Born seismograms using coupled free oscillations: the effects of strong coupling and anisotropy

Abstract

We have developed an expression for the first‐order Born waveform perturbation for long‐period seismic records on an aspherical earth, using an anelastic monopole reference model. We have derived both an explicitly anelastic first‐order Born term u1(r, t) and an approximate, but much simpler, expression in which quasi‐degenerate modal coupling is represented by secular terms in the time domain. We designate this expression the ‘strong’ Born approximation to identify the presence of ‘strong’ quasi‐degenerate coupling. Earlier applications of Born theory to surface wave seismograms have typically neglected the coupling between different modal dispersion branches. The strong Born approximation is linear in the aspherical model, but the secular terms restrict its accuracy to ‘short’ times after event onset, typically fewer than 10 hr. Additional accuracy can be gained by treating the self‐coupling of isolated multiplets explicitly by formally summing the Born series using a projection of the aspherical operator L1 onto the multiplet in question. We call this the ‘stronger’ Born approximation, which is a non‐linear functional of the aspherical model. The stronger Born approximation is similar to, but formally less accurate than, the subspace projection algorithm. We verified the accuracy of synthetic seismograms calculated with the ‘strong’ and ‘stronger’ Born approximations against Galerkin coupled‐mode synthetics using a zonally symmetric, weakly anisotropic upper mantle model. The Born seismograms replicate successfully the ‘quasi‐Love’ waveforms that diagnose spheroidal‐toroidal coupling, suggesting that the strong Born approximation is adequate to model the interaction of free‐oscillation coupling partners that are closely spaced in the frequency domain, at least for short records. We performed a waveform inversion test using three‐component synthetic seismograms from 297 source‐receiver pairs. Once spheroidal—toroidal coupling is incorporated in the inverse formulation, the waveform perturbations associated with the anisotropic parameters are clearly distinct from waveform perturbations associated with the isotropic parameters. Although the model space used in this experiment is highly restricted compared to the real Earth, these results suggest that the trade off between anisotropy and isotropic lateral structure may be less problematic in a fully‐coupled waveform inversion than in a tomographic inversion of surface wave phase delays. Copyright © 1993, Wiley Blackwell. All rights reserved