...L.I. Lobkovsky Abstract The difficulties and contradictions of the classical concept of plate tectonics are discussed. It was shown the postulate of rigid plates and Euler’s theorem on the motion of rigid body with one fixed point, which is the basis of the kinematic description of plate tectonics...

... acting as small circles of rotation initiating external rifting and spreading in the craton along great circles, as expressed in Eulers Theorem. The thin cratonic crust separated to form narrow basins floored by oceanic crust, the precursors of the greenstone belts. Thus the high grade mobile belt...

... of different initial centres of rotation, but always spiralled in to the same solution, as shown in Figure 3 . Everett thought up the iterative process—with successive halvings and reversals—from scratch, but it was essentially an application of Euler’s theorem and was apparently the first in this field...

... the field from deeper sources. The derivative approach of separating anomalies of shallow, intermediate, and deep sourves is, however, qualitative. Semiautomatic source location methods, such as the Euler method (also variously referred to in the literature as Euler's theorem on homogeneous functions...

... because this anomaly does not seem to be produced by an ideal single-point source and thus the Euler’s solutions are not reliable. In fact, it seems that it is generated by a complex source or multiple sources (a nonideal source). Let us recall that Euler deconvolution is grounded on the Euler theorem...

...G. Florio; M. Fedi; R. Pasteka Abstract Standard Euler deconvolution is applied to potential-field functions that are homogeneous and harmonic. Homogeneity is necessary to satisfy the Euler deconvolution equation itself, whereas harmonicity is required to compute the vertical derivative from data...

... discontinuity, situated between the upper and inner mantle. Ayllón et al. (1977, p. 75) and Anadón et al. (1981, p. 33) presented an alternative explanation for those movements supported by Euler’s theorem. In introducing plate tectonics, some textbook authors explained the meaning of tectonics...

... advance in using this path. Minkowski functionals are a complete set of geometrical features as established by Hadwiger’s theorem ( Santaló, 1976 ). A class of objects to which Hadwiger’s theorem applies is the class of sets that can be viewed as the union of a finite number of convex objects...

... properties ( Pilkington and Todoeschuck, 1993 ; Herrmann, 1997 ; Marsan and Bewan, 1999 ; Fedi and Florio, 2006 ). Based on equation  1 , Euler’s theorem ( Olmsted, 1961 ) shows that if f is continuously differentiable and homogeneous of degree n in R , the homogeneity...

.... Rather, there are many theorems, usually establishing just abstract mathematical conditions and making it difficult to devise the type of geological information needed to guarantee a unique solution. In Part I of these companion papers, we show that translating the mathematical uniqueness conditions...

... they simultaneously invert for seafloor conductivity and the respective rotation matrix (using Euler angles). Aside from these approaches, the inclusion of the third component (the vertical one) is usually not considered in reorientation operations. A basic approach to incorporate the third sensor components...

... and, ultimately, provided information on their depths, shapes and morphology from a combined analysis of their spectral content, characteristic gradient signatures and modelling responses. In addition, mass deficiencies have been estimated, directly from the anomaly map, by the use of Gauss's theorem without any...

....” The answer to all of this is: no problem. Mantura appears not to understand the basic geometrics involved in moving a rigid plate on the surface of a sphere. Although there are other mathematical schemes for describing the movement of a plate across the globe, Euler’s theorem is the simplest for the mind’s...

... be combined in a unique way to obtain the effective elasticity tensor that then can be used in the moment tensor expression. Moreover, the Green’s function of the medium is not differentiable at the bimaterial interface, which prevents writing down the moment tensor form of the representation theorem...

... data. The application of the method was also tested on a pseudogravity gradient tensor derived from total magnetic field data over the Särna area in west-central Sweden. Combined with Euler deconvolution, the method provides useful complementary information for interpretation of aeromagnetic data...

... to a horizontal slab of known position (Smith’s theorem; Smith, 1961 ) and (2) the estimated source has a known and homogeneous density and is compact. In addition to these ambiguities, inverse problems are unstable and require regularization (e.g.,  Li and Oldenburg, 1996 ; Pilkington, 1997 ; Zhdanov, 2002...

...Valentine Mikhailov; Armand Galdeano; Michel Diament; Alexei Gvishiani; Sergei Agayan; Shamil′ Bogoutdinov; Elena Graeva; Pascal Sailhac Abstract Results of Euler deconvolution strongly depend on the selection of viable solutions. Synthetic calculations using multiple causative sources show...

... computational advantages of the former gravity-field algorithms. 13 11 2000 05 12 2001 © 2002 Society of Exploration Geophysicists. All rights reserved. 2002 Haáz (1953) derives the gravity gradient tensor for uniform prismatic polyhedra using a complex variable theory and Euler's...

... scatterer. Starting with a Green's function representation for seismic interferometry, they derive the generalized optical theorem and a consistent non-linear scattering matrix for point scatterers. Denli and Huang state that effective and reliable reservoir monitoring is critically important...

... measurements on anisotropic material. The authors show that by using Green's functions and double-sided Neumann boundary conditions in the integral equation (representation theorem) for the wave equation, that source-side deghosting of data that have already had receiver-side deghosting applied may...