The quantitative investigation of nonstationary interference wave fields in layered-homogeneous elastic media with plane-parallel interfaces. I. Statements of problems and rational methods of their solution

The proposed series of Notes of Scientific seminars of PBMI (Petersburg Branch of Mathematical Institute) are devoted to important division of seismic wave propagation's theory connected in general sense with the systematic investigation of the interference wave's fields in layered elastic media. In this domain a few of completed results which can influence on the level of physical representations on regularizes in propagation of the real (comparable low-frequency) wave fields in the model's media from sufficiently general classes are obtained yet. The restrictiveness of the model's representation of the applied theory of the seismic wave propagation which is situated on the basis of the all modern seismology and geophysical prospecting are as it is known on the reason of serious difficulties which they now are experiencing now.
In issues of this present series it is assumed to illuminate the results of investigations which have the aim to extend the model's representation of the modern seismology and geophysical prospecting on the classes of blocked-structured media which contains the thin-layered traced or non-traced (heterogeneous) formations.
In present (the first issue of series) the new effective approach to quantitative investigation of the non stationary interference wave fields in layered-homogeneous isotropic elastic media with plane-parallel interfaces is stated. The rational statements of the problem and the rational methods of their solution are discussed. The quantitative estimations of the wave field in different regions of a medium are based on the wide application of the contour integral method with combination of the modern numerical methods of the investigations of the dispersion equation's roots of problem, with the methods of the construction of the correspondent stationary contours of the phase functions and with the calculation of the spectral functions of fields by the methods of numerical integration along these contours... (look the contents) Unfortunately it is not succeeded to place in the present issue the whole material intended for this one (because of technical reasons). It was necessary to put its applicable (to the concrete problems), which should be a culmination of present investigation in to the next issue of these series. Bibligraphy: 10 titles.