Multiplicity of elastic wave propagation in random polycrystals

Abstract

The coherent elastic wave in untextured polycrystals, central to ultrasonic and seismic characterization, was recently observed to have two modes per polarization at short wavelengths. However, their physical origin and amplitude partition have remained open. We address both by theory, grain-scale numerical simulations and a grain velocity estimate. The first-order smoothing approximation, simplified by the far-field approximation, predicts three waves, which are the classical effective wave and one for each type of scattered wave (longitudinal and transverse). At long wavelengths, only the effective wave is weakly attenuated. At short wavelengths, one of the other two waves joins it with comparable attenuation, whereas the third stays far more attenuated. A new residue method, which needs no fitting, gives the same pattern for the amplitude partition, with the two waves sharing the coherent field and the third carrying little. The simulations reveal exactly these two modes, for transverse waves in iron and longitudinal waves in strongly anisotropic SrMgSn, and never the third. The wavefields reveal the mechanism, in which the incident wave is extinguished within one grain correlation length and the coherent field is rebuilt by forward multiple scattering. Strikingly, a grain velocity estimate from single-crystal constants provides independent evidence, tracing the two modes to plane waves of the individual grains and closely reproducing their velocities. Observability of multiple waves is thus set by attenuation and amplitude partition together, and short-wavelength measurements in random media must allow for more than one coherent mode.