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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Altimetry data and the elastic stress tensor of subduction zones

The stress field in the lithosphere caused by the distribution of density anomalies associated to the geoidal undulations observed by the GEOS-3 and SEASAT Earth satellites in the Tonga region was studied. Different models of the lithosphere were generated with different assumptions on the density distribution and geometry, all generating a geoid profile almost identical to the observed one. The first model is the Airy isostatic hypothesis which consists of a crust of density 2.85 laying on a lithosphere of density 3.35. The models obtained with different compensation depths give residual shortwavelength anomalies of the order of several tens of mgal and several tens of meters geoidal undulations. It indicates that there is no isostasy of the Airy type in the Tonga region because the observed geoid has very smooth undulation of about 25 m over a distance of 2000 km. The Pratt isostatic hypothesis is used in a model consisting of a crust of variable density laying on a lithosphere of higher density. This model gives smaller residual anomalies but still shows that there is no isostasy of the Pratt type in the Tonga region because the observed geoidal undulation are much smaller and smoother than the residual undulations associated to the Pratt model of isostasy.

Caputo, M.↗
NASA NTRS1994

Preliminary estimates of Gulf Stream characteristics from TOPEX data and a precise gravimetric geoid

TOPEX sea surface height data has been used, with a gravimetric geoid, to calculate sea surface topography across the Gulf Stream. This topography was initially computed for nine tracks on cycles 21 to 29. Due to inaccurate geoid undulations on one track, results for eight tracks are reported. The sea surface topography estimates were used to calculate parameters that describe Gulf Stream characteristics from two models of the Gulf Stream. One model was based on a Gaussian representation of the velocity while the other was a hyperbolic representation of velocity or the sea surface topography. The parameters of the Gaussian velocity model fit were a width parameter, a maximum velocity value, and the location of the maximum velocity. The parameters of the hyperbolic sea surface topography model were the width, the height jump, position, and sea surface topography at the center of the stream. Both models were used for the eight tracks and nine cycles studied. Comparisons were made between the width parameters, the maximum velocities, and the height jumps. Some of the parameter estimates were found to be highly (0.9) correlated when the hyperbolic sea surface topography fit was carried out, but such correlations were reduced for either the Gaussian velocity fits or the hyperbolic velocity model fit. A comparison of the parameters derived from 1-year TOPEX data showed good agreement with values derived by Kelly (1991) using 2.5 years of Geosat data near 38 deg N, 66 deg W longitude. Accuracy of the geoid undulations used in the calculations was of order of +/- 16 cm with the accuracy of a geoid undulation difference equal to +/- 15 cm over a 100-km line in areas with good terrestrial data coverage. This paper demonstrates that our knowledge or geoid undulations and undulation differences, in a portion of the Gulf Stream region, is sufficiently accurate to determine characteristics of the jet when used with TOPEX altimeter data. The method used here has not been shown to be more accurate than methods that average altimeter data to form a reference surface used in analysis to obtain the Gulf Stream characteristics. However, the results show the geoid approach may be used in areas where lack of current meandering reduces the accuracy of the average surface procedure.

Rapp, Richard H.↗
NASA NTRS1973

A noncoherent model for microwave emissions and backscattering from the sea surface

The two-scale (small irregularities superimposed upon large undulations) scattering theory proposed by Semyonov was extended and used to compute microwave apparent temperature and the backscattering cross section from ocean surfaces. The effect of the small irregularities upon the scattering characteristics of the large undulations is included by modifying the Fresnel reflection coefficients; whereas the effect of the large undulations upon those of the small irregularities is taken into account by averaging over the surface normals of the large undulations. The same set of surface parameters is employed for a given wind speed to predict both the scattering and the emission characteristics at both polarizations.

Wu, S. T.↗
NASA NTRS1974

The geoid: Definition and determination

The determination of the geoid has been one of the prime goals of geodesy. Knowledge of geoid undulations with respect to some reference surface was needed for the determination of the figure of the earth, for the precise reduction of distance measurements to a reference ellipsoid, and for the determination of the geocentric location of points on the surface of the earth. Currently and in the future, undulation information can also be used in geophysical studies related to crustal structures and in oceanographic studies related to sea surface topography. The actual determination of global geoids has been carried out by using gravimetric data, satellite‐derived information related to the gravitational field of the earth, or a combination of the two techniques. Regional geoid determinations have been made by astrogeodetic techniques. For some applications of undulation information, undulation standard deviations of the order of ±5 m would be sufficient. Such an accuracy can be obtained by using data currently available. In the past few years, renewed interest in the geoid arose when the concept of satellite altimetry was proposed to measure the distance from the satellite to some area on the ocean surface.

