  In inverse scattering problem, it is well-known that subspace migration
yields very accurate locations of small perfectly conducting cracks when
applied frequency is known. In contrast, when applied frequency is unknown,
inaccurate locations are identified via subspace migration with wrong frequency
data. However, this fact has been examined through the experimental results so,
the reason of such phenomenon has not been theoretically investigated. In this
paper, we analyze mathematical structure of subspace migration with unknown
frequency by establishing a relationship with Bessel function of order zero of
the first kind. Identified structure of subspace migration and corresponding
results of numerical simulation answer that why subspace migration with unknown
frequency yields inaccurate location of cracks and gives an idea of
improvement.
