  Gravitational wave echoes from the black holes have been suggested as a
crucial observable to probe the spacetime in the vicinity of the horizon. In
particular, it was speculated that the echoes are closely connected with
specific characteristics of the exotic compact objects, and moreover, possibly
provide an access to the quantum nature of gravity. Recently, it was shown that
the discontinuity in the black hole metric substantially modifies the
asymptotical behavior of quasinormal frequencies. In the present study, we
proceed further and argue that a discontinuity planted into the metric
furnishes an alternative mechanism for the black hole echoes. Physically, the
latter may correspond to an uneven matter distribution inside the surrounding
halo. To demonstrate the results, we first numerically investigate the temporal
evolution of the scalar perturbations around a black hole that possesses a
nonsmooth effective potential. It is shown that the phenomenon persists even
though the discontinuity can be located further away from the horizon with
rather insignificant strength. Moreover, we show that the echoes in the present
model can be derived analytically based on the modified pole structure of the
associated Green function. The asymptotical properties of the quasinormal mode
spectrum and the echoes are found to be closely connected, as both features can
be attributed to the same origin. In particular, the period of the echoes in
the time domain $T$ is shown to be related to the asymptotic spacing between
successive poles along the real axis in the frequency domain
$\Delta(\Re\omega)$, by a simple relation
$\lim\limits_{\Re\omega\to+\infty}\Delta(\Re\omega) = 2\pi/T$. The potential
astrophysical implications of the present findings are addressed.
