ALBERT

Description: Full-waveform inversion (FWI) of shallow-seismic surface waves is able to reconstruct lateral variations of subsurface elastic properties. Line-source simulation for point-source data is required when applying algorithms of 2-D adjoint FWI to recorded shallow-seismic field data. The equivalent line-source response for point-source data can be obtained by convolving the waveforms with $\sqrt{t^{-1}}$ ( t : traveltime), which produces a phase shift of /4. Subsequently an amplitude correction must be applied. In this work we recommend to scale the seismograms with $\sqrt{2 r v_{\rm ph}}$ at small receiver offsets r , where v ph is the phase velocity, and gradually shift to applying a $\sqrt{t^{-1}}$ time-domain taper and scaling the waveforms with $r\sqrt{2}$ for larger receiver offsets r . We call this the hybrid transformation which is adapted for direct body and Rayleigh waves and demonstrate its outstanding performance on a 2-D heterogeneous structure. The fit of the phases as well as the amplitudes for all shot locations and components (vertical and radial) is excellent with respect to the reference line-source data. An approach for 1-D media based on Fourier–Bessel integral transformation generates strong artefacts for waves produced by 2-D structures. The theoretical background for both approaches is presented in a companion contribution. In the current contribution we study their performance when applied to waves propagating in a significantly 2-D-heterogeneous structure. We calculate synthetic seismograms for 2-D structure for line sources as well as point sources. Line-source simulations obtained from the point-source seismograms through different approaches are then compared to the corresponding line-source reference waveforms. Although being derived by approximation the hybrid transformation performs excellently except for explicitly back-scattered waves. In reconstruction tests we further invert point-source synthetic seismograms by a 2-D FWI to subsurface structure and evaluate its ability to reproduce the original structural model in comparison to the inversion of line-source synthetic data. Even when applying no explicit correction to the point-source waveforms prior to inversion only moderate artefacts appear in the results. However, the overall performance is best in terms of model reproduction and ability to reproduce the original data in a 3-D simulation if inverted waveforms are obtained by the hybrid transformation.