This paper is devoted to provide a solid mathematical foundation for a promising imaging technique based on the acoustic radiation force, which acts as a dipolar source. From the rigorously established asymptotic expansions of near-and far-field measurements of the transient wave induced by the anomaly, we design asymptotic imaging methods leading to a quantitative estimation of physical and geometrical parameters of the anomaly.

In this work, we present an explicit expression for the Green function in a visco-elastic medium. We choose Szabo and Wu's frequency power law model to describe the visco-elastic properties and derive a generalized visco-elastic wave equation. We express the ideal Green function (without any viscous effect) in terms of the viscous Green function using an attenuation operator. By means of an approximation of the ideal Green function, we address the problem of reconstructing a small anomaly in a visco-elastic medium from wavefield measurements.