| Abstract: | The theory is explained and practical applications are shown for a numerical procedure in seismology. Particularly the problems concerning the generation of waves under the action of external pressures, and their propagation, in non-homogeneous, both elastic and absorbing media, have been carried out. These problems have been assumed mono-dimensional and refer to plane and spherical waves. The procedure is based on the solution, by means of series, of the wave differential equation, non-homogeneous, and with non-constant coefficients. It is a direct numerical method whose advantage is, mainly, the possibility of tackling, without great difficulties, problems regarding non-homogeneous elastic and absorbing media. On the contrary the methods which require the theoretical expression of the solutions by means of formulae, generally, present conceptual and numerical difficulties. As examples of application of this procedure, the following cases have been carried out by means of numerical calculations. a) Propagation of a wave, initially of symmetrical shape, in a viscoelastic medium; from the results it appears that the wave propagates without losing its symmetry, i.e. without sensible dispersion. A theoretical analysis has been carried out to justify this result, showing that the dispersion in viscoelastic media is noticeable only for relatively high frequencies. It seems that the practical absence of dispersion in field experiments do not exclude necessarily the viscoelastic character of absorption. b) Generation of plane waves under the effect of a uniform pressure distributed on the plane surface of a medium. The way the length and the shape of the generated wave depends not only on the type of pressure acting on the surface but also on the near surface impedance variations has been studied. c) Generation of a spherical wave under the action of a pressure in a spherical hole. The examples treated show how the length and shape of the wave depends on the radius of the hole. Particularly the frequencies of the wave spectrum are proportional to this radius, for a given type of pressure acting in the hole. The characteristics of this procedure would also permit the study of media for which the stress-strain relations are not univocal and linear (non linear absorption). This study, interesting for the wave propagation in rocks, is worth while to be carried out in a special paper. |
