  Viscoelastic behavior in geological materials controls a wide range of
geophysical phenomena, such as mantle convection. We present a new method for
measuring attenuation in single crystals of minerals and in reference materials
over a frequency range of 1-1e-4 Hz via nanoindentation. In the experiments, we
calculate the phase lag between a sinusoidal load applied to the tip of the
nanoindenter and its displacement into and out of the tested sample, which
provides a measure of the inverse quality factor 1/Q (i.e., attenuation) of the
sample. Experiments were conducted on polymethyl methacrylate (PMMA), indium,
halite, olivine and quartz. Attenuation spectrum from our tests on PMMA and
indium are in excellent agreement with reported values from past studies. We
quantified the natural damping of the nanoindenter and show that it becomes
comparable to that of the samples at frequencies greater than 0.1 Hz, but is
much lower at lower frequencies.