Richard H. Rapp↗
NASA NTRS1975

Methods for the computation of detailed geoids and their accuracy

Two methods for the computation of geoid undulations using potential coefficients and 1 deg x 1 deg terrestrial anomaly data are examined. It was found that both methods give the same final result but that one method allows a more simplified error analysis. Specific equations were considered for the effect of the mass of the atmosphere and a cap dependent zero-order undulation term was derived. Although a correction to a gravity anomaly for the effect of the atmosphere is only about -0.87 mgal, this correction causes a fairly large undulation correction that was not considered previously. The accuracy of a geoid undulation computed by these techniques was estimated considering anomaly data errors, potential coefficient errors, and truncation (only a finite set of potential coefficients being used) errors. It was found that an optimum cap size of 20 deg should be used. The geoid and its accuracy were computed in the Geos 3 calibration area using the GEM 6 potential coefficients and 1 deg x 1 deg terrestrial anomaly data. The accuracy of the computed geoid is on the order of plus or minus 2 m with respect to an unknown set of best earth parameter constants.

Rapp, R. H.↗
NASA NTRS1979

Evolution of Martian polar landscapes - Interplay of long-term variations in perennial ice cover and dust storm intensity

The discovery of a new type of Martian polar terrain, called undulating plain, is reported and the evolution of the plains and other areas of the Martian polar region is discussed in terms of the trapping of dust by the perennial ice cover. High-resolution Viking Orbiter 2 observations of the north polar terrain reveal perennially ice-covered surfaces with low relief, wavelike, regularly spaced, parallel ridges and troughs (undulating plains) occupying areas of the polar terrain previously thought to be flat, and associated with troughs of considerable local relief which exhibit at least partial annual melting. It is proposed that the wavelike topography of the undulating plains originates from long-term periodic variations in cyclical dust precipitation at the margin of a growing or receding perennial polar cap in response to changes in insolation. The troughs are proposed to originate from areas of steep slope in the undulating terrain which have lost their perennial ice cover and have become incapable of trapping dust. The polar landscape thus appears to record the migrations, expansions and contractions of the Martian polar cap.

Cutts, J. A.↗
NASA NTRS1988

Modeling and estimation of a low degree geopotential model from terrestrial gravity data

The development of appropriate modeling and adjustment procedures for the estimation of harmonic coefficients of the geopotential, from surface gravity data was studied, in order to provide an optimum way of utilizing the terrestrial gravity information in combination solutions currently developed at NASA/Goddard Space Flight Center, for use in the TOPEX/POSEIDON mission. The mathematical modeling was based on the fundamental boundary condition of the linearized Molodensky boundary value problem. Atmospheric and ellipsoidal corrections were applied to the surface anomalies. Terrestrial gravity solutions were found to be in good agreement with the satellite ones over areas which are well surveyed (gravimetrically), such as North America or Australia. However, systematic differences between the terrestrial only models and GEMT1, over extended regions in Africa, the Soviet Union, and China were found. In Africa, gravity anomaly differences on the order of 20 mgals and undulation differences on the order of 15 meters, over regions extending 2000 km in diameter, occur. Comparisons of the GEMT1 implied undulations with 32 well distributed Doppler derived undulations gave an RMS difference of 2.6 m, while corresponding comparison with undulations implied by the terrestrial solution gave RMS difference on the order of 15 m, which implies that the terrestrial data in that region are substantially in error.

Pavlis, Nikolaos K.↗
NASA NTRS1992

Features of wavy vortices in a curved channel from experimental and numerical studies

Results are reported from an experimental study obtaining evidence of time-dependent, wavy vortex motions associated with undulating and twisting Dean vortices in a curved channel with 40-to-1 aspect ratio, and mild curvature (radius ratio = 0.979). The results are compared with direct numerical simulations of time-dependent 3D Navier-Stokes equations using boundary conditions in the spanwise and streamwise directions. When viewed in cross section, experimental visualizations of undulating and twisting vortex flows show rocking motion and changes in the direction of the flow between vortices that are like those observed in the simulations. Experimental spectra show that undulating vortices are replaced by the higher-frequency, shorter streamwise wavelength twisting vortices at higher Reynolds numbers. When undulating vortices are present, experimental power spectra and visualizations give frequencies that are somewhat lower than the most unstable frequencies predicted by linear stability analysis.

