however, was accompanied by 'trapdoor' faulting on a steeply dipping fracture system within the caldera. Repeated trapdoor faulting over geological time has formed an arcuate intra-caldera ridge within Sierra Negra and may have acted to relax stresses above the magma chamber, inhibiting summit eruptions. Similar processes may help explain large uplift unaccompanied by eruptive activity at other volcanoes.

Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms.

Two-dimensional (2-D) phase unwrapping, that is, deducing unambiguous phase values from a 2-D array of values known only modulo 2pi, is a key step in interpreting data acquired with synthetic aperture radar interferometry. Noting the recent network formulation of the phase unwrapping problem, we apply here some well-established ideas of network theory to formalize the problem, analyze its complexity, and derive algorithms for its solution. It has been suggested that the objective of phase unwrapping should be to minimize the total number of places where unwrapped and wrapped phase gradients differ. Here we use network constructions to show that this so-called minimum L0-norm problem is NP-hard, or one that complexity theory suggests is impossible for efficient algorithms to solve exactly. Therefore we must instead find approximate solutions; we present two new algorithms for doing so. The first uses the network ideas of shortest paths and spanning trees to improve on the Goldstein et al. residue-cut algorithm [Radio Sci. 23, 713 (1988)]. Our improved algorithm is very fast, provides complete coverage, and allows user-defined weights. With our second algorithm, we extend the ideas of linear network flow problems to the nonlinear L0 case. This algorithm yields excellent approximations to the minimum L0 norm. Using interferometric data, we demonstrate that our algorithms are highly competitive with other existing algorithms in speed and accuracy, outperforming them in the cases presented here.

Phase unwrapping through fringe-line detection in synthetic aperture radar interferometry.

Interferometric synthetic aperture radar presents a new technology for performing high-resolution topographic mapping. One of the factors critical to mapping accuracy is phase unwrapping. This paper presents a new algorithm that unwraps phase through fringe-line detection. The algorithm is effective in preventing error propagation, it preserves the image resolution, and, in the mean time, it produces negligible local errors. An edge-segment linking approach and a curve-fitting approach are investigated, and their performances are compared. Test results of the algorithm are shown with the actual interferometric SEASAT synthetic aperture radar images over large-relief terrain near Yellowstone National Park with a short baseline, and results are shown over relatively flat terrain in Death Valley of California with a long baseline.

Remote sensing of ocean currents.

A method of remotely measuring near-surface ocean currents with a synthetic aperture radar (SAR) is described. The apparatus consists of a single SAR transmitter and two receiving antennas. The phase difference between SAR image scenes obtained from the antennas forms an interferogram that is directly proportional to the surface current. The first field test of this technique against conventional measurements gives estimates of mean currents accurate to order 20 percent, that is, root-mean-square errors of 5 to 10 centimeters per second in mean flows of 27 to 56 centimeters per second. If the full potential of the method could be realized with spacecraft, then it might be possible to routinely monitor the surface currents of the world's oceans.

Thickness of Saturn's Rings Inferred from Voyager 1 Observations of Microwave Scatter.

Earth-based telescopic observations indicate that Saturn's rings are about 1 kilometer thick, while spacecraft measurements and theoretical considerations give an upper bound of about 100 meters. Analysis of a shielding effect present in radio occultation provides a sensitive new measure of the ring thickness. On the basis of this effect, Voyager 1 microwave measurements of near-forward scatter imply a thickness ranging from less than 10 meters in ring C to about 20 and 50 meters in the Cassini division and ring A, respectively. Monolayer models do not fit the observations in the latter two regions. The discrepancy between the Earth-based and spacecraft measurements may be due to warps in the ring plane or effects of tenuous material outside the primary ring system.