  The Einstein Telescope (ET) is a proposed third-generation gravitational-wave
(GW) underground observatory. It will have greatly increased sensitivity
compared to current GW detectors, and it is designed to extend the observation
band down to a few Hz. At these frequencies, a major limitation of the ET
sensitivity is predicted to be due to gravitational fluctuations produced by
the environment, most importantly by the seismic field, which give rise to the
so-called Newtonian noise (NN). Accurate models of ET NN are crucial to assess
the compatibility of an ET candidate site with the ET sensitivity target also
considering a possible reduction of NN by noise cancellation. With NN models
becoming increasingly complex as they include details of geology and
topography, it is crucial to have tools to make robust assessments of their
accuracy. For this purpose, we derive a lower bound on seismic NN spectra,
which is weakly dependent on geology and properties of the seismic field. As a
first application, we use the lower limit to compare it with NN estimates
recently calculated for the Sardinia and Euregio Meuse-Rhine (EMR) candidate
sites. We find the utility of the method, which shows an inconsistency with the
predictions for the EMR site, which indicates that ET NN models require further
improvement.
