  A major problem in solving multi-waves inverse problems is the presence of
critical points where the collected data completely vanishes. The set of these
critical points depend on the choice of the boundary conditions, and can be
directly determined from the data itself. To our knowledge, in the most
existing stability results, the boundary conditions are assumed to be close to
a set of CGO solutions where the critical points can be avoided. We establish
in the present work new weighted stability estimates for an electro-acoustic
inverse problem without assumptions on the presence of critical points. These
results show that the Lipschitz stability far from the critical points
deteriorates near these points to a logarithmic stability.
