A simple transformation, for a point Theoretical Considerations on the surface of a spherical mod... more A simple transformation, for a point Theoretical Considerations on the surface of a spherical model and for the corresponding local velocity, has been used to We will define at a point M(a,e,$) of a study the propagation of a disturbance along the spherical surface a local angular velocity surface. Using a Gaussian beam computation and consider the simple wave equation for the scheme,rays are traced and seismograms obtained propagation of a disturbance for a few spherical models with lateral heterogeneities. In the results, deviations from the first order perturbation theory for normal modes are displayed.
Thomson’s formulas (1872) that give the position of the magnetic centre of a magnet and the first... more Thomson’s formulas (1872) that give the position of the magnetic centre of a magnet and the first results on the global geomagnetic field were sufficient to show that the source of this field had a disymmetry in the equatorial plane. To confirm this with Schmidt’s (1934) explicit formulas giving the position of the optimal eccentric dipole, numerical calculus was necessary. To obtain their relatively simple formulas, Thomson and Schmidt used lengthy algebra that was avoidable.
A north-south wide-angle fan-profile through the Yarlung Zangbo suture, across the Lhasa block an... more A north-south wide-angle fan-profile through the Yarlung Zangbo suture, across the Lhasa block and through the Bangong-Nujiang suture shows several significant and sharp changes in crustal thickness. Both sutures appear as vertical 20-km steps in the Moho and may have been the loci for eastward strike-slip motion of the Tibetan lithosphere.
Jean-Maurice Monnoyer m'a introduit à la philosophie de la perception et à la métaphysique contem... more Jean-Maurice Monnoyer m'a introduit à la philosophie de la perception et à la métaphysique contemporaine. Il m'a convaincu de m'intéresser au toucher. Il m'a décidé à entreprendre ce travail et m'a permis de le terminer, par son aide, ses conseils et ses encouragements constants. Je lui exprime ma plus profonde gratitude.
Jean-Maurice Monnoyer m'a introduit à la philosophie de la perception et à la métaphysique contem... more Jean-Maurice Monnoyer m'a introduit à la philosophie de la perception et à la métaphysique contemporaine. Il m'a convaincu de m'intéresser au toucher. Il m'a décidé à entreprendre ce travail et m'a permis de le terminer, par son aide, ses conseils et ses encouragements constants. Je lui exprime ma plus profonde gratitude.
Five clinonietric stations have been installed in Normandy to determine the deformation of the gr... more Five clinonietric stations have been installed in Normandy to determine the deformation of the ground due to tidal loads in the Channel. The attraction of the water sheet is computed for every hour during the period of observation. The effect of the deformation of the ground (tilt plus variation of attraction) is evaluated and compared to the attraction of the water loads.
Earth flattening methods are developed to obtain simultaneous approximate expressions of propagat... more Earth flattening methods are developed to obtain simultaneous approximate expressions of propagators and Green matrices for body force and dislocation sources in a gravitating sphere. p, density; p , mean density; u = X/(X t 2p); ur = p / ( h t 2p); a = ( I t uf = 1uf = (1 t u)/2; f 2 = n(n t 1); o, angular frequency; m' = po2R2/p; s2 = m2f 2 t 2; v2 = f X/pw2R2; G , Newton's constant; g, acceleration of gravity; a = pgR/p; p = pR44-p = d m 7 = p R m . At the surface of the Earth these dimensionless numbers are about 2. d=-2(4a-1) t o , c=-(m2t2dt2a), e=-(m2+2-4uf2);I, unit matrix;n,complex conjugate of l7. denotes a transposition. If M is a 2n x 2n matrix we define the n x n blocks , M by We shall follow the treatment a? Alterman, Jarosch & Pekeris (1959) -hereafter AJPtreatment for the Fourier-Legendre transform Y of the displacment-stress-gravity vector.
Kennett has shown how the equations of elastodynamics may be derived from a variational principle... more Kennett has shown how the equations of elastodynamics may be derived from a variational principle (see also Lanczos, Germain) and attempted to extend this method to the ' Minor Matrix ' system (Gilbert & Backus).
The introduction of vertical and horizontal slownesses as independent variables in the transport ... more The introduction of vertical and horizontal slownesses as independent variables in the transport equation allows us to obtain an explicit expression for the amplitude variation along a ray in a vertically stratified medium. This expression can be used to introduce the dynamical characteristics in the inverse problem of refraction seismology. For the scalar wave equation the ratio of squared amplitudes is a rational functional of some function of the local slowness, the parametrization of which leads to a system of linear homogeneous equations. For P seismic waves the same functional is obtained for the ratio of squared amplitudes weighted by the density.
As the structure of P -SV wave equation matrix allows its diagonalization, it is possible to obta... more As the structure of P -SV wave equation matrix allows its diagonalization, it is possible to obtain the expression of an approximate propagator, the only approximation consisting in using a series of homogeneous layers to represent the stratification of the medium and the effect of sphericity.
