  The power law of aftershock evolution was proposed by Hirano in 1924 and
introduced by Utsu into seismology in the second half of the last century. The
Hirano-Utsu law is widely used in studying the relaxation of earthquake source
after the main shock of an earthquake. The prevailing view in the literature is
that the Hirano-Utsu law is an improved version of Omori's hyperbolic law,
formulated in 1894. The author disagrees with this notion. The paper proposes
an axiomatic approach to the study of aftershocks. A phenomenological parameter
of the source, called the deactivation coefficient, was introduced. The theory
is based on axioms that do not contain any a priori statements regarding the
form of the law of aftershock evolution. Formulas for the deactivation
coefficient are derived from the axioms, allowing one to experimentally
establish the truth or falsity of the Hirano-Utsu and Omori laws. A two-stage
mode of source relaxation was discovered. In the first stage, called the Omori
epoch, the Omori law is strictly followed. The Omori epoch ends with a
bifurcation, after which aftershock activity becomes unpredictable. Omori's law
is not fulfilled at the second stage of evolution. The Hirano-Utsu law is not
fulfilled either at the first or second stage. Keywords: earthquake source,
main shock, relaxation, deactivation coefficient, evolution equation, inverse
problem, Omori epoch, bifurcation, two-stage relaxation mode.
