In quantitatively estimating interference wave fields by methods of function theory, the initial integration path is subjected to deformation in the complex (() For the convenience of the reader, here we outline general information (borrowed from [1, w on the location of the roots ( = (~,(x) of the dispersion equations of the problems from [2, 3] on the principal sheet of the (() plane. The main purpose of this section is to study the roots of the above equations on the second sheet of the complex (() plane whose parts adjacent to the cuts often prove to be essential to implementing the method of contour integration when we quantitatively estimate the spectral functions of displacement fields.1. We shall write dispersion equations (12) and (20) when we drew the cuts from the branch points of the radicals to infinity along the real axis without intersecting the point ( = 0. In what follows, we need some results from [11, although the main problem is to obtain necessary information about the location of the roots of the dispersion equations on the second sheet of the complex plane, the passage to which is carried out by intersecting the cut (7, c~ and by bypassing only one branch point ( = 7 of the radical/3((). hi this connection, the paper is subdivided into three parts. In the first part, we discuss the reasons that stimulated us to direct our attention to the study of the roots of tile dispersion equation not only on the