Abstract
We develop an enclosure-type reconstruction scheme to identify penetrableobstacles in acoustic waves with anisotropic medium in $\mathbb{R}^{3}$.The main difficulty of treating this problem lies in the fact thatthere are no complex geometrical optics solutions available for theacoustic equation with anisotropic medium in $\mathbb{R}^{3}$. Instead,we will use another type of special solutions called oscillating-decayingsolutions. Even though that oscillating-decaying solutions are definedonly on the half space, we are able to give necessary boundary inputsby the Runge approximation property. Moreover, since we are consideringa Helmholtz-type equation, we turn to Meyers' $L^{p}$ estimate tocompare the integrals coming from oscillating-decaying solutions andthose from reflected solutions.
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