Seismic waveform modeling and surface wave tomography in a three-dimensional Earth: asymptotic and non-asymptotic approaches

We investigate the impact of the theoretical limitations brought by asymptotic methods on upper-mantle tomographic models deduced from long-period surface wave data (period >80 s), by performing a synthetic test using a non-asymptotic formalism. This methodology incorporates the effects of back and multiple forward scattering on the wave field by summing normal modes computed to third order of perturbations directly in the 3D Earth, and models the sensitivity to scatterers away from the great-circle path. We first compare the methods we used for the forward problem, both theoretically and numerically. Then we present results from the computation of 7849 synthetic Love waveforms in an upper mantle model consisting of two heterogeneities with power up to spherical harmonic degree 12. The waveforms are subsequently inverted using a 0th order asymptotic formalism (equivalent to a path-average approximation in the surface waves domain). We show that the main structures are retrieved, but that the theoretical noise on the output model is of the same order as the noise due to the path-coverage and a priori constraints