  It is well known that a hypothetical compact object that looks like an
Einsteinian (Schwarzschild or Kerr) black hole everywhere except a small region
near its surface should have the ringdown profile predicted by the Einstein
theory at early and intermediate times, but modified by the so-called echoes at
late times. A similar phenomenon appears when one considers an Einsteinian
black hole and a shell of matter placed at some distance from it, so that
astrophysical estimates could be made for the allowed mass of the black hole
environment. While echoes for both systems have been extensively studied
recently, no such analysis has been done for a system featuring phenomena
simultaneously, that is, echoes due to new physics near the surface/event
horizon and echoes due to matter at some distance from the black hole. Here,
following [9, 11], we consider a traversable wormhole obtained by identifying
two Schwarzschild metrics with the same mass M at the throat, which is near the
Schwarzschild radius, and add a nonthin shell of matter at a distance. This
allows us to understand how the echoes of the surface of the compact object are
affected by the astrophysical environment at a distance. The straightforward
calculations for the time-domain profiles of such a system support the
expectations that if the echoes are observed, they should most probably be
ascribed to some new physics near the event horizon rather than some
"environmental" effect.
