An example of the natural cubic splines used to construct the 1-D earth models, following eq. (8). The coefficients a_i represent V_P values in the outer core (yellow diamonds), drawn from the prior model distribution ρ(m). The black line shows the resulting V_P profile f (z) in the outer core, which is constructed by summing the products a_iψ_i(z) for the four splines (dashed).