Comparing one-step full-spectrum inversion with two-step splitting function inversion in normal mode tomography

Abstract

Earth's normal modes, or whole Earth oscillations, provide important constraints on Earth's large-scale 3-D structure. In addition to constraining shear and compressional wave velocities, they are the only seismic data sensitive to density perturbations. Density is particularly difficult to determine, and previous studies have found contradicting results, hence the method chosen to invert normal mode data for 3-D structure becomes important. In the problem of inverting the measured frequency spectra for an earth model, we can take two approaches: (i) a one-step full-spectrum inversion, where normal mode spectra are directly inverted for a mantle model and (ii) a two-step splitting function inversion, where first the spectra are inverted for splitting functions, which are then inverted for a mantle model. Here we compare the methodology and results of both approaches, continuing the work done by Li et al. and Durek & Romanowicz, and extending it to higher spherical harmonic degrees. Using exactly the same normal mode data set, we use both inversion approaches to make 3-D shear wave velocity mantle models. Both approaches give models consistent with previous tomographic studies, although spectral misfits are consistently lower for the one-step full-spectrum inversion. We also show that we cannot draw any conclusions on odd-degree structure in the lower mantle with the currently available normal mode data sets.