  Seismic mapping of the top of the inner core indicates two distinct areas of
high P-wave velocity, the stronger one located beneath Asia, and the other
located beneath the Atlantic. This two-fold pattern supports the idea that a
lower-mantle heterogeneity can be transmitted to the inner core through outer
core convection. In this study, a two-component convective dynamo model, where
thermal convection is near critical and compositional convection is strongly
supercritical, produces a substantial inner core heterogeneity in the rapidly
rotating strongly driven regime of Earth's core. While the temperature profile
that models secular cooling ensures that the mantle heterogeneity propagates as
far as the inner core boundary (ICB), the distribution of heat flux at the ICB
is determined by the strength of compositional buoyancy. A large heat flux
variation $q^*$ of $O(10)$ at the core-mantle boundary (CMB), where $q^*$ is
the ratio of the maximum heat flux difference to the mean heat flux at the CMB,
produces a core flow regime of long-lived convection in the east and
time-varying convection in the west. Here, the P-wave velocity estimated from
the ICB heat flux in the dynamo is higher in the east than in the west, with
the hemispherical difference of the same order as the observed lower bound,
0.5%. Additional observational constraints are satisfied in this regime -- the
variability of high-latitude magnetic flux in the east is lower than that in
the west; and the stratified F-layer at the base of the outer core, which is
fed by the mass flux from regional melting of the inner core and magnetically
damped, attains a steady-state height of $\sim$ 200 km.
