  We revisit the problem of recovering wave speeds and density across a curved
interface from reflected wave amplitudes. Such amplitudes have been exploited
for decades in (exploration) seismology in this context. However, the analysis
in seismology has been based on linearization and mostly flat interfaces. Here,
we present a nonlinear analysis allowing curved interfaces, establish
uniqueness and provide a reconstruction, while making the notion of amplitude
precise through a procedure rooted in microlocal analysis.
