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Flexural models of trench/outer rise topography of coronae on Venus with axisymmetric spherical shell elastic plates

Magellan altimetry has revealed that many coronae on Venus have trenches or moats around their peripheries and rises outboard of the trenches. This trench/outer rise topographic signature is generally associated with the tectonic annulus of the corona. Sandwell and Schubert have interpreted the trench/outer rise topography and the associated tectonic annulus around coronae to be the result of elastic bending of the Venus lithosphere (though the tectonic structures are consequences of inelastic deformation of the lithosphere). They used two-dimensional elastic plate flexure theory to fit topographic profiles across a number of large coronae and inferred elastic lithosphere thicknesses between about 15 and 40 km, similar to inferred values of elastic thickness for the Earth's lithosphere at subduction zones around the Pacific Ocean. Here, we report the results of using axisymmetric elastic flexure theory for the deformation of thin spherical shell plates to interpret the trench/outer rise topography of the large coronae modeled by Sandwell and Schubert and of coronae as small as 250 km in diameter. In the case of a corona only a few hundred kilometers in diameter, the model accounts for the small planform radius of the moat and the nonradial orientation of altimetric traces across the corona. By fitting the flexural topography of coronae we determine the elastic thickness and loading necessary to account for the observed flexure. We calculate the associated bending moment and determine whether the corona interior topographic load can provide the required moment. We also calculate surface stresses and compare the stress distribution with the location of annular tectonic features.

Moore, W.

A spatial domain Stokes flow model for the gravity and topography of the middle latitudes of Venus

A novel modeling technique is developed and applied to the long-wavelength gravity, topography, and internal density structure of Venus. The focus of this study is to employ data on the gravity and topography of Venus, which are obtained from the Pioneer Venus Orbiter mission, to enhance understanding some key aspects of the internal structure of the planet. A modeling strategy utilizing 'stokeslets' or basic units of slow viscous flow (governed by the Stokes equations) to duplicate the observed gravity and topography is implemented.

Bills, Bruce G.

The effect of topography on radar scattering from vegetated areas

This paper shows how the radar scattering from vegetated areas is affected by the topography of the surface underneath the vegetation. It is shown, using a discrete scatterer model, that the dominant scattering mechanism may change drastically when the ground surface is tilted relative to the horizontal. In the case of a horizontal ground surface, total scattering may be dominated by scattering off the tree trunks, followed by a reflection off the ground surface. For a relatively small tilt in the ground surface (about 2 deg from horizontal), the ground-trunk interaction term may be replaced by scattering from the branches alone as the dominant scattering mechanism. We also show that the effect of the topography is more pronounced for scattering by longer wavelengths, and discuss the implications on algorithms designed to infer forest woody biomass and soil and vegetation moisture using polarimetric SAR data. The effect of the topography on the scattering behavior from forested areas is illustrated with images acquired by the NASA/JPL three-frequency polarimetric SAR over the Black Forest in Germany.

Van Zyl, Jakob J.

New Mars free-air and Bouguer gravity: Correlation with topography, geology and large impact basins

Free-air and Bouguer gravity anomalies from a 50x50 field (MGM635), derived at the Goddard Space Flight Center, with global topography, geology, and the distribution of large impact basins was compared. The free-air gravity anomalies were derived from re-analysis of Viking Orbiter and Mariner 9 tracking data and have a spatial resolution of 250-300 km. Bouguer anomalies were calculated using a 50x50 expansion of the current Mars topography and the GSFC degree 50 geoid as the equipotential reference surface. Rotational flattening was removed using a moment of inertia of 0.365 and the corrections from Table B2 of Sleep and Phillips. Crustal density and mean density were assumed to be 2.9 and 3.93 gm/cm(sup 3). The spherical harmonic topography used has zero mean elevation, and differs from the USGS maps by about 2 km. Comparisons with global geology use a simplified map with about 1/3 the number of units on the current maps. For correlation with impact basins, the recent compilation by Schultz and Frey was used.

