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NASA NTRS1988

Geoid and topography for infinite Prandtl number convection in a spherical shell

Geoid anomalies and surface and lower-boundary topographies are calculated for numerically generated thermal convection for an infinite Prandtl number, Boussinesq, axisymmetric spherical fluid shell with constant gravity and viscosity, for heating both entirely from below and entirely from within. Convection solutions are obtained for Rayleigh numbers Ra up to 20 times the critical Ra in heating from below and 27 times critical for heating from within. Geoid parallels surface undulations, and boundary deformation generally increases with increasing cell wavelength. Dimensionless geoid and topography in heating from below are about 5 times greater than in heating from within. Values for heating from within correlate more closely with geophysical data than values from heating from below, suggesting a predominance of internal heating in the mantle. The study emphasizes that dynamically induced topography and geoid are sensitive to the mode of heating in the earth's mantle.

Bercovici, D.↗

NASA NTRS1988

Dependence of image grey values on topography in SIR-B images

This paper focuses on the use of a high resolution digital elevation model (DEM) to aid in rectifying and enhancing synthetic aperture radar images. Using a synthetic backscatter image, the SIR-B images are manually rectified and resampled to remove geometric distortions caused by topography. In a second step, an improved reflectance function of incidence angle is derived from the DEM and the rectified image and this function is used to reduce radiometric effects of topography yielding an albedo image which clearly shows the thematic, as opposed to topographic content of the image. The procedure is tested on four SIR-B images of a scene in Argentina (crossover point) that is imaged under different azimuth and incidence angles. The similarity of the resulting images indicates that the procedure effectively reduces artefacts from the images that are dependent on topography.

Domik, G.↗

NASA NTRS1988

Earth rotation and core topography

The NASA Geodynamics program has as one of its missions highly accurate monitoring of polar motion, including changes in length of day (LOD). These observations place fundamental constraints on processes occurring in the atmosphere, in the mantle, and in the core of the planet. Short-timescale (t less than or approx 1 yr) variations in LOD are mainly the result of interaction between the atmosphere and the solid earth, while variations in LOD on decade timescales result from the exchange of angular momentum between the mantle and the fluid core. One mechanism for this exchange of angular momentum is through topographic coupling between pressure variations associated with flow in the core interacting with topography at the core-mantel boundary (CMB). Work done under another NASA grant addressing the origin of long-wavelength geoid anomalies as well as evidence from seismology, resulted in several models of CMB topography. The purpose of work supported by NAG5-819 was to study further the problem of CMB topography, using geodesy, fluid mechanics, geomagnetics, and seismology. This is a final report.

Hager, Bradford H.↗

NASA NTRS1989

The role of topography in geodetic gravity field modelling

Masses associated with the topography, bathymetry, and its isostatic compensation are a dominant source of gravity field variations, especially at shorter wavelengths. On global scales the topographic/isostatic effects are also significant, except for the lowest harmonics. In practice, though, global effects need not be taken into account as such effects are included in the coefficients of the geopotential reference fields. On local scales, the short-wavelength gravity variations due to the topography may, in rugged terrain, be an order of magnitude larger than other effects. In such cases, explicit or implicit terrain reduction procedures are mandatory in order to obtain good prediction results. Such effects may be computed by space-domain integration or by fast Fourier transformation (FFT) methods. Numerical examples are given for areas of the Canadian Rockies. In principle, good knowledge of the topographic densities is required to produce the smoothest residual field. Densities may be determined from sample measurements or by gravimetric means, but both are somewhat troublesome methods in practice. The use of a standard density, e.g., 2.67 g/cu cm, may often yield satisfactory results and may be put within a consistent theoretical framework. The independence of density assumptions is the key point of the classical Molodensky approach to the geodetic boundary value problem. The Molodensky solutions take into account that land gravity field observations are done on a non-level surface. Molodensky's problem may be solved by integral expansions or more effective FFT methods, but the solution should not be intermixed with the use of terrain reductions. The methods are actually complimentary and may both be required in order to obtain the smoothest possible signal, least prone to aliasing and other effects coming from sparse data coverage, typical of rugged topography.

Forsberg, R.↗

NASA NTRS1990

Erosional development of bedrock spur and gully topography in the Valles Marineris, Mars

Gully networks separated by resistant bedrock spurs are a common erosional feature along the escarpments that border the Valles Marineris. The resistant spur topography is best developed where the base of the slope is truncated by linear scarps interpreted as fault scarps. Regional variations in slope morphology imply that spur and gully topography undergoes a systematic progressive degradation through time associated with the erosional destruction of the basal fault scarps. The comparative morphometry of the divide networks indicates that the density of the spur networks and the number of first-order unbranched spurs decreases as the basal slope break becomes more sinuous. Abstraction of the spurs occurs through regolith storage in adjacent gullies at the slope base and the most degraded slope forms are entirely buried in talus. The basal fault scarps apparently control regolith transport by allowing debris to drain from the slope. As these basal scarps decay the slope base becomes increasingly sinuous and the slopes become transport limited. Dry mass-wasting may be the most important process acting on these slopes where a continually lowered base level is required to maintain the spur topography. In contrast to the Martian slopes, range front fault escarpments in the western U.S. show no systematic trend in spur network geometry as they are eroded. These weathering limited slopes are controlled by the more efficient removal of regolith through fluvial processes which rapidly create quasi-equilibrium drainage networks.

