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In the context of providing a mathematical framework for the propagation ofultrasound waves in a random multiscale medium, we consider the scattering ofclassical waves (modeled by a divergence form scalar Helmholtz equation) by abounded object with a random composite micro-structure embedded in an unboundedhomogeneous background medium. Using quantitative stochastic homogenizationtechniques, we provide asymptotic expansions of the scattered field in thebackground medium with respect to a scaling parameter describing the spatialrandom oscillations of the micro-structure. Introducing a boundary layercorrector to compensate the breakdown of stationarity assumptions at theboundary of the scattering medium, we prove quantitative $L^2$- and $H^1$-error estimates for the asymptotic first-order expansion. The theoreticalresults are supported by numerical experiments.

Scattered wavefield in the stochastic homogenization regime