Ligrani, P. M.↗
NASA NTRSDate not supplied

Large Impact Features on Icy Galilean Satellites: Implications for Ice Shell Thickness and Habitability.

Nowhere in the solar system are impact morphologies observed in greater variety than on the icy Galilean satellites. This is very likely a consequence of the structural and thermal state of the crust at the time of impact, and perhaps impact velocity. We have conducted a multi-disciplinary investigation to study how these features formed. The particular combination of geophysical factors and impactor characteristics that is shared by these satellites is likely responsible for these features. We have derived Digital Terrain Models for a number of these features, which have been used as a tool for producing facies maps. Impact features on Ganymede and Callisto are relatable to impact features on Europa, with implications for its ice shell history. We have identified two broad classes of these impact features: (a) Crater forms, which variously include pits, central domes, and crater rims; and (b) Palimpsests (including pene-palimpsests), which all have smooth enclosed central plains, an extensive outer undulating plains unit, concentric arcuate ridges(in the case of pene-palimpsests), and no recognizable rim. The very large, measured volume of the undulating plains unit of the pene-palimpsest Buto, Ganymede, substantially exceeds the amount of target material that could have been both melted and excavated by the impact event itself. Therefore, we conclude that the undulating plains material was derived from a fluid or “slushy” layer in the near-surface target at the time of impact. The recognition of undulating plains as the dominant unit in Memphis and Nidaba, two other palimpsests on Ganymede that we have mapped(which display highly variable crater counts, with Buto being the least cratered),leads us to a working hypothesis that these plains only form where and when the target has substantial near surface fluid or “slush.” By extension, all other impact features on Ganymede and Callisto, such as those with central pits and central domes, formed in targets with no pre-existing, or at most inconsequential, amounts of fluid or “slush.” Supporting this conclusion, modeling by members of our group indicates that the present topography of impact features with central pits and domes can be largely explained by the behavior of ice alone, with no or little contribution from fluids. Our study supports explanations for the formation and final appearance of palimpsests (and pene-palimpsests) that are entirely applicable to this feature class, and sharply distinct from explanations for other impact features (crater forms) on Ganymede and Callisto.

Jeffrey M Moore↗
NASA NTRS1979

Estimation of the ocean geoid near the Blake Escarpment using GEOS-3 satellite altimetry

The accuracy with which the local ocean geoid structure could be determined using satellite altimetry data was investigated. The undulation and along-track component of the vertical deflection for selected passes of GEOS-3 near the Blake Escarpment were estimated and compared with independent analogous estimates based on U. S. Navy surface gravimetric survey data. The results of these comparisons show agreement in the geoid undulation values generally to within one or two meters. The nature of the discrepancy in the undulation values was primarily that of a bias error believed to be due essentially to radial orbit uncertainties. The agreement between the vertical deflection estimates was not significantly affected by orbit uncertainties over the track lengths considered in this study (100 - 1500 km), and the comparisons show typical rms differences of between one and two arc secs. In addition, the capability of the altimeter to resolve short wavelength features of the geoid was determined. This analysis involved spectrum and cross spectrum analysis of sets of closely spaced parallel subtracks to determine statistically significant short wavelength geoid resolution capability. The results of this analysis show that resolution can be achieved down to wavelengths as short as 30 km - 80 km depending on regional geoid variations.

Brammer, R. F.↗
NASA NTRS1986

Spherical harmonic expansions of the Earth's gravitational potential to degree 360 using 30' mean anomalies

