LOW-FREQUENCY ELASTIC-WAVE SCATTERING BY AN INCLUSION - LIMITS OF APPLICATIONS

The present investigation considers various approximations for the pro blem of low-frequency elastic waves scattered by a single, small inclu sion of constant elastic parameters. For the Rayleigh approximation co ntaining both near- and far-field terms, the scattered amplitudes are investigated as a function of distance from the scatterer. Near-field terms are found to be dominant for distances up to two wavelengths, af ter which far-field solutions correctly describe the scattered field. At a distance of two wavelengths the relative error between the total and the far-field solution is about 15 per cent and decreases with inc reasing distance. Deriving solutions for the linear and quadratic Rayl eigh-Born approximation, the relative error between the non-linear Ray leigh approximation and the linear and quadratic Rayleigh-Born approxi mation as a function of the scattering angle and the parameter perturb ation is investigated. The relative error reveals a strong dependence on the scattering angle, while the addition of the quadratic term sign ificantly improves the approximation for all scattering angles and par ameter perturbations. An approximation for the error caused by lineari zation of the problem, based entirely on the perturbations of the para meters from the background medium, and its validity range are given. W e also investigate the limit of the wave parameter for Rayleigh scatte ring and find higher values than previously assumed. By choosing relat ive errors of 5 per cent, 10 per cent and 20 per cent between the exac t solution and the Rayleigh approximation, we find the upper limits fo r the parameter k(p)R to be 0.55, 0.7 and 9.9, respectively.