Strong constraints can be placed on the origin of heterogeneity of seismic wave velocities and density if the observed ratios of various parameters are compared with mineral physics predictions. They include the shear to compressional wave velocity heterogeneity ratio, Rs/p≡Δ log Vs/Δ log Vp, the bulk sound to shear wave velocity heterogeneity ratio, Rϕ/s≡Δ log Vϕ/Δ log Vs, and the density to velocity heterogeneity ratio, R&rgr;/s,p≡Δ log &rgr;/Δ log Vs,p. Using mineral physics considerations, we calculate these ratios in the lower mantle corresponding to the thermal and chemical origin of velocity and density heterogeneity. Both anharmonic and anelastic effects are considered for thermal origin. Anharmonic effects are estimated from the theoretical calculations as well as from laboratory measurements which show a marked increase in Rs/p with pressure from ~1.5 to ~2.1 in the lower mantle. Such a trend is marginally consistent with seismological observations showing an increase in Rs/p with depth (from ~1.7 to ~3.2 in the lower mantle). However, anharmonic effect alone cannot explain inferred low R&rgr;/s (2.7) and corresponding negative values of Rϕ/s (and R&rgr;/s) in the deep lower mantle which cannot be accounted for by thermal or simple chemical heterogeneity such as the heterogeneity in the Fe/(Fe+Mg) and/or Mg/(Mg+Si) ratios. Possible causes of anomalies in this region are discussed, including the role of anisotropy and a combined effect of heterogeneity in Fe and Ca content. ¿ 2001 American Geophysical Union