Scattering of elastic waves by an elastic or viscoelastic cylinder

The scattering of elastic waves by an elastic or viscoelastic cylinder is investigated numerically. The analytical solutions of the scattered and internal fields excited by a normally incident plane P wave or SV  wave are derived in a concise form. Solutions for cylindrical P ‐wave incidence and for some special cases of the cylinder medium and the matrix medium are also evaluated explicitly. Numerical results for directivity patterns, scattering cross‐sections and synthetic seismograms are given for both non‐absorbing and absorbing cylinders. Results show that the directivity patterns that undergo a mode conversion (the P–SV  scattering and the SV –P scattering) are invariant as ka increases, k being the wavenumber and a the cylinder radius, the P–P scattering and the SV –SV  scattering concentrate to the forward direction and all scattering waves ( P–P , SV –SV  and P–SV  or SV –P ) grow into more complicated structures. The interference of diffracted and transmitted waves causes the maxima and minima in the curves of scattering cross‐sections, and the small high‐frequency peaks that appear in a low‐velocity non‐absorbing cylinder correspond to the resonance scattering. The total scattered field is mainly the superposition of the geometrically transmitted waves ( P 1  P 2  P 1  , P 1  P 2  S 1 and P 1  S 2  S 1 for P ‐wave incidence and S 1  S 2  S 1  , S 1  S 2  P 1 and S 1  P 2  P 1 for SV ‐wave incidence) that go through the cylinder and the diffracted waves ( P 1  P^ 1  P 1 and P 1  P^ 1  S 1 for P ‐wave incidence and S 1  Ŝ 1  S 1 and S 1  P^ 1  P 1 for SV ‐wave incidence) that propagate on the matrix side of the cylinder interface. The arrival times and the waveforms of these different wave pulses depend on the positions of the observation points and the elastic parameters of the medium.