Frey, Herbert

Spectral study of Venus global topography and geoid from Magellan and PVO data

An analysis of newly available global harmonic models for topography and geoid on Venus was conducted. It was found that the power spectral density for Venus topography has a power law dependence on wave-number characteristic of Brown Noise, similar to what is found for the Earth. However, the Venus topography spectrum presents a rollover at lower degree (l = 3) than is observed for the Earth spectrum and has smaller amplitudes than that of the Earth's. The Venus geoid also obeys a power law relationship, at least for small values of l, but with a smaller slope and more power (for l greater than 3) than the Earth geoid.

Kucinskas, A. B.

Mapping of sea bottom topography

Under suitable conditions the bottom topography of shallow seas is visible in remote sensing radar imagery. Two experiments were performed to establish which remote sensing technique or combination yields optimal imaging of bottom topography and which hydro-meteorological conditions are favorable. A further goal is to gain experience with these techniques. Two experiments were performed over an area in the North Sea near the measuring platform Meetpost Noordwijk (MPN). The bottom topography in the test area is dominated by sand waves. The crests of the sand waves are perpendicular to the coast line and the dominating (tidal-)current direction. A 4x4 sq km wide section of the test area was studied in more detail. The first experiment was undertaken on 16 Aug. 1989. During the experiment the following remote sensing instruments were used: Landsat-Thematic Mapper, and NASA/JPL Airborne Imaging Radar (AIR). The hydro-meteorological conditions; current, wind, wave, and air and water temperature were monitored by MPN, a ship of Rijkswaterstaat (the OCTANS), and a pitch-and-roll WAVEC-buoy. The second experiment took place on 12 July 1992. During this experiment data were collected with the NASA/JPL polarimetric synthetic aperture radar (SAR), and a five-band helicopter-borne scatterometer. Again the hydro-meteorological conditions were monitored at MPN and the OCTANS. Furthermore, interferometric radar data were collected.

Calkoen, C. J.

A preliminary evaluation of ocean topography from the TOPEX/POSEIDON mission

We have analyzed 50 ten-day cycles of TOPEX/POSEIDON (T/P) altimeter data to evaluate the ocean dynamic topography and its temporal variations. We have employed data from both the U.S. and French altimeters along with the NASA precision orbits in this analysis. Errors in the diurnal and semidiurnal components of the Cartwright-Ray tide model have been significantly reduced using a correction developed from a combination of JGM-2 and OSU91A was employed, as well as a geoid model based solely on OSU91A. The long wavelengths of the comparisons to historical data, although geoid error still corrupts the dynamic topography for wavelengths shorter than 2500 km. The root mean square (RMS) variability is similar to previous results from Geosat, with bakground 'noise' approaching 3 cm RMS. The computed annual and semiannual variations are also similar to previous Geosat results, although the hemispheric distribution of the annual heating cycle is much better presented in the T/P results. They also compare reasonably well with the Levitus hydrographic compilation in the northern hemisphere, although the T/P variations generally have larger amplitudes. Ten-day average maps of variations in sea level compare well with simulations measurements at ocean tide gauges, with RMS differences of less than 4 cm and correlations greater than 0.6 for most of the island gauges. Time-longitude plots of these sea level variations at different latitudes in the Pacific clearly show the presence of equatorial Kelvin waves and Rossby waves, with the wave speeds agreeing well with theoretical and observed values. Measurement of variations in global sea level over cycles 2-51 have an RMS variability of 6.3 mm and a rate of change of -3.5 +/- 8 mm/yr, the uncertainty primarily due to insufficient averaging of the interannual and periodic sea level variations. These results show that the accuracy of the T/P measurements of sea level has dramatically improved over previous missions, with estimated time variable errors of 4 cm or less. Although geographically correlated orbit errors have also been reduced to the few centimeter level, further improvement in determinations of the mean dynamic topography will be difficult to obtain until a more accurate model of the marine geoid is available.

Nerem, R. S.

A 360-degree and -order model of Venus topography

This report presents the most recent spherical harmonic topography model of Venus developed at Jet Propulsion Laboratory. It was produced by a spherical harmonic analysis of the most complete set of Magellan altimetry data, augmented by Pioneer Venus and Venera data. The harmonic coefficients of the topography were computed to degree and order 360. Compared to previous topography models, this one has the highest correlation with the gravity field of Venus.

