Fig. 2: Depth dependence of elastic moduli and seismic velocities for pyrolite composition listed in Table 1¹⁵.

a Shear and bulk moduli. The anomalous behaviour of the bulk modulus, K¹¹ (K = − V(dP/dV), where V is volume and P is pressure) is due to the iron octahedron volume collapse during the spin-state change⁴ associated with the spin crossover. As previously shown¹¹, the pressure onset, the pressure range of the HS-LS crossover, and associated anomalies in K are temperature dependent (same legend all panels). The shear modulus, G, (G = τ/γ, where τ is the shear stress and γ is the shear strain) is not significantly affected by the octahedron volume reduction and increases monotonically with increasing pressure and decreasing temperature. b S-wave (\({V}_{s}=\sqrt{G/\rho }\)) and c P-wave (\({V}_{p}=\sqrt{(K+4/3G)/\rho }\)) velocity for pyrolite at different temperatures. The average mantle temperature profile (black) is calculated by setting the starting temperature to 1873 K at 660 km, and integrating the adiabatic temperature gradient¹⁵ through the lower mantle. The blue/magenta curves were calculated using the same technique, but decreasing/increasing the temperature at 660 km by ±500 K. In the mixed-spin region, the softening of K¹¹ causes a reduction in P-wave velocity sensitivity to isobaric temperature variations¹⁴, while the S-wave velocity remains sensitive to such temperature variations. Consequently, the expected seismic signal of iron-bearing Fp in the lower mantle consists of a disruption of vertically coherent thermal structures in P-velocities, whereas a coherent thermal structure is apparent in the S-velocities^12,14. Additional compositions shown in Supplementary Fig. 1 demonstrate the calculated seismic velocities dependence on Fp proportion.