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The aim of this article is to present and rigorously analyze topologicalsensitivity based algorithms for detection of diametrically small inclusions inan isotropic homogeneous elastic formation using single and multiplemeasurements of the far-field scattering amplitudes. A $L^2-$cost functional isconsidered and a location indicator is constructed from its topologicalderivative. The performance of the indicator is analyzed in terms of thetopological sensitivity for location detection and stability with respect tomeasurement and medium noises. It is established that the location indicatordoes not guarantee inclusion detection and achieves only a low resolution whenthere is mode-conversion in an elastic formation. Accordingly, a weightedlocation indicator is designed to tackle the mode-conversion phenomenon. It issubstantiated that the weighted function renders the location of an inclusionstably with resolution as per Rayleigh criterion.

Topological Sensitivity Based Far-Field Detection of Elastic Inclusions