Abstract:
this work presents an application of the transient electromagnetic geophysical method in the area of basin of resende, rio de janeiro, brazil. ln this basin, it was made in 2001, a geophysical survey of 88 soundings seeking to contribute for the knowledge of the hydrogeological potential of the area. this area is densely industrialized, so noise tends to hinder the use of the method. the data were interpreted using an 1-d inversion algorithm where the resistivity in depth is estimated from the induced voltage time decay. surface shows highly conductive layers (~5ω.m) and the value of 200ω.m for the transition resistivity coresponding to the geoelectric basement was suggested from lithology and stratigraphy data of the basin together with a fine adjustment gauged in the 3-d gravity model of the basin. from the 1-d inversion we built up a pseudo-3d geoelectric image of the basement geometry. despite the physical properties involved (density and resistivity) does not have any relationship between them, the topography of a previous gravity basement was used to estimate depths that were not reached by the tem signal. the resulting surface has a topography which is assumed be representative of the basin's basement. so, the use the tem method in basin of resende allowed to estimate the lateral limits of the basin and to propose limits in depth. three areas can be depicted: a structural high flanked by two structural lows (depocenters), one to east and the other to west of the basin.

Abstract:
This paper presents an application of the gravimetric method using
terrestrial and aerial data collected in one sector of the Parecis Basin,
Brazil. The data received latitude and elevation corrections and also the
Eotvos correction in the aerial survey case. Maps of Free-Air anomaly and
Bouguer anomaly were obtained. These maps allowed us to identify the Pimenta
Bueno Graben, which is an attractive region for oil and gas prospecting. Finally,
the maps were compared and correlated to tectonic domains of the Pimenta Bueno
Graben region.

Abstract:
This current paper
discusses an application of the aerial radiometric method in the Itaboraí Region,
located in Rio de Janeiro State, Brazil. Radiometric data acquired by aircraft
registered in counts per second of potassium, thorium and uranium channels were
processed generating radiometric maps of the entire region. The generated maps
provide important information regarding the superficial geology. At last, all
the radiometric information gained is correlated with geological and
topographical knowledge of the Itaboraí Region.

Abstract:
This work presents the magnetometric method application in the Carajás Mineral Province, located in the south of the Pará state, Brazil. This is a region rich in iron ore in hematite form distributed in the Itacaiúnas Belt. The available gross magnetometric data were corrected and subtracted from the IGRF (International Geomagnetic Reference Field). Subsequently, magnetic anomaly, vertical derivative, horizontal derivatives and analytical signal maps were made that allowed to identify the main faults and the geological bodies of the region.

Abstract:
An alternate Hamiltonian H different from Ostrogradski's one is found for the Lagrangian L = L(q, \dot q, \ddot q). We add a suitable divergence to L and insert a=q and b=\ddot q. Contrary to other approaches no constraint is needed because \ddot a = b is one of the canonical equations. Another canonical equation becomes equivalent to the fourth-order Euler-Lagrange equation of L. Usually, H becomes quadratic in the momenta, whereas the Ostrogradski approach has Hamiltonians always linear in the momenta. For non-linear L=F(R), G=dF/dR \ne 0 the Lagrangians L and \hat L=\hat F(\hat R) with \hat F=2R/G\sp 3-3L/G\sp 4, \hat g_{ij}=G\sp 2g_{ij} and \hat R=3R/G\sp 2 - 4L/G \sp 3 give conformally equivalent fourth-order field equations being dual to each other. This generalizes Buchdahl's result for L=R^2. The exact fourth-order gravity cosmological solutions found by Accioly and Chimento are interpreted from the viewpoint of the instability of fourth-order theories and how they transform under this duality. Finally, the alternate Hamiltonian is applied to deduce the Wheeler-De Witt equation for fourth-order gravity models more systematically than before.

Abstract:
We prove the theorem valid for (Pseudo)-Riemannian manifolds $V_n$: "Let $x \in V_n$ be a fixed point of a homothetic motion which is not an isometry then all curvature invariants vanish at $x$." and get the Corollary: "All curvature invariants of the plane wave metric $$ds \sp 2 \quad = \quad 2 \, du \, dv \, + \, a\sp 2 (u) \, dw \sp 2 \, + \, b\sp 2 (u) \, dz \sp 2 $$ identically vanish." Analysing the proof we see: The fact that for definite signature flatness can be characterized by the vanishing of a curvature invariant, essentially rests on the compactness of the rotation group $SO(n)$. For Lorentz signature, however, one has the non-compact Lorentz group $SO(3,1)$ instead of it. A further and independent proof of the corollary uses the fact, that the Geroch limit does not lead to a Hausdorff topology, so a sequence of gravitational waves can converge to the flat space-time, even if each element of the sequence is the same pp-wave.

Abstract:
We analyze the presumptions which lead to instabilities in theories of order higher than second. That type of fourth order gravity which leads to an inflationary (quasi de Sitter) period of cosmic evolution by inclusion of one curvature squared term (i.e. the Starobinsky model) is used as an example. The corresponding Hamiltonian formulation (which is necessary for deducing the Wheeler de Witt equation) is found both in the Ostrogradski approach and in another form. As an example, a closed form solution of the Wheeler de Witt equation for a spatially flat Friedmann model and L=R\sp 2 is found. The method proposed by Simon to bring fourth order gravity to second order can be (if suitably generalized) applied to bring sixth order gravity to second order. In the Erratum we show that a spatially flat Friedmann model need not be geodesically complete even if the scale factor a(t) is positive and smooth for all real values of the synchronized time t.

Abstract:
We present three reasons for rewriting the Einstein equation. The new version is physically equivalent but geometrically more clear. 1. We write $4 \pi$ instead of $8 \pi$ at the r.h.s, and we explain how this factor enters as surface area of the unit 2--sphere. 2. We define the Riemann curvature tensor and its contractions (including the Einstein tensor at the l.h.s.) with one half of its usual value. This compensates not only for the change made at the r.h.s., but it gives the result that the curvature scalar of the unit 2--sphere equals one, i.e., in two dimensions, now the Gaussian curvature and the Ricci scalar coincide. 3. For the commutator $[u,v]$ of the vector fields $u$ and $v$ we prefer to write (because of the analogy with the antisymmetrization of tensors) $$[u,v]\ = \ \frac{1}{2} \, ( \, u\, v \ - \ v \, u \,)$$ which is one half of the usual value. Then, the curvature operator defined by $$ \nabla_{[u} \ \nabla_{v]} \quad - \quad \nabla_{[u,\,v]}$$ (where $\nabla $ denotes the covariant derivative) is consistent with point 2, i.e., it equals one half of the usual value.

Abstract:
The following four statements have been proven decades ago already, but they continue to induce a strange feeling: - All curvature invariants of a gravitational wave vanish - in spite of the fact that it represents a nonflat spacetime. - The eigennullframe components of the curvature tensor (the Cartan ''scalars'') do not represent curvature scalars. - The Euclidean topology in the Minkowski spacetime does not possess a basis composed of Lorentz--invariant neighbourhoods. - There are points in the de Sitter spacetime which cannot be joined to each other by any geodesic. We explain that our feeling is influenced by the compactness of the rotation group; the strangeness disappears if we fully acknowledge the noncompactness of the Lorentz group. Output: Imaginary coordinate rotations from Euclidean to Lorentzian signature are very dangerous.

Abstract:
The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined by the length of a space--like geodesic.