Synthetic normal-mode spectra: a full-coupling perspective

Abstract:

Normal-mode spectra may be used to investigate the large-scale anelastic structure of the entire earth. The relevant theory was developed a few decades ago, however, mainly due to computational limitations, several approximations are commonly employed, and thus far the full merits of the complete theory have not been taken advantage of. In this study, we present an exact algebraic form of the theory for an aspherical, anelastic and rotating earth model in which either complex or real spherical harmonic bases are used. Physical dispersion is incorporated into the quadratic eigenvalue problem by expanding the logarithmic frequency term to 2^nd order. In addition, we carry out numerical experiments up to 3 mHz to quantitatively evaluate the accuracy of commonly used approximate mode synthetics. We find that (1) approximating mode frequencies for realistic earth models with an average over degenerate frequencies of two coupled modes for physical dispersion, Coriolis effects and perturbed kinematic energy terms gives rise to subtle differences in mode spectra; (2) taking into account the exact normalization of modes instead of the one for a spherical, non-rotation model improves mode spectra by ~2%; (3) consideration of mode coupling in a narrow frequency band yields up to 10% discrepancies in mode spectra compared with wide-band coupling, indicating that the popular splitting function approach may introduce slight biases in normal-mode tomography.