  Elastic anomalies produced by the spin crossover in ferropericlase have been
documented by both first principles calculations and high pressure-temperature
experiments. The predicted signature of this spin crossover in the lower mantle
is, however, subtle and difficult to geophysically observe within the mantle.
Indeed, global seismic anomalies associated with spin transitions have not yet
been recognized in seismologic studies of the deep mantle. A sensitive seismic
parameter is needed to determine the presence and amplitude of such a spin
crossover signature. The effects of spin crossovers on Bullen's parameter,
$\eta$, are assessed here for a range of compositions, thermal profiles, and
lateral variations in temperature within the lower mantle. Velocity anomalies
associated with the spin crossover in ferropericlase span a depth range near
1,000 km for typical mantle temperatures. Positive excursions of Bullen's
parameter with a maximum amplitude of $\sim$ 0.03 are calculated to be present
over a broad depth range within the mid-to-deep lower mantle: these are largest
for peridotitic and harzburgitic compositions. These excursions are highest in
amplitude for model lower mantles with large lateral thermal variations, and
with cold downwellings having longer lateral length-scales relative to hot
upwellings. We conclude that predicted deviations in Bullen's parameter due to
the spin crossover in ferropericlase for geophysically relevant compositions
may be sufficiently large to resolve in accurate seismic inversions of this
parameter, and could shed light on both the lateral variations in temperature
at depth within the lower mantle, and the amount of ferropericlase at depth.
