Fig. 7

Magnetic correlations of the coupled Earth dynamo model. a The modulus of the variance-normalized magnetic covariance matrix, showing the correlation between the poloidal field coefficients at the core surface (y-axis) and the poloidal field coefficients at various depth levels (x-axis). Correlations are shown up to spherical harmonic degree 10. Coefficients are ordered according to a one-dimensional scheme where all admissible values of the degree n are grouped together for a given value of the order m, leading to iso-m blocks of decreasing size along the diagonal of the matrix. The two blue tracks have (n,m) _x =(n,m) _y =(1,0) (track 1) and (n,m) _x =(3,2), (n,m) _y =(2,1) (track 2). b Same as a, for the toroidal field coefficients at various depth levels. Note that correlations are undefined at the core surface, since the toroidal field vanishes there, by virtue of the insulating magnetic boundary condition. The two red tracks have (n,m) _x =(3,1), (n,m) _y =(2,1) (track 1) and (n,m) _x =(4,2), (n,m) _y =(5,2) (track 2). c Modulus of correlation along the tracks defined above. ICB and CMB stand for inner-core boundary and core-mantle boundary, respectively