On the role of reflections, refractions and diving waves in full-waveform inversion

ABSTRACT Full‐waveform inversion suffers from local minima, due to a lack of low frequencies in 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 a perturbation in a reference model consisting in two homogeneous isotropic acoustic half‐spaces and the assumption of infinitely large apertures available in the data, 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. Diving waves can be included if the deeper part of the homogeneous model is replaced by one that has a vertical velocity gradient. We study this spectrum in more detail by separately considering scattering of direct, reflected and head waves, as well as singly and multiply reflected diving waves for a gradient model. Taking the reflection coefficient of the deeper reflector into account, we obtain sensitivity estimates for each wavetype. 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. If the deeper part has a constant positive velocity gradient with depth, all the energy eventually returns to the source‐receiver line, given a sufficiently large acquisition aperture. This will improve the sensitivity of the scattered reflected and refracted wavefields to perturbations in the background model. The same happens for a zero velocity gradient but with a very high impedance contrast between the two half‐spaces, which results in a large reflection coefficient.