Sensitivity analysis of acoustic waveform inversion to velocity anomalies in the near-surface using the Fréchet derivative

Seismic waveform inversion (WI) has been applied to high- resolution velocity model building at all scales, but how truthful are the amplitudes of velocity anomalies recovered in the WI models? Previous sensitivity analysis of WI has focused on estimating model uncertainties, understanding the radiation patterns of different geophysical parameters, and separating the tomography and migration mode of WI in the wavenumber-domain. Few of the studies explore if the WI is equally sensitivity to high and low velocity anomalies, whereas nonlinear traveltime tomography (TT) is known to be more sensitive to high velocity anomalies than low velocity anomalies because of wavefront healing. In this paper, we analyze the sensitivity of WI to velocity anomalies by first comparing the amplitudes of wavefield perturbations generated by injected high and low velocity anomalies. We provide theoretical calculations for a point scatter and numerical simulations for a velocity anomaly with a size equivalent to a fraction of the dominant wavelength. Then, we perform WI tests to recover high and low velocity anomalies of equal velocity or slowness perturbations. Acoustic waveform modeling and inversion are used for simplicity. The preliminary results show acoustic WI is potentially more sensitive to low velocity anomalies than high velocity anomalies. The joint inversion of traveltime and waveform data is advocated for near-surface velocity estimation, since the different sensitivity of TT and acoustic WI can be complementary to each other.

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