  Various studies have confirmed the possibility of identifying the location of
a set of small inhomogeneities via a direct sampling method; however, when
their permeability differs from that of the background, their location cannot
be satisfactorily identified. However, no theoretical explanation for this
phenomenon has been verified. In this study, we demonstrate that the indicator
function of the direct sampling method can be expressed by the Bessel function
of order one of the first kind and explain why the exact locations of
inhomogeneities cannot be identified. Numerical results with noisy data are
exhibited to support our examination.
