  We prove existence of strongly continuous evolution systems in L^2 for
Schroedinger-type equations with non-Lipschitz coefficients in the principal
part. The underlying operator structure is motivated from models of paraxial
approximations of wave propagation in geophysics. Thus, the evolution direction
is a spatial coordinate (depth) with additional pseudodifferential terms in
time and low regularity in the lateral variables. We formulate and analyze the
Cauchy problem in distribution spaces with mixed regularity. The key point in
the evolution system construction is an elliptic regularity result, which
enables us to precisely determine the common domain of the generators. The
construction of a solution with low regularity in the coefficients is the basis
for an inverse analysis which allows to infer the lack of lateral regularity in
the medium from measured data.
