  We have developed a scheme for reducing LIGO suspension thermal noise close
to violin-mode resonances. The idea is to monitor directly the
thermally-induced motion of a small portion of (a ``point'' on) each suspension
fiber, thereby recording the random forces driving the test-mass motion close
to each violin-mode frequency. One can then suppress the thermal noise by
optimally subtracting the recorded fiber motions from the measured motion of
the test mass, i.e., from the LIGO output. The proposed method is a
modification of an analogous but more technically difficult scheme by
Braginsky, Levin and Vyatchanin for reducing broad-band suspension thermal
noise. The efficiency of our method is limited by the sensitivity of the sensor
used to monitor the fiber motion. If the sensor has no intrinsic noise (i.e.
has unlimited sensitivity), then our method allows, in principle, a complete
removal of violin spikes from the thermal-noise spectrum. We find that in
LIGO-II interferometers, in order to suppress violin spikes below the
shot-noise level, the intrinsic noise of the sensor must be less than
\~2*10^{-13}cm/sqrt(Hz). This sensitivity is two orders of magnitude greater
than that of currently available sensors.
