Scattering of elastic waves by an elastic or viscoelastic cylinder

The scattering of elastic waves by an elastic or viscoelastic cylinder is i nvestigated numerically. The analytical solutions of the scattered and inte rnal fields excited by a normally incident plane P wave or SV wave are deri ved in a concise form. Solutions for cylindrical P-wave incidence and for s ome special cases of the cylinder medium and the matrix medium are also eva luated explicitly. Numerical results for directivity patterns, scattering c ross-sections and synthetic seismograms are given for both non-absorbing an d absorbing cylinders. Results show that the directivity patterns that unde rgo a mode conversion (the P-SV scattering and the SV-P scattering) are inv ariant as ka increases, k being the wavenumber and a the cylinder radius, t he P-P scattering and the SV-SV scattering concentrate to the forward direc tion 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 wave s 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-absorb ing cylinder correspond to the resonance scattering. The total scattered fi eld is mainly the superposition of the geometrically transmitted waves (P1P 2P1, P1P2S1 and P1S2S1 for P-wave incidence and S1S2S1 , S1S2P1 and S1P2P1 for SV-wave incidence) that go through the cylinder and the diffracted wave s (P-1(P) over cap(1)P(1) and P-1(P) over cap(1)S(1) for P-wave incidence a nd S-1(S) over cap(1)S(1) and S-1(P) over cap(1)P(1) for SV-wave incidence) that propagate on the matrix side of the cylinder interface. The arrival t imes and the waveforms of these different wave pulses depend on the positio ns of the observation points and the elastic parameters of the medium.