Two potential coefficient fields that are complete to degree and order 360 have been computed. One field (OSU86E) excludes geophysically predicted anomalies while the other (OSU86F) includes such anomalies. These fields were computed using a set of 30' mean gravity anomalies derived from satellite altimetry in the ocean areas and from land measurements in North America, Europe, Australia, Japan and a few other areas. Where no 30' data existed, 1 deg x 1 deg mean anomaly estimates were used if available. No rigorous combination of satellite and terrestrial data was carried out. Instead advantage was taken of the adjusted anomalies and potential coefficients from a rigorous combination of the GEML2' potential coefficient set and 1 deg x 1 deg mean gravity anomalies. The two new fields were computed using a quadrature procedure with de-smoothing factors. The spectra of the new fields agree well with the spectra of the fields with 1 deg x 1 deg data out to degree 180. Above degree 180 the new fields have more power. The fields have been tested through comparison of Doppler station geoid undulations with undulations from various geopotential models. The agreement between the two types of undulations is approximately + or - 1.6 m. The use of a 360 field over a 180 field does not significantly improve the comparison. Instead it allows the comparison to be done at some stations where high frequency effects are important. In addition maps made in areas of high frequency information (such as trench areas) clearly reveal the signal in the new fields from degree 181 to 360.

Rapp, Richard H.↗
NASA NTRS1991

Analysis of altimetry over the Aral Sea

Satellite based altimetric data taken by GEOS-3, SEASAT, and GEOSAT over the Aral Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25 by 0.25 degree grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180 by 180 geopotential model is taken as the empirical model. The collocation procedure is performed with a set of local residual empirical covariance functions. For comparison, Rapp's global covariance functions and Jordan's self-consistent theoretical covariance functions based on Jordan's formulation and on locally derived parameters are also used to grid geoid undulations and to predict gravity anomalies. The sensitivity of the collocation results to the choice of covariance functions is discussed.

Au, Andrew Y.↗
NASA NTRS2006

Various Ambiguities in Re-constructing Laser Pulse Parameters

We think that mode lock laser pulses are generated by the summation process that take place between the monochromatic EM filed frequencies as if they interact with each other as shown in equation 1. In reality, the pulse generation is a collaborative interaction process between EM fields and various material medium. When we carry out the actual mode lock analysis, we do take into account of interpaly between all the temporal dynamics of the cavity gain medium, cavity round trip time and the response time of the intra cavity element (saturable absorber, Kerr medium, etc.). that really enforces the locking of the phase of the cavity spontaneous emissions. On a conceptual level, this simplistic representation of the mode locking by Eq.1 ignores all these critical physical processes. When we try to analyze a pulsed field, again we start by representing it very much like this equation, even though we can only detect the square modulus of this complex field and loose a lot of phase related information to the detectors quantum whims and their time constants. The key parameters for a light pulse are as follows. Foremost is the (i) carrier frequency, which cannot be described or imagined without its state of undulation expressed as its (ii) phase. Next is our imagined time finite (iii) carrier envelope that provides the temporal boundary of the field amplitude strength of the undulating E-field. The final parameter is the (iv) state of polarization or the unique plane along which the strength of the E-field gradient undulates. None of these filed characteristics are made self-evident to us by the fields themselves. We do not see light. Light does not see light. Light beams pass through each other without altering each others energy distribution unless there are interacting material molecules (dipoles) within the physical volume of superposition of the beams. In contrast, we can sense the material particles. Material particles sense each other and they cannot pass through each other without interacting with (scattering from) each other. Thus the interpretation of the superposition phenomenon of multiple fields on detectors should not be lumped under the mysterious "wave-particle duality" philosophy. The phenomenon of superposition can be understood better when we focus on the actual process experienced by the detecting dipoles when allowed by QM rules, they respond to and sum all the induced stimulations due to all the superposed fields followed by the proportionate energy absorption giving rise to the fringes we observe. We will present various experimental results to illustrate our arguments. Our position is that such detector behavior driven interpretations rather than the generally implied field-field interaction driven explanations, will help us better understand the ultimate nature of light and hence invent better and newer devices and instruments.

Roychoudhuri, Chandrasekhar↗
NASA NTRS2024

Filament Wound Composite Analysis Using the NASA Multiscale Analysis Tool (NASMAT) and Finite Element Analysis

