  A theoretical foundation is developed for active seismic reconstruction of
fractures endowed with spatially-varying interfacial condition
(e.g.~partially-closed fractures, hydraulic fractures). The proposed indicator
functional carries a superior localization property with no significant
sensitivity to the fracture's contact condition, measurement errors, and
illumination frequency. This is accomplished through the paradigm of the
$F_\sharp$-factorization technique and the recently developed Generalized
Linear Sampling Method (GLSM) applied to elastodynamics. The direct scattering
problem is formulated in the frequency domain where the fracture surface is
illuminated by a set of incident plane waves, while monitoring the induced
scattered field in the form of (elastic) far-field patterns. The analysis of
the well-posedness of the forward problem leads to an admissibility condition
on the fracture's (linearized) contact parameters. This in turn contributes
toward establishing the applicability of the $F_\sharp$-factorization method,
and consequently aids the formulation of a convex GLSM cost functional whose
minimizer can be computed without iterations. Such minimizer is then used to
construct a robust fracture indicator function, whose performance is
illustrated through a set of numerical experiments. For completeness, the
results of the GLSM reconstruction are compared to those obtained by the
classical linear sampling method (LSM).
