The Earth’s crystalline inner core (IC) solidifies from the liquid Fe alloy of the outer core (OC), which releases latent heat and light elements sustaining the geodynamo. Variability in solidification regime at the inner core boundary (ICB) may result in compositional and thermal multi-scale mosaic of the IC surface and dissimilarity of its hemispheres. Both the mosaic and hemisphericity are poorly constrained, not least due to a lack of available sampling by short-period reflected waves. Measured amplitude ratio of seismic phases of PKiKP and PcP reflected, respectively, off the inner and outer boundary of the liquid core, yields direct estimate of the ICB density jump. This parameter is capable of constraining the inner – outer core compositional difference and latent energy release, but is not well known (0.2–1.2 g/cub cm), and its distribution is obscure. Travel time measurements of PKiKP and PcP waveforms can be useful in terms of getting an insight into fine structure of ICB and its topography. We analyse a new representative sample of pre-critical PKiKP/PcP differential travel times and amplitude ratios that probes the core’s spots under Southeastern Asia and South America . We observe a statistically significant systematic bias between the measurements collected in western and eastern hemispheres, and carefully examine its origin. Separating the effects of core-mantle boundary (CMB) and ICB on the measured differentials is particularly challenging and we acknowledge that a whole class of physically valid models involving D” heterogeneities and lateral variation in lower mantle attenuation can be addressed to account for the observed hemisphericity. However, we find that variance in PKiKP-PcP differential travel times measured above the epicentral distance of 16 degrees is essentially due to mantle heterogeneities. Analysis of data below this distance indicates the ICB density jump under Southeastern Asia can be about 0.3 g/cub. cm, which is three times as small as under South America where also the thickness of the liquid core can be by 1-3 km in excess of the one in the East. The findings are interpretable as evidence for IC hemispherical asymmetry whereby crystallization dominates in the West and melting in the East (and not vice versa) or in terms of two disconnected mosaic patches with contrasting properties.