The scattering operator of acoustics maps sound speed singularities of a
medium to singularities in the observed pressure field. Using
geometrical optics (and its variants to handle caustics), the scattering
operator can be written as Fourier integral operator. Under certain
conditions on the sound speed, back-projecting the pressure field is
equivalent to application of a pseudodifferential operator to the
unknown sound speed singularities. Since pseudodifferential operators
preserve singularities, we can recover sound speed singularities.
In this talk we will examine what happens for electromagnetic and
elastic waves where the situation is quite different. The scattering
operator is considerably more complicated and one has to use Fourier
integral operators with singular symbols to represent it. The
back-projection process shows that in general, the resulting image
consists of two parts. One has singularities correctly placed and the
other produces artifacts. We will discuss how and when one can remove
such artifacts.
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