  We establish the equations which translate a conservation law for the problem
of the seismic response of an above-ground structure (e.g., building, hill or
mountain) of arbitrary shape and inquire whether both the implicit (formal) and
explicit (numerical) solutions for the response obey this law for the case of a
cylindrical, rectangular protuberance. Both the low-order (poor approximations
of the response) as well as higher-order (supposedly better approximations)
turn out to satisfy the conservation of flux relation, which means that the
satisfaction of this relation is a necessary, but not sufficient, means for
determining whether a solution to the scattering problem is valid.