Fiber reinforced composite materials, owing to their tailorable thermomechanical and functional properties, allow one to produce a structure that is stronger, stiffer, and lighter than its metal counterpart while performing the same function, yielding a more efficient structure. This not only allows for the improvement of current technologies like aircraft structures, but also enables new technologies like gaseous hydrogen storage for mobility applications, which are otherwise impractical when manufactured using traditional metals due to weight and space restrictions or material embrittlement. However, the use of composites imposes greater design and manufacturing challenges on an engineer, since they are heterogenous, having a distinct structure across multiple length scale, behave generally anisotropically at the structural level and require complex manufacturing and processing methods. Capturing this complex behavior requires detailed numerical simulations, including the modeling of microstructural features like undulations, voids, and fiber alignment. In this paper, multiple repeating unit cells (RUCs), representing filament wound composites, are developed (via a script provided in the Appendix) and analyzed. The refinement of these RUCs is varied, and the analyses are performed using both the Abaqus finite element software and the NASA Multiscale Analysis Tool (NASMAT). A study is undertaken to compare the predicted effective elastic properties of the wound RUC to a laminate representation of the wound RUC, which neglects the undulations. Additionally, two different sets of periodic boundary conditions (PBCs) have been examined. One approximates the real boundary conditions using a standard approach and the other represents the PBCs exactly through the use of an offset. Lastly, a comparison of the local elastic stress fields is made among the models and approaches. Since wound structures are often approximated as laminated structures, it is important to understand the degree to which this assumption is valid, namely by first comparing the elastic constants and local elastic fields. This will provide, on the one hand, information concerning the bulk mechanical behavior and, on the other hand, insights concerning local load distributions and likely damage initiation sites.

Composites↗
NASA NTRS1973

The earth's gravitational field from the combination of satellite and terrestrial data

This paper reviews techniques and results in the combination of gravimetric and satellite data. The estimation of mean anomalies for use in combination studies is discussed with the location of current gravity material being described. Specific techniques for combination solutions are discussed for various models. These models include those where the gravitational field is represented by a set of potential coefficients, or by a set of discrete blocks distributed on the earth. The potential coefficient solutions compared are those of the SAO Standard Earth II and III, the Goddard Earth Model 4, and a solution by the author. These solutions are compared in terms of coefficients, undulation and anomaly differences, and implied anomaly degree variances. In addition, comparisons were made through terrestrial anomaly comparisons, astrogeodetic undulation comparisons, and orbit fitting tests.

Rapp, R. H.↗
NASA NTRS1976

The effect of remote zones on the accuracy of evaluating the Molodensky

An analytical method is presented for determining the error in computing the gravity anomaly from the Molodensky integral if geoidal undulation data in remote zones are neglected. The error is given in terms of the usual degree variance and a set of parameters which are functions only of the size of the area in which undulation data are taken. A numerical calculation using Kaula's degree variances indicates that it is necessary to integrate the Molodensky integral over approximately a hemisphere in order to reduce the effect of neglected data to the order of 1 milligal in the computation of gravity anomaly.

Buglia, J. J.↗
NASA NTRS1976

Detailed gravimetric geoid computations in North America

A detailed gravimetric geoid has been computed for the Eastern United States and the Northwestern Atlantic Ocean by combining the Goddard Space Flight Center GEM-8 earth gravity model with the available 15 x 15 arcmin and 1 x 1 deg mean free air surface gravity observations. The short wavelength undulations were computed by applying Stokes' formula to the 15 x 15 arcmin and 1 x 1 deg surface data. The long wavelength undulations were provided by the GEM-8 model. The gravimetric geoid has been compared with Geoceiver derived and astrogeodetically determined geoid heights in the United States and the rms agreement is on the order of 1.5 meters. Excellent agreement in shape has been found between the detailed geoid and geoidal profiles derived from GEOS-III altimeter data in the Northwest Atlantic Ocean.

Marsh, J. G.↗
NASA NTRS1976

The influence of the atmosphere on geoid and potential coefficient determinations from gravity data

For the precise computation of geoid undulations the effect of the attraction of the atmosphere on the solution of the basic boundary value problem of gravimetric geodesy must be considered. This paper extends the theory of Moritz for deriving an atmospheric correction to the case when the undulations are computed by combining anomalies in a cap surrounding the computation point with information derived from potential coefficients. The correction term is a function of the cap size and the topography within the cap. It reaches a value of 3.0 m for a cap size of 30 deg, variations on the decimeter level being caused by variations in the topography. The effect of the atmospheric correction terms on potential coefficients is found to be small, reaching a maximum of 0.0055 millionths at n = 2, m = 2 when terrestrial gravity data are considered. The magnitude of this correction indicates that in future potential coefficient determination from gravity data the atmospheric correction should be made to such data.

Rummel, R.↗