A simple transformation, for a point Theoretical Considerations on the surface of a spherical mod... more A simple transformation, for a point Theoretical Considerations on the surface of a spherical model and for the corresponding local velocity, has been used to We will define at a point M(a,e,$) of a study the propagation of a disturbance along the spherical surface a local angular velocity surface. Using a Gaussian beam computation and consider the simple wave equation for the scheme,rays are traced and seismograms obtained propagation of a disturbance for a few spherical models with lateral heterogeneities. In the results, deviations from the first order perturbation theory for normal modes are displayed.
Thomson’s formulas (1872) that give the position of the magnetic centre of a magnet and the first... more Thomson’s formulas (1872) that give the position of the magnetic centre of a magnet and the first results on the global geomagnetic field were sufficient to show that the source of this field had a disymmetry in the equatorial plane. To confirm this with Schmidt’s (1934) explicit formulas giving the position of the optimal eccentric dipole, numerical calculus was necessary. To obtain their relatively simple formulas, Thomson and Schmidt used lengthy algebra that was avoidable.
A north-south wide-angle fan-profile through the Yarlung Zangbo suture, across the Lhasa block an... more A north-south wide-angle fan-profile through the Yarlung Zangbo suture, across the Lhasa block and through the Bangong-Nujiang suture shows several significant and sharp changes in crustal thickness. Both sutures appear as vertical 20-km steps in the Moho and may have been the loci for eastward strike-slip motion of the Tibetan lithosphere.
Jean-Maurice Monnoyer m'a introduit à la philosophie de la perception et à la métaphysique contem... more Jean-Maurice Monnoyer m'a introduit à la philosophie de la perception et à la métaphysique contemporaine. Il m'a convaincu de m'intéresser au toucher. Il m'a décidé à entreprendre ce travail et m'a permis de le terminer, par son aide, ses conseils et ses encouragements constants. Je lui exprime ma plus profonde gratitude.
Jean-Maurice Monnoyer m'a introduit à la philosophie de la perception et à la métaphysique contem... more Jean-Maurice Monnoyer m'a introduit à la philosophie de la perception et à la métaphysique contemporaine. Il m'a convaincu de m'intéresser au toucher. Il m'a décidé à entreprendre ce travail et m'a permis de le terminer, par son aide, ses conseils et ses encouragements constants. Je lui exprime ma plus profonde gratitude.
Five clinonietric stations have been installed in Normandy to determine the deformation of the gr... more Five clinonietric stations have been installed in Normandy to determine the deformation of the ground due to tidal loads in the Channel. The attraction of the water sheet is computed for every hour during the period of observation. The effect of the deformation of the ground (tilt plus variation of attraction) is evaluated and compared to the attraction of the water loads.
Earth flattening methods are developed to obtain simultaneous approximate expressions of propagat... more Earth flattening methods are developed to obtain simultaneous approximate expressions of propagators and Green matrices for body force and dislocation sources in a gravitating sphere. p, density; p , mean density; u = X/(X t 2p); ur = p / ( h t 2p); a = ( I t uf = 1uf = (1 t u)/2; f 2 = n(n t 1); o, angular frequency; m' = po2R2/p; s2 = m2f 2 t 2; v2 = f X/pw2R2; G , Newton's constant; g, acceleration of gravity; a = pgR/p; p = pR44-p = d m 7 = p R m . At the surface of the Earth these dimensionless numbers are about 2. d=-2(4a-1) t o , c=-(m2t2dt2a), e=-(m2+2-4uf2);I, unit matrix;n,complex conjugate of l7. denotes a transposition. If M is a 2n x 2n matrix we define the n x n blocks , M by We shall follow the treatment a? Alterman, Jarosch & Pekeris (1959) -hereafter AJPtreatment for the Fourier-Legendre transform Y of the displacment-stress-gravity vector.
Kennett has shown how the equations of elastodynamics may be derived from a variational principle... more Kennett has shown how the equations of elastodynamics may be derived from a variational principle (see also Lanczos, Germain) and attempted to extend this method to the ' Minor Matrix ' system (Gilbert & Backus).
The introduction of vertical and horizontal slownesses as independent variables in the transport ... more The introduction of vertical and horizontal slownesses as independent variables in the transport equation allows us to obtain an explicit expression for the amplitude variation along a ray in a vertically stratified medium. This expression can be used to introduce the dynamical characteristics in the inverse problem of refraction seismology. For the scalar wave equation the ratio of squared amplitudes is a rational functional of some function of the local slowness, the parametrization of which leads to a system of linear homogeneous equations. For P seismic waves the same functional is obtained for the ratio of squared amplitudes weighted by the density.
As the structure of P -SV wave equation matrix allows its diagonalization, it is possible to obta... more As the structure of P -SV wave equation matrix allows its diagonalization, it is possible to obtain the expression of an approximate propagator, the only approximation consisting in using a series of homogeneous layers to represent the stratification of the medium and the effect of sphericity.
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