  The aim of this article is to present and rigorously analyze topological
sensitivity based algorithms for detection of diametrically small inclusions in
an isotropic homogeneous elastic formation using single and multiple
measurements of the far-field scattering amplitudes. A $L^2-$cost functional is
considered and a location indicator is constructed from its topological
derivative. The performance of the indicator is analyzed in terms of the
topological sensitivity for location detection and stability with respect to
measurement and medium noises. It is established that the location indicator
does not guarantee inclusion detection and achieves only a low resolution when
there is mode-conversion in an elastic formation. Accordingly, a weighted
location indicator is designed to tackle the mode-conversion phenomenon. It is
substantiated that the weighted function renders the location of an inclusion
stably with resolution as per Rayleigh criterion.
