Multiscale aspects of waveform tomography

We consider the inference of medium velocity from transmitted acoustic waves. Typically, the measurements are done in a narrow frequency band. As a result the sensitivity of the data with respect to velocity perturbations varies dramatically with the scale of the perturbation. ‘Smooth’ perturbations will cause a phase shift, whereas perturbations that vary on the wavelength-scale cause amplitude variations. We investigate how to incorporate this scale dependent behavior in the formulation of the inverse problem.