In highly heterogeneous media, waves don't propagate ballistically. They can interact several times with the heterogeneities of the medium and enter the multiple scattering regime. In this regime, classical imaging techniques, based on direct or singly scattered waves fail. Multiply scattered waveforms (coda) are too complex for being exactly modeled but are perfectly reproducible and very sensitive to small variations of the medium. Recent works demonstrated the possibility of measuring small velocity variations with diffuse waves, either at the geophysical scale (seismic coda) or at the material scale (ultrasonic coda). These works are mainly focused in monitoring global or regional changes of the medium. The present thesis deals with the possibility of using coda waves to study local changes of the medium. Two complementary studies are developed: The forward problem addresses the modeling of the coda variations generated by a local change. We distinguish the case of a structural change (strong impedance contrast) from the case of a velocity change (small impedance contrast). The inverse problem consists in using the coda variations measurements to locate and characterize the changes that occurred. Potential applications may concern, among others, monitoring of geological structures and non-destructive testing of heterogeneous materials. This in mind, we illustrate the different studies with numerical simulations of acoustic and seismic waves and with ultrasound experiments in concrete blocks.