Rappaport, Nicole

An Inversion of Gravity and Topography for Mantle and Crustal Structure on Mars

Analysis of the gravity and topography of Mars presently provides our primary quantitative constraints on the internal structure of Mars. We present an inversion of the long-wavelength (harmonic degree less than or equal to 10) gravity and topography of Mars for lateral variations of mantle temperature and crustal thickness. Our formulation incorporates both viscous mantle flow (which most prior studies have neglected) and isostatically compensated density anomalies in the crust and lithosphere. Our nominal model has a 150-km-thick high-viscosity surface layer over an isoviscous mantle, with a core radius of 1840 km. It predicts lateral temperature variations of up to a few hundred degrees Kelvin relative to the mean mantle temperature, with high temperature under Tharsis and to a lesser extent under Elysium and cool temperatures elsewhere. Surprisingly, the model predicts crustal thinning beneath Tharsis. If correct, this implies that thinning of the crust by mantle shear stresses dominates over thickening of the crust by volcanism. The major impact basins (Hellas, Argyre, Isidis, Chryse, and Utopia) are regions of crustal thinning, as expected. Utopia is also predicted to be a region of hot mantle, which is hard to reconcile with the surface geology. An alternative model for Utopia treats it as a mascon basin. The Utopia gravity anomaly is consistent with the presence of a 1.2 to 1.6 km thick layer of uncompensated basalt, in good agreement with geologic arguments about the amount of volcanic fill in this area. The mantle thermal structure is the dominant contributor to the observed geoid in our inversion. The mantle also dominates the topography at the longest wavelengths, but shorter wavelengths (harmonic degrees greater than or equal to 4) are dominated by the crustal structure. Because of the uncertainty about the appropriate numerical values for some of the model's input parameters, we have examined the sensitivity of the model results to the planetary structural model (core radius and core and mantle densities), the mantle's viscosity stratification, and the mean crustal thickness. The model results are insensitive to the specific thickness or viscosity contrast of the high-viscosity surface layer and to the mean crustal thickness in the range 25 to 100 km. Models with a large core radius or with an upper mantle low-viscosity zone require implausibly large lateral variations in mantle temperature.

Kiefer, Walter S.

The Laser Vegetation Imaging Sensor (LVIS): A Medium-Altitude, Digitization-Only, Airborne Laser Altimeter for Mapping Vegetation and Topography

The Laser Vegetation Imaging Sensor (LVIS) is an airborne, scanning laser altimeter designed and developed at NASA's Goddard Space Flight Center. LVIS operates at altitudes up to 10 km above ground, and is capable of producing a data swath up to 1000 m wide nominally with 25 m wide footprints. The entire time history of the outgoing and return pulses is digitized, allowing unambiguous determination of range and return pulse structure. Combined with aircraft position and attitude knowledge, this instrument produces topographic maps with decimeter accuracy and vertical height and structure measurements of vegetation. The laser transmitter is a diode-pumped Nd:YAG oscillator producing 1064 nm, 10 nsec, 5 mJ pulses at repetition rates up to 500 Hz. LVIS has recently demonstrated its ability to determine topography (including sub-canopy) and vegetation height and structure on flight missions to various forested regions in the U.S. and Central America. The LVIS system is the airborne simulator for the Vegetation Canopy Lidar (VCL) mission (a NASA Earth remote sensing satellite due for launch in 2000), providing simulated data sets and a platform for instrument proof-of-concept studies. The topography maps and return waveforms produced by LVIS provide Earth scientists with a unique data set allowing studies of topography, hydrology, and vegetation with unmatched accuracy and coverage.

Blair, J. Bryan

X-Ray Topography of Tetragonal Lysozyme Grown by the Temperature-Controlled Technique

Growth-induced defects in lysozyme crystals were observed by white-beam and monochromatic X-ray topography at the National Synchrotron Light Source (NSLS) at the Brookhaven National Laboratory (BNL). The topographic methods were non-destructive to the extent that traditional diffraction data collection could be performed to high resolution after topography. It was found that changes in growth parameters, defect concentration as detected by X-ray topography, and the diffraction quality obtainable from the crystals were all strongly correlated. In addition, crystals with fewer defects showed lower mosaicity and higher diffraction resolution as expected.

Stojanoff, V.

