Abstract :
In commonly studied coefficient identification problems in wave propagation it
is assumed that the wavefield data being measured arises in response to a known source
function, often an idealization such as a delta function. However it may be the case that
the source is itself difficult or impossible to know with any precision, thus some works have
treated the source itself, subject to some constraints, as an unknown in the problem, together
with the coefficient(s) of interest. In this paper we will discuss two problems of this type
involving the determination of an unknown impedance in a one dimensional wave equation
from corresponding transmission data. In the first version it is assumed that the phase of
the Fourier transform of the source function is known, but not its amplitude. In the second
version no specific knowledge of the source is assumed, but some restrictions are imposed on
the locations of the complex zeros of its Fourier transform. The strategy in both cases is to
first infer the data for a related inverse spectral problem.
