Applied aspects of studying the roots of dispersion equations on nonprincipal sheets of a complex plane

In quantitatively estimating interference wave fields by methods of function theory, the initial integration path is subjected to deformation in the complex (ζ) plane. As a result of this deformation, sometimes the contour λ may go into other sheets of the Riemann (ζ) surface. This forces us to study the integrands and, in particular, the dispersion equation of the problem on the other sheets of the (ζ) plane. Similar questions are discussed for the case where a layer SH is in contact with two elastic half-spaces. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 225, 1996, pp. 62–90. Translated by T. N. Surkova.