Sergii Dukhopelnykov, Federica Di Michele, Donato Pera, Bruno Rubino, Kateryna Stiepanova
abstract:
In this paper, we consider the problem of seismic wave propagation based on the
homogeneous Helmholtz equation with two cylindrical tunnel inclusions under
perfectly welded interface conditions. The exact analytical solution of the
model is obtained using a boundary method that involves series expansions of
incident and reflected SH waves in terms of cylindrical wave functions, as well
as coordinate transformations between different reference systems.
We also examine the convergence of the approximate solution of the truncated
system to the solution of the corresponding infinite system, and compute the
relative error. This brief communication focuses on the role of introducing a
normalizing coefficient in the truncation order of the resulting infinite block
matrix equation in the study of seismic wave propagation boundary value problems
for cylindrical inclusions in a half-space.
Mathematics Subject Classification: 35Q72, 74B15
Key words and phrases: Scattering of SH waves, Helmholtz equation, Graf's Theorem, two underground structures, cylindrical inclusions