The signal of mantle anisotropy in the coupling of normal modes

We investigate whether the coupling of normal mode (NM) multiplets can help us constrain mantle anisotropy. We first derive explicit expressions of the generalized structure coefficients of coupled modes in terms of elastic coefficients, including the Love parameters describing radial anisotropy and the parameters describing azimuthal anisotropy (J(c), J(s), K-c, K-s, M-c, M-s, B-c, B-s, G(c), G(s), E-c, E-s, H-c, H-s, D-c and D-s). We detail the selection rules that describe which modes can couple together and which elastic parameters govern their coupling. We then focus on modes of type S-0(l) - T-0 (l+1) and determine whether they can be used to constrain mantle anisotropy. We show that they are sensitive to six elastic parameters describing azimuthal anisotropy, in addition to the two shear-wave elastic parameters L and N ( i.e. V-SV and V-SH). We find that neither isotropic nor radially anisotropic mantle models can fully explain the observed degree two signal. We show that the NM signal that remains after correction for the effect of the crust and mantle radial anisotropy can be explained by the presence of azimuthal anisotropy in the upper mantle. Although the data favour locating azimuthal anisotropy below 400 km, its depth extent and distribution is still not well constrained by the data. Consideration of NM coupling can thus help constrain azimuthal anisotropy in the mantle, but joint analyses with surface-wave phase velocities is needed to reduce the parameter trade-offs and improve our constraints on the individual elastic parameters and the depth location of the azimuthal anisotropy.