  This paper is concerned with the factorization method with a single far-field
pattern to recover an arbitrary convex polygonal scatterer/source in linear
elasticity. The approach also applies to the compressional (resp. shear) part
of the far-field pattern excited by a single compressional (resp. shear) plane
wave. The one-wave factorization is based on the scattering data for a priori
given testing scatterers. It can be regarded as a domain-defined sampling
method and does not require forward solvers. We derive the spectral system of
the far-field operator for rigid disks and show that, using testing disks, the
one-wave factorization method can be justified independently of the classical
factorization method.