Patton, Peter C.↗

NASA NTRS1990

Spatial cross-correlation of Antarctic Sea ice and seabed topography

A time series of derived sea ice concentrations as observed about Antarctica by the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) satellite in 1983 is considered. The degree of spatial cross correlation between these data and seabed topography is quantified. The approach is to implement a statistical image processing filter designed to extract local patterns of spatial cross correlation over the entire sea ice field as it undergoes daily changes. Throughout the sea ice, it was found that large scale variations in sea ice concentration correlate systematically with variations in the topography of the seabed. Generally speaking, high concentrations of sea ice occur over deep ocean, whereas areas of encavement, early dissipation and polynya formation develop over topographic features of high elevation. The latter was studied in detail with respect to the features Maud Rise, Astrid Ridge and the continental shelf in the Cosmonaut and Ross Seas. In each case, it is shown that an encavement in sea ice, a polynya, or both develops in the vicinity of the feature in question. As these results are quantified in terms of spatial cross correlation, a potential role is inferred for seabed topography in such fluctuations in the sea ice about Antarctica.

Deveaux, Richard D.↗

NASA NTRS1990

On oscillatory flow over topography in a rotating fluid

Quasi-geostrophic beta-plane motion of a homogeneous liquid over topography is considered for situations in which there is a time-periodic forcing of a zonal current. Such an oscillatory current generates a topographic Rossby wave response that has a complicated, but periodic, temporal structure. The linear solution grows resonances at all integer values of the beta-parameter. The nonlinear analysis demonstrates that for weak friction and forcing, the resonances are bent and multiple equilibria of the time-dependent Rossby wave states are possible in certain parameter ranges. While the basic forced flow in the absence of topography has no time-mean, the nonlinear amplitude equations show that a mean retrograde (westward) Eulerian zonal flow is generated in the interactions of the forced flow with the topography.

Hart, J. E.↗

NASA NTRS1990

Dynamic sea surface topography, gravity, and improved orbit accuracies from the direct evaluation of Seasat altimeter data

A gravitational model incorporating Seasat altimetry, surface gravimetry, and satellite tracking data has been determined in terms of global spherical harmonics complete to degree and order 50. This model, PGS-3337, uses altimeter data as a dynamic observation of the satellite's height above the sea surface. A solution for the ocean's dynamic topography is recovered simultaneously with the orbit parameters, gravity, and ocean tidal terms. The recovered dynamic topography reveals the global long wavelength circulation of the oceans with a resolution of 2000 km and is very similar to the mean upper ocean dynamic height derived from historical ship observations. The PGS-3337 geoid has an uncertainty of 60 cm rms globally but 25 cm rms over the ocean because of the altimeter measurements. Seasat orbits determined in this solution have an estimated accuracy for the radial position of 20 cm rms. The difference between the altimeter observed sea height and the geoid plus dynamic topography model is 30 cm rms. Contained in these residuals are the sea height variability, as well as errors from the geoid, orbits, tidal models, and altimeter range measurement. This performance level is 2 to 3 times better than that achieved with previous Goddard gravitational models.

Marsh, J. G.↗

NASA NTRS1990

Processes of crustal formation and evolution on Venus - An analysis of topography, hypsometry, and crustal thickness variations

Processes of crustal formation and evolution are examined, and the role of crustal thickness variation in the production of topography is assessed. Evidence for crustal composition, age, average crustal thickness, and total crustal volume on Venus is reviewed. It is shown that the present crustal volume of Venus is comparable to that of the present earth. The geologic evidence for variations in crustal thickness on Venus are outlined, and specific examples of regions of apparent crustal thickening are assessed. These observations are compared to a simple model of Airy isostasy using global Venus topography and the end-member hypothesis (that the topography of Venus could result solely from crustal thickness variations). Models to account for these observations are proposed.

Head, James W.↗

NASA NTRS1992

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.↗

NASA NTRS1992

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.↗

NASA NTRS1993

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.↗

NASA NTRS1993

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↗

NASA NTRS1993

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.↗

NASA NTRS1992

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.↗

NASA NTRS1994

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.↗

NASA NTRS1994

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↗

NASA NTRS1996

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.↗