Full waveform inversion suffers from local minima, due to a lack of low frequencies in the data. A reflector below the zone of interest may, however, help in recovering the long-wavelength components of a velocity perturbation, as demonstrated in a paper by Mora. With the Born approximation for the perturbation in a reference model consisting of two homogeneous isotropic acoustic halfspaces, analytic expressions can be found that describe the spatial spectrum of the recorded seismic signal as a function of the spatial spectrum of the inhomogeneity. We study this spectrum in more detail by separately considering direct, reflected and head waves. Taking the reflection coefficient of the deeper reflector into account, we obtain sensitivity estimates for each of these types of waves. Although the head waves have a relatively small contribution to the reconstruction of the velocity perturbation, compared to the other waves, they contain reliable long-wavelength information that can be beneficial for full waveform inversion.


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