Combination of altimetry data from different satellite missions

Substantial altimetry datasets collected by different satellites have only become available during the past five years, but the future will bring a variety of new altimetry missions, both parallel and consecutive in time. The characteristics of each produced dataset vary with the different orbital heights and inclinations of the spacecraft, as well as with the technical properties of the radar instrument. An integral analysis of datasets with different properties offers advantages both in terms of data quantity and data quality. This thesis is concerned with the development of the means for such integral analysis, in particular for dynamic solutions in which precise orbits for the satellites are computed simultaneously. The first half of the thesis discusses the theory and numerical implementation of dynamic multi-satellite altimetry analysis. The most important aspect of this analysis is the application of dual satellite altimetry crossover points as a bi-directional tracking data type in simultaneous orbit solutions. The central problem is that the spatial and temporal distributions of the crossovers are in conflict with the time-organised nature of traditional solution methods. Their application to the adjustment of the orbits of both satellites involved in a dual crossover therefore requires several fundamental changes of the classical least-squares prediction/correction methods. The second part of the thesis applies the developed numerical techniques to the problems of precise orbit computation and gravity field adjustment, using the altimetry datasets of ERS-1 and TOPEX/Poseidon. Although the two datasets can be considered less compatible that those of planned future satellite missions, the obtained results adequately illustrate the merits of a simultaneous solution technique. In particular, the geographically correlated orbit error is partially observable from a dataset consisting of crossover differences between two sufficiently different altimetry datasets, while being unobservable from the analysis of altimetry data of both satellites individually. This error signal, which has a substantial gravity-induced component, can be employed advantageously in simultaneous solutions for the two satellites in which also the harmonic coefficients of the gravity field model are estimated.

Mapeamento da isoterma de Curie na Bacia do Parnaíba estimada através da profundidade da base das fontes magnéticas

Located on the western edge of the Brazilian northeast, the Parnaíba Basin is an intra cratonic basin with oil production. This study aims at understanding its genesis and evolution, using aeromagnetic and gravity data. We used the spectral analysis of aeromagnetic data to map the depth to the bottom of the magnetic sources in order to assimilate this depth with the depth of the Curie isotherm, and infer the geothermal gradient. Using the spectral analysis technique, we succeeded in mapping the surface of the depth to the bottom of magnetic sources (SBFM), which marks the depth that occur magnetization. In the Parnaíba Basin the SBFM presented depths around -20,5 and -28,5 , which was consistent with an inversion of the same dataset using the technique of Magnetization Vector Inversion (MVI). Furthermore, SBFM topography correlates well with Moho depth, which was estimated from satellite gravimetric data from the GOCE mission (Gravity Field and Steady-State Ocean Circulation Explorer). Assuming that SBFM coincides with the Curie isotherm of magnetite (ICM), defined as the surface at which magnetite ( ) looses its ferromagnetic properties, it was possible to estimate the geothermal gradient. The geothermal gradient in the basin showed values between 19.2 and 26.5 , allowing to estimate the heat flow for the Parnaíba basin after assuming a conductivity of 2.69 . The resulting heat flow values ranged between 51.6 and 71.3 , which is consistent with values found in other works throughout the South American continent. Lithospheric thickness using an empirical relationship, finding values between -65.8 and -89.2 . We propose that thermal structure of Parnaíba basin is influenced by a deep thermal anomaly. This anomaly has heated the lithosphere beneath the basin and has resulted in relatively thin values for the lithospheric thickness and relatively high surface heat flow values. The origin of the anomaly is not clear, but the correlation between Curie depth and Moho topography, suggests that tectonic extension processes could have played a role.

Mean dynamic topography of the North Indian Ocean

A satellite-only Mean Dynamic Topography (MDT) of the North Indian Ocean is estimated from the DIRR5 geoid and CNES_CLS11 mean sea surface (Schaffer et al. 2012). DIRR5 geoid is estimated from the latest release (Release 5) of GOCE gravity data according to previous studies (e.g., Johannessen et al. 2003; Raj, 2014). Note that this MDT estimated is referenced to a time period of 7 years (1993-1999). A correction data obtained from AVISO is later used to convert the MDT to a time reference of 20 years (1993-2012). More details are given in Raj (2016).

