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

A conservation law for testing methods of prediction of the seismic wave response of a protuberance emerging from flat ground