  After the main shock of an earthquake the aftershocks are observed. According
to Omori's law, the frequency of aftershocks decreases hyperbolically over
time. We noticed that, strictly speaking, Omori's law paradoxically contradicts
the law of energy conservation. The contradiction is that the excitation of
each aftershock consumes a finite portion of the source's energy, so that the
total energy released by the source tends to infinity over time. The paradox is
formally theoretical, but its analysis has proved useful. Eliminating the
contradiction between Omori's law and the fundamental law of conservation of
energy allowed us to further understand the nature of the phenomenological
theory of aftershocks. We used the concept of deactivation of a source after
the formation of a main rupture in it. We have based the theory on the original
aftershock evolution equation, which has the form of a first-order linear
differential equation. Two ways to eliminate the paradoxical situation are
indicated. Key words: earthquake source, aftershock, evolution equation,
deactivation coefficient, inverse problem, Omori epoch, source bifurcation,
logistic equation, Hirano-Utsu formula.
