  Theoretical calculations of sound-wave velocities of materials at extreme
conditions are of great importance to various fields, in particular geophysics.
For example, the seismic data on sound-wave propagation through the solid
iron-rich Earth's inner core have been the main source for elucidating its
properties and building models. As the laboratory experiments at very high
temperatures and pressures are non-trivial, ab initio predictions are
invaluable. The latter, however, tend to disagree with experiment. We notice
that many attempts to calculate sound-wave velocities of matter at extreme
conditions in the framework of quantum-mechanics based methods have not been
taking into account the effect of anharmonic atomic vibrations. We show how
anharmonic effects can be incorporated into ab initio calculations and
demonstrate that in particular they might be non-negligible for iron in Earth's
core. Therefore, we open an avenue to reconcile experiment and ab initio
theory.