Inferences About the Early Moon From Gravity and Topography

Recent spacecraft missions to the Moon have significantly improved our knowledge of the lunar gravity and topography fields, and have raised some new and old questions about the early lunar history. It has frequently been assumed that the shape of the Moon today reflects an earlier equilibrium state and that the Moon has retained some internal strength. Recent analysis indicating a superisostatic state of some lunar basins lends support to this hypothesis. On its simplest level, the present shape of the Moon is slightly flattened by 2.2 +/- 0.2 km while its gravity field, represented by an equipotential surface, is flattened only about 0.5 km. The hydrostatic component to the flattening arising from the Moon's present day rotation contributes only 7 m. This difference between the topographic shape of the MOon and the shape of its gravitational equipotential has frequently been explained as the "memory" of an earlier moon that was rotating faster and had a correspondingly larger hydrostatic flattening. To obtain this amount of hydrostatic flattening from rotation alone, and accounting for the contribution of the present-day gravity field, the Moon's rotation rate would need to be about 15x greater than at present, leading ot a period of < 2 days. Maintaining its synchronous rotation with Earth would require a radius for the Moon's orbit of approximately 9 Earth Radii. Unfortunately, our confidence in the observed lunar flattening is not as great as we would like. The uncertainty of .02 km may not properly reflect the limitations of the Clementine dataset, which did not sample poleward of latitudes 81 N and 79 S. Also, the large variation of topography +/- 8 km seen on the MOon dwarfs our estimate fo the flattening. Further the lunar south pole is on the edge of, or possibly inside the massive deep, South Pole-Aitken Basin. Thus, polar radii could be underestimated. This would yield a smaller flattening, which would imply a greater lunar rotation period and orbital radius. However, Basin compensation states and analyses of support and relaxation of topography at long wavelengths point to a lunar shape that has retained a flattening from an earlier faster rotation period.

Smith, D. E.

Modelling and Estimation of Dynamic Ocean Topography Within Global Geopotential Solutions

In this poster, we will present a report on the ongoing investigation "Improved Gravitational and Dynamic Height Models Through the use of Oceanographic Data." we have used a two year mean (1993-1994) of the Dynamic ocean Topography (DOT) field implied by the Semtner and Chervin POCM_4B model, and developed normal equations in surface spherical harmonics to degree and order 30. These normal equations, were combined with normal equations derived from TOPEX and ERS-1 altimeter data over the same time period. Combination solutions (based on satellite tracking data, altimeter data, surface gravity data and OCM data) were were developed Test solutions were obtained estimating the DOT field to 2Ox2O and 3ox3O. These solutions were tested with independent DOT values computed over 38 WOCE hydrographic sections, which contained a total of 3072 stations and represented 216000 km of travelled lines. The weighted standard deviation of the differences between the DOT obtained from the hydrographic data and and the field estimated from the joint combination solutions was computed for each of the test models, the weighted standard deviation for the baseline combination solution excluding the POCM4_B data was 9.7 cm for a DOT solution to 30x30, where introducing the POCM4_B data into the combination model reduced the standard deviation to 9.2 cm, indicating the the introduction of oceanographic information benefits the solution for the dynamic ocean topography. We will discuss the weighting schemes applied and the method of solution. Another aspect of our investigation involves testing alternate parametric representations of the dynamic height field. We looked at the alternative representations in terms of the Proudman functions (PF), and compared these to the use of spherical harmonics (SH) to represent the dynamic ocean topography, using once again the 1993 and 1994 output of the POCM4_B OCM as the reference model. A significant advantage of PF's over SH's is that the former require no "fill-in" values over areas where the DOT is undefined. We show that the PF and SH results using equal number of parameters agree quite well in overall content. In addition, PFs appear better suited for representation of high frequency signals close to the signal boundary. The development of the PF solutions for the DOT will be described and the statistics of the comparisons will be presented.

Lemoine, Frank G.

