Seismic waveform modelling in a 3-D Earth using the Born approximation: potential shortcomings and a remedy
Résumé
S U M M A R Y Although the use of the first-order Born approximation for the computation of seismic observ-ables and sensitivity kernels in 3-D earth models shows promise for improving tomographic modelling, more work is necessary to systematically determine how well such methods forward model realistic seismic data compared with more standard asymptotic methods. Most work so far has been focused on the analysis of secondary data, such as phase velocity, rather than time domain waveforms. We here compare synthetic waveforms obtained for simple models using standard asymptotic approximations that collapse the sensitivity to 3-D structure on the great circle plane and those obtained using the 3-D linear Born approximation, with accurate numerical 3-D synthetics. We find, not surprisingly, that 3-D Born more accurately models the perturbation effects of velocity anomalies that are comparable in wavelength to or are smaller than the first Fresnel zone. However, larger wavelength and amplitude anomalies can easily produce large phase delays that cause the first-order (linear) Born approximation to break down, whereas asymptotic methods that incorporate the effect of heterogeneity in the phase rather than in the amplitude of the waveform are more robust. Including a path average phase delay to the Born calculated waveforms significantly improves their accuracy in the case of long-wavelength structure, while still retaining the ability to correctly model the effect of shorter-wavelength structure. Tests in random models with structural wavelengths consistent with existing global seismic models indicate that the linear Born approximation frequently breaks down in realistic earth models, with worse misfit for first and second orbit Rayleigh and higher mode surface waveforms than the great-circle based approximations at all distances tested (>20 •). For fundamental modes, the average misfit for the waveforms calculated with the linear Born formalism is quite poor, particularly for distances larger than 60 •. The modified Born formalism consistently improves the fit relative to the linear Born waveforms, but only outperforms the great-circle based approximations for the higher mode surface waveforms. We note, however, that phase delay kernels for multitaper measurements of fundamental mode Rayleigh wave phase velocities developed from the Born approximation do not demonstrate the problems associated with the linear waveform kernels. There is general agreement with measurements and moderate improvement relative to phase delays predicted by the path-average approximation.
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