A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Contribuição de uma seção gravimétrica transversal ao estudo da estruturação litosférica na porção setentrional da Província Borborema, NE do Brasil

Este trabalho apresenta um modelo gravimétrico 2,5D gerado a partir de 315 novas estações gravimétricas levantadas ao longo de uma seção transversal NW-SE com 750 km de extensão na porção setentrional da Província Borborema, NE do Brasil. A modelagem gravimétrica foi aplicada separadamente nas componentes regional e residual do campo gravitacional. A modelagem 2,5D das anomalias regionais revelou que a profundidade da interface crosta-manto varia de 28 a 32 km, considerando uma densidade média de 2,8 g/cm3 para a crosta continental e de 3,3 g/cm3 para o manto litosférico. As anomalias residuais de alta frequência foram interpretadas a partir do contraste de densidade da crosta superior, com uma espessura não superior a 10 km, e uma ampla associação litológica, com densidades variando de 2,55 a 2,9 g/cm3. A configuração geotectônica litosférica atual da Província Borborema é claramente resultado da ruptura dos continentes Sul-Americano e Africano no Mesozoico, na qual boa parte dos vestígios das estruturas tectônicas de grandes profundidades formadas durante a orogênese Brasiliana/Pan-Africana foi mascarada pelo último episódio tectônico responsável pela fragmentação do Gondwana Ocidental. _______________________________________________________________________________________ ABSTRACT

Magnetic Field Due to the Self-Gravity-Induced Electric Polarization of a Rotating Massive Body

he notion of the gravity-induced electric field has been applied to an entire self-gravitating massive body. The resulting electric polarization of the otherwise neutral body, when taken in conjunction with the latter's rotation, is shown to generate an axial-magnetic field of the right type and order of magnitude for certain astrophysical objects. In the present treatment the electric polarization is calculated in the ion-continuum Thomas-Fermi approximation while the electrodynamics of the continuous medium is treated in the nonrelativistic approximation.

Gravitational field of a straight cosmic string in the framework of higher-derivative gravity

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the derection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter.

Scattering of photons by an external gravitational field in the framework of higher-derivative gravity

The scattering of photons by a static gravitational field, treated as an external field, is discussed in the context of gravity with higher derivatives. It is shown that the R-2 sector of the theory does not contribute to the photon scattering, whereas the R-mu nu(2) sector produces dispersive (energy-dependent) photon propagation.

Two-dimensional background field gravity: A Hamilton-Jacobi analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gravitational field of a straight cosmic string in the framework of higher-derivative gravity

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the deflection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter. © 2008 World Scientific Publishing Company.

On the long standing issue of an R phi(2) coupling between gravity and a massless free scalar field

Using 2-body trees on a flat space background, it is shown that the actions A[g, φ] = (Latin small letter esh) d4x√-g [(R/2K) + (1/2)(gμν ∂μφ∂νφ + λRφ2)] and Ā[ḡ, φ̄] = (Latin small letter esh) d4x√ - ḡ [(R̄/2k) + (1/2) ḡμν∂μφ̄∂ νφ] describe the same theory at the tree-level in this case. We also demonstrate the quantum equivalence (at one-loop) of the barred and unbarred systems for λ == -1/6 (conformal coupling).

On the motion of particles in covariant Horava-Lifshitz gravity and the meaning of the A-field

We studied the low energy motion of particles in the general covariant. version of Horava-Lifshitz gravity proposed by Horava and Melby-Thompson. Using a scalar field coupled to gravity according to the minimal substitution recipe proposed by da Silva and taking the geometrical optics limit, we could write an effective relativistic metric for a general solution. As a result, we discovered that the equivalence principle is not in general recovered at low energies, unless the spatial Laplacian of A vanishes. Finally, we analyzed the motion on the spherical symmetric solution proposed by Horava and Melby-Thompson, where we could find its effective line element and compute spin-0 geodesics. Using standard methods we have shown that such an effective metric cannot reproduce Newton's gravity law even in the weak gravitational field approximation. (C) 2011 Elsevier B.V All rights reserved.

Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

There are several classes of homogeneous Fermi systems that are characterized by the topology of the energy spectrum of fermionic quasiparticles: (i) gapless systems with a Fermi surface, (ii) systems with a gap in their spectrum, (iii) gapless systems with topologically stable point nodes (Fermi points), and (iv) gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality class 3. The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of class 3 are the effective gauge and gravitational fields. The great advantage of superfluid 3He-A is that we can perform experiments by using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to class 4. They have gapless fermionic quasiparticles with a “relativistic” spectrum close to gap nodes, which allows application of ideas developed for superfluid 3He-A.