Preliminary Correlations of Gravity and Topography from Mars Global Surveyor

The Mars Global Surveyor (MGS) spacecraft is currently in a 400-km altitude polar mapping orbit and scheduled to begin global mapping of Mars in March of 1999. Doppler tracking data collected in this Gravity Calibration Orbit prior to the nominal mapping mission combined with observations from the MGS Science Phasing Orbit in Spring - Summer 1999 and the Viking and mariner 9 orbiters has led to preliminary high resolution gravity fields. Spherical harmonic expansions have been performed to degree and order 70 and are characterized by the first high spatial resolution coverage of high latitudes. Topographic mapping by the Mars Orbiter Laser Altimeter on MGS is providing measurements of the height of the martian surface with sub-meter vertical resolution and 5-30 m absolute accuracy. Data obtained during the circular mapping phase are expected to provide the first high resolution measurements of surface heights in the southern hemisphere. The combination of gravity and topography measurements provides information on the structure of the planetary interior, i.e. the rigidity and distribution of internal density. The observations can also be used to address the mechanisms of support of surface topography. Preliminary results of correlations of gravity and topography at long planetary wavelengths will be presented and the implications for internal structure will be addressed.

Zuber, M. T.

Implications of MOLA Global Roughness, Statistics, and Topography

New insights are emerging as the ongoing high-quality measurements of the Martian surface topography by Mars Orbiter Laser Altimeter (MOLA) on board the Mars Global Surveyor (MGS) spacecraft increase in coverage, resolution, and diversity. For the first time, a global characterization of the statistical properties of topography is possible. The data were collected during the aerobreaking hiatus, science phasing, and mapping orbits of MGS, and have a resolution of 300-400 m along track, a range resolution of 37.5 cm, a range precision of 1-10 m for surface slopes up to 30 deg., and an absolute accuracy of topography of 13 m. The spacecraft's orbit inclination dictates that nadir observations have latitude coverage of about 87.1S to 87.1N; the addition of observations obtained during a period of off-nadir pointing over the north pole extended coverage to 90N. Additional information is contained in the original extended abstract.

Aharonson, O.

Stationary Wave Activity Simulated by the NASA Ames MGCM Incorporating New MOLA Topography Data

Annual simulations of Mars' atmosphere have been conducted with the NASA Ames Mars General Circulation Model (MGCM) using the newly-acquired MOLA topography data. The data is provided at 1 x 1 deg resolution, and is used by the MGCM at 7.5 x 9 deg resolution. The vertical domain in the simulations reported here extends to around 80 km. Simulated stationary wave activity is examined in each hemisphere as a function of season (at every 30 deg of Ls), dust loading (dust visible opacities of 0.3, 1, and 3), and topography (comparing results with MOLA vs. Smith-Zuber topography). Additional information is contained in the original extended abstract.

Bridger, A. F. C.

The Mystery of the Mars North Polar Gravity-Topography Correlation(Or Lack Thereof)

Maps of moderately high resolution gravity data obtained from the Mars Global Surveyor (MGS) gravity calibration orbit campaign and high precision topography obtained from the Mars Orbiter Laser Altimeter (MOLA) experiment reveal relationships between gravity and topography in high northern latitudes of Mars. Figure 1 shows the results of a JPL spherical harmonic gravity model bandpass filtered between degrees 6 and 50 contoured over a MOLA topographic image. A positive gravity anomaly exists over the main North Polar cap, but there are at least six additional positive gravity anomalies, as well as a number of smaller negative anomalies, with no obvious correlation to topography. Additional information is contained in the original extended abstract.

Phillips, R. J.

Shape and Topography of Mars

Observations by the Mars Orbiter Laser Altimeter (MOLA) on the Mars Global Surveyor (MGS) spacecraft are showing a new planet in its range of topography and in the detail of the geological features. MGS arrived at Mars in Sept 1997 and since Feb. 28, 1999 the laser altimeter has operated continuously. By the end of April 2000 MOLA had acquired over 350 million measurements of the planet's shape and topography. These observations show a strong down-hill topographic gradient from the south pole to the north pole with an extremely low and flat basin encompassing most of the northern hemisphere. Large outflow channels are seen in the Chyrse region that strongly suggest considerable quantities of water once flowed into the lower northern hemisphere from the south. The northern icecap, which rises to a height of three kilometers above the surrounding terrain, is shown to be largely composed of water ice and at the center of a large basin. The southern hemisphere is about five kilometers higher than the low northern plains and dominated by the Hellas impact basin whose ejecta is the major contributor to the topography of the hemisphere and the crustal dichotomy. The south polar icecap, which is part of a much larger region of layered terrain composed of water ice and dust, reaches an elevation of nearly five kilometers and except for the large Tharsis volcanoes is the highest part of the planet.

Smith, David E.