Multiple Scattering of Elastic Waves in Polycrystals

TL;DR

This paper advances the modeling of elastic wave scattering in polycrystals by solving the Dyson equation with a second-order smoothing approximation, capturing more complex multiple scattering effects across all frequency regimes.

Contribution

It introduces the second-order smoothing approximation (SOSA) for solving the Dyson equation, enabling more accurate modeling of multiple scattering in polycrystals beyond first-order methods.

Findings

SOSA captures recurrent scattering effects missed by FOSA.

Multiple scattering effects are significant in the stochastic regime, especially for shear waves.

The method applies across all frequency regimes without restrictive approximations.

Abstract

Elastic waves that propagate in polycrystalline materials attenuate due to scattering of energy out of the primary propagation direction in addition to becoming dispersive in their group and phase velocities. Attenuation and dispersion are modeled through multiple scattering theory to describe the mean displacement field or the mean elastodynamic Green's function. The Green's function is governed by the Dyson equation and was solved previously (Weaver, 1990) by truncating the multiple scattering series at first-order, which is known as the first-order smoothing approximation (FOSA). FOSA allows for multiple scattering but places a restriction on the scattering events such that a scatterer can only be visited once during a particular multiple scattering process. In other words, recurrent scattering between two scatterers is not permitted. In this article, the Dyson equation is solved using the second-order smoothing approximation (SOSA). The SOSA permits scatterers to be visited twice during the multiple scattering process and, thus, provides a more complete picture of the multiple scattering effects on elastic waves. The derivation is valid at all frequencies spanning the Rayleigh, stochastic, and geometric scattering regimes without additional approximations that limit applicability in strongly scattering cases (like the Born approximation). The importance of SOSA is exemplified through analyzing specific weak and strongly scattering polycrystals. Multiple scattering effects contained in SOSA are shown to be important at the beginning of the stochastic scattering regime and are particularly important for transverse (shear) waves. This step forward opens the door for a deeper fundamental understanding of multiple scattering phenomena in polycrystalline materials.