We consider an N-layered elastic medium which is perfectly insulated from its embedding space. Each layer has unit two-way vertical traveltime, and a coincident source-receiver pair is located just below the top interface. If the insulated medium is excited in the remote past, the power spectrum of the resulting impulsive normal-incidence synthetic seismogram is a pure line spectrum; because no random elements exist in the system at the time of measurement, this spectrum is a minimum entropy spectrum. If we add white noise to the seismogram, the power spectrum becomes a maximum entropy spectrum. The maximum entropy spectrum can thus be decomposed into the sum of a minimum entropy spectrum plus white noise; this spectral decomposition is due to Pisarenko (1973). If the insulated medium is excited at time t = 0, the resulting synthetic seismogram differs rather remarkably from the seismogram obtained for excitation